# Is there a strict definition for what is atonal?



## Zellibrung

I've recently been exploring atonal music, but I'm having trouble if there is actually some line that demarcates tonal and atonal. 

Is there an empirical way to always determine the difference between a piece that has modal changes and that is atonal? or are they one in the same(or shades of gray)? 

For example, If I played a piece that is in C and then at the end I played every sharp once I'd assume it'd still be considered to be in C. 

Additionally, I'd like to know if there's a definite line between 12 tone serialism and anything else. From the wikipedia article I read there were only 4 rules to serialism, that seemed there could be room for someone to "cheat" essentially and come up with something fairly tonal with the use of different voices, note lengths, etc. even if the frequency of all notes were equal.

All in all, I don't seem to have a full grasp of when a piece would cross over from being tonal to atonal, or if such a thing exists. Anyone know?


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## EdwardBast

Zellibrung said:


> I've recently been exploring atonal music, but I'm having trouble if there is actually some line that demarcates tonal and atonal.


There is no line. The reasons the discourse is parsed as an either or proposition - tonal vs. atonal - are political. Reality is a smooth continuum between various degrees and vectors of tonal gravity, that is, attraction to a given pitch or set of pitches.



Zellibrung said:


> Is there an empirical way to always determine the difference between a piece that has modal changes and that is atonal? or are they one in the same(or shades of gray)?
> 
> For example, If I played a piece that is in C and then at the end I played every sharp once I'd assume it'd still be considered to be in C.


I'm not sure what you mean in this context by "modal changes."

It would probably be considered a poorly composed piece in C.



Zellibrung said:


> Additionally, I'd like to know if there's a definite line between 12 tone serialism and anything else. From the wikipedia article I read there were only 4 rules to serialism, that seemed there could be room for someone to "cheat" essentially and come up with something fairly tonal with the use of different voices, note lengths, etc. even if the frequency of all notes were equal.


Rules are for school children. What would be the point of writing a tonal 12-tone piece? For the fun? The glory? Destiny? Adventure? Romance? 



Zellibrung said:


> All in all, I don't seem to have a full grasp of when a piece would cross over from being tonal to atonal, or if such a thing exists. Anyone know?


It's a judgment call. Different more or less coherent groups of people reach a consensus on what works belong in what category and then try to make everyone else join their consensus. Convert or be burnt at the stake. Used to be a weekly exercise here on TC


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## Woodduck

EdwardBast said:


> There is no line. The reasons the discourse is parsed as an either or proposition - tonal vs. atonal - are political. Reality is a smooth continuum between various degrees and vectors of tonal gravity, that is, attraction to a given pitch or set of pitches.
> 
> Different more or less coherent groups of people reach a consensus on what works belong in what category and then try to make everyone else join their consensus. Convert or be burnt at the stake. Used to be a weekly exercise here on TC


Yeah. Remember the fistfights over the Berg Sonata, said by some to be in b minor, and the Schoenberg Piano Suite, said by some to have tonics in it?

Those were golden days. Now we're reduced to arguing about tonality in Wagner. I thought that was a settled question, but... Oh well. It's something to occupy my free time.


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## Lenny

EdwardBast said:


> Rules are for school children. What would be the point of writing a tonal 12-tone piece? For the fun? The glory? Destiny? Adventure? Romance?


I vote for romance. Writing 12-tone pieces is a sure highway to bling bling.


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## BabyGiraffe

Play something that sounds random or dissonant = atonal. It doesn't have to be truly random. Using structures that can't be perceived also makes your music random.
You can learn how to voice lead triads and dissonant chords in the pitch space making completely tonal music with 12 keys - check all the videos and books on the Neo-Riemannian theory and the out of copyright "Harmonic materials of modern music" by Howard Hanson.
We are pretty limited in our hearing and memory. And what we hear is distorted compared to the sound in real world.
https://en.wikipedia.org/wiki/Fletcher–Munson_curves
Most of the so called atonal music is not atonal at all, we just can't recognise/enjoy the patterns.

What MOST people enjoy - intervals with factors of 2 and 3 and scales based on them(octaves, fifths, fourths), rhythms with factors of 2 and 3, 5-7 steps scales, harmonies with factors of 2, 3 and 5 (5/4 is major, 6/5 is minor).
Some cultures have developed more complex music with factors of 7 (african based jazz, blues and traditional tirbal drumming which is not groovy for the normal westener), middle Eastern/north African/ Balkan/ Indian rhythms/microtones with factors of 11, 13 or 17.
Ancient Greek and Roman Pythagorean enharmonic scales with factors of 31 (which weren't very enjoyble to the normal people even back then and were used mostly in sacred rituals, by mystics etc). The traditional Indonesian music also uses 29 or higher primes.
It's interesting to note that the different numbers sound different, occultists and Pythagoreans have theories about their meaning, functions etc.
12et is a mixed bag, approximating different primes, so you can play distorted versions not only of 2,3,5 limit Western scales, but also some pseudo-African and Oriental. Still, they make more sense than the avantgarde stuff which is based on completely distorted harmony (clusters etc), misunderstanding of the human cognition, psychology, acoustic and mathematical principles. 
If you want symmetry in your music like equal divisions of the octave or some other intervals that don't sound horrible, you have to apply the same kind of math that the ancient guys like Pythagoras -based on superparticular ratios.


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## mtmailey

There is no strict rules BUT if music uses all notes on the scale which is 12 then it is atonal.People just want others to use the traditional systems.The easy key signatures are C,G,F majors .I use the often you know.


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## Razumovskymas

My (very volatile) position right now is that one can only TRY to be atonal.


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## Woodduck

Razumovskymas said:


> My (very volatile) position right now is that one can only TRY to be atonal.


Provocative. Tell us more.


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## Zellibrung

EdwardBast said:


> There is no line. The reasons the discourse is parsed as an either or proposition - tonal vs. atonal - are political. Reality is a smooth continuum between various degrees and vectors of tonal gravity, that is, attraction to a given pitch or set of pitches.


I suppose that would make sense considering that some pieces are described as "very tonal".



EdwardBast said:


> I'm not sure what you mean in this context by "modal changes."


I think I meant to say key changes.



EdwardBast said:


> Rules are for school children. What would be the point of writing a tonal 12-tone piece? For the fun? The glory? Destiny? Adventure? Romance?


It's only that I wasn't sure if the rules were also a reflection of some underlying reality. A better term would probably be guidelines. As for why, adventure would probably be the closest out of those choices. In general, I was trying to get a better idea of concepts like dissonance and atonality, and finding where the boundaries and extremes were would help for a better understanding of these concepts and how they can be used.

At the same time, the idea of a relatively "nice" sounding 12-tone piece does still seem like an interesting idea, that could yield interesting results(though it seems that for some people that would be going against the whole point of making atonal music). The idea of order within chaos appeals to me.

In my own attempts at writing sometimes a piece would appear to be in a 10 note scale, though I had never specifically set out to make it that way, and from a theory standpoint I had no idea what to make of it or why it wasn't as dissonant as I had expected.

Though I never thought he intended to make a tonal 12-tone piece, my initial impression of Schoenberg was that he considered it a challenge to make something decent from what theorists generally assumed would be just be a cacaphony.



BabyGiraffe said:


> You can learn how to voice lead triads and dissonant chords in the pitch space making completely tonal music with 12 keys - check all the videos and books on the Neo-Riemannian theory and the out of copyright "Harmonic materials of modern music" by Howard Hanson.
> We are pretty limited in our hearing and memory. And what we hear is distorted compared to the sound in real world.
> https://en.wikipedia.org/wiki/Fletcher–Munson_curves
> Most of the so called atonal music is not atonal at all, we just can't recognise/enjoy the patterns.


This looks like just the sort of stuff I've been looking for. I'll have to read further into all of this.


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## Razumovskymas

Woodduck said:


> Provocative. Tell us more.


I'm shifting already as we speak. You see my opinions are much like auditive events in time without much relation to each other, like the tones in an atonal piece of music.


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## EdwardBast

Zellibrung said:


> I
> It's only that I wasn't sure if the rules were also a reflection of some underlying reality. A better term would probably be guidelines. As for why, adventure would probably be the closest out of those choices. In general, I was trying to get a better idea of concepts like dissonance and atonality, and finding where the boundaries and extremes were would help for a better understanding of these concepts and how they can be used.
> 
> At the same time, the idea of a relatively "nice" sounding 12-tone piece does still seem like an interesting idea, that could yield interesting results(though it seems that for some people that would be going against the whole point of making atonal music). The idea of order within chaos appeals to me.


I was being silly with my response on this point. I agree that whatever gets a composer to an interesting work is worth trying!

I know of (and knew) teachers of composition who believed in an underlying aesthetic ideal, who discouraged using rows emphasizing thirds or any other sequences with triadic or tonal implications.


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## Woodduck

EdwardBast said:


> I know of (and knew) teachers of composition who believed in an underlying aesthetic ideal, who discouraged using rows emphasizing thirds or any other sequences with triadic or tonal implications.


This is the Originalist, or Schoenberg-Scalia, Doctrine of Constitutional Dodecaphony.


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## fluteman

Woodduck said:


> This is the Originalist, or Schoenberg-Scalia, Doctrine of Constitutional Dodecaphony.


Schoenberg-Scalia! I knew reading this thread would be worth it! You and Edward Bast rightly observe that this is such an emotionally-charged political or even religious issue around here it's hardly worth pursuing. For me, the broad range of possible definitions of "atonal" is one indication of how varied music can be. Yet people don't seem to ask for definitions of music, which seems to me a more interesting and fundamental question.


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## Razumovskymas

Woodduck said:


> Provocative. Tell us more.


IF one "sees" the true beauty of an atonal/serial or dodecaphonic piece of music like the way Millionrainbows describes. As I understand he puts it more or less like this (correct me if I'm wrong Millionrainbows) : letting go of every tonal reference and not trying to cling on to anything that might look a bit tonal (~sensuous) but YET experiencing a relation between the different intervals, spaces... THEN (in my eyes) that piece of music kind of becomes tonal in some way.

Of course it al depends on how you define atonal but I sense an inevitable paradox.


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## Bettina

fluteman said:


> Schoenberg-Scalia! I knew reading this thread would be worth it! You and Edward Bast rightly observe that this is such an emotionally-charged political or even religious issue around here it's hardly worth pursuing. For me, the broad range of possible definitions of "atonal" is one indication of how varied music can be. *Yet people don't seem to ask for definitions of music, which seems to me a more interesting and fundamental question.*


Actually, that topic does come up fairly often, usually in the context of discussing Cage's 4'33".


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## Vox Gabrieli

fluteman said:


> Yet people don't seem to ask for definitions of music, which seems to me a more interesting and fundamental question.


"_Why do people try so hard to explain the beauty of music, thus depriving it of its mystery?_"

An underappreciated quote from Bernstein's Norton Lectures.


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## isorhythm

Woodduck said:


> Yeah. Remember the fistfights over the Berg Sonata, *said by some to be in b minor*, and the Schoenberg Piano Suite, said by some to have tonics in it?.


Said by some including Berg! I'm willing to give him that.


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## Woodduck

Gabriel Ortiz said:


> "_Why do people try so hard to explain the beauty of music, thus depriving it of its mystery?_"
> 
> An underappreciated quote from Bernstein's Norton Lectures.


Never fear. Despite all explanations, the mystery remains.


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## Woodduck

isorhythm said:


> Said by some including Berg! I'm willing to give him that.


It does cadence in b minor. I'm willing to give you that.


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## Woodduck

fluteman said:


> Schoenberg-Scalia! I knew reading this thread would be worth it! You and Edward Bast rightly observe that this is such an emotionally-charged political or even religious issue around here it's hardly worth pursuing. For me, *the broad range of possible definitions of "atonal"* is one indication of how varied music can be. Yet people don't seem to ask for definitions of music, which seems to me a more interesting and fundamental question.


How many useful definitions of atonality can you think of? I can come up with only one: "in music consisting of tones, the absence of a tonal system, i.e. a hierarchical system governing the relationships between those tones, including a central tone at the base of that hierarchy functioning as a point of departure, resolution, or repose."

"Atonal" and "atonality" may be thrown about carelessly, but the above is the conception that anchors my thinking on the subject. It allows me to say with assurance that Schoenberg's _Erwartung_ is atonal but Wagner's _Tristan_ is not. I think the debates arise mainly because, first, music may have both tonal and non-tonal aspects, and, second, because different people hear different things in what they're listening to.


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## Bettina

Gabriel Ortiz said:


> "_Why do people try so hard to explain the beauty of music, thus depriving it of its mystery?_"
> 
> An underappreciated quote from Bernstein's Norton Lectures.


That's ironic coming from Bernstein, who gave hundreds of lectures on the inner workings of music!


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## fluteman

Bettina said:


> Actually, that topic does come up fairly often, usually in the context of discussing Cage's 4'33".


