# Is the Perfect Fourth a Dissonance? If So, Why?



## millionrainbows

From WIK: 
The perfect fourth may be derived from the harmonic series as the interval between the third and fourth harmonics. The term perfect identifies this interval as belonging to the group of perfect intervals, so called because they are neither major nor minor (unlike thirds, which are either minor or major) but perfect.
The perfect fourth is a perfect interval like the unison, octave, and perfect fifth, and it is a sensory consonance. In common practice harmony, however, it is considered a stylistic dissonance in certain contexts, namely in two-voice textures and whenever it appears above the bass. If the bass note also happens to be the chord's root, the interval's upper note almost always temporarily displaces the third of any chord, and, in the terminology used in popular music, is then called a suspended fourth.
In the 13th century, the fourth and fifth together were the concordantiae mediae (middle consonances) after the unison and octave, and before the thirds and sixths. The fourth came in the 15th century to be regarded as dissonant on its own, and was first classed as a dissonance by Johannes Tinctoris in his Terminorum musicae diffinitorium (1473). In practice, however, it continued to be used as a consonance when supported by the interval of a third or fifth in a lower voice.
Modern acoustic theory supports the medieval interpretation insofar as the intervals of unison, octave, fifth and fourth have particularly simple frequency ratios. The octave has the ratio of 2:1, for example the interval between a' at A440 and a'' at 880 Hz, giving the ratio 880:440, or 2:1. The fifth has a ratio of 3:2, and its complement has the ratio of 3:4. Ancient and medieval music theorists appear to have been familiar with these ratios, see for example their experiments on the monochord.

It sounds to me like the treatment of the perfect fourth as dissonant is just a stylistic convention, based on harmony in thirds.

From WIK:
Suspended Fourth: The term is borrowed from the contrapuntal technique of suspension, where a note from a previous chord is carried over to the next chord, and then resolved down to the third or tonic, suspending a note from the previous chord. However, in modern usage, the term concerns only the notes played at a given time; in a suspended chord, the added tone does not necessarily resolve and is not necessarily "prepared" (i.e., held over) from the prior chord. As such, in C-F-G, F would resolve to E (or E♭), but in rock and popular music, "the term is used to indicate only the harmonic structure, with no implications about what comes before or after," though preparation of the fourth occurs about half the time and traditional resolution of the fourth occurs usually. In modern jazz, a third can be added to the chord voicing, as long as it is above the fourth.

In Western music, dissonance is the quality of sounds that seems unstable and has an aural need to resolve to a stable consonance. Both consonance and dissonance are words applied to harmony, chords, and intervals and, by extension, to melody, tonality, and even rhythm and metre. *Although there are physical and neurological facts important to understanding the idea of dissonance, the precise definition of dissonance is culturally conditioned-definitions of and conventions of usage related to dissonance vary greatly among different musical styles, traditions, and cultures.* Nevertheless, the basic ideas of dissonance, consonance, and resolution exist in some form in all musical traditions that have a concept of melody, harmony, or tonality. Dissonance being the complement of consonance it may be defined, as above, as non-coincidence of partials, lack of fusion or pattern matching, or as complexity.

Understanding a particular musical style's treatment of dissonance-what is considered dissonant and what rules or procedures govern how dissonant intervals, chords, or notes are treated-is key in understanding that particular style. For instance, harmony is generally governed by chords, which are collections of notes defined as tolerably consonant by the style. (There is likely, however, to be a hierarchy of chords, with some considered more consonant and some more dissonant.) Any note that does not fall within the prevailing harmony is considered dissonant. A given style typically pays attention to how its musical structure approaches dissonance (in steps is less jarring, a leap is more jarring), and even more to how they resolve (almost always by step), to how they fit within the meter and rhythm (dissonances on strong beats are more emphatic, those on weaker beats less vital), and to how they lie within the phrase (dissonances tend to resolve at phrase's end).


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## Woodduck

In brief: since "dissonance" and "consonance" have more than one definition, since in any definition they are relative to each other, and since talking about sensory phenomena without reference to specific sounds is apt to lock us in a theoretical ivory tower out of touch with reality, the answer is "yes and no."

Wishing to avoid confinement in the ivory tower, I take exception to Wiki's statement that a perfect fourth is a "sensory consonance." From a purely sensory (acoustical) standpoint, the effect of consonance or dissonance depends on the clash of partials. Hence the degree of dissonance audible in an interval can depend on the timbre of the instruments that play it and the register in which it's played. Example: on the piano, intervals played high on the keyboard sound "pure," while those played low are rich in audible partials. In the high register, a perfect fourth and a perfect fifth both sound consonant, but played in the bass register the fifth sounds fairly pure while the fourth sounds muddy and harsh.


