# ...How to Listen To and Understand Atonal Music?



## Gargamel

Been familiarizing myself with plenty of atonal music over the decades. My approach is just very melodical, but what I lack is the know-how to analyze it like analyzing tonal music. Although writings on 12-tone music often focus on the rows, that's not how most people listen to it. (The scottish composer Jonathan Harvey, studying with both Babbitt and Stockhausen, expressed doubts whether it's even possible to hear the series, or partitions of the series.)

I've tried if I can see, whether different motifs and themes can be outlined by the intervals they span. Example: Berg's String Quartet Op. 3. The first motif spans 8 semitones. The continuation spans 4 semitones, which is conversely the same as 8, and when the motive is repeated, it's 4 semitones lower. The next motif spans 10 (conversely 2) semitones. The accompaniment is starchly differentiated by avoidance of these aforementioned interval spans. Now, I can't make deeper sense of it than that. (I've also tried to hear atonal music, to no avail, in terms of bass movement).


----------



## Phil loves classical

I don't believe there is a single way to listen, since different composers composed atonal music differently. These are just my thoughts, I don't profess to be an expert. But did do quite a bit to try to understand what's going on.

Webern's Variations is the easiest to follow which highlight certain transformations. I can hear a lot of the retrogrades and inversions, since there is little else to distract the ear, and it's slow enough to follow, but I honestly doubt I could follow them without having experimented a bit of that stuff on my own. He follows with a technical consistency through. Schoenberg is more loose so I don't bother with listening too intently. I view his music as kind of like Classical or Romantic music in disguise, and it's fun to hear certain gestures in other idioms but with this alien sort of language. It's like watching the acting in a foreign language film. I didn't know what to listen to in Carter for a long time, but i think it's just his way of organizing in certain arrangements of register and rhythm. I don't think the pitches are to be picked out, nor really matter (it has a very fluid consistency because of the chord technique he uses frequently) unlike with Webern. With the Serialists, it's again rhythms, registers, timbres. I can make certain patterns out sometimes, sometimes not, but it sounds mesmerizing nonetheless. Ferneyhough keeps me on my toes, he strings unpredictable rhythms together.


----------



## SanAntone

I don't try to "understand" any music, tonal or atonal. I just listen and it is the same process for either.


----------



## GucciManeIsTheNewWebern

SanAntone said:


> I don't try to "understand" any music, tonal or atonal. I just listen and it is the same process for either.


While I agree with this and think atonal should just be listened to like any other music (it breaks my heart that some have the misconception it's some purely intellectual, unmusical exercise), I think OP is looking more for ways to appreciate the theory behind it or how to make better sense of it. I love listening to the end product, but I also wish I knew the theory behind how it actually worked better which could give me even a deeper appreciation of what's going on. But you're right: if i'm listening to Beethoven, I'm not really actively thinking "Wow! Look at how he employed that neopolitan sixth which sets up the cadence into the new key of the subtonic in the development section!" though I'm sure lots of people on this forum do.


----------



## Guest

Is the process of 'understanding' atonal music significantly different from 'understanding tonal music? Surely one needs to listen to it, study the score, come to know what the composer is doing and how/why it works, have the background knowledge to be able to do either?

I have only a rudimentary knowledge of musical theory, enough to be able to read music to Initial Grade :trp:.
I can't spot a diminished 4th or an augmented 7th. I know Sibelius' 4th Symphony makes significant use of the tritone - but I can't hear that it does. I'd like to 'understand' more about the technical side of musical construction, and I'd also like to know more about why major sounds happy and minor sounds sad...

Haviing said that, there's other things I'm prioritising studying, so musical theory will have to wait. In the meantime, I'll continue to listen, read about and increase my understanding of music incrementally.


----------



## Gargamel

GucciManeIsTheNewWebern said:


> While I agree with this and think atonal should just be listened to like any other music (it breaks my heart that some have the misconception it's some purely intellectual, unmusical exercise), I think OP is looking more for ways to appreciate the theory behind it or how to make better sense of it. I love listening to the end product, but I also wish I knew the theory behind how it actually worked better which could give me even a deeper appreciation of what's going on. But you're right: if i'm listening to Beethoven, I'm not really actively thinking "Wow! Look at how he employed that neopolitan sixth which sets up the cadence into the new key of the subtonic in the development section!" though I'm sure lots of people on this forum do.


I don't think it's necessary to identify the rows to make good sense of serial music, or time to follow Carter. I'm rather very familiar with the serial procedures, and it doesn't help me to make much sense of a given piece. Further, it's virtually impossible for most people to make sense of music in this way when the row is being (trichordally) partitioned as in Babbitt's or Martino's music.

I should like to hear serial music in the same way that I listen to Berg's string quartet or any free atonal music: in terms of hierarchies and how motifs and phrases are differentiated by their interval spans. The strong beats seem to outline some kind of hierarchies vaguely analoguous to tonal music's scale degrees but I can't tell exactly how.


----------



## Phil loves classical

MacLeod said:


> *Is the process of 'understanding' atonal music significantly different from 'understanding tonal music?* Surely one needs to listen to it, study the score, come to know what the composer is doing and how/why it works, have the background knowledge to be able to do either?
> 
> I have only a rudimentary knowledge of musical theory, enough to be able to read music to Initial Grade :trp:.
> I can't spot a diminished 4th or an augmented 7th. I know Sibelius' 4th Symphony makes significant use of the tritone - but I can't hear that it does. I'd like to 'understand' more about the technical side of musical construction, and I'd also like to know more about why major sounds happy and minor sounds sad...
> 
> Haviing said that, there's other things I'm prioritising studying, so musical theory will have to wait. In the meantime, I'll continue to listen, read about and increase my understanding of music incrementally.


i think it shouldn't be, but for practical reasons it is, at least for most people at the beginning, because we're used to tonal building blocks but not atonal ones. I'm thinking a tone row is just part of a method, and not something important in itself to pick out and wonder at. Schoenberg was hoping he'd be the next grand-daddy like Bach, and that most music afterwards would be 12-tone based, and people would make lullabies out of it (a loose paraphrase or interpretation on my part). But as I recall from Bernstein's lecture, at the end of his life he wrote a tonal piece, some people felt he was selling out, and he seemed to change his stance and acknowledged tonal hierarchies can't be denied or something.


----------



## GucciManeIsTheNewWebern

Phil loves classical said:


> i think it shouldn't be, but for practical reasons it is, at least for most people at the beginning, because we're used to tonal building blocks but not atonal ones. I'm thinking a tone row is just part of a method, and not something important in itself to pick out and wonder at. Schoenberg was hoping he'd be the next grand-daddy like Bach, and that most music afterwards would be 12-tone based, *and people would make lullabies out of it* (a loose paraphrase or interpretation on my part). But as I recall from Bernstein's lecture, at the end of his life he wrote a tonal piece, some people felt he was selling out, and he seemed to change his stance and acknowledged tonal hierarchies can't be denied or something.