Oh, right. I forgot about that. Of course, those threads usually turn into a series of jokes. I wish some of that sense of humor could be applied more generally.


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## fluteman

Woodduck said:


> How many useful definitions of atonality can you think of? I can come up with only one: "in music consisting of tones, the absence of a tonal system, i.e. a hierarchical system governing the relationships between those tones, including a central tone at the base of that hierarchy functioning as a point of departure, resolution, or repose."
> 
> "Atonal" and "atonality" may be thrown about carelessly, but the above is the conception that anchors my thinking on the subject. It allows me to say with assurance that Schoenberg's _Erwartung_ is atonal but Wagner's _Tristan_ is not. I think the debates arise mainly because, first, music may have both tonal and non-tonal aspects, and, second, because different people hear different things in what they're listening to.


That's all fine, but I also see more narrow definitions advanced here, perhaps for the reasons you suggest. In the end, defining "tonal" or "music", or any word, only holds so much importance for me. I don't like packing mere words with heavy political or religious freight. That's what Senator McCarthy did with "communist". I go back to the comment of Lewis Carroll's Humpty Dumpty in Through The Looking Glass.


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## Lindenbaum

"Atonal" is a rather limited characteristic of a piece of music I think. For instance, a Wagner piece, a Debussy piece, a Schoenberg piece, a Shostakovich piece, and a Ligeti piece might each be in some way atonal. Its more useful to describe a piece as, say serial, or employing just very extended and chromatic common practice techniques, etc.


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## millionrainbows

Zellibrung said:


> I've recently been exploring atonal music, but I'm having trouble if there is actually some line that demarcates tonal and atonal.
> 
> Is there an empirical way to always determine the difference between a piece that has modal changes and that is atonal? or are they one in the same(or shades of gray)?
> 
> For example, If I played a piece that is in C and then at the end I played every sharp once I'd assume it'd still be considered to be in C.
> 
> Additionally, I'd like to know if there's a definite line between 12 tone serialism and anything else. From the wikipedia article I read there were only 4 rules to serialism, that seemed there could be room for someone to "cheat" essentially and come up with something fairly tonal with the use of different voices, note lengths, etc. even if the frequency of all notes were equal.
> 
> All in all, I don't seem to have a full grasp of when a piece would cross over from being tonal to atonal, or if such a thing exists. Anyone know?


I don't think the line is clear, because tonality weakens by degrees.

Besides that, "atonal" is an _exclusive_ term which means "music that is not tonal." It does not have to define _all_ _the ways_ in which music can be "not tonal," but simply excludes music that is not tonal; i.e., music which does not derive its structure from a _harmonic hierarchy.
_
This means that, for instance, Bartok using the diminished scale and creating a "quasi-tonality" by establishing fleeting local tone centers (derived from the way the diminished scale divides the octave into 3 parts) is not tonal, because it does not establish an overall harmonic hierarchy which governs the entire octave, and the "centers" are based on geometric divisions of the diminished scale (12 ÷ 3 = 4), not on a harmonically-derived hierarchy (which you can hear).

Yet, other "harmonic hierarchies" _are possible_ other than CP tonality's major/minor system. Debussy's use of the whole tone scale, though it creates instability, is best described as a "different" tonality rather than "atonal," since it uses the WT scale as a "scale" with 6 possible tonal centers, but no stable fifth.

You have to think about these issues, you can't expect a couple of terms like "tonal/atonal" to explain everything.


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## millionrainbows

Razumovskymas said:


> IF one "sees" the true beauty of an atonal/serial or dodecaphonic piece of music like the way Millionrainbows describes. As I understand he puts it more or less like this (correct me if I'm wrong, millionrainbows) : letting go of every tonal reference and not trying to cling on to anything that might look a bit tonal (~sensuous) but YET experiencing a relation between the different intervals, spaces... THEN (in my eyes) that piece of music kind of becomes tonal in some way.
> 
> Of course it all depends on how you define atonal but I sense an inevitable paradox.


I agree with the way you are approaching the hearing, but I would not call it "tonal;" I would say "harmonic." Yes, it's 'tonal' insofar as all sound is harmonic, and has some sense of gravity as an individual event or interval; but not 'tonal' as it applies to an entire octave, or scale, governed by a single tonic note.

Even an interval all by itself, like F-Bb (fourth), has a 'tonal meaning.' We tend to automatically hear a fourth as "tonic on top." So intervals in isolation have their own little gravity fields.


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## EdwardBast

millionrainbows said:


> This means that, for instance, Bartok using the *diminished scale* and creating a "quasi-tonality" by establishing fleeting local tone centers (derived from the way the diminished scale divides the octave into *3 parts*) is not tonal, because it does not establish an overall harmonic hierarchy which governs the entire octave, and the "centers" are based on geometric divisions of the diminished scale (12 ÷ 3 = 4), not on a harmonically-derived hierarchy (which you can hear).


The standard term for this scale in classical theory is _octatonic_. "Diminished scale" is used in jazz theory.

I think you mean 4 parts, not 3. It is the _hexatonic_ scale, sometimes called the Bartok scale, that divides the octave into three parts.



millionrainbows said:


> Yet, other "harmonic hierarchies" _are possible_ other than CP tonality's major/minor system. Debussy's use of the whole tone scale, though it creates instability, is best described as a "different" tonality rather than "atonal," since it uses the WT scale as a "scale" with 6 possible tonal centers, but no stable fifth.


Describing it as a different tonality would just be messy. If you are going to associate the term tonality with hierarchy, it is not wise to use the term with respect to a scale which has no intrinsic hierarchy. Wouldn't it be easier and less confusing to call music in a whole tone scale something like "whole tone" music?

Monty Python illustrates this problem succinctly. Pay attention particularly to the bit beginning at :52:


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## BabyGiraffe

millionrainbows said:


> Even an interval all by itself, like F-Bb (fourth), has a 'tonal meaning.' We tend to automatically hear a fourth as "tonic on top." So intervals in isolation have their own little gravity fields.


We don't hear any tonics, dominants and so on. We hear relations. Play or listen to a 100 hz sound wave. Then another at 150 hz . Are you going to hear the ratios or some indoctrinated musical theories from 16-18 century about what is what. 
There are too many things build on sand in the music theory - from the way we notate, the note names, how we label the different intervals, all the different harmonic, counterpoint etc theories (it is sad that some kids still learn from counterpoint books stating that M3rds are dissonant - it was only true for the Pythagorean tuning) and so on. People in the past didn't knew much about the sound waves, frequency bands, acoustics, dissonance curves etc, didn't have way to measure frequencies, didn't have modern oscilloscopes, spectrographs etc.
It's sad the same mantras repeated over and over.
It's easy to check the ratios of the different notes and scales and see why harmony works, which scales are actually symmetrical and based on different math sequences, why some things sound pleasant and why some horrible, why "atonality" is impossible and so on. The most sad part is about the equal divisions of the octave. There is a reason why they sound horrible - not only they are not equal, they make absolutely no sense to our brains.


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## EdwardBast

BabyGiraffe said:


> We don't hear any tonics, dominants and so on. We hear relations.


What do you think tonics and dominants are? They are notes or chords heard in _relation_ to a broader tonal context. Essentially, these terms and their relatives describe networks of *relations*!



BabyGiraffe said:


> Play or listen to a 100 hz sound wave. Then another at 150 hz . Are you going to hear the ratios or some indoctrinated musical theories from 16-18 century about what is what.


Obviously we _hear_ both! What we _understand_ when listening to music is the relationships between notes chords and contrapuntal lines as described in "musical theories from 16-18 century." Everyone who has listening competence with music of this era has an intuitive understanding of what is correct within the style and what is not. You are confusing acoustic phenomena with musical ones. We listen to the latter.



BabyGiraffe said:


> There are too many things build on sand in the music theory - from the way we notate, the note names, how we label the different intervals, all the different harmonic, counterpoint etc theories (it is sad that some kids still learn from counterpoint books stating that M3rds are dissonant - it was only true for the Pythagorean tuning) and so on.


No one, let alone kids, learns that M3rds are dissonant. Where did you get this idea? For those who understand harmony, counterpoint and notation the theories make good sense. Do you have any specific complaints?



BabyGiraffe said:


> People in the past didn't knew much about the sound waves, frequency bands, acoustics, dissonance curves etc, didn't have way to measure frequencies, didn't have modern oscilloscopes, spectrographs etc.


So? And if they did how would this have affected music theory and counterpoint?



BabyGiraffe said:


> It's sad the same mantras repeated over and over.
> It's easy to check the ratios of the different notes and scales and see why harmony works, which scales are actually symmetrical and based on different math sequences, why some things sound pleasant and why some horrible, why "atonality" is impossible and so on.


Using acoustic analysis to explain aesthetic issues with respect to harmony and melodic materials is like using chemical analysis to teach cooking.



BabyGiraffe said:


> The most sad part is about the equal divisions of the octave. There is a reason why they sound horrible - not only they are not equal, they make absolutely no sense to our brains.


They don't sound horrible, nor do harmonies built on equal divisions. No one with musical sense believes they do. Diminished and augmented chords are used to great and beautiful effect everywhere in classical music, as are whole tone, octatonic, and hexatonic scales and symmetrical triadic cycles. What on earth are you talking about?


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## BabyGiraffe

EdwardBast said:


> What do you think tonics and dominants are? They are notes or chords heard in _relation_ to a broader tonal context. Essentially, they describes networks of *relations*!
> 
> Obviously we _hear_ both! What we _understand_ when listening to music is the relationships between notes chords and contrapuntal lines as described in "musical theories from 16-18 century." Everyone who has listening competence with music of this era has an intuitive understanding of what is correct within the style and what is not. You are confusing acoustic phenomena with musical ones. We listen to the latter.
> 
> No one, let alone kids, learn that M3rds are dissonant. Where did you get this idea? For those who understand harmony, counterpoint and notation the theories make good sense. Do you have any specific complaints?
> 
> So? And if they did how would this have affected music theory and counterpoint?
> 
> Using acoustic analysis to explain aesthetic issues with respect to harmony and melodic materials is like using chemical analysis to teach cooking.
> 
> They don't sound horrible, nor do harmonies built on equal divisions. No one with musical sense believes they do. Diminished and augmented chords are used to great and beautiful effect everywhere in classical music, as are whole tone, octatonic, and hexatonic scales and symmetrical triadic cycles. What on earth are you talking about?


There is no difference between the acoustic and musical. There is a reason why certain things sound good to us and it's easy to understand and describe all the musical relations and facts with simple math. The Western notation and music theory is not useful and not practical describing, notating and analyzing most of the global music. But guess what, math is very capable of doing it.
I'm just saying that the views of certain individuals here have nothing in common with the reality. 
Especially when you start to talk about dividing the octave in parts etc. If you want to actually do such things, you have to use these things 
https://en.wikipedia.org/wiki/Superparticular_ratio
and they don't give your "symmetrical chords and scales".


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## EdwardBast

BabyGiraffe said:


> There is no difference between the acoustic and musical. There is a reason why certain things sound good to us and it's easy to understand and describe all the musical relations and facts with simple math. The Western notation and music theory is not useful and not practical describing, notating and analyzing most of the global music. But guess what, math is very capable of doing it.


Every sentence in this is egregiously wrong or misguided. I'll just number the sentences 1-4.
1. This is reductivist nonsense. It's like saying that since the world is made up of quarks, biology can be understood with particle physics. What you are missing is that higher order arrangements of matter and sounds have emergent properties that cannot be reduced to their substructural bases. New principles govern the higher levels of organization.
2. see 1 ^^^. Precisely the same error. 
3. Duh! Western music theory is good for describing western art music. The theory of Indian Classical music is good for describing … need I continue? 
4. No, see 1. Precisely the same error. You will have no better luck explaining any type of music because every system of musical organization ever conceived is governed by emergent properties that don't neatly reduce to acoustic properties.

You need to read about the aesthetic theory of emergent properties. Monroe Beardsley does a good short introduction to this in his _Aesthetics from Ancient Greece to the Present_, Jerrold Levinson treats it in more detail in Chapter 7 of his _Music, Art and Metaphysics_.


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## fluteman

EdwardBast said:


> The standard term for this scale in classical theory is _octatonic_. "Diminished scale" is used in jazz theory.
> 
> I think you mean 4 parts, not 3. It is the _hexatonic_ scale, sometimes called the Bartok scale, that divides the octave into three parts.
> 
> Describing it as a different tonality would just be messy. If you are going to associate the term tonality with hierarchy, it is not wise to use the term with respect to a scale which has no intrinsic hierarchy. Wouldn't it be easier and less confusing to call music in a whole tone scale something like "whole tone" music?
> 
> Monty Python illustrates this problem succinctly. Pay attention particularly to the bit beginning at :52:


Merely "liking" your post isn't enough, as it includes a classic and apt Monty Python skit. The one I cite most often in discussion groups like this is below, especially the exchange at 1:00.