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## caters

I actually answered a question on Stack Exchange about 12TET intervals and how dissonant they are. I don't mind posting it here.

I don't know if this is the true dissonance ranking but here is my personal ranking:

*Rank -1*

*Unison*

This I don't really consider to be an interval because the 2 notes are exactly identical. So, that is why I gave it the negative rank.

*Rank 0*

*Octave and Perfect fifth*

These are the 2 most open intervals and so it isn't surprising that these intervals would be the most consonant. I don't consider the seventh to be open because when you invert it, it becomes a second. Octaves technically invert to a unison but practically speaking, they self-invert, meaning that an octave becomes another octave. Fifths invert to fourths so there isn't much difference. Also, these intervals are fundamental to any tuning system. Without them, the entire field of music theory would fall apart.

*Rank 1*

*Perfect fourth, Major third, and Major sixth*

Unlike some people who view the perfect fourth as dissonant, I don't, at least outside of contrapuntal contexts. It isn't as consonant as the perfect fifth but it isn't all that dissonant either. Some might argue "If it doesn't appear in the harmonic series, than it is dissonant", basing their argument off of the supposed fact that the note of the perfect fourth never appears, but then that would lead to the tritone being more consonant than the perfect fourth which is just wrong.Thirds and sixths tend to be consonant but the major ones are understandably more consonant than their minor counterparts.

*Rank 2
*
*Minor third and Minor seventh
*
This again isn't agreed upon but I view these 2 intervals as being consonant but not as consonant. This is partly because, when you combine the two intervals, you get a very peaceful sounding minor seventh chord.

*Rank 3*

*Major seventh and Major second*

These 2 intervals are both quite dissonant, the second especially. But they still have a lower ranking than the last few intervals.

*Rank 4*

*Minor second and Minor sixth*

Now this might seem odd, after all the minor sixth shows up everywhere. But here's the thing. When it shows up as part of a chord, I rank it based on how consonant the chord is in root position. When it is all by itself with no harmonic context, at least to me, it sounds augmented, more specifically like an augmented fifth. And augmented fifths are dissonant.

*Rank 5*

*Tritone*

This is the only rank besides the negative rank that has a single interval. To put it simply, the tritone is *the most dissonant interval*, not just a very dissonant interval. Part of the reason is that it divides the octave cleanly in half. Now you might think that octave symmetry should make it very consonant. But in fact, this usually turns out not to be the case. For example, the whole tone scale, as a scale is relatively consonant. But harmonically, it is extremely dissonant. All the fifths are either diminished or augmented. This makes for some weird harmonic progressions. So actually, symmetry is kind of a guarantee for extreme dissonance. That is, unless you consider Dorian to be symmetric(which most don't, when most people say symmetry in music theory, they mean octave symmetry, not palindrome symmetry).

But like I said, this is my own personal ranking of the intervals. The objective ranking in 12TET may very well be different. But this personal ranking does all have to do with 12TET since it is the only tuning system I use.

In conclusion, I would say that outside of counterpoint, the perfect fourth is just as consonant as the major third and major sixth and thus is not just a sensory consonance but a true consonance.


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## isorhythm

I think you answered your own question - it depends which sense of the word dissonance you mean. Nothing mysterious here.


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## millionrainbows

Woodduck said:


> Wishing to avoid confinement in the ivory tower, I take exception to Wiki's statement that a perfect fourth is a "sensory consonance." From a purely sensory (acoustical) standpoint, the effect of consonance or dissonance depends on the clash of partials. Hence the degree of dissonance audible in an interval can depend on the timbre of the instruments that play it and the register in which it's played. Example: on the piano, intervals played high on the keyboard sound "pure," while those played low are rich in audible partials. In the high register, a perfect fourth and a perfect fifth both sound consonant, but played in the bass register the fifth sounds fairly pure while the fourth sounds muddy and harsh.


I have to disagree totally with this. Why? Because I think you are avoiding any scientific or quantitative definition of consonance and are "saving it" for your CP argument that says a perfect fourth above the tonic is a dissonance. It makes little sense to say "played in the bass register the fifth sounds fairly pure while the fourth sounds muddy and harsh" without saying why. After all, there is little qualitative difference between 2:3 and 3:4.



> ...since "dissonance" and "consonance" have more than one definition...


Not really. The 5th and the 4th are considered to be "perfect intervals": The perfect fourth is a perfect interval like the unison, octave, and perfect fifth, and it is a *sensory consonance*.

The fourth is only_ considered, not __defined_ to be dissonant in CP harmony.

In common practice harmony the fourth is _considered_ a stylistic dissonance in certain contexts, namely in two-voice textures and whenever it appears above the bass. If the bass note also happens to be the chord's root, the interval's upper note almost always temporarily displaces the third of any chord, and, in the terminology used in popular music, is then called a suspended fourth.