Imagine that. Even though it's a funny joke, I wonder if theoretically it's super far fetched. People's minds have been conditioned over the course of several centuries to process tonal music as more pleasing, and dissonance and atonal music as jarring, creepy, tense etc. which is why composers of horror movie scores make use of it. While a lot of atonal music is indeed creepy and unsettling, I don't categorically attach these constructed emotions/interpretations to it which are more artificial societal constructs associated with the music. To me, it's just another way of writing music with an equally broad spectrum of expression and pallette of tones and colors, something known to people who've actually spent quality time with the music.

So going back to the lullaby, if music somehow underwent some kind of immediate aesthetic/cultural revolution under Schönberg, whether a baby could actually find a 12-tone lullaby relaxing, or if our brains are physically wired to find tonal music more pleasing - after all, there's a reason we started out with tonality and not atonality. I personally find lots of atonal music very pleasing and relaxing, but would a baby, who has nothing to interpret the music with but the physical wirings of its brain? Perhaps there's none of that societal 'conditioning' at all, or (which I'm inclined to believe) it's a bit of column A and column B.


----------



## Phil loves classical

^ I recall there were some studies done, and dissonance causes certain brain patterns showing discomfort. I think it's wired in. It's possible to overcome it by looking at context and stuff, but all things equal, it wouldn't be pleasing to a baby. I'd be very skeptical feeding that sort of music first, it could make the baby unbalanced. I noticed this when I left Spotify on at night while sleeping a few times, Penderecki Thernody and Bartok's Music for Percussion (that timpani glissando!)... scared me. Ravel's Piano Concerto in G, 2nd movement, made me feel this amazing sort of ecstasy. Even Richard Marx's Right Here Waiting sounded good when I was sleeping once. I normally hate that song.


----------



## SanAntone

> Is the process of 'understanding' atonal music significantly different from 'understanding tonal music? Surely one needs to listen to it, study the score, come to know what the composer is doing and how/why it works, have the background knowledge to be able to do either?


If you are trying to "know what the composer is doing and how/why it works" you're not really listening to the music, _as music_. I have a degree in Music Theory and Composition. I know a lot about music theory, and about serial composition, tone rows, etc. But I NEVER draw on that knowledge when I am listening to music by Schönberg, Webern, or Berg, etc.

Studying a score or analyzing or reading an analysis of a composition can be worthwhile, but it is a separate activity and should be done for its own end - not as preparation for listening to a piece of music, IMO. But for me, and I know enough about composing and have had enough conversations with other composers, and composition teachers to know that the last thing a composer wants if for his process to be front and center and on the audience's mind.

Just like it is for tonal music, the hope is for the music to speak to us as music - not as a tone-puzzle, filled with permutations, inversions, retrogrades and other manipulations of a tone row.

My thinking is this: if an atonal work does not engage your heart and excite your intelligence, then it is not working as music, or you are not in the mood for that kind of music. Learning how it was put together might be an interesting pastime - but is no replacement for experiencing the music, real time, no differently than what happens as you listen to your favorite tonal composers.

At least that's how I look at it.


----------



## Guest

SanAntone said:


> If you are trying to "know what the composer is doing and how/why it works" you're not really listening to the music, _as music_. I have a degree in Music Theory and Composition. I know a lot about music theory, and about serial composition, tone rows, etc. But I NEVER draw on that knowledge when I am listening to music by Schönberg, Webern, or Berg, etc.
> 
> Studying a score or analyzing or reading an analysis of a composition can be worthwhile, but it is a separate activity and should be done for its own end - not as preparation for listening to a piece of music, IMO. But for me, and I know enough about composing and have had enough conversations with other composers, and composition teachers to know that the last thing a composer wants if for his process to be front and center and on the audience's mind.
> 
> Just like it is for tonal music, the hope is for the music to speak to us as music - not as a tone-puzzle, filled with permutations, inversions, retrogrades and other manipulations of a tone row.
> 
> My thinking is this: if an atonal work does not engage your heart and excite your intelligence, then it is not working as music, or you are not in the mood for that kind of music. Learning how it was put together might be an interesting pastime - but is no replacement for experiencing the music, real time, no differently than what happens as you listen to your favorite tonal composers.
> 
> At least that's how I look at it.


I'm not recommending any particular process for _listening _to music. I was responding to the question about how to go about _understanding _its form, making the point that the same activities you might engage in to understand tonal could be the same for atonal.

As for the idea that music must be listened to 'as music' (and not as...what?), such prescription seems to me unnecessary. We are each entitled to listen to music in whatever way we will. If someone wants to do a mechanistic analysis, let them get on with it. If someone wants to wallow in whatever emotional or spiritual response they gain from it, that's fine.


----------



## Gargamel

MacLeod said:


> I'm not recommending any particular process for _listening _to music. I was responding to the question about how to go about _understanding _its form, making the point that the same activities you might engage in to understand tonal could be the same for atonal.
> 
> As for the idea that music must be listened to 'as music' (and not as...what?), such prescription seems to me unnecessary. We are each entitled to listen to music in whatever way we will. If someone wants to do a mechanistic analysis, let them get on with it. If someone wants to wallow in whatever emotional or spiritual response they gain from it, that's fine.


When listening to tonal music, one subconsciously hears hierarchies which can also be analyzed: Octaves doublings are insignificant. Fifths are usually less important than thirds. Sevenths and fourths are more important than most tones. Similarly in atonal music, there exists hierarchies, which serial stuff doesn't adequately explain. Some intervals have more significance than others, which I tried to highlight with the Berg example. (E. g. it doesn't matter much whether an interval is eight semitones or four, because they're equivalent.)


----------



## Eclectic Al

Another non-expert here.

The OP here was about atonal music, but nearly all the discussion has been about serial or avant garde music.

I read on Wikipedia that (for instance) Scriabin's late piano sonatas are pretty much atonal.

Now I find music like that very appealing, and some music by the early serialists (eg some Webern). Take Berg's violin concerto - is that a piece which is deemed to be atonal, as that's another which I can readily relate to. However, I seem to recall it is sometimes criticised because the serial procedures adopted contain too many tonal implications, as though that thereby sells out the atonal religion. Do I recall correctly?

I have never been able to get anything from later serialists or members of avant garde tendencies, but is it fair to say that there are other atonal approaches aside from theirs? The mainstream music that seems to have most in common with such styles is the horror movie soundtrack, which suggests it would be wrong to say that such music has no emotional content. However, as someone who doesn't listen to it much I just tend to find it destabilising in a way that I do not find pleasant. Can someone suggest a piece of out-and-out atonal or avant garde music which is pleasant to listen to fairly casually?


----------



## Gargamel

Eclectic Al said:


> Can someone suggest a piece of out-and-out atonal or avant garde music which is pleasant to listen to fairly casually?


Examples of some highly melodic composers:
Roger Sessions (Symphonies 5 and 8), Andre Jolivet (Piano concerto, Piano sonata no. 2 and the symphonies), Bernstein (Symphony no. 3 'Kaddish'), Kenneth Leighton (Piano concerto no. 3). Babbitt's late music is also comparatively pleasant (Septet but Equal, String quartet no. 6) and jazzy (Canonical form).