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## fluteman

EdwardBast said:


> Every sentence in this is egregiously wrong or misguided. I'll just number the sentences 1-4.
> 1. This is reductivist nonsense. It's like saying that since the world is made up of quarks, biology can be understood with particle physics. What you are missing is that higher order arrangements of matter and sounds have emergent properties that cannot be reduced to their substructural bases. New principles govern the higher levels of organization.
> 2. see 1 ^^^. Precisely the same error.
> 3. Duh! Western music theory is good for describing western art music. The theory of Indian Classical music is good for describing … need I continue?
> 4. No, see 1. Precisely the same error. You will have no better luck explaining any type of music because every system of musical organization ever conceived is governed by emergent properties that don't neatly reduce to acoustic properties.
> 
> You need to read about the aesthetic theory of emergent properties. Monroe Beardsley does a good short introduction to this in his _Aesthetics from Ancient Greece to the Present_, Jerrold Levinson treats it in more detail in Chapter 7 of his _Music, Art and Metaphysics_.


I don't want to get too deeply into this debate, except to note that BabyGiraffe sounds suspiciously like someone who learns his living at least partly as a performing musician, and Edward Bast like someone who earns his as a musicologist / scholar / teacher. (Both of you could be composers and arrangers.) If I'm right about that, you two are profoundly different species and will never come near a meeting of the minds, even if this thread continues for another thousand posts.


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## Phil loves classical

Atonal in the strictest definition is the lack of a tonal center or key. But that does not mean there can't be harmonic relationships between individual notes. There are pieces with a lot of dissonance and passing notes but still tonal, that can be hard to distinguish from certain atonal works but containing a lot of harmonic relationships, just no centre. This may be where the lines get blurred, as they both seem to aim for the same thing, freedom from conventional melody. Baby Giraffe is right in that the intervals that sound pleasant are based on simpler mathematical ratios like dominants, perfect fourths, (why not M3rds though?).


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## Woodduck

Phil loves classical said:


> Baby Giraffe is right in that the intervals that sound pleasant are based on simpler mathematical ratios like dominants, perfect fourths, (why not M3rds though?).


Musical context and acculturation have more to do with what sounds pleasant than does the physics of sound. You're echoing BabyGiraffe's reductionism.


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## Phil loves classical

Woodduck said:


> Musical context and acculturation have more to do with what sounds pleasant than does the physics of sound. You're echoing BabyGiraffe's reductionism.


I thought it was like a scientific fact that those intervals sound right or pleasant to even a beginner in music, like something deeply ingrained in us, and have to do with the ratio of frequencies.


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## BabyGiraffe

EdwardBast said:


> Every sentence in this is egregiously wrong or misguided. I'll just number the sentences 1-4.
> 1. This is reductivist nonsense. It's like saying that since the world is made up of quarks, biology can be understood with particle physics. What you are missing is that higher order arrangements of matter and sounds have emergent properties that cannot be reduced to their substructural bases. New principles govern the higher levels of organization.
> 2. see 1 ^^^. Precisely the same error.
> 3. Duh! Western music theory is good for describing western art music. The theory of Indian Classical music is good for describing … need I continue?
> 4. No, see 1. Precisely the same error. You will have no better luck explaining any type of music because every system of musical organization ever conceived is governed by emergent properties that don't neatly reduce to acoustic properties.
> 
> You need to read about the aesthetic theory of emergent properties. Monroe Beardsley does a good short introduction to this in his _Aesthetics from Ancient Greece to the Present_, Jerrold Levinson treats it in more detail in Chapter 7 of his _Music, Art and Metaphysics_.


All the musical systems are based on acoustics. You can't understand what is going on, if your music knowledge is based on the standard Western theory which was created around the major scale - note names, name of the intervals, scale degrees etc. Sight reading Liszt's chromatic runs in F# are painful and most musician hate to play in this key. Why? Because of the way it has to be notated.
Analyzing anything that deviates from the harmony manuals (even Mozart does this) is impossible in this paradigm and you have to develop some warped systems to explain why is the music working when someone is "breaking" the rules of Western music. Of course, noone is breaking any rules and anyone who says that doesn't have an idea about why and how things work.

The theory of the Indian Classical music is good for describing the Western music, if you are willing to use their terms and add all the theory of harmony and counterpoint describing it in just intonation. They are playing the same 5-limit systems, but without all the simplifications (and with some occasional 7-limit intervals, but you can hear them too in the Western acapella singing too ). 
It's easy to describe both with terms like Euclidian distance norms, vals, just intonantion hobbit scales, formal periods, tempering of commas and other tuning jargon. It's just not practical to understand music with acoustic theories, if you want to limit your knowledge to pop music or some other style.


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## arpeggio

In music theory class in college we had a definition that we used. This definition has been used by many members.

Based on the discussions here, I have no idea what it would be. Most of the time I have no idea what you guys are talking about even from the pro-atonal crowd. My music theory professor made more sense.

I do know this. During the first fifty years of my life I disliked Schoenberg. Now that I understand him I am being told by many experts here that his music is junk and I am wasting my time listening to him. Heaven protect me from the wrath of the powers that be if I start to understand Xenakis.


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## Guest

Gabriel Ortiz said:


> "_Why do people try so hard to explain the beauty of music, thus depriving it of its mystery?_"
> 
> An underappreciated quote from Bernstein's Norton Lectures.


I guess I'd need to listen to the whole lecture to understand his point. Taken out of context, it's a nonsense: why do people try so hard to explain life?



Phil loves classical said:


> Baby Giraffe is right in that the intervals that sound pleasant are based on simpler mathematical ratios like dominants, perfect fourths, (why not M3rds though?).


Well, I don't know how many "tonal" composers consciously used maths to construct their works, but I suspect that Mozart wrote his 40th because of how it sounded (and because of its relationship to his previous works and the cultural context of the period) not because of how the maths worked.

The fact that maths can be used to provide one "explanation" of music does not give it some _preeminence _in understanding what it is about music that enthrals or repels.


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## BabyGiraffe

MacLeod said:


> The fact that maths can be used to provide one "explanation" of music does not give it some _preeminence _in understanding what it is about music that enthrals or repels.


Music is all about the same basic principles that can be described using math and apply to any aspect of our appreciation of the good art (some system like the 12-tone composition and similar could be attractive to some alien species, but we can't comprehend them).
You can check Ptolemy about the way Ancient Greeks and Romans used to teach and understand musical concepts.

This is what you hear when you listen to Bach, Mozart or any "good" music.

Enthrals:

















This is the 21st century.

Repels:

(Modernist painting that sold for 26 millions.)







(34 millions)









Galio Galilei said that:
"Philosophy is written in that great book which ever lies before our eyes - I mean the universe - but we cannot understand it if we do not first learn the language and grasp the symbols, in which it is written. This book is written in the mathematical language, and the symbols are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word of it; without which one wanders in vain through a dark labyrinth."

The Assayer (1623), as translated by Thomas Salusbury (1661), p. 178, as quoted in The Metaphysical Foundations of Modern Science (2003) by Edwin Arthur Burtt, p. 75.

There are more than enough studies on acoustics, human cognition etc that you can research on your own, if you are interested in these topics and math behind them.


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## Art Rock

BabyGiraffe said:


> Repels:
> 
> View attachment 95250
> 
> .


Richter is one of my all-time favourite artists. I adore his abstracts. If you don't like them, fine, but so not assume that others do not.


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## BabyGiraffe

Art Rock said:


> Richter is one of my all-time favourite artists. I adore his abstracts. If you don't like them, fine, but so not assume that others do not.


I didn't say that there are no people that don't like such patterns.
_Most _ people don't care about random blobs just like most people don't care about random sound collages without perceivable structure.
You have your own perception, but it's not universal.


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## Art Rock

EDIT: never mind. Nietzsche was right.


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## Guest

BabyGiraffe said:


> Music is all about the same basic principles that can be described using math and apply to any aspect of our appreciation of the good art (some system like the 12-tone composition and similar could be attractive to some alien species, but we can't comprehend them).
> You can check Ptolemy about the way Ancient Greeks and Romans used to teach and understand musical concepts.
> 
> This is what you hear when you listen to Bach, Mozart or any "good" music.
> 
> [...]
> 
> There are more than enough studies on acoustics, human cognition etc that you can research on your own, if you are interested in these topics and math behind them.


Thank you. I think you miss my point, which was not to challenge the idea that there is a mathematical explanation, but to challenge the idea that such an explanation must be pre-eminent in our understanding.

What I _hear_ - a highly personal experience - cannot be represented by maths or a painting, even though I know the sounds and their relationships are amenable to a formal mathematical analysis. As far as I am concerned, it is what I hear that is pre-eminent in my understanding.


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## BabyGiraffe

MacLeod said:


> Thank you. I think you miss my point, which was not to challenge the idea that there is a mathematical explanation, but to challenge the idea that such an explanation must be pre-eminent in our understanding.
> 
> What I _hear_ - a highly personal experience - cannot be represented by maths or a painting, even though I know the sounds and their relationships are amenable to a formal mathematical analysis. As far as I am concerned, it is what I hear that is pre-eminent in my understanding.


Your reactions to stimuli can be personalized and we can be trained to react in a certain way to different situations, but there are natural affinities to some patterns, frequency ranges etc.
Some people are trying to compose music for animals (like cats, monkeys, parrots) that is fitting their hearing range, vocalizations, hertbeat. It's interesting that the parrots are the only animals that respond with interest to our rhythms and their dances are pretty close to these of humans dancing to the same rhythm.


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## EdwardBast

BabyGiraffe said:


> All the musical systems are based on acoustics. You can't understand what is going on, if your music knowledge is based on the standard Western theory which was created around the major scale - note names, name of the intervals, scale degrees etc. Sight reading Liszt's chromatic runs in F# are painful and most musician hate to play in this key. Why? Because of the way it has to be notated.
> Analyzing anything that deviates from the harmony manuals (even Mozart does this) is impossible in this paradigm and you have to develop some warped systems to explain why is the music working when someone is "breaking" the rules of Western music. Of course, noone is breaking any rules and anyone who says that doesn't have an idea about why and how things work.


You are talking in vague generalities. What do you mean by musical systems? What specific complaints do you have about note names and intervals? Can you give an example of something deviating "from the harmony manuals that is impossible in this paradigm"? What warped systems are you talking about? Could you give a single concrete example of anything you are addressing?


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## EdwardBast

BabyGiraffe said:


> There are more than enough studies on acoustics, human cognition etc that you can research on your own, if you are interested in these topics and math behind them.


Actually we are interested in music theory, which is why we are here in the Music Theory Forum. It is hard to tell if you have a clear understanding of what western music theory is about. You seem to be confusing it with acoustic theory. What does it mean to you to analyze a work by Mozart?


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## Woodduck

Phil loves classical said:


> I thought it was like a scientific fact that those intervals sound right or pleasant to even a beginner in music, like something deeply ingrained in us, and have to do with the ratio of frequencies.


It is not a scientific fact, nor even "like" one. Can you point to scrupulously controlled studies done with humans who have no knowledge of any music (young children, for example)? Such studies, which would eliminate the factors of musical and cultural experience, would be the only way to prove your simplistic theory of what sounds "pleasant" to humans as such. In fact, it's easily shown, and has been shown by studies of the musical perceptions of people in different cultures, that pleasure does not necessarily correlate with the complexity of frequency ratios. Physiologically, intervals with simple ratios are less stimulating than those with more complex ratios, but a lack of stimulation is not necessarily experienced as pleasant. It may simply be uninteresting.


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## Guest

BabyGiraffe said:


> It's interesting that the parrots are the only animals that respond with interest to our rhythms and their dances are pretty close to these of humans dancing to the same rhythm.


Not quite the response I was expecting, which might have gone something like:



BabyGiraffe said:


> "OK, fair enough, I get that you don't give primacy to the maths of it all and yes, of course, I can see that for some/many people, it's what they hear and how they respond to it (intellectually, emotionally, physically, spiritually) that is of greatest importance. I can nevertheless point you to sources that show that Mozart/Beethoven/Bach/ understood the maths and consciously composed according to the maths and not just for the sheer love of the sounds."


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## millionrainbows

EdwardBast said:


> The standard term for this scale in classical theory is _octatonic_. "Diminished scale" is used in jazz theory.


Hey, you're standard.



EdwardBast said:


> I think you mean 4 parts, not 3. It is the _hexatonic_ scale, sometimes called the Bartok scale, that divides the octave into three parts.


Yes, that's right, 4 parts.



EdwardBast said:


> Describing it as a different tonality would just be messy. If you are going to associate the term tonality with hierarchy, it is not wise to use the term with respect to a scale which has no intrinsic hierarchy.


That's not necessarily true. A WT scale can have 6 possible "roots" and you can build augmented triads on each step. "Intrinsic hierarchy?" What's that?



EdwardBast said:


> Wouldn't it be easier and less confusing to call music in a whole tone scale something like "whole tone" music?