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## Becca

There is no "scientific or quantitative definition of consonance", it is a highly subjective, even socially based concept. Yes you can find some which almost everyone will agree on but, as obvious from this thread, there is a large, fuzzy middle ground with substantial disagreement which is the antithesis of quantitative let alone scientific definition.


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## millionrainbows

caters said:


> I don't know if this is the true dissonance ranking but here is my personal ranking:
> 
> Rank -1: Unison
> 
> Rank 0: Octave and Perfect fifth
> 
> Rank 1: Perfect fourth, Major third, and Major sixth


This is somewhat contradictory, since you yourself observed that the fifth and fourth are inversions, with only one step of difference in their size.

I must reject your "personal" ranking of dissonance. From WIK:


Perfect consonances:
unisons and octaves
perfect fourths and perfect fifths

Imperfect consonances:
major thirds and minor sixths
minor thirds and major sixths


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## Woodduck

millionrainbows said:


> I have to disagree totally with this. Why? Because I think you are avoiding any scientific or quantitative definition of consonance and are "saving it" for your CP argument that says a perfect fourth above the tonic is a dissonance. It makes little sense to say "played in the bass register the fifth sounds fairly pure while the fourth sounds muddy and harsh" without saying why. After all, there is little qualitative difference between 2:3 and 3:4.
> 
> Not really. The 5th and the 4th are considered to be "perfect intervals": The perfect fourth is a perfect interval like the unison, octave, and perfect fifth, and it is a *sensory consonance*.
> 
> The fourth is only_ considered, not __defined_ to be dissonant in CP harmony.
> 
> In common practice harmony the fourth is _considered_ a stylistic dissonance in certain contexts, namely in two-voice textures and whenever it appears above the bass. If the bass note also happens to be the chord's root, the interval's upper note almost always temporarily displaces the third of any chord, and, in the terminology used in popular music, is then called a suspended fourth.


Do you seriously intend this as an argument?

I addressed, with precisely stated intention, the idea of SENSORY dissonance, and you think it's meaningful to respond with "I think you are avoiding any scientific or quantitative definition of consonance"?

I'm just going to let you think about that howling nonsequitur while I go have some breakfast.


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## millionrainbows

Becca said:


> There is no "scientific or quantitative definition of consonance", it is a highly subjective, even socially based concept. Yes you can find some which almost everyone will agree on but, as obvious from this thread, there is a large, fuzzy middle ground with substantial disagreement which is the antithesis of quantitative let alone scientific definition.


It can be a subjective, socially based concept in CP music, but we must also consider this ranking, using ideas and terminology found in Western CP theory:

Perfect consonances:


unisons and octaves
perfect fourths and perfect fifths

Imperfect consonances:


major thirds and minor sixths
minor thirds and major sixths

You're "hedging your bet" just like Woodduck, saving it up for your coming contention that "a perfect fourth is considered a dissonance" retort.

You're not "defining" anything, either; you're just pointing out that "consonance and dissonance" are merely "concepts" which change in different contexts, while ignoring all points to the contrary: ratios, numbers, vibrations, and physical and neurological facts important to understanding the _idea _of dissonance.

I even think WIK takes it too far when it calls these ideas and considerations "definitions":

WIK: "...the precise definition of dissonance is culturally conditioned-definitions of and conventions of usage related to dissonance vary greatly among different musical styles, traditions, and cultures."

So how can these be "definitions?"

definition: A statement of the meaning of a word or word group or a sign or symbol (dictionary definitions); A statement expressing the essential nature of something.


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## millionrainbows

Woodduck said:


> Do you seriously intend this as an argument?
> 
> I addressed, with precisely stated intention, the idea of SENSORY dissonance, and you think it's meaningful to respond with "I think you are avoiding any scientific or quantitative definition of consonance"?


When you make statements like "I take exception to Wiki's statement that a perfect fourth is a "sensory consonance," I can see exactly where you're going with this: down the same academic blind alley. 

If you don't _acknowledge_ the FACT of sensory consonance/dissonance, then why does it even matter that you "addressed" it? You apparently missed breakfast, and are out to lunch.


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## Woodduck

millionrainbows said:


> When you make statements like "I take exception to Wiki's statement that a perfect fourth is a "sensory consonance," I can see exactly where you're going with this: down the same academic blind alley.
> 
> *If you don't acknowledge the FACT of sensory consonance/dissonance*, then why does it even matter that you "addressed" it?


In post #2 I cite, with a specific example, a variable which affects the SENSORY PERCEPTION OF DISSONANCE (determined by the clash of audible partials), yet you say that I "don't acknowledge the fact of sensory dissonance"? Huh? Are you trying to gaslight everyone here?