----------



## SanAntone

MacLeod said:


> I'm not recommending any particular process for _listening _to music. I was responding to the question about how to go about _understanding _its form, making the point that the same activities you might engage in to understand tonal could be the same for atonal.
> 
> As for the idea that music must be listened to 'as music' (and not as...what?), such prescription seems to me unnecessary. We are each entitled to listen to music in whatever way we will. If someone wants to do a mechanistic analysis, let them get on with it. If someone wants to wallow in whatever emotional or spiritual response they gain from it, that's fine.


The title of the thread is "...How to *Listen To* and Understand Atonal Music?"

The idea of "understanding" music is completely separate from listening to music. My advice is to simply listen to atonal music and forget trying to understand it. The understanding, such as it is, comes with exposure. Or not. Atonal music may never speak to some of us, and that's okay. There is no law that says that atonal music must be understood or appreciated or liked.

If after giving it a good try and sampling several different composers and works the music still does not engage you - then move on and forget about it.



> The OP here was about atonal music, but nearly all the discussion has been about serial or avant garde music.
> 
> Can someone suggest a piece of out-and-out atonal or avant garde music which is pleasant to listen to fairly casually?


I find much of Webern's music to be pleasant to listen to, his Symphony, op 21, for example. But you may not. It does have the advantage of being short.


----------



## Guest

^ Well, you give your advice and I'll give mine.


----------



## Gargamel

SanAntone said:


> The title of the thread is "...How to *Listen To* and Understand Atonal Music?"
> 
> The idea of "understanding" music is completely separate from listening to music. My advice is to simply listen to atonal music and forget trying to understand it. The understanding, such as it is, comes with exposure. Or not.


Your advice is not satisfactory. After immensing oneself with atonal music for decades (I'm able to whistle most of Schoenberg's, Berg's and Webern's works from beginning to end), there comes a limit -- as with tonal music -- where exposure alone doesn't further *understanding*. Again refer to my first post how I'm attempting to keep track of the musical patterns.


----------



## Gargamel

Well it's a disappointment, you guys who know so much about tonal music know almost nothing about atonal music, and there's only talk about tone rows.


----------



## Oscar South

I personally find that beginning my approach into atonal pieces with a journey into understanding the orchestration, dynamic, form and context of the piece yields a lot more insight into the harmony than a direct attack at the harmony itself would.

In fact -- with the wisdom of a few more years of practice than I once had (I was very 'harmony obsessed' through my musical development), I would say that I also get a lot more out of tonal musical works with that approach too! Harmony often feels like an afterthought once you've developed an understanding into those attributes of a piece.


----------



## Torkelburger

There is not just one way of composing atonal music. There are all kinds of methods and procedures. The only thing they all have in common is just that they don't have a tonal center. Not every atonal piece even has a melody (such as in some Ligeti pieces). Some don't have harmony either (such as solo instrumental pieces).

A good resource to see some of these different procedures in use for atonal composition is on Samuel Andreyev's YouTube channel. He analyzes a lot of modern music and much of it is atonal (does not fall under Stravinskian, 12-tone, or tonal techniques). Here are a few videos that show atonal technique:


























Also, a good place to start for atonal analysis is Schoenberg's Drei Klavierstucke, Op. 11. You can see in this video how the intervals from just the first 5 bars are turned up-side down, backwards, upside-down and backwards, used harmonically, etc., etc. in every note and bar in the rest of the piece.


----------



## SeptimalTritone

Gargamel said:


> Your advice is not satisfactory. After immensing oneself with atonal music for decades (I'm able to whistle most of Schoenberg's, Berg's and Webern's works from beginning to end), there comes a limit -- as with tonal music -- where exposure alone doesn't further *understanding*. Again refer to my first post how I'm attempting to keep track of the musical patterns.


Looks like you have more than well understood second Viennese music at an intuitive sonic level, but are genuinely wishing to understand the mechanics of why it works for your own interest (and not just as a crutch or replacement for gut level musical understanding). This is good.

I've found Jack Boss's book on 12-tone Schoenberg https://www.amazon.com/Schoenbergs-Twelve-Tone-Music-Symmetry-Musical/dp/1107624924 helpful. It covers how the music strives for thematic/contrapuntal goals and moves toward/away from them and eventually realizes them. You'll learn more than merely a dry stamp-collector's catalogue of which tone row inversion goes where - you'll gain an understanding of musical development in a Schoenberg work.

The second chapter on the Suite for Piano op 25 is excellent and is alone worth the book, albeit hard work. But it's worth it.

I've also enjoyed Kathryn Bailey's book on Webern here https://www.amazon.com/Twelve-Note-Music-Anton-Webern/dp/0521547962


----------



## SanAntone

SeptimalTritone said:


> Looks like you have more than well understood second Viennese music at an intuitive sonic level, but are genuinely wishing to understand the mechanics of why it works for your own interest (and not just as a crutch or replacement for gut level musical understanding). This is good.
> 
> I've found Jack Boss's book on 12-tone Schoenberg https://www.amazon.com/Schoenbergs-Twelve-Tone-Music-Symmetry-Musical/dp/1107624924 helpful. It covers how the music strives for thematic/contrapuntal goals and moves toward/away from them and eventually realizes them. You'll learn more than merely a dry stamp-collector's catalogue of which tone row inversion goes where - you'll gain an understanding of musical development in a Schoenberg work.
> 
> The second chapter on the Suite for Piano op 25 is excellent and is alone worth the book, albeit hard work. But it's worth it.
> 
> I've also enjoyed Kathryn Bailey's book on Webern here https://www.amazon.com/Twelve-Note-Music-Anton-Webern/dp/0521547962


Interesting. I wasn't aware of the Boss book but I have Kathryn Bailey's book on Webern.

While books like these can be valuable for study (I've got a bunch of them: George Perle's 2-vols on the Berg operas, books on the music of Boulez, Carter, Stravinsky, Cage, etc.) and it can be interesting reading about how these composers worked, it doesn't help me to appreciate the music. As I wrote earlier, my "understanding" (for lack of a better term) of a piece of music is entirely gotten from listening to it.

But we might be using the word "understanding" differently.


----------



## Gargamel

Torkelburger said:


> There is not just one way of composing atonal music. There are all kinds of methods and procedures. The only thing they all have in common is just that they don't have a tonal center. Not every atonal piece even has a melody (such as in some Ligeti pieces). Some don't have harmony either (such as solo instrumental pieces).
> 
> A good resource to see some of these different procedures in use for atonal composition is on Samuel Andreyev's YouTube channel. He analyzes a lot of modern music and much of it is atonal (does not fall under Stravinskian, 12-tone, or tonal techniques). Here are a few videos that show atonal technique:
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
> Also, a good place to start for atonal analysis is Schoenberg's Drei Klavierstucke, Op. 11. You can see in this video how the intervals from just the first 5 bars are turned up-side down, backwards, upside-down and backwards, used harmonically, etc., etc. in every note and bar in the rest of the piece.


Looking how it goes up-side down, backwards, upside-down and backwards, it's fairly kindergarden stuff. The difficulty for me is "why this transposition? Why does the motif start at this pitch?" because what atonal music lacks is root movement. The first video link shows an example (Schoenberg's passacaglia) which is structured on bass movement but that's just the nature of a passacaglia and not something you can generally base your analysis on.