Yes, as a subset of "tonality." You could call it a "whole tone tonality," but not "atonal" in the way Debussy uses it. Schoenberg used the WT scale as two areas a half-step apart, since there are only two WT scales in the total chromatic, and this was also a "quasi-tonality," especially because the minor second is related to the fifth as a tritone, and this was used to create a form of disguised I-V progression.


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## millionrainbows

BabyGiraffe said:


> The most sad part is about the equal divisions of the octave. There is a reason why they sound horrible - not only they are not equal, they make absolutely no sense to our brains.


I don't agree; whole tone runs sound especially shimmering, and that's why Debussy used them: we were getting closer to achieving true ET.

Also, in ET, the fifths are only 2 cents flat, and most people can't even hear a two cent difference (I was tested, and I can, but just barely). So ET favors fifths, which allows for root movement and stability of triads.


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## EdwardBast

millionrainbows said:


> That's not necessarily true. A WT scale can have 6 possible "roots" and you can build augmented triads on each step. "Intrinsic hierarchy?" What's that?


I should have written that WT scales are intrinsically non-hierarchical, meaning there is nothing about the relations of the pitches that favors any pitch in the scale over any other.



millionrainbows said:


> Yes, as a subset of "tonality." You could call it a "whole tone tonality," but not "atonal" in the way Debussy uses it. Schoenberg used the WT scale as two areas a half-step apart, since there are only two WT scales in the total chromatic, and this was also a "quasi-tonality," especially because the minor second is related to the fifth as a tritone, and this was used to create a form of disguised I-V progression.


"Okay Bruce. No confusion there. What do you think Bruce?" 
"I'm fine with it Bruce. But we better ask Bruce what he thinks."
"Okay, I will. Hey Bruce, what's your opinion on this?
"Huh?"

(Terminology is better when it differentiates unlike things rather than making them sound the same.)


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## millionrainbows

EdwardBast said:


> I should have written that WT scales are intrinsically non-hierarchical, meaning there is nothing about the relations of the pitches that favors any pitch in the scale over any other.


You called it a whole tone *scale,* so you have to recognize the parameters of that designation. Scales are most often presented as spanning an octave, with a 'starting note'. This already implies a tonic, because scales are "intrinsically" tonal devices.

With this, it's easy to make an hierarchy, by building triads on each scale step, and giving them a function.

The only thing that "function" does is project an hierarchy of triads, in relation to the tonic, by degree of consonance.

So, to an extent, these structures are created "automatically" as a consequence of constructing triads on the scale-steps. 

In the case of the whole-tone scale, if it is referenced in a tonal context, it is inherently an unstable "deconstructing" element, tonally speaking; the best it can manage is a "suspended" feel, or altered dominant; but it can definitely be used to suggest tonal areas of function. 

Like Thelonious Monk did, it can be used as a dominant element, reinforcing a dominant 7 sound. 

Example: in C major, a whole-tone scale beginning on G (G-A-B-C#-D#-F) suggests a G aug 9, or a G7b5. Let's build some triads, from C: (C-D-E-F#(Gb)-G#(Ab)-A#(Bb).

I: C-E-Gb: Cb5, C-E-G#: C aug, which repeats on every scale step, since the scale is symmetrical. This makes it usable for those functions on each step. Any "modal" permutation (starting on D, E, F#, etc) are simply reiterations, and are essentially identical, and will yield the same content. Limited, but flexible.

Additionally, the whole-tone is a 6-note scale, so there are only 2 of them per octave. This allows 2 areas of tonality to be created, a semitone apart. Since the semitone can be a tritone substitution (the "chromatic/fifths" connection), this creates a "I-V" contrast which can be exploited tonally. Debussy did this. Schoenberg also used a row constructed on similar lines to "suggest" this same effect, although in essence, his tone-row is not "tonal" in a structural sense.


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## Phil loves classical

Woodduck said:


> It is not a scientific fact, nor even "like" one. Can you point to scrupulously controlled studies done with humans who have no knowledge of any music (young children, for example)? Such studies, which would eliminate the factors of musical and cultural experience, would be the only way to prove your simplistic theory of what sounds "pleasant" to humans as such. In fact, it's easily shown, and has been shown by studies of the musical perceptions of people in different cultures, that pleasure does not necessarily correlate with the complexity of frequency ratios. Physiologically, intervals with simple ratios are less stimulating than those with more complex ratios, but a lack of stimulation is not necessarily experienced as pleasant. It may simply be uninteresting.


What I mean by pleasant is the degree of consonance, which is why they call "perfect" fourths and fifths? These ratios 3:2 for perfect fifth, 4:3 for perfect fourth and 2:1 for octave are the the basics of harmony and tonality, no? The human ear is sensitive to these relative frequencies or harmonics.


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## Woodduck

_What I mean by pleasant is the degree of consonance, which is why they call "perfect" fourths and fifths? These ratios 3:2 for perfect fifth, 4:3 for perfect fourth and 2:1 for octave are the the basics of harmony and tonality, no? The human ear is sensitive to these relative frequencies or harmonics._

Acoustically, the terms "consonance" and "dissonance" are indeed identified with the simplicity or complexity of frequency ratios. Unfortunately, consonance and dissonance are also concepts in Western harmonic theory which refer to the stability or self-sufficiency of a chord versus its instability or need for resolution, as well as purely psychological concepts equivalent to "pleasantness" and "unpleasantness." The relationships between acoustical consonance and dissonance, the artistic uses of intervals, and subjective pleasure, are not simple.

It's a mistake to confuse, as you have, these three ways of using the terms "consonance" and "dissonance."


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## Phil loves classical

Woodduck said:


> _What I mean by pleasant is the degree of consonance, which is why they call "perfect" fourths and fifths? These ratios 3:2 for perfect fifth, 4:3 for perfect fourth and 2:1 for octave are the the basics of harmony and tonality, no? The human ear is sensitive to these relative frequencies or harmonics._
> 
> Acoustically, the terms "consonance" and "dissonance" are indeed identified with the simplicity or complexity of frequency ratios. Unfortunately, consonance and dissonance are also concepts in Western harmonic theory which refer to the stability or self-sufficiency of a chord versus its instability or need for resolution, as well as purely psychological concepts equivalent to "pleasantness" and "unpleasantness." The relationships between acoustical consonance and dissonance, the artistic uses of intervals, and subjective pleasure, are not simple.
> 
> It's a mistake to confuse, as you have, these three ways of using the terms "consonance" and "dissonance."


Here is a discussion on Wikipedia I just found. There is a more objective definition and also a more subjective definition of the pleasant tie with consonance. There is use of musical context that affects consonance and dissonance wasn't discussed earlier.

https://en.m.wikipedia.org/wiki/Consonance_and_dissonance


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## fluteman

Woodduck said:


> The relationships between acoustical consonance and dissonance, the artistic uses of intervals, and subjective pleasure, are not simple.


There you have it. And that's why threads like this go nowhere despite numerous intelligent comments. This subject cannot be summed up in a couple of sentences. If you restrict the discussion to traditional western harmony, and traditional western music principles generally, and a narrow cultural context, as some of the posters here implicitly do, you can make some observations about the relationship of harmony, consonance, dissonance, etc. to emotional and psychological impact. Even there, the listener's own background, psychological and intellectual makeup and expectations play a large role in the impact of the music he or she hears. So you need to make a lot of assumptions about the audience as well before any of these generalizations have any validity.


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## EdwardBast

millionrainbows said:


> You called it a whole tone *scale,* so you have to recognize the parameters of that designation. Scales are most often presented as spanning an octave, with a 'starting note'. This already implies a tonic, because scales are "intrinsically" tonal devices.


One line in and you have already made a logical and factual mess of it. "Most often" does not mean always. One can start on any note in a WT collection, so no implied tonic. Some scales are modal, not tonal. In short, I don't have the time or interest to go on a bug hunt through the rest of your post.


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## BabyGiraffe

Consonance vs dissonance - there is nothing subjective here outside of the social conditioning. Brainwashing someone with complex and clashing sounds eventually may distort his natural perceptions and he/she can start to like, but this doesn't make it more pleasing for the majority.

About the whole tone in 12et - it's scale is a sequence of intervals that modulates throughout different keys. If you really want to hear equal divisions of octave, you have to use epimoric ratios.

Divide the octave two times and you have a 3-limit chord: 1/1-3/2-2/1(CGC). 
Divide it three times and you get a 5-limit chord- 1/1 - 4/3-5/3-2/1 (CFA(-16 cents compared to 12et))
Four times - 7-limit chord: 1/1-5/4-3/2-7/4 -2/1. (CE(-14c)GBb(-31 c)) Can be heard often performed by a capella groups. There is a wonderful a capella version of Nimrod on youtube where you can hear it clearly along with other pure chords.
Five times -7-limit- 1/1- 6/5 - 7/5 - 8/5 - 9/5- 2/1 (dominant ninth in inversion that actually sounds decent, because the notes don't clash too much - as they would in 12et).
Six times - 1/1- 7/6 - 4/3 - 3/2 - 5/3 -11/6 - to me it sounds very North African , probably can even work as a chord unlike the whole tone scale.
Diving seven times gives us 13-limit scale having more in common with the whole tone scale than the previous 11-limit scale, if you don't mind adding or subtracting around 20-30 cents per note and one additional note.
8 times - scale containing harmonic 1 to 16. Pretty popular in Asia and Africa as a gamut for pentatonic subsets. Composers like Bartok invoke this scale, but it sounds distorted in 12et.
You can do the math using a calculator and check that these (or any other superparticular division) are all equal and musical sounding.
The same ratios can be used as rhytms or polyrhythms. There are more than enough studies about the parallels between the pitch contents and the rhythms used in the Middle Eastern and African music; and African or Carnatic rhythmical concepts can be used for creation of JI scales that are harmonious not only to the root, but also between themselves .


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## EdwardBast

BabyGiraffe said:


> Consonance vs dissonance - there is nothing subjective here outside of the social conditioning. Brainwashing someone with complex and clashing sounds eventually may distort his natural perceptions and he/she can start to like, but this doesn't make it more pleasing for the majority.
> 
> About the whole tone in 12et - it's scale is a sequence of intervals that modulates throughout different keys. If you really want to hear equal divisions of octave, you have to use epimoric ratios.
> 
> Divide the octave two times and you have a 3-limit chord: 1/1-3/2-2/1(CGC).
> Divide it three times and you get a 5-limit chord- 1/1 - 4/3-5/3-2/1 (CFA(-16 cents compared to 12et))
> Four times - 7-limit chord: 1/1-5/4-3/2-7/4 -2/1. (CE(-14c)GBb(-31 c)) Can be heard often performed by a capella groups. There is a wonderful a capella version of Nimrod on youtube where you can hear it clearly along with other pure chords.
> Five times -7-limit- 1/1- 6/5 - 7/5 - 8/5 - 9/5- 2/1 (dominant ninth in inversion that actually sounds decent, because the notes don't clash too much - as they would in 12et).
> Six times - 1/1- 7/6 - 4/3 - 3/2 - 5/3 -11/6 - to me it sounds very North African , probably can even work as a chord unlike the whole tone scale.
> Diving seven times gives us 13-limit scale having more in common with the whole tone scale than the previous 11-limit scale, if you don't mind adding or subtracting around 20-30 cents per note and one additional note.
> 8 times - scale containing harmonic 1 to 16. Pretty popular in Asia and Africa as a gamut for pentatonic subsets. Composers like Bartok invoke this scale, but it sounds distorted in 12et.
> You can do the math using a calculator and check that these (or any other superparticular division) are all equal and musical sounding.
> The same ratios can be used as rhytms or polyrhythms. There are more than enough studies about the parallels between the pitch contents and the rhythms used in the Middle Eastern and African music; and African or Carnatic rhythmical concepts can be used for creation of JI scales that are harmonious not only to the root, but also between themselves .


Okay, I understand. What you are talking about is a subject on the periphery of music theory where it intersects with acoustics. When theorists talk about analysis, this is not what they mean. When they talk about why a progression works, they are not thinking about ratios of any kind. They are talking about counterpoint and voice-leading and root movement. With the vocabulary you are using above, you could address virtually none of the quotidian concerns of music theorists.


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## Vox Gabrieli

Bettina said:


> That's ironic coming from Bernstein, who gave hundreds of lectures on the inner workings of music!


It's the thought that counts. :tiphat:


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## fluteman

BabyGiraffe said:


> Consonance vs dissonance - there is nothing subjective here outside of the social conditioning. Brainwashing someone with complex and clashing sounds eventually may distort his natural perceptions and he/she can start to like, but this doesn't make it more pleasing for the majority.