----------



## Torkelburger

> Looking how it goes up-side down, backwards, upside-down and backwards, it's fairly kindergarden stuff.


Pitches appearing in different transformations adds unity and cohesion to a piece that might otherwise sound random in a non-tonal context. Further, the varying rhythms (some of them difficult), textures, articulations, dynamics, octave displacements, transpositions, etc., etc. add the needed layers of complexity. And the technique in the piece is not so simple that I seriously doubt 99.9% of any group of listeners would realize that measure 13 is derived from measure 4, even when reading the score. So your comment is moot.



> The difficulty for me is "why this transposition? Why does the motif start at this pitch?" because what atonal music lacks is root movement.


Lacking root movement is not any sort of shortcoming of atonal music. Do not try and shoehorn atonal music to fit the mold and customs of tonal music and then criticize it for not meeting that standard.

To choose a certain transposition or start a motif at a certain pitch in atonal composition, the composer is most likely trying to accomplish one or more of the following--the avoidance of note fatigue, the avoidance of tonal implications. As an atonal composer, you want to avoid repetition of a certain note(s) that may give too much precedence to that note(s) above the others and therefore mistakenly create an auditory "fatigue". You generally want a universal cycling through all twelve pitches similar to 12-tone composition but not as systematic a process in order to keep a chromatic freshness to the sound. Webern, in particular, excelled in this kind of atonal writing (see Bagatelles for String Quartet for example). You also want to avoid a series of notes that might denote a key, triad, scale, anything tonal, etc. So in order to accomplish that, a composer must choose the best transposition to accomplish these goals. It becomes extremely difficult to do in 12-tone composition counterpoint.



> The first video link shows an example (Schoenberg's passacaglia) which is structured on bass movement but that's just the nature of a passacaglia and not something you can generally base your analysis on.


As with most atonal music, Schoenberg's passacaglia is structured on a specific pitch class set and interval vector and is first stated in the bass-ostinato. The analysis is based on this as the melodic material, harmonies, and accompaniment all come from this same pitch class set and interval vector. The video explained this in laymen terms.


----------



## SanAntone

Gargamel said:


> Looking how it goes up-side down, backwards, upside-down and backwards, it's fairly kindergarden stuff. The difficulty for me is "why this transposition? Why does the motif start at this pitch?" because what atonal music lacks is root movement. The first video link shows an example (Schoenberg's passacaglia) which is structured on bass movement but that's just the nature of a passacaglia and not something you can generally base your analysis on.


If you don't it know it, this book by *Charles Wuorinen* offers a good basic explanation of atonal composition:

Simple Composition

View attachment 144149


Don't let the title fool you.


----------



## Gargamel

Torkelburger said:


> Pitches appearing in different transformations adds unity and cohesion to a piece that might otherwise sound random in a non-tonal context. Further, the varying rhythms (some of them difficult), textures, articulations, dynamics, octave displacements, transpositions, etc., etc. add the needed layers of complexity. And the technique in the piece is not so simple that I seriously doubt 99.9% of any group of listeners would realize that measure 13 is derived from measure 4, even when reading the score. So your comment is moot.
> 
> Lacking root movement is not any sort of shortcoming of atonal music. Do not try and shoehorn atonal music to fit the mold and customs of tonal music and then criticize it for not meeting that standard


When I said "kindergarden stuff", I meant it's easier for me to get acquainted with the music through these transformations than it is from other analytic viewpoints, although I could not always tell which building block is related to which, and with combinatorial schemes such as Babbitt's (whose music and theory I'm extremely well acquainted with) it's almost impossible to analyze from this viewpoint being a layman.



Torkelburger said:


> To choose a certain transposition or start a motif at a certain pitch in atonal composition, the composer is most likely trying to accomplish one or more of the following--the avoidance of note fatigue, the avoidance of tonal implications. As an atonal composer, you want to avoid repetition of a certain note(s) that may give too much precedence to that note(s) above the others and therefore mistakenly create an auditory "fatigue". You generally want a universal cycling through all twelve pitches similar to 12-tone composition but not as systematic a process in order to keep a chromatic freshness to the sound. Webern, in particular, excelled in this kind of atonal writing (see Bagatelles for String Quartet for example). You also want to avoid a series of notes that might denote a key, triad, scale, anything tonal, etc. So in order to accomplish that, a composer must choose the best transposition to accomplish these goals. It becomes extremely difficult to do in 12-tone composition counterpoint.


Maybe try contrasting it with to traditional (Bach or Fux) counterpoint? Consonant intervals being relagated to weak beats?


----------



## SeptimalTritone

Gargamel said:


> When I said "kindergarden stuff", I meant it's easier for me to get acquainted with the music through these transformations than it is from other analytic viewpoints, although I could not always tell which building block is related to which, and with combinatorial schemes such as Babbitt's (whose music and theory I'm extremely well acquainted with) it's almost impossible to analyze from this viewpoint being a layman.


So go check out the Jack Boss book I mentioned above. Start with the analysis of the op 25 prelude. It does more than pedantically count tone rows - it fully explains the musical narrative of the work and how the tone rows are placed together to arrive towards/away from a _musical goal_.

For a more gentle introduction explaining what makes atonal music "click", you could try Charles Rosen's _Schoenberg_ book. In fact, you should start with that. You can easily find the pdf online for free at the moment. 



Gargamel said:


> Maybe try contrasting it with to traditional (Bach or Fux) counterpoint? Consonant intervals being relagated to weak beats?


In Schoenberg, resolution of dissonance is not the greatest driving factor propelling the music as it would be in Beethoven. Generally in Schoenberg's counterpoint there's a certain management of dissonance - it doesn't randomly and suddenly wind up on a stable root position triad, or randomly wind up on a dense tone cluster.

But still, dissonant-constant resolution a la Bach/Fux counterpoint is not the main driving force. Take, e.g., the end of the first movement of Schoenberg's string quartet 4. It ends on a hexachord, but it sounds conclusive! This is because other mechanics like the rhythm of chromatic cycling (like Torkelberger mentioned in Webern's six bagatelles, but also play a role in most atonal/serial Second-Viennese works) play a greater role. Further, (generalized) motivic/harmonic/contrapuntal development is also more important in this music - it fuels the developmental narrative.

I'd suggest starting by reading the Charles Rosen book. It's short, and an accessible and breezy read. It will tell you what mechanics matter more in this music. Then perhaps follow it up with the Jack Boss book for detailed analysis of specific works.


----------



## Gargamel

SeptimalTritone said:


> I'd suggest starting by reading the Charles Rosen book. It's short, and an accessible and breezy read. It will tell you what mechanics matter more in this music. Then perhaps follow it up with the Jack Boss book for detailed analysis of specific works.


Oh, thanks. I also once started Wuorinen's book but for some reason never finished it.


----------



## Torkelburger

Gargamel said:


> Maybe try contrasting it with to traditional (Bach or Fux) counterpoint? Consonant intervals being relagated to weak beats?


I'll add my two cents worth. Comparing and contrasting atonal passacaglias to Bach's wouldn't be very productive in my opinion. Atonal music does not use the same expressive devices as tonal music. It does not use triadic harmony, root movement, keys/tonality, scales, etc. to generate expressiveness.

Atonal music must rely on intervals for expressive purposes, both harmonically and melodically. For example, harmonically occurring minor ninths and minor seconds are very tense while harmonically occurring thirds and sixths are expressively calmer. The options increase melodically. For instance, a melodically *ascending* minor ninth emotes something different than a *descending* minor ninth, etc. even though it's the same interval.


----------



## Torkelburger

So why does an atonal composer write a passacaglia then? The answer is he has chosen it as a form best suited to make his musical argument comprehensible to the listener. This is best explained in Aaron Copland's book _What to Listen for In Music_, which applies to the periods of music from Baroque through Contemporary. The book is especially useful to modern composers because it answers the question of "I have this musical idea (either Stravinskian, 12-tone, atonal, etc.). How do I get the audience to comprehend this idea?"

There are two choices, and only two-to repeat the idea or not to repeat the idea. Each option has several subsets and each subset can be broken down even further so it can get rather complicated. For repetition of the idea you have: repetition through sectional forms (two and three part forms, rondo, and you can even add modern-invented forms like mirror forms and minimalism); repetition through variation (basso ostinato, passacaglia, chaconne, theme and variations, (and minimalism)); repetition through contrapuntal forms (canon, invention, fugue, etc.); repetition through developmental forms (sonata form). Non-repetition forms include free forms, text-based forms, opera/drama/ballet, film music, programmatic forms)-or you could just have a very, very short piece like Webern would sometimes compose.

Copland explains how each of these forms (except the modern forms I mentioned) presents an idea as a unique musical argument in a way the listener can comprehend. Now, as a composer, certain ideas will be better suited for a certain form over others and the composer must find the right one for this particular idea. For example, the rhythms in atonal music are often asymmetrical, with odd groupings, ties over the downbeat, complex rhythms, changing meters, and odd meters. An idea with those characteristics would probably not be well suited for a passacaglia and the composer would have to choose something else. You couldn't relegate consonant intervals to weak beats as in your question, as the weak beats would always be changing and there may not even be an identifiable pulse to the music.


----------



## Torkelburger

One book you should also read if you are interested in either analyzing or composing atonal music is _The Structure of Atonal Music_ by Allen Forte. It explains the basic concepts, vocabulary, and language that analysts and composers of atonal music use. Pitch class sets, interval vectors, relations and set complexes. As an atonal composer, pitch class set theory has been extremely helpful in composition. The interval vectors not only show you what intervals occur in the pitch class set, but also the ones that do not occur and are not available. That helps you in designing the specific sound and character you want to achieve.


----------



## Torkelburger

Lastly, I recommend the book _Serial Composition_ by Reginald Smith Brindle. There are two chapters that may interest you. One chapter is about writing counterpoint (there are several chapters about counterpoint) but this one in particular is about two-part counterpoint and, while in a 12-tone context, discusses the importance of intervals and expression and how to write with a specific expressive goal in mind, even within the confines of a 12-tone row. Another chapter deals with how to write free atonality and analyzes two atonal pieces in great depth. It goes through a step by step thought process of how they were composed.


----------



## Gargamel

Torkelburger said:


> Copland explains how each of these forms (except the modern forms I mentioned) presents an idea as a unique musical argument in a way the listener can comprehend. Now, as a composer, certain ideas will be better suited for a certain form over others and the composer must find the right one for this particular idea. For example, the rhythms in atonal music are often asymmetrical, with odd groupings, ties over the downbeat, complex rhythms, changing meters, and odd meters. An idea with those characteristics would probably not be well suited for a passacaglia and the composer would have to choose something else. You couldn't relegate consonant intervals to weak beats as in your question, as the weak beats would always be changing and there may not even be an identifiable pulse to the music.


Hmm, there is often identifiable pulse in Schoenberg, which Boulez famously attacked him for. (Or was it the fact that he abided to old forms?) But Schoenberg always denied that he (unlike Strauss in his mind) was revolutionary and emphasized his closeness to tonal contemporaries such as Max Reger.


----------



## Torkelburger

Gargamel said:


> Hmm, there is often identifiable pulse in Schoenberg, which Boulez famously attacked him for. (Or was it the fact that he abided to old forms?) But Schoenberg always denied that he (unlike Strauss in his mind) was revolutionary and emphasized his closeness to tonal contemporaries such as Max Reger.


Yes, you're right. And I've always liked that about Schoenberg. I love both approaches, actually. But yes, I was referring to the style developed by his followers much later when atonality became popular and mainstream among composers around the late 40's through early 70's. Literally hundreds of composers could be named, but to my mind come: Luciano Berio, Mario Davidovsky, Luigi Dallapiccola*, Luigi Nono, Leon Kirchner, Elliott Carter...

*(Actually, Dallapiccola had occasionally written some canonic material in extremely complex rhythm and mixed meters. Nothing like fugues or passacaglias that I remember, but some nice canons).


----------



## millionrainbows

This is a very good book. It's valuable because it provides a much-needed bird's-eye-view of serial thought, and how it has influenced all modern music, not just serial music.

Just the title itself is indicative of how the author puts 12-tone and set theory under the same larger umbrella of "serialism," and how this type of more mathematical thought has influenced all areas of modern music.


----------



## nv420

tl;dr - for me how to listen depends on aesthetics and not tonality

Because "atonal" is a fairly sweeping category, I personally would think it would depend more on the aesthetic of the music how I'd recommend listening to it rather than the tonality or lack thereof. As a fair few people on here have stated, a lot of Second Viennese music is actually pretty similar to classical and romantic-era music in many ways. You still have your melodies and chordal movements even if they sound a bit different from that of C.P.E. music. Check the opening of this Schoenberg concerto out. 



To me it honestly sounds pretty melodic in a lot of areas, and some of the harmonies kind of sound almost jazzy to me. So I personally don't have to listen to it any differently than I'd listen to the more harmonically adventurous late romantics like Scriabin.

But there's also "atonal" music that is aesthetically super different to this here. Like if you consider spectralist stuff like this (



) atonal, speaking only for myself I think it requires a different kind of listening out of me. It's less about hearing lines and counterpoint and rhythm, and more about placing yourself in an environment of sounds that you can experience, kind of like ambient music. (I really like ambient music and that's how I got into composers like Scelsi and Ligeti and the spectralists.)

Again, I can speak only for myself here.


----------



## nv420

I'd second the Jack Boss book. He was actually my teacher for a post-tonal theory class I took and that guy knows his stuff when it comes to Second Viennese School music in particular (also a very nice and humorous bloke).


----------



## Gargamel

If Schoenberg's violin concerto was tonal, this is what it might sound:





(Or that one Zemlinsky piece, I can't remember which one it was.)


----------



## Phil loves classical

^ To me sounds similar to saying "If Obama was white, he would be like this...", but I can see where your coming from. His idiom is still post-Romantic.

I've read some of John Rahn's Basic Atonal Theory. In the intro he made a good point that from infancy we developed a set of "tonal filters". He also boldly stated "not all atonal music is good music. *In fact, most contemporary music is not very good.*". That was back in 1980 when the book was published. I wonder how much he actually analysed the music to say it. How do you say Babbitt is good, but xyz composer's atonal music sucks (assuming it's still by trained composers)?