Then how do you explain the gradual evolution of western music, where first only the unison was considered consonant, then the fifth, and finally the third, eventually resulting in a harmonic system based on the triad? How do you explain why the Well Tempered Clavier sounds slightly dissonant when played with a scale that is not equal tempered, even though Bach likely did not have the then-newly developed and far from universal equal-tempered scale in mind when he wrote it? How is it that a certain scales sound North African, or Middle Eastern, or Indian, or Japanese, i.e., foreign, strange, and at least slightly unpleasant, to western ears? Music is like milk. If you've been raised on cow's milk, goat's milk tastes a little strange and bad, and vice versa. The ear naturally adapts to the sounds of its environment, no "brainwashing" needed. And it's been convincingly demonstrated to me that the ear will eventually accept intervals one might consider harshly dissonant and unpleasant as perfectly pleasant if exposed to them long enough.
All of which is to say, the subjective element of hearing is considerable, and complex.


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## arpeggio

If I don't like it, it is atonal


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## Woodduck

BabyGiraffe said:


> Consonance vs dissonance - there is nothing subjective here outside of the social conditioning. *Brainwashing* someone with complex and clashing sounds eventually may distort his natural perceptions and he/she can start to like, but this doesn't make it more pleasing for the majority.


This persistent identification of acoustical consonance with pleasantness contains, at most, half a grain of truth, and tells us nothing of value. Even if it could be shown that a majority of people with no experience of actual music would find an isolated perfect fifth more pleasant than an isolated minor third, what would that tell us about how these sounds are perceived and enjoyed in music? The answer is: almost nothing.

Do you find music consisting of nothing but unison melody more "pleasant" than music with harmony? Music consisting of octaves and perfect fifths more "pleasant" than music containing thirds? Music with suspensions or chromaticism less "pleasant" than simple successions of triads? Assuming that the answer is "no" in every case - why? Have you been "brainwashed"?

We generally enjoy the sound of dissonant intervals resolving to more consonant ones, but it is the contrast and the resolving, not the consonance as such, that we enjoy most. Tension and relaxation, activity and rest, succeeding each other: without yang, yin quickly palls and bores - and the reverse likewise. Tension and activity are, at least, evidence of life. Perfect repose is death.


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## isorhythm

^^Exactly this - a piece consisting only of the most consonant intervals would sound pretty bad.


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## BabyGiraffe

isorhythm said:


> ^^Exactly this - a piece consisting only of the most consonant intervals would sound pretty bad.


All the vocal church music is bad then, if we use your definitions. All the Indian classical music is bad then (using 22 notes per octave for perfect badness and being unable to modulate to other distant keys - such idiots). 
Why do you think that many people cry when they hear perfect harmony - because it's bad. Even vulgar pop/rock/electronic songs can sound as sacred as something from Palestrina, if they were recorded in perfect badness.
Some instruments like our voices, unfretted string instruments, trombones etc are capable of producing such bad harmony.

Why does Bach wouldn't sound great in JI - because you can't play him in JI with 12 keys. You will need way more than that. Check the millionrainbows' link about Bach's tuning. The problem is not in acoustics or Bach's music, it is in the physical limitations of the human limbs, memory and the design of our instruments. 
Why do we need more more dissonant and distorted intervals - because they add interest. Oriental music used to be described by the 19th century writers as too sensual and even decadent. Wide microtonal pitch inflections and melismas using neutral intervals would be out of place when you want to invoke holiness with your chords and melodies instead of lust or agitation. 
The most perfect instruments capable of the most perfect consonance are the synthesizers - they can play unisons without any phasing effects (good luck doing this with natural instruments) and this sound is completely flat, uninteresting and boring to us. 
If someone finds the traditional world music strange, it's because he is being exposed too much to contemporary midi based pop/electronic. If even untrained person can recognize 25 cents difference between two notes, there are 48 notes per octave.

Do you think that you have heard all of them? What happens when someone is exposed to anything outside of his comfort zone?
Atonal composers using system that is not made to handle anything more than 3-limit chords - octaves and fifths (5-limit intervals like M3 and m3 are distorted in 12et) are writing music that sounds horribly out of tune using cluster and similar.
The exotic Chinese, Arabic etc intervals didn't appear out of nothing, it's all math. There was a conference in Egypt in 1932 where people from North Africa and Middle East tried to make unified musical system. It failed, because some of the people thought that 24et or any other tempered system will ruin the beaty of their music. 
https://en.wikipedia.org/wiki/Cairo_Congress_of_Arab_Music


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## millionrainbows

EdwardBast said:


> One line in and you have already made a logical and factual mess of it. "Most often" does not mean always. One can start on any note in a WT collection, so no implied tonic. Some scales are modal, not tonal. In short, I don't have the time or interest to go on a bug hunt through the rest of your post.


Debussy used the WT scale in a tonal way. The problem is, the WT scale is not a good example for defining any aspect of tonality, since it is harmonically vague (flatted fifths, symmetrical) and also based on a geometrical (not acoustical) division of the 12 note chromatic octave. It is in "both worlds."

I don't have time to pursue these vagaries either, which were presented for the purposes of your argumentation, and have served no clarifying purpose.


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## millionrainbows

Dissonance and consonance are not absolutes; they represent relationships. All sound starts with one note, which is "1" or 1:1, and goes from there. 2:1, 3:1, 4:1, etc.
Tonality is based on this; "1" is tonic, and the functions built on the steps of the scale are ratios of that: in C, G is 3:2, F is 4:3, E is 5:4, Eb is 6:5.

We generally enjoy the sound of dissonant intervals resolving to more consonant ones, but it is the contrast and the resolving, not the consonance as such, that we enjoy most. Tension and relaxation, activity and rest, succeeding each other...

I don't see how you can separate the two, except for purposes of argumentation.

I think Baby Giraffe needs to proceed with prudence, because this is a big, gnarly area, and he already seems to have created more tension than resolution. Also, the critics out there need to lighten up.

As I've said elsewhere, in the 'religion and music' threads, consonance or "the drone" of 1:1 has always had a spiritual or quasi-religious significance.

Gregorian chant shows this 'drone-like' quality, which was there before harmony developed. The fifth (of organum) came next, so in the development of harmony, the overtone relation to "1" has shown itself to manifest naturally.


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## Barbebleu

arpeggio said:


> If I don't like it, it is atonal


Well you nearly have it summed up. If it doesn't grate on your ears it is not atonal!


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## fluteman

Barbebleu said:


> Well you nearly have it summed up. If it doesn't grate on your ears it is not atonal!


Atonal this, atonal that.
Some say the fundamental elements of music are melody, rhythm, harmony and timbre. I was taught something similar as a child. Others reasonably list additional elements such as dynamics. Whatever the exact makeup of the list of fundamental elements, I think it's safe to say humans have a natural affinity for listening to all of them, often in regular structures and patterns. That makes sense. We naturally listen for patterns to help us make sense of our world, in human language, animal sounds, even to gauge the weather, and in the post-industrial era, many synthetic sounds.
So why do some here focus so much on just one of these elements, i.e., harmony? Why not talk about arrhythmic music, which certainly became a big thing in the 20th century? In fact, radical experiments with rhythm, dynamics and timbre seemed to be more significant trends in modern music in the second half of the 20th century. You certainly hear it with Boulez, Xenakis and the electronic composers. Experiments with harmony were already old news for them.


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## Woodduck

fluteman said:


> Atonal this, atonal that.
> Some say the fundamental elements of music are melody, rhythm, harmony and timbre. I was taught something similar as a child. Others reasonably list additional elements such as dynamics. Whatever the exact makeup of the list of fundamental elements, I think it's safe to say humans have a natural affinity for listening to all of them, often in regular structures and patterns. That makes sense. We naturally listen for patterns to help us make sense of our world, in human language, animal sounds, even to gauge the weather, and in the post-industrial era, many synthetic sounds.
> *So why do some here focus so much on just one of these elements, i.e., harmony? * Why not talk about arrhythmic music, which certainly became a big thing in the 20th century? In fact, radical experiments with rhythm, dynamics and timbre seemed to be more significant trends in modern music in the second half of the 20th century. You certainly hear it with Boulez, Xenakis and the electronic composers. Experiments with harmony were already old news for them.


I've asked that question too. I can think of several reasons:

1. Harmony in Western music became, through the elaboration of tonality, the principal vehicle of formal design which made varied and large-scale forms possible. Increasing chromaticism posed problems of structure which Schoenberg's 12-tone system was purportedly designed to solve.

2. Schoenberg, following Wagner, was preoccupied with harmony, and atonal harmony disturbed people in a way that, say, Stravinsky's irregular rhythms didn't.

3. There has never been, to my knowledge, a systematic theory of melody, rhythm or timbre corresponding to harmonic theory.

4. Harmony can be related in obvious ways to physical science - the acoustics of sound - and those with a scientific bent can have fun doing math, rolling out graphs and charts, pointing up correspondences, and propounding theories about why music sounds the way it does.

At this point in history there may not be anything new to say about the West's harmonic heritage, but atonality will remain a wall that every classical music listener runs smack into. The other elements of music are interesting, but they don't pose comparable problems. And so we keep talking about harmony.


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## BabyGiraffe

Woodduck said:


> I've asked that question too. I can think of several reasons:
> 
> 1. Harmony in Western music became, through the elaboration of tonality, the principal vehicle of formal design which made varied and large-scale forms possible. Increasing chromaticism posed problems of structure which Schoenberg's 12-tone system was purportedly designed to solve.
> 
> 2. Schoenberg, following Wagner, was preoccupied with harmony, and atonal harmony disturbed people in a way that, say, Stravinsky's irregular rhythms didn't.
> 
> 3. There has never been, to my knowledge, a systematic theory of melody, rhythm or timbre corresponding to harmonic theory.
> 
> 4. Harmony can be related in obvious ways to physical science - the acoustics of sound - and those with a scientific bent can have fun doing math, rolling out graphs and charts, pointing up correspondences, and propounding theories about why music sounds the way it does.
> 
> At this point in history there may not be anything new to say about the West's harmonic heritage, but atonality will remain a wall that every classical music listener runs smack into. The other elements of music are interesting, but they don't pose comparable problems. And so we keep talking about harmony.


Harmony is the simplest thing to analyse and harmony is dependant of the gamut you are using. (For example there is are no options for harmony in a typical 7tone Oriental scale - most of them are pentatonic collections with added 2 microtonal pitches, so you will have only 1 or 2 chords that don't clash per scale. To make a decent oriental scale that supports harmony, you will have to use way more than 7 pitches.) 
Different gamuts will have different harmonic theories and different things that work in them (Vishnegradsky's "diatonic" in 24et is a MOS based on generator 11 or 13, the diatonic in 12et is based on generator 7 or 5), but they still obey to acoustics.
I think that there are melody theories in Schillinger's book using different vectors and axis. 
There are also many theories of rhythm, but they are too math heavy and this is the reason why they aren't taught at school (books that deal with specific ethnic rhythms are probably all that any composer would need - Messiaen studied Indian theories, but there are Balkan, African, Oriental and )
Timbre - plenty of books that deal with acoustics. Again you need math. Search Amazon or Jstor (for articles about timbre).

And what are the problems that atonality represents?


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## isorhythm

If anyone's looking for a lucid explanation of what BabyGiraffe is talking about, I'd recommend Kyle Gann's online articles. It's not relevant to what the rest of us are talking about in this thread, however.


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## BabyGiraffe

isorhythm said:


> If anyone's looking for a lucid explanation of what BabyGiraffe is talking about, I'd recommend Kyle Gann's online articles. It's not relevant to what the rest of us are talking about in this thread, however.


Well I was just respoding to the previous comment about harmony.

Here is something interesting:

"The overtone series … still contains many problems that will have to be faced. And if for the
time being we still manage to escape those problems, it is due to little else than a compromise
between the natural intervals and our inability to use them - that compromise which we call
the tempered system, which amounts to an indefinitely extended truce. This reduction of the
natural relations to manageable ones cannot permanently impede the evolution of music; and
the ear will have to attack the problems, because it is so disposed. Then our scale will be
transformed into a higher order, as the church modes were transformed into major and minor
modes. Whether there will then be quarter tones, eighth, third, or (as Busoni thinks) sixth
tones, or whether we will move directly to a 53-tone scale … we cannot foretell. Perhaps this
new division of the octave will even be untempered and will not have much left over in
common with our scale."

Arnold Schoenberg, Theory of Harmony, page 25

He knew some acoustics and still wrote atonal music for piano that clashes with the way it is tuned... Extended chords and polytonal clusters are interesting problems for the performers. I wonder how wind, brass, string players decide the exact values of the pitches, that can be played without discords - the practice to notate exactly the intonation is contemporary and many orchestral recordings deliver different interpretations of famous pieces - Wagner is the obvious case.