----------



## Gargamel

Phil loves classical said:


> ^ To me sounds similar to saying "If Obama was white, he would be like this...", but I can see where your coming from. His idiom is still post-Romantic.


It's got almost the same melody as Schoenberg's violin concerto, duh.


----------



## Phil loves classical

Gargamel said:


> It's got almost the same melody as Schoenberg's violin concerto, duh.


Almost as in how exactly?


----------



## BabyGiraffe

Phil loves classical said:


> ^ To me sounds similar to saying "If Obama was white, he would be like this...", but I can see where your coming from. His idiom is still post-Romantic.
> 
> I've read some of John Rahn's Basic Atonal Theory. In the intro he made a good point that from infancy we developed a set of "tonal filters". He also boldly stated "not all atonal music is good music. *In fact, most contemporary music is not very good.*". That was back in 1980 when the book was published. I wonder how much he actually analysed the music to say it. How do you say Babbitt is good, but xyz composer's atonal music sucks (assuming it's still by trained composers)?


How can you say that X/Y/Z is good, but M/N/R's composer tonal  music sucks (assuming it's still by trained composers)?


----------



## Gargamel

Phil loves classical said:


> Almost as in how exactly?











I transposed the Schoenberg concerto, illegally with C clefs, so the beginnings of the two pieces are the exact same pitch. And had I bothered to transpose the notes themselves, I could have shown you that the continuation in the bass strings (Scharwenka, M. 10-13) is the same as the violin melody (Schoenberg, M. 1-3).


----------



## Gargamel

SeptimalTritone said:


> So go check out the Jack Boss book I mentioned above. Start with the analysis of the op 25 prelude. It does more than pedantically count tone rows - it fully explains the musical narrative of the work and how the tone rows are placed together to arrive towards/away from a _musical goal_.
> 
> For a more gentle introduction explaining what makes atonal music "click", you could try Charles Rosen's _Schoenberg_ book. In fact, you should start with that. You can easily find the pdf online for free at the moment.
> 
> In Schoenberg, resolution of dissonance is not the greatest driving factor propelling the music as it would be in Beethoven. Generally in Schoenberg's counterpoint there's a certain management of dissonance - it doesn't randomly and suddenly wind up on a stable root position triad, or randomly wind up on a dense tone cluster.


My uneducated guess would be that it has something to do with melodic movement, whether it's going up or down. (Some people use the terms "conjoint", "disjoint" or "paralel" movement for the relationship of two voices.) It's quite strictly controlled to accommodate for either dissonance or consonance in traditional counterpoint, but for 2nd viennese school melodies, you often hear "up" which should be "down" in tonal music and so on. Take, for instance, the few first melodies of Wozzeck, and imagine what it would sound like if just a few of those melodic movements/vectors were inverted (so that up becomes down and vice versa). With only such a trifling modification, it would sound like a nursery rhyme!

(Probably lots of exceptions to the rule which I just described! For example, the melodic line in the beginning of Schoenberg's piano concerto sounds rather tonal, but then, in the second phrase it goes a bit minor where tonally you _should_ be hearing major! Maybeh.)


----------



## Tikoo Tuba

I think the driving relationship is Space . Rhythmic intervals are ideally indeterminate . 
The performer must actually be one artist making this fundamental choice . Playing in
a consort gets very psychic with a multi-dimensional sensibility .


----------



## millionrainbows

If we were going to try to understand atonal music by listening to it, what does its nature suggest we listen for?
Since we know it is not tonal, we should not be listening to detect a tonal center.
Since most listeners are already conditioned to listen to music in terms of a tonal center, first we must get past this obstacle, which can be difficult. 
Once we do that, we can hear the music as relative _relationships,_ in terms of _intervals._ If you know all 6 intervals by ear, and can name them, you are well on your way to understanding that aspect.


----------



## Gargamel

millionrainbows said:


> If we were going to try to understand atonal music by listening to it, what does its nature suggest we listen for?
> Since we know it is not tonal, we should not be listening to detect a tonal center.
> Since most listeners are already conditioned to listen to music in terms of a tonal center, first we must get past this obstacle, which can be difficult.
> Once we do that, we can hear the music as relative _relationships,_ in terms of _intervals._ If you know all 6 intervals by ear, and can name them, you are well on your way to understanding that aspect.


Although what you said is exceedingly obvious, almost ridiculous, it did lead me on to a rather remarkable idea about _harmonic practice_ in atonal music. What kind of intervals are necessary for tonal music? The answer is, equal intervals, and strong tonal chords are always built of equal-interval chords made up of thirds. For music to be atonal, equal-interval chords are unnecessary. So composers of atonal music consciously avoid equal-interval chords built of thirds. Other equal-interval chords such as those built on perfect fourths may be used, as Webern uses in Variations Op. 27. This leaves the question, when and how can weak tonal chords such as Sus be used? Berg likes to emphasize tonal undercurrents in his late works such as Lulu, perhaps sometimes by employing weak tonal chords, but more importantly the way he doubles the tonic/fundamental in the bass, outlining tonal chord progressions in this way even when the musical structure itself is atonal.


----------



## SanAntone

millionrainbows said:


> If we were going to try to understand atonal music by listening to it, what does its nature suggest we listen for?
> Since we know it is not tonal, we should not be listening to detect a tonal center.
> Since most listeners are already conditioned to listen to music in terms of a tonal center, first we must get past this obstacle, which can be difficult.
> Once we do that, we can hear the music as relative _relationships,_ in terms of _intervals._ If you know all 6 intervals by ear, and can name them, you are well on your way to understanding that aspect.


I don't have a problem listening to atonal music, in fact, I don't have a clue as to what you are talking about: "listen to music in terms of a tonal center" - I never have this problem since I just listen to the sound of the music. It either pleases me or not, but I certainly never approach it from the perspective of tonal centers, etc.


----------



## millionrainbows

Gargamel said:


> Although what you said is exceedingly obvious, almost ridiculous, it did lead me on to a rather remarkable idea about _harmonic practice_ in atonal music. What kind of intervals are necessary for tonal music? The answer is, equal intervals, and strong tonal chords are always built of equal-interval chords made up of thirds. For music to be atonal, equal-interval chords are unnecessary. So composers of atonal music consciously avoid equal-interval chords built of thirds. Other equal-interval chords such as those built on perfect fourths may be used, as Webern uses in Variations Op. 27. This leaves the question, when and how can weak tonal chords such as Sus be used? Berg likes to emphasize tonal undercurrents in his late works such as Lulu, perhaps sometimes by employing weak tonal chords, but more importantly the way he doubles the tonic/fundamental in the bass, outlining tonal chord progressions in this way even when the musical structure itself is atonal.


You might find Schoenberg's Structural Functions of Harmony (available in softcover) interesting. In it, he talks about root movement in terms of intervals, and explains how intervals can suggest tonality, or movement to (or away from) a root station.


----------



## millionrainbows

SanAntone said:


> I don't have a problem listening to atonal music, in fact, I don't have a clue as to what you are talking about: "listen to music in terms of a tonal center" - I never have this problem since I just listen to the sound of the music. It either pleases me or not, but I certainly never approach it from the perspective of tonal centers, etc.


I find this hard to believe, since you have previously stated: "I majored in music theory and composition and know the standard methods of analyzing classical music..."


----------



## SanAntone

millionrainbows said:


> I find this hard to believe, since you have previously stated: "I majored in music theory and composition and know the standard methods of analyzing classical music..."


I did graduate with a degree in music theory and composition, but when I listen to music I am not "analyzing on the fly."


----------



## millionrainbows

SanAntone said:


> I did graduate with a degree in music theory and composition, but when I listen to music I am not "analyzing on the fly."


You don't have to analyze to listen for tonal centers. I just used a theory term to communicate this way of listening to you.


----------



## SanAntone

millionrainbows said:


> You don't have to analyze to listen for tonal centers. I just used a theory term to communicate this way of listening to you.


If that's how you want to listen to atonal music. I don't want to listen for tonal centers in atonal music.


----------



## millionrainbows

SanAntone said:


> If that's how you want to listen to atonal music. *I don't want to listen for tonal centers in atonal music.*


??? 
In my post #54, I said 



> If we were going to try to understand atonal music by listening to it, what does its nature suggest we listen for?





> Since we know it is not tonal, *we should not be listening to detect a tonal center.*


----------



## SanAntone

> f we were going to try to understand atonal music by listening to it, what does its nature suggest we listen for?
> Since we know it is not tonal, we should not be listening to detect a tonal center.


So it seems we agree that we should not be listening for tonal centers when listening to atonal music.

I'm glad we got that straightened out.


----------



## millionrainbows

The real point is that we can listen to *tonal* music in terms of tonal centers without having to 'analyze it on the fly.'


----------



## Woodduck

Gargamel said:


> Although what you said is exceedingly obvious, almost ridiculous, it did lead me on to a rather remarkable idea about _harmonic practice_ in atonal music. *What kind of intervals are necessary for tonal music? The answer is, equal intervals, and strong tonal chords are always built of equal-interval chords made up of thirds.* For music to be atonal, equal-interval chords are unnecessary. So *composers of atonal music consciously avoid equal-interval chords built of thirds.*


The thirds in major and minor triads are not equal. In both cases, one of the thirds is major, the other minor. A triad consisting of equal intervals would be either diminished or augmented, and neither of those, in itself, implies a clear tonal center. Liszt exploits the equal-interval augmented triad and gives his Faust Symphony a splendidly atonal beginning:


----------



## millionrainbows

There are 6 intervals, the others being inversions: m2, M2, m3, M3, fourth, and tritone.

As I see things, the intervals most useful to tonality are fourths and fifths, because when cycled (stacked), they generate the entire chromatic scale before looping back in to themselves, as in C-G-A-E-B etc. for fifths and C-F-Bb-Eb-Ab etc. for fourths. In this sense they are non-recursive, and encourage travel within a key by fourths and fifths (I-IV, V-I, etc), or travel to new keys by that interval.

The other intervals M2, m3, M3, and the tritone are recursive and they cycle back on themselves 'within the octave,' thus staying within smaller 'chromatic orbits' than fourths & fifths, and encouraging chromatic movement, except for the m2, which with the fourth/fifth, are the only two intervals that generate the entire chromatic when cycled.

In terms of harmonic sonority, intervals can be considered vertically. By themselves, intervals can suggest tonality or 'roots', which I go into in my blogs. For atonality, which has no 'root movement,' these effects can still have suggestive power.

https://www.talkclassical.com/blogs/millionrainbows/1007-root-movement.html


----------



## Gargamel

Woodduck said:


> The thirds in major and minor triads are not equal. In both cases, one of the thirds is major, the other minor. A triad consisting of equal intervals would be either diminished or augmented, and neither of those, in itself, implies a clear tonal center. Liszt exploits the equal-interval augmented triad and gives his Faust Symphony a splendidly atonal beginning:


Don't be like that. We both know what I'm talking about. The term "equal-interval chords" can be misleading, but that's the only term I know of used to describe the opposite to "mixed-interval chords". Functionally speaking, triads and seventh chords are not "mixed-interval chords", since the tonal system grants the major third and the minor third an equal status or function amongst various degrees.
From Wikipedia: "Chords characterized by one consistent interval, or primarily but with alterations, are equal-interval chords."


----------



## Woodduck

Gargamel said:


> Don't be like that. We both know what I'm talking about. The term "equal-interval chords" can be misleading, but that's the only term I know of used to describe the opposite to "mixed-interval chords". Functionally speaking, triads and seventh chords are not "mixed-interval chords", since the tonal system grants the major third and the minor third an equal status or function amongst various degrees.
> From Wikipedia: "Chords characterized by one consistent interval, or primarily but with alterations, are equal-interval chords."


I don't think my objection is misguided. The notion of "equal-interval chords" in which the intervals are in fact unequal except by a convention of notation (they're equidistant on the staff) seems to me no more than a physical description stating the obvious: that common practice tonality is based on triadic harmony and atonality is not. Perhaps that's all you meant to say?


----------



## Gargamel

Woodduck said:


> I don't think my objection is misguided. The notion of "equal-interval chords" in which the intervals are in fact unequal except by a convention of notation (they're equidistant on the staff) seems to me no more than a physical description stating the obvious: that common practice tonality is based on triadic harmony and atonality is not. Perhaps that's all you meant to say?


Triads and seventh chords are consistently made up of a *succession* of thirds. I think the word "succession" here is key. A triad is a succession of two thirds; a seventh is a succession of three thirds. When we say "succession of thirds", without specifying if it's a major or minor third, we are uniformly refering to one type of intervallic information. Tonality is here just a context that tells you whether it's a major or minor third. You can call it what you want, but I think my use of the term "equal-interval chord" as in the Wikipedia article on "Mixed-interval chord": _"a mixed-interval chord is a chord not characterized by one consistent interval. Chords characterized by one consistent interval, or primarily but with alterations, are equal-interval chords. Mixed interval chords "lend themselves particularly" to atonal music since they tend to be dissonant."_

Perhaps I meant to conjecture, that even if tonal features such as partial major/minor chord progressions may be included in atonal music, there are strong reasons not to stack up multiple thirds. (Berg, for instance, explicitly puts up perfectly tonal harmonies, but often with only single third interval.)


----------



## BabyGiraffe

Gargamel said:


> Triads and seventh chords are consistently made up of a *succession* of thirds. I think the word "succession" here is key. A triad is a succession of two thirds; a seventh is a succession of three thirds. When we say "succession of thirds", without specifying if it's a major or minor third, we are uniformly refering to one type of intervallic information. Tonality is here just a context that tells you whether it's a major or minor third. You can call it what you want, but I think my use of the term "equal-interval chord" as in the Wikipedia article on "Mixed-interval chord": _"a mixed-interval chord is a chord not characterized by one consistent interval. Chords characterized by one consistent interval, or primarily but with alterations, are equal-interval chords. Mixed interval chords "lend themselves particularly" to atonal music since they tend to be dissonant."_
> 
> Perhaps I meant to conjecture, that even if tonal features such as partial major/minor chord progressions may be included in atonal music, there are strong reasons not to stack up multiple thirds. (Berg, for instance, explicitly puts up perfectly tonal harmonies, but often with only single third interval.)