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## fluteman

Woodduck said:


> I've asked that question too. I can think of several reasons:
> 
> 1. Harmony in Western music became, through the elaboration of tonality, the principal vehicle of formal design which made varied and large-scale forms possible. Increasing chromaticism posed problems of structure which Schoenberg's 12-tone system was purportedly designed to solve.
> 
> 2. Schoenberg, following Wagner, was preoccupied with harmony, and atonal harmony disturbed people in a way that, say, Stravinsky's irregular rhythms didn't.
> 
> 3. There has never been, to my knowledge, a systematic theory of melody, rhythm or timbre corresponding to harmonic theory.
> 
> 4. Harmony can be related in obvious ways to physical science - the acoustics of sound - and those with a scientific bent can have fun doing math, rolling out graphs and charts, pointing up correspondences, and propounding theories about why music sounds the way it does.
> 
> At this point in history there may not be anything new to say about the West's harmonic heritage, but atonality will remain a wall that every classical music listener runs smack into. The other elements of music are interesting, but they don't pose comparable problems. And so we keep talking about harmony.


Well, if that's so, I'll just have to continue as an outsider to all of this, because I don't understand this special status of harmony. Hearing "Stravinsky's irregular rhythms" for the first time was a profound experience for me, far more so than hearing Schoenberg's "atonality" for the first time, and perhaps the most profound single experience I've ever had listening to music. When I was 17 and finally got to perform Stravinsky for the first time (Ragtime) it was an equally profound experience.

And as a classical music listener myself, I can't agree that "atonality will remain a wall that every classical music listener runs smack into", at least not any more than any of these other "walls". Remember that the ideas of 20th century modernists have long since filtered into our popular music, TV, movies and popular culture in general. Some here dismiss all that as "sound effects", but everyone born since 1960 (at least) has grown up with those sounds. In fact, it is the symphonies and string quartets of Haydn and Mozart that are increasingly walls that younger generations run smack into and quickly turn away (never mind four-hour Wagner operas), a sad situation that will only worsen if we neglect music education.


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## millionrainbows

It seems to me that harmony, as a relation of all tones to a central tonic tone, is a natural phenomenon which developed out of natural phenomena. We all can relate to "the drone" as a center of being, as a manifestation of our own being, as a spiritual manifestation of being.


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## Woodduck

fluteman said:


> And as a classical music listener myself, I can't agree that "atonality will remain a wall that every classical music listener runs smack into", at least not any more than any of these other "walls". Remember that the ideas of 20th century modernists have long since filtered into our popular music, TV, movies and popular culture in general. Some here dismiss all that as "sound effects", but everyone born since 1960 (at least) has grown up with those sounds. In fact, it is the symphonies and string quartets of Haydn and Mozart that are increasingly walls that younger generations run smack into and quickly turn away (never mind four-hour Wagner operas), a sad situation that will only worsen if we neglect music education.


I think you underestimate the fundamental appeal of tonality to the human brain. Do you think it's accidental that most of the world's music has always exhibited tonality of some kind? I'm betting it always will. Tonality doesn't have to be Mozart's or Wagner's kind. Schoenberg's attack on tonal centers and hierarchies was and remains an anomaly, regardless of its influence in the 20th century and regardless of the segment of classical music listeners who have embraced the resulting music for its own peculiar qualities. The brave new world you're suggesting we're in is far from the world I know, where the postman still does not whistle tone rows. We're all subjected to involuntary listening to music in public places every day, but how much of what we hear is atonal? Mozart may eventually become as alien to us as the classical music of India, but the reasons will be cultural, not neurological.


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## millionrainbows

Woodduck said:


> I think you underestimate the fundamental appeal of tonality to the human brain. Do you think it's accidental that most of the world's music has always exhibited tonality of some kind? I'm betting it always will. Tonality doesn't have to be Mozart's or Wagner's kind.


Yes, "tonality" in that general sense seems to be a naturally occurring thing, since it is based on the way we hear: a fundamental tone and its harmonics. Any scale can be considered to be a "harmonic model."

But ultimately, this is "harmonic" hearing, with 'tonality' as a subset of that.

Other "givens" of hearing are:

---we tend to hear whatever is in the low bass as a 'tonic,' with higher tones related to that as subservient, like harmonics.

---we hear intervals according to harmonic principles: fourths sound as tonic on top, fifths sound as tonic on bottom.

Thus, any combination of sounds we hear, as harmonic phenomena, will be subject to these criteria. Even atonal music has this harmonic quality, but it is more random and less sustained, and certainly not integrated into its syntax in a holistic way as tonalities based on scales are. Still, from moment to moment, we hear each singularity as having harmonic meaning in the above ways.

"Tonality" in a general sense can be considered as a special version of tone-centeredness, which relates entire scales (which cover an octave) to a tonic. Usually, these scales are less than the full 12, so tonality is a "limiting" factor on the total chromatic.

Just because 12-tone music is chromatic, and constantly changes this 'root reference,' does not mean it is an "attack" on tonality; in this sense, it is simply a constantly changing reference, since all harmonic entities are heard as relating to a 'center,' even if this is self-sustaining on a moment-by moment level, and applies to all singularities and sound events.

Even isolated intervals and chords are heard as having a "tonal" identity, relating to whatever pitch seems to be the center.



Woodduck said:


> Schoenberg's attack on tonal centers and hierarchies was and remains an anomaly, regardless of its influence in the 20th century and regardless of the segment of classical music listeners who have embraced the resulting music for its own peculiar qualities.


Primitive or folk musics are usually tonal, and based on harmonics found in strings and pipes. Harmonics occur roughly as octave, fifth, major third, minor seventh, and variants of that. The pentatonic scale is one of those "entities" that goes hand-in-hand with tonality. It models the harmonics with its 1-3-5-7 color notes. Most folk music does not have 12 notes. Most folk music is pentatonic.






Schoenberg was aware of all 12 notes of our Western system (based on Pythagoran ideas), and used them all. All this means is that he followed the harmonic series further; see Harmonielehre.



Woodduck said:


> The brave new world you're suggesting we're in is far from the world I know, where the postman still does not whistle tone rows. We're all subjected to involuntary listening to music in public places every day, but how much of what we hear is atonal?


All that means is that most simplistic music does not use all 12 notes, but uses simpler pentatonic ideas.



Woodduck said:


> Mozart may eventually become as alien to us as the classical music of India, but the reasons will be cultural, not neurological.


No, it will mean the people have gone further than simple 5 and 7-note scales, and will be able to listen instant-by-instant.


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## Woodduck

millionrainbows said:


> No, it will mean the people have gone further than simple 5 and 7-note scales, and will be able to listen instant-by-instant.


You mean the way Stravinsky's duck listens?


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## fluteman

Woodduck said:


> I think you underestimate the fundamental appeal of tonality to the human brain. Do you think it's accidental that most of the world's music has always exhibited tonality of some kind? I'm betting it always will. Tonality doesn't have to be Mozart's or Wagner's kind. Schoenberg's attack on tonal centers and hierarchies was and remains an anomaly, regardless of its influence in the 20th century and regardless of the segment of classical music listeners who have embraced the resulting music for its own peculiar qualities. The brave new world you're suggesting we're in is far from the world I know, where the postman still does not whistle tone rows. We're all subjected to involuntary listening to music in public places every day, but how much of what we hear is atonal? Mozart may eventually become as alien to us as the classical music of India, but the reasons will be cultural, not neurological.


Well, nearly every artistic revolutionary is ultimately an anomaly in a sense. Very few of them have the everlasting, all-encompassing impact they envision and aspire to have. Schoenberg certainly didn't, if his goal was to permanently and universally replace the traditional western diatonic scale. Stravinsky didn't either. But anyone from my generation will recognize the theme from "Jaws", which John Williams adapted from the Sacrificial Dance of The Rite of Spring. Not long ago I brought my kids to a Pixar movie, and a preview for another, upcoming Pixar movie ("Ice Age 3", I think) prominently featured Aarvo Part's Spiegel im Spiegel, which I have heard in other movies as well. To this day, the Theme for The Twilight Zone by French avant-garde composer Marius Constant, with obvious atonal elements, is more familiar to anyone who grew up in America's TV age than anything Wagner ever wrote. (Sorry!) 
In fact, when we were kids, whistling or humming the Twilight Zone Theme signified we thought something was spooky or weird. I'm sure some postal workers have whistled it too. The truth is, "Schoenberg's attack on tonal centers", as you put it, didn't forever and completely destroy the idea of tonal centers. But it did have a permanent influence on how we hear music.
Ed.: Also, I see no practical way to fully and definitively separate the cultural (or perhaps more accurately, the environmental) from the neurological elements in how we hear music, though someday scientists may be able to help with that.


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## BabyGiraffe

millionrainbows said:


> Yes, "tonality" in that general sense seems to be a naturally occurring thing, since it is based on the way we hear: a fundamental tone and its harmonics. Any scale can be considered to be a "harmonic model."
> 
> But ultimately, this is "harmonic" hearing, with 'tonality' as a subset of that.
> 
> Other "givens" of hearing are:
> 
> ---we tend to hear whatever is in the low bass as a 'tonic,' with higher tones related to that as subservient, like harmonics.
> 
> ---we hear intervals according to harmonic principles: fourths sound as tonic on top, fifths sound as tonic on bottom.
> .


If they are on the bottom, they aren't 4ths or 5ths, because generate overtones. They are the tonics. 
We hear waves that vibrate at certain rates and are measured in Hz. We don't hear western, eastern or alien theory. When you play 2 waves against each other we also hear combinatiorial waves that are sum and difference of the original pitches. Our ear's mechanism also further distorts what we hear.
Atonal music is just playing some "funky" ratios as chords and almost unrelated ratios as tonics while avoiding repetitions of the pitch material, so the brain of the listeners is cofused even more. True atonality is impossible, all these techniques are tricks.


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## millionrainbows

BabyGiraffe said:


> If they are on the bottom, they aren't 4ths or 5ths, because generate overtones. They are the tonics.


Okay, consider a middle-range fourth C-F, and you will hear its "tonic" as the top note F. Place it somewhere in the bass.

Consider C-G, and you will hear its "tonic" as the lower note C. Place it somewhere in the bass.

The point being that a 'tonic' is implied in these intervals.


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## millionrainbows

Woodduck said:


> You mean the way Stravinsky's duck listens?


No; just the opposite.


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## millionrainbows

BabyGiraffe said:


> We hear waves that vibrate at certain rates and are measured in Hz. We don't hear western, eastern or alien theory.


Theory is not based on one note; it is based on whole systems, which include scales.



BabyGiraffe said:


> When you play 2 waves against each other we also hear combinatiorial waves that are sum and difference of the original pitches.


But primarily, we hear the main relationships between the two fundamentals, which we express as a ratio. Sum and difference pitches are for organ builders.



BabyGiraffe said:


> Our ear's mechanism also further distorts what we hear.


Not basically; we still hear a fourth as a fourth, even if the ratio is not exact.



BabyGiraffe said:


> Atonal music is just playing some "funky" ratios as chords and almost unrelated ratios as tonics…


Atonal music does not have "tonics."



BabyGiraffe said:


> ...while avoiding repetitions of the pitch material, so the brain of the listeners is cofused even more.


No, that is not the intent of writing atonal music. If it confuses listeners, that's their problem.



BabyGiraffe said:


> True atonality is impossible...


Tonality can be avoided to the point that it is, for all practical purposes, atonal or non-existent. Still, all sound has "harmonic" significance, in that all harmonic entities can be heard as having a 'tonic' if one wishes. When it gets to this point, I prefer to hear them as "colors."



BabyGiraffe said:


> ...all these techniques are tricks.


No, they are techniques. If you feel you have been "tricked," ask for your money back, and buy a Lynrd Skynrd CD instead.


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## BabyGiraffe

We hear patterns. When the pattern is too complex or intentionally obscured by shifting registers, tempo changes, klangfarbenmelodie, avoiding repeats - I call this a trick.
Each note and chord has a tonic and the tonic implies some kind of tonality.
Even in the standard theory as taught in the schools/ universities, inversions are treated as different chords that resolve and move in a specific way, not as the same thing as the root position chord. 
You are basically practicing misinformation in this thread.


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## fluteman

BabyGiraffe said:


> We hear patterns.


That's right. But sometimes, artists confound our expectations and intentionally create something that is patternless, or more accurately, has patternless elements combined with patterned elements, since art always follows some rule or structural principle. This doesn't just apply to harmony, or to music. You can see this begin to develop in a significant way with the French impressionist painters of the late 19th century.


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## millionrainbows

BabyGiraffe said:


> We hear patterns. When the pattern is too complex or intentionally obscured by shifting registers, tempo changes, klangfarbenmelodie, avoiding repeats - I call this a trick.


Whatever. A lot of this is intentional, to avoid tonal associations.



BabyGiraffe said:


> Each note and chord has a tonic and the tonic implies some kind of tonality.


On a certain micro-harmonic level, this may be somewhat true, but there are people who can resist hearing everything tonally. For me, "tonality" must cover a larger span of time, and must relate to previous events. Much atonal music does not do this.



BabyGiraffe said:


> Even in the standard theory as taught in the schools/ universities, inversions are treated as different chords that resolve and move in a specific way, not as the same thing as the root position chord.


Inversions are inversions because they relate to the tonic. Take the same chord, C-E-G, and invert it according to atonality, and you get the literal inversion: C-Ab-F.


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## BabyGiraffe

millionrainbows;1259290
You haven't thought about this very much said:


> Nope, I guess you haven't thought too much - CEG inverts to CEbG. CEGC inverts to CAbFC.


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## millionrainbows

BabyGiraffe said:


> Nope, I guess you haven't thought too much - *CEG inverts to CEbG.* CEGC inverts to CAbFC.


No, that's incorrect. A literal inversion, by interval, of C-E-G results in C-Ab-F.

You seem to be contradicting your own statement by saying "C-E-G-C inverts to C-Ab-F-C," which is correct.


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## BabyGiraffe

millionrainbows said:


> No, that's incorrect. A literal inversion, by interval, of C-E-G results in C-Ab-F.
> 
> You seem to be contradicting your own statement by saying "C-E-G-C inverts to C-Ab-F-C," which is correct.


Sorry, this was a mistake in the order.
So, 4 3 = CEG inverts to 3 4 = C Db G
4 3 5 = CEGC inverts to 5 3 4 = C F Ab C
Also known as vertical flip transformation.


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## JAS

Welcome to the world created by barbarians tearing down established institutions and tradition.


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## millionrainbows

Is anybody still interested in drawing a strict line between tonal and atonal? Because I think to do so would be extremely valuable in understanding both tonality, its mutant offspring, and atonality, and its offspring.

In the case of Bartok, its hard to say, because he was both. 

Some may not agree with this, but Alban Berg as well, because he was so idiosyncratic in his use of the "method" (which Schoenberg preferred to call it). He also used tonal elements. He was very loose in his application of 12-tone theory, and sometimes used very arbitrary or "mystical" numerology and number sequences which had nothing to do with the method as such. In this sense, he was anti-rational and a bit of a mystic.

To add to the confusion, there are certain "mechanical" or geometric aspects in some scales and materials, such as the diminished scale and the whole-tone scale. These scales are both "tonal" and "atonal" in that they have a certain recognizable harmonic sound, yet they are based on geometric projections of intervals, and symmetrical divisions of the octave. It depends on how they are used, like Debussy (who used them tonally).

People need to understand that the 12-note division of the octave is arbitrary, favors the fifth, and is very geometric by nature (12 can be divided by 1,2,3,4, or 6, and retain symmetry).


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## Razumovskymas

millionrainbows said:


> Is anybody still interested in *drawing a strict line between tonal and atonal*? Because I think to do so would be extremely valuable in understanding both tonality, its mutant offspring, and atonality, and its offspring.


If you want to do that you first have to have an agreement of a strict definition of "tonal" and "atonal" and I think that's impossible. Even you aren't really 100% consistent in your descriptions of atonality.

As I understand it now "atonality" is just the intention to avoid as much previous historically evolved patterns as possible, nothing more than that. And that's an interesting and valuable starting point obviously to look at music. But I don't think it's necessary to find the strict line. But if that is your holy grail, I'll be happy to follow your quest because it's quite entertaining from time to time.


----------



## BabyGiraffe

Razumovskymas said:


> If you want to do that you first have to have an agreement of a strict definition of "tonal" and "atonal" and I think that's impossible. Even you aren't really 100% consistent in your descriptions of atonality.
> 
> As I understand it now "atonality" is just the intention to avoid as much previous historically evolved patterns as possible, nothing more than that. And that's an interesting and valuable starting point obviously to look at music. But I don't think it's necessary to find the strict line. But if that is your holy grail, I'll be happy to follow your quest because it's quite entertaining from time to time.


Tonality = clear relations to a base pitch/root/fundamental frequency/tonic or whatever is called. Modal scales are also tonal.
Atonal = obscured relations, because the scale is dissonant or constantly modulating.

Here is another explanation of tonality.

"A psychological phenomenon having as its chief characteristic a tonal polarity around a 1 Identity; the sounding of various of the identities -- either Odentities or Udentities -- with a Numerary Nexus will create this polarity, and the smaller the >odd-number identities played the stronger the polarity.

Acoustically, the identities of a tonality represent the maximal consonance of any given number of stipulated identities because of the Numerary Nexus:

the tones of the triad 8/7 - 10/7 - 12/7 -- with the Numerary Nexus 7 -- are in the relation 8:10:12, or 4:5:6 (Identities 1-5-3), and create a polarity around 8/7, the 1 Odentitiy. This is the maximal consonance that three different tonal identities in music can attain.

Were the triad 10/7 - 12/7 - 7/7 (= 1/1) chosen, with the relation between the tones of 5:6:7 (Identities 5-3-7), the polarity around 8/7 would still be created, though it would not be as strong.

Essentially, Partch is saying that any collection of musical pitches whose frequencies can be expressed as proportional relationships which form a subset of an arithmetic series, will exhibit tonality.

He is assuming octave-equivalence, thus, only the odd factors really matter. The lower the odd numbers are, the stronger the perceived sensation of tonality"



millionrainbows said:


> Is anybody still interested in drawing a strict line between tonal and atonal? Because I think to do so would be extremely valuable in understanding both tonality, its mutant offspring, and atonality, and its offspring.
> 
> People need to understand that the 12-note division of the octave is arbitrary, favors the fifth, and is very geometric by nature (12 can be divided by 1,2,3,4, or 6, and retain symmetry).


People need to understand that you are talking about logarithmic division of the octave. And the equal logarithmic divisions sounds pretty bad compared to linear divisions.
Linear division of the octave gives us nice tonal scales and chords.
Linear vs Logarithmic = Fifth vs Tritone, Augmented vs I6/4 chord, Diminished 7 vs Major add 7/4 (barbershop seventh) etc.
Which division sounds better?
I'm not sure that 12et favours the fifth (or the fourth) that much. You can hear all kinds of stuff in it. The typical Hollywood sci-fi/fantasy cliches with tritone progressions are from 17-limit, the various "symmetrical" scales are also higher limit.


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## Razumovskymas

"obscured relations"

"another explanation"

"psychological phenomenon"

"talking about"

"sounds better"

"I'm not sure"

"all kinds of stuf"

"identities"

"he is assuming"



I don't think we're quite there yet :lol:


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## millionrainbows

BabyGiraffe said:


> Tonality = clear relations to a base pitch/root/fundamental frequency/tonic or whatever is called.


Yes, but we need to specify the exact nature of that hierarchy, and how, and if, it relates to linear time.

Most people think of "tonality" as taking place over periods of time; and/or as applied to scales and octaves, which does not take into account purely vertical instances of "harmonic hierarchy", and I think you need to see that difference clearly.

"Tonalities" are models of harmonic hierarchies, spread out over time, but there are harmonic hierarchies which can exist independently of that.



fluteman said:


> Modal scales are also tonal.


I agree with that if the mode is considered as a scale; but be aware that academics view modes as strictly melodic formulae, with no tonality.



fluteman said:


> Atonal = obscured relations, because the scale is dissonant or constantly modulating.


No; you need to work on that.



fluteman said:


> Here is another explanation of tonality.
> 
> "A psychological phenomenon having as its chief characteristic a tonal polarity around a 1 Identity; the sounding of various of the identities -- either Odentities or Udentities -- with a Numerary Nexus will create this polarity, and the smaller the >odd-number identities played the stronger the polarity.
> 
> Acoustically, the identities of a tonality represent *the maximal consonance of any given number of stipulated identities* because of the Numerary Nexus:
> 
> the tones of the triad 8/7 - 10/7 - 12/7 -- with the Numerary Nexus 7 -- are in the relation 8:10:12, or 4:5:6 (Identities 1-5-3), and create a polarity around 8/7, the 1 Odentitiy. This is the maximal consonance that three different tonal identities in music can attain.
> 
> Were the triad 10/7 - 12/7 - 7/7 (= 1/1) chosen, with the relation between the tones of 5:6:7 (Identities 5-3-7), the polarity around 8/7 would still be created, though it would not be as strong.
> 
> Essentially, Partch is saying that any collection of musical pitches whose frequencies can be expressed as proportional relationships which form a subset of an arithmetic series, will exhibit tonality.


This is applicable to collections of pitches ("stipulated identities"). These might as well be scales, since they are subservient members of a collection of pitches (relationships), and he preserves octave-equivalence; this meets all my criteria for a scale, related to a "1" which is an octave.



fluteman said:


> He is assuming octave-equivalence, thus, only the odd factors really matter. The lower the odd numbers are, the stronger the perceived sensation of tonality.


This does not apply to atonal music, in which vertical constructs are the only harmonic factors. You say they are "obscured," but this is because they have no vertical relation to a "1" over a consistent linear space of time. They relate internally, only to themselves, and then by comparison to ones that precede or follow; not to an overall "1".



fluteman said:


> People need to understand that you are talking about logarithmic division of the octave. And the equal logarithmic divisions sound pretty bad compared to linear divisions.


YOU need to understand that the 12-division is a rough approximation of the Pythagoran "stacking of fifths" and that it is only 2 cents off for each fifth. Thirds are what really sound worse.



fluteman said:


> Linear division of the octave gives us nice tonal scales and chords.


Yes, and that is because of _fifths only,_ not triads. Western tonality is based on root movement, and fifths create stable root stations for these chords.



fluteman said:


> Linear vs Logarithmic = Fifth vs Tritone, Augmented vs I6/4 chord, Diminished 7 vs Major add 7/4 (barbershop seventh) etc.
> Which division sounds better?


You seem to be missing the point that the Western tonal system is _meant _to be unstable, to create movement. It's not based on consonance per say, as an end in itself. That's why we have F in the C scale.



fluteman said:


> I'm not sure that 12et favours the fifth (or the fourth) that much. You can hear all kinds of stuff in it. The typical Hollywood sci-fi/fantasy cliches with tritone progressions are from 17-limit, the various "symmetrical" scales are also higher limit.


The 17-tone division is not used as a 17-tone scale. It is used for the options, when creating smaller scales out of it, for better fifths or thirds. There are all sorts of hybrid scales which come out of it, but none of them uses all 17 notes.


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## BabyGiraffe

Razumovskymas said:


> "obscured relations"
> 
> "another explanation"
> 
> "psychological phenomenon"
> 
> "talking about"
> 
> "sounds better"
> 
> "I'm not sure"
> 
> "all kinds of stuf"
> 
> "identities"
> 
> "he is assuming"
> 
> I don't think we're quite there yet :lol:


I don't think _you_ are quite anywhere yet... 
Let me ask you: which ratio looks more harmonic and useful - 1.41666666667 or 1.5? Which one is easier to comprehend - Tritone or Fifth?


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## BabyGiraffe

millionrainbows said:


> Yes, but we need to specify the exact nature of that hierarchy, and how, and if, it relates to linear time.
> 
> Most people think of "tonality" as taking place over periods of time; and/or as applied to scales and octaves, which does not take into account purely vertical instances of "harmonic hierarchy", and I think you need to see that difference clearly.
> 
> "Tonalities" are models of harmonic hierarchies, spread out over time, but there are harmonic hierarchies which can exist independently of that.
> 
> *Tonality is a sensation of strong resolution to the most stable pitch in a given pitch class set. Nothing to do with harmony. You can make distorted tonalities using more higher limit generators for your scale. Vishegradsky's favourite scale is basically tempered version of such scale based on stacked 11/8s (around 550 cents). There is a good resource on him and other composers that worked in 24et online.*
> 
> This does not apply to atonal music, in which vertical constructs are the only harmonic factors. You say they are "obscured," but this is because they have no vertical relation to a "1" over a consistent linear space of time. They relate internally, only to themselves, and then by comparison to ones that precede or follow; not to an overall "1".
> 
> YOU need to understand that the 12-division is a rough approximation of the Pythagoran "stacking of fifths" and that it is only 2 cents off for each fifth. Thirds are what really sound worse.
> 
> *12et division is not a rough approximation of Pythagorean tuning. If you take pure JI major scale and start transposing, you will get the circle of fifths (or fourths). The only thing that you need to do is to temper the syntonic comma. Pythagoras' tuning is pretty crappy in my opinion with even worse thirds than 12et.*
> 
> Yes, and that is because of _fifths only,_ not triads. Western tonality is based on root movement, and fifths create stable root stations for these chords.
> 
> *Western tonality is based on triads. You can always check the tuning that Bach, Mozart and friends used. Almost pure M3 and bad fifths.*
> 
> You seem to be missing the point that the Western tonal system is _meant _to be unstable, to create movement. It's not based on consonance per say, as an end in itself. That's why we have F in the C scale.
> 
> *You have F in the C scale, because it's one of the most consonant intervals. P5, P4, M6, M3, m3 and 7/4, septimal tritone 7/5 are the most consonant intervals in the octave.
> *
> 
> The 17-tone division is not used as a 17-tone scale. It is used for the options, when creating smaller scales out of it, for better fifths or thirds. There are all sorts of hybrid scales which come out of it, but none of them uses all 17 notes.
> *17-limit means that the fraction will contain a factor of 17... Noone is talking about division of 17 tones (which is historically 3 limit thing as used by the arabs/turks).*


...... 
......
......