Triad is a succession of thirds only in a scale where these thirds belong to the same interval class. So, not in 12 equal where step 3 and 4 don't belong to the same interval class - so, your remark about stacking thirds makes no sense (in theory only: in practice I doubt that most listeners won't hear in more than 9 different note melodies alterations of pitches instead of unique "scale degrees").
Still, if you want to compose dodecaphonic music, you have to think in 12 equal logic, not in 7 (in 7 equal major and minor "thirds" are mapped to the same step, so 7-tone music can be triadic - or tetradic, because 7/6 is mapped also to the same degree as 5/4 and 6/5; in 12 equal 7/6 is mapped to 6/5 => so seventh chords of jazz and romantic music can be interpreted as septimal consonances, for example the dominant seventh can be thought as 4:5:6:7 = 1-5/4-3/2-7/4 and the whole 12 equal as kind of scale, equivalent to diatonic one, but heavily tempered; if we want more accuracy - 7/6 and minor third being different pitches, we can extend to septimal meantone ((31 equal is perfect)) or two other 12 tone scales in 22 or 27 equal.)
Honestly, it's pretty hard to make real atonal music, because every possible progression has some harmonical interpretations.


----------



## millionrainbows

Gargamel said:


> Triads and seventh chords are consistently made up of a *succession* of thirds. I think the word "succession" here is key. A triad is a succession of two thirds; a seventh is a succession of three thirds. When we say "succession of thirds", without specifying if it's a major or minor third, we are uniformly refering to one type of intervallic information. Tonality is here just a context that tells you whether it's a major or minor third. You can call it what you want, but I think my use of the term "equal-interval chord" as in the Wikipedia article on "Mixed-interval chord": _"a mixed-interval chord is a chord not characterized by one consistent interval. Chords characterized by one consistent interval, or primarily but with alterations, are equal-interval chords. Mixed interval chords "lend themselves particularly" to atonal music since they tend to be dissonant."_
> 
> Perhaps I meant to conjecture, that even if tonal features such as partial major/minor chord progressions may be included in atonal music, there are strong reasons not to stack up multiple thirds. (Berg, for instance, explicitly puts up perfectly tonal harmonies, but often with only single third interval.)


I'd use the term "tertian."
https://en.wikipedia.org/wiki/Tertian


----------



## millionrainbows

BabyGiraffe said:


> Triad is a succession of thirds only in a scale where these thirds belong to the same interval class. So, not in 12 equal where step 3 and 4 don't belong to the same interval class - so, your remark about stacking thirds makes no sense (in theory only: in practice I doubt that most listeners won't hear in more than 9 different note melodies alterations of pitches instead of unique "scale degrees").
> Still, if you want to compose dodecaphonic music, you have to think in 12 equal logic, not in 7 (in 7 equal major and minor "thirds" are mapped to the same step, so 7-tone music can be triadic - or tetradic, because 7/6 is mapped also to the same degree as 5/4 and 6/5; in 12 equal 7/6 is mapped to 6/5 => so seventh chords of jazz and romantic music can be interpreted as septimal consonances, for example the dominant seventh can be thought as 4:5:6:7 = 1-5/4-3/2-7/4 and the whole 12 equal as kind of scale, equivalent to diatonic one, but heavily tempered; if we want more accuracy - 7/6 and minor third being different pitches, we can extend to septimal meantone ((31 equal is perfect)) or two other 12 tone scales in 22 or 27 equal.)
> Honestly, it's pretty hard to make real atonal music, because every possible progression has some harmonical interpretations.


.....Harmonical?


----------



## millionrainbows

Beethoven used root movement by thirds, as in the transitions in the Ninth. This kind of root movement is doubly interesting because not only does it move to distant key areas quickly, it also has the effect of "outlining triads" with the roots. Like, if you moved chords from Cmaj-Amin-Fmaj-Dmin. This has the effect of outlining a Dmin7 chord, D-F-A-C.

In terms of their "cycling" properties, minor thirds have a value of 3 (semitones) and cycle within the octave as 3X4=12, and major thirds are a value of 4 semitones, so 4X3=12.

In triadic terms, these are diminished seventh and augmented chords. The diminished seventh is so called because it "diminishes" the fifth of a triad, so it has an "inward-going" effect. 
The augmented chord has "augmented" or expanded the fifth, so it has an "outward-going" effect.

These have corresponding effects on our perception of tonality. Holst's use of augmented triads has the effect of creating a sense of "harmonic vertigo," as if the tonality were expanding.

Diminished structures will have the opposite effect, of a "shrinking" collapse of tonality, which will tend towards the chromatic, as the diminished scale is made of m3rds and semitones.

Augmented structures 'expand' because the augmented scale can be mapped to the whole tone scale, and is a symmetrical construction of whole steps, which give a scale-like feeling of movement "away" from a note.

Thirds can be considered n terms of root movement, or melodic implications.

A third moving down is getting stronger or "ascending" in root feeling: we hear the second note as root, or resting point.

A third up is getting weaker or "descending" in root feeling: we hear the first note as root, but we have moved away from it to a weaker note; thus, it is "descending" or weakening the sense of tonality.

By 'weak' or 'strong' is meant simply either 'strengthening' and reinforcing a root or key center, or 'weakening' the root or key, and moving away from it, to perhaps another key.

That's why Beethoven used root movement of chords by _descending_ thirds, Cmaj-Amin-Fmaj-Dmin (in the transitions of the Ninth) because he was traveling to new root stations, and in downward-moving thirds we hear each succeeding root as stronger than the last.


----------



## BabyGiraffe

millionrainbows said:


> .....Harmonical?


Adj.	1.	harmonical - involving or characterized by harmony
(or an obsolete form of harmonic)

Btw, your interpretations of harmony only in terms of 12 equal characteristics are too limited, my friend, you can play valid 5-limit temperaments in 9 to 19 notes per octave without problems (20 and 21 are probably too "enharmonic" for simple triadic harmony, but maybe even they can be used, if someone is careful). 22+ notes per octave is well tuned 7-limit (more dissonant harmonies can be found in bigger divisions).


----------



## millionrainbows

BabyGiraffe said:


> Adj. 1. harmonical - involving or characterized by harmony
> (or an obsolete form of harmonic)
> 
> Btw, your interpretations of harmony only in terms of 12 equal characteristics are too limited, my friend, you can play valid 5-limit temperaments in 9 to 19 notes per octave without problems (20 and 21 are probably too "enharmonic" for simple triadic harmony, but maybe even they can be used, if someone is careful). 22+ notes per octave is well tuned 7-limit (more dissonant harmonies can be found in bigger divisions).


You need to 'grok,' to begin with, why there are 12 notes, why they became equal, learn to generalize, and forget all this 5-limit stuff.


----------



## Gargamel

Why is all composition taught to consist of four parts? Although there is no need for resolution in atonal music, the idea of having four voices is persisent. Maybe it's just most practical to teach it that way, or if you need to sustain a sense of indeterminate root, the 4-part chord with the least possible transpositions would be the dim7 chord?


----------