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## Razumovskymas

BabyGiraffe said:


> I don't think _you_ are quite anywhere yet...
> Let me ask you: which ratio looks more harmonic and useful - 1.41666666667 or 1.5? Which one is easier to comprehend - Tritone or Fifth?


I love tritones as well as fifths :tiphat:

I tend to believe perception of harmony is more cultural then natural so I'm not really bothered by ratios that LOOK good.


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## Razumovskymas

But hey look what happens if you do the ratio of the tritone to the power two!!

Looks good doesn't it!


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## millionrainbows

baby giraffe said:


> Tonality is a sensation of strong resolution to the most stable pitch in a given pitch class set. Nothing to do with harmony.


Serialism has nothing to do with harmony, either.

Harmony does not apply to atonal music, except in instant-by-instant occurrences, in which vertical constructs are the only harmonic factors.

You say they are "obscured," but this is because they have no vertical relation to a "1" over a consistent linear space of time (i.e. they are not tonal). They relate internally, only to themselves, and then by comparison to ones that precede or follow; not to an overall "1," or even to a vertical aggregate of "tonalities" that Partch presents. These Partch "tonalities" are based on harmonic factors. Atonal music is not.

You need to understand that the 12-division is a rough approximation of the Pythagoran "stacking of fifths" and that it is only 2 cents off for each fifth. Thirds are what really sound worse.



baby giraffe said:


> 12et division is not a rough approximation of Pythagorean tuning.


Yes it is, but I didn't say that. I said 12ET was derived from the Pythagoran-derived procedure of stacking fifths, which came from the school of Pythagoras.



baby giraffe said:


> If you take pure JI major scale and start transposing, you will get the circle of fifths (or fourths).


That doesn't make sense at all. Transpose to where? Where do you think the circle of fifths came from? It's what our 12-note division of the octave is based on. Just intonation cannot "tranpose." It is rooted on a base pitch.



baby giraffe said:


> The only thing that you need to do is to temper the syntonic comma. Pythagoras' tuning is pretty crappy in my opinion with even worse thirds than 12et.


I'm not talking about the Pythagoran scale at all; I referred to the Pythagoran-derived procedure of stacking fifths, which came from the school of Pythagoras.


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## millionrainbows

In the end, it's not possible to draw a line between tonality and atonality, because many of the mechanisms overlap, and have dual natures.

The diminished and whole tone scales are both geometric and tonal; they are based on projected intervals (min 4 and maj 2), and divide the 12-note octave evenly and symmetrically. Yet, they both have a certain tonal dimension which can be used tonally, as Wagner and Debussy did.

Atonal music does have a harmonic dimension, though unlike tonality, the harmonic verticalities are not derived from systematic harmonic considerations, but only by momentary, or comparative sequences (comparing dissonances _relative _to what precedes or follows).

So like all set-derived chromatic music, the harmony is "relative" to everything around it, not by relation to an overriding, system-wide "1" or tonic note.

That's why it makes no sense to discuss 'just' intonation, or perfect intervals, in the context of atonality, since it is music which is not derived from harmonic considerations.


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## BabyGiraffe

millionrainbows said:


> Serialism has nothing to do with harmony, either. Why are you in this thread?
> 
> Harmony does not apply to atonal music, except in instant-by-instant occurrences, in which vertical constructs are the only harmonic factors.
> 
> You say they are "obscured," but this is because they have no vertical relation to a "1" over a consistent linear space of time (i.e. they are not tonal). They relate internally, only to themselves, and then by comparison to ones that precede or follow; not to an overall "1," or even to a vertical aggregate of "tonalities" that Partch presents. These Partch "tonalities" are based on harmonic factors. Atonal music is not.
> 
> You need to understand that the 12-division is a rough approximation of the Pythagoran "stacking of fifths" and that it is only 2 cents off for each fifth. Thirds are what really sound worse.
> 
> Yes it is, but I didn't say that. I said 12ET was derived from the Pythagoran-derived procedure of stacking fifths, which came from the school of Pythagoras.
> 
> That doesn't make sense at all. Transpose to where? Where do you think the circle of fifths came from? It's what our 12-note division of the octave is based on. Just intonation cannot "tranpose." It is rooted on a base pitch.
> 
> I'm not talking about the Pythagoran scale at all; I referred to the Pythagoran-derived procedure of stacking fifths, which came from the school of Pythagoras.


Just intonation can't transpose? Why don't you try to sing something, then switch the tonality. It's not that hard...
If you start transposing the major scale in just intonation, you will get the 12 Western pitches. The difference between C major and F major, or C major and G major is a comma + 1 another note. 12 chromatic steps can be derived by tempering the commas.
Indians/ arabs etc use gamuts with stacked pure scales, so you don't have to retune to play another tonality.
About atonal music - there is a difference between what listener hears and composer's intentions. As long as there are recognizable intervals, the music will have some kind of tonality. 
I've yet to hear music based on noise, pitchbends etc that actually sounds decent.


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## millionrainbows

BabyGiraffe said:


> Just intonation can't transpose? Why don't you try to sing something, then switch the tonality. It's not that hard...


That's a shift of the base, not a transposition. What note do you transpose to? Do you use the 12-note scale, or the 53-tone scale?



BabyGiraffe said:


> 12 chromatic steps can be derived by tempering the commas.


That sounds like ET to me, or very similar. From WIK:

The term syntonic temperament has been used to describe the combination of (a) the continuum of tunings in which the tempered perfect fifth (P5) is the generator and the octave is the period; (b) comma sequences that start with the syntonic comma (i.e., in which the syntonic comma is tempered to zero, making the generated major third as wide as two generated major seconds); and (c) the "tuning range" of P5 temperings in which (0 >= the width of the generated minor second >= the width of the generated major second) is true. This combination is necessary and sufficient to define a set of relationships among tonal intervals that is constant across the syntonic temperament's tuning range. Hence, it also defines a constant mapping -- all across the tuning continuum -- between (a) the notes at these tonal intervals, and (b) the corresponding partials of a pseudo-harmonic timbre. Hence, the relationship between the syntonic temperament and its note-aligned timbres can be seen as a generalization of the special relationship between Just Intonation and the Harmonic Series.




BabyGiraffe said:


> About atonal music - there is a difference between what listener hears and composer's intentions. As long as there are recognizable intervals, the music will have some kind of tonality.


No. if there is an interval, it will have a harmonic identity, but that is not tonality except as a vertical harmonic phenomena. If we stretch the definition of "tonality" to that degree, it becomes meaningless. Please use another term.


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## Razumovskymas

millionrainbows said:


> In the end, it's not possible to draw a line between tonality and atonality, because many of the mechanisms overlap, and have dual natures.
> 
> The diminished and whole tone scales are both geometric and tonal; they are based on projected intervals (min 4 and maj 2), and divide the 12-note octave evenly and symmetrically. Yet, they both have a certain tonal dimension which can be used tonally, as Wagner and Debussy did.
> 
> Atonal music does have a harmonic dimension, though unlike tonality, the harmonic verticalities are not derived from systematic harmonic considerations, but only by momentary, or comparative sequences (comparing dissonances _relative _to what precedes or follows).
> 
> *So like all set-derived chromatic music, the harmony is "relative" to everything around it, not by relation to an overriding, system-wide "1" or tonic note.
> *
> That's why it makes no sense to discuss 'just' intonation, or perfect intervals, in the context of atonality, since it is music which is not derived from harmonic considerations.


that seems like a useful approach! (for me personally)


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## BabyGiraffe

millionrainbows said:


> That's a shift of the base, not a transposition. What note do you transpose to? Do you use the 12-note scale, or the 53-tone scale?
> 
> That sounds like ET to me, or very similar. From WIK:
> 
> The term syntonic temperament has been used to describe the combination of (a) the continuum of tunings in which the tempered perfect fifth (P5) is the generator and the octave is the period; (b) comma sequences that start with the syntonic comma (i.e., in which the syntonic comma is tempered to zero, making the generated major third as wide as two generated major seconds); and (c) the "tuning range" of P5 temperings in which (0 >= the width of the generated minor second >= the width of the generated major second) is true. This combination is necessary and sufficient to define a set of relationships among tonal intervals that is constant across the syntonic temperament's tuning range. Hence, it also defines a constant mapping -- all across the tuning continuum -- between (a) the notes at these tonal intervals, and (b) the corresponding partials of a pseudo-harmonic timbre. Hence, the relationship between the syntonic temperament and its note-aligned timbres can be seen as a generalization of the special relationship between Just Intonation and the Harmonic Series.
> 
> 
> 
> No. if there is an interval, it will have a harmonic identity, but that is not tonality except as a vertical harmonic phenomena. If we stretch the definition of "tonality" to that degree, it becomes meaningless. Please use another term.


Nope, it a transposition. Deep scales do this trick. Just transpose to a scale degree. 
(For example: Take pure major scale in just intonation, transpose to G, you will keep the same pitches and get 27/16 which is a comma away from the wolf M6 and can be used to harmonize the D note and 45/32 - the diatonic tritone. )
https://en.wikipedia.org/wiki/Deep_scale_property


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## millionrainbows

BabyGiraffe said:


> Nope, it a transposition. Deep scales do this trick. Just transpose to a scale degree.
> (For example: Take pure major scale in just intonation, transpose to G, you will keep the same pitches and get 27/16 which is a comma away from the wolf M6 and can be used to harmonize the D note and 45/32 - the diatonic tritone. )
> https://en.wikipedia.org/wiki/Deep_scale_property


That only preserves some of the intervals, not all, and these are different for each different transposition. I thought you were interested in pure intervals.

What does this have to do with atonality? What is your agenda?


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## Nicksievers

There is definitely shades of grey. Atonality really is just extreme chromaticism which was really started by Beethoven. Listen through much of Beethoven, then Brahms, Strauss and finally early Schoenberg and you will understand perfectly. Schoenberg's Book of the Hanging Gardens is considering the first purely atonal piece, however you can hear that it almost is composed against tonality where every harmonic expectation is denied. Though the expectations still exist through consonance and dissonance as natural phenomena. In my opinion you can always deny these expectations to create atonality but our ear will always search for consonance. I believe Schoenberg's "Emancipation of Dissonance" is impossible because of our biological connection to the overtone series.


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## Phil loves classical

There is no strict definition of atonality. The most general one is a lack of tonal centre. But as Bernstein said in a lecture, there had been no system as of yet that destroys completely the relationships of the 12 tones to each other, including dodecaphony.


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## millionrainbows

Phil loves classical said:


> There is no strict definition of atonality. The most general one is a lack of tonal centre. But as Bernstein said in a lecture, there had been no system as of yet that destroys completely the relationships of the 12 tones to each other, including dodecaphony.


There is probably nothing which fits the term "strict" on this question.

That being said, it could be argued that the 12-tone and serial (set) methods do indeed "destroy" tonality's structural/harmonic functions, at least in an objective sense, and thus "destroy" tonality.

Subjectively, the beauty of music and the "salvation" of dodecaphony is in the harmonic realm of the ear/brain, where we tend to perceive tonality even when it is not intended by the composer or enabled by tonal harmonic hierarchies and structures. This is subjective, however, and since it lies in the realm of experience and the 'metaphysical,' cannot be "strictly proven."

However, if we are theoretically literate, we can know objectively whether or not a music is truly tonal or not, but we must acknowledge the objective proof as such, and disregard the subjective, if we are to "strictly" prove that something is tonal, or not.

But "art" is subjective, right? Herein lies the contradiction of questions like this.

It is ridiculous to try to expect "strict" answers or "objective proof" to questions of tonality, unless one is willing to submit to objective, theoretical proof of methods and theory, and unless one can accept as "givens" certain criteria for the establishment of tonality or its absence (as a structural component, not subjective experience).

In other words, we must ideally keep the subjective realm of experience completely separate from the objective realm. This applies to all metaphysical realms, such as religion. That's why I think it is ridiculous for self-professed "atheists" to justify their stance on "objective" criteria, such as the unprovability of the existence of God.

Otherwise, who am I to question anyone's "pie in the sky?" I see a duckie, and there's Santa, and that one looks like a tonal center, and there's some whipped cream…wow, those floor tiles are creating triangular patterns, at least from my perspective in this bathroom stall...


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## ancore

I guess if you dont feel the tonality that counts as atonal


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## millionrainbows

ancore said:


> I guess if you dont feel the tonality that counts as atonal


That would be a totally subjective definition of tonality, and I don't think that tonality & its principles are totally subjective. There are certain objective factors involved.

Of course, if you think that whatever you hear is the gospel truth, I won't argue with your perceptions.


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