From my post:

_"...talking about *sensory* phenomena without reference to specific sounds is apt to lock us in a theoretical ivory tower...I take exception to Wiki's statement that a perfect fourth is a 'sensory consonance.' From a *purely sensory *(acoustical) standpoint, the *effect* of consonance or dissonance depends on the clash of partials. Hence the degree of dissonance *audible* in an interval can depend on the timbre of the instruments that play it and the register in which it's played." _

(I assumed that it's generally known that the different timbres of instruments are a function of the different patterns of overtones those instruments produce. I also assumed an acquaintance with the fact that lower tones, in general, generate more audible overtones than higher ones.)

An acoustical fact here explains a fact of SENSORY perception: because the SENSATION of dissonance is influenced by the audibility of clashing overtones, an interval can SOUND more or less dissonant depending on the overtones emitted by the sound source. Therefore, a perfect fourth cannot simply be called a "sensory consonance" or a "sensory dissonance," but will be heard as more or less consonant or dissonant depending, in part, on how much clash can be perceived among the overtones produced by the sound source.

Obviously, this particular aspect of sensory perception is just one factor influencing our perception of consonance and dissonance. But the concrete specifics governing sensory perception - how a specific instance of sound strikes us - appear not to figure into your thinking, which seems so bound to theory as to exclude obvious auditory factors. This theoretical bias leads you to want to make the question simpler than it is. Whether or nor a perfect fourth should be _classified_ as a consonance according to some scale of dissonance is not what I was addressing, and I made this clear when I said "I take exception to Wiki's statement that a perfect fourth is a SENSORY consonance."

My point is anything but "academic," and in fact it seems that in your fondness for using that term as a derogation you're engaging in projection. The only "academic blind alley" around here is the one you're apparently stuck in - the one that leads to the ivory tower from which you issue _ex cathedra_ pronouncements while pretending to invite discussion. Do you want your thread title's questions examined from all points of view, or is this thread just a lecture in disguise?


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## Bwv 1080

Quartal harmony is a staple of modal jazz and not particularly dissonant in that context, but in common practice tonality, yes. So depends on the context


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## millionrainbows

Woodduck said:


> ...a perfect fourth cannot simply be called a "sensory consonance" or a "sensory dissonance," but will be heard as more or less consonant or dissonant depending, in part, on how much clash can be perceived among the overtones produced by the sound source...
> ...the *concrete specifics* governing sensory perception - *how a specific instance of sound strikes u*s - appear not to figure into your thinking, which seems so bound to theory as to exclude obvious *auditory factors*. This theoretical bias leads you to want to make the question simpler than it is.


These are all subjective hoo-hah. There is nothing "concrete" about "how a sound strikes us."

"Auditory factors" correspond with vibrations, ratios, in this case 3:4, which is a relatively simple whole-number ratio.

The perfect fourth, along with the perfect fifth, are birds of a feather, they are each other's inverse, and harmonically, they create strong suggestions of tonal gravity: the fifth is heard as "root" on bottom, and the fourth as "root" on top.

The fourth and fifth are the Western divisors of the octave, and create the Western triumvirate of I-IV-V.

Additionally, they are the only two intervals that are not recursive within one octave; i.e., when "stacked" they both produce all 12 chromatic notes; the fifth: (7 X 12 = 84) and the fourth: (5 X 12 = 60). This quality they share with no other intervals. These two "brother" intervals were made to travel outside the octave into new territory, tonally speaking.

If the fourth is "singled out" and separated from the fifth as "dissonant," just because the fourth above the root creates a tendency to reinforce another key, then this is an artificial distinction, made necessary by the instability of the major scale, with its fourth above the root.

The fourth is not "dissonant;" this is an artificial convenience of Western tonality and the harmonic deficiencies of its chosen scale, the major scale, which is designed for instability and harmonic root movement.


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## millionrainbows

Bwv 1080 said:


> Quartal harmony is a staple of modal jazz and not particularly dissonant in that context, but in common practice tonality, yes. So depends on the context


Are you talking about how fourths _sound, _or how they are considered? That's two different things. Woodduck seems to be focussed on how the fourth is _considered_ in a Western CP context.

To me, and to any physicist, consonance and dissonance are based on auditory factors which BTW happen to perfectly correspond with interval ratios. Your "context" is totally subjective and means essentially nothing. It is part of a "belief system" which originated in Christian religion, and still persists.


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## Woodduck

millionrainbows said:


> *These are all subjective hoo-hah. There is nothing "concrete" about "how a sound strikes us."*
> 
> "Auditory factors" correspond with vibrations, ratios, in this case 3:4, which is a relatively simple whole-number ratio.
> 
> The perfect fourth, along with the perfect fifth, are birds of a feather, they are each other's inverse, and harmonically, they create strong suggestions of tonal gravity: the fifth is heard as "root" on bottom, and the fourth as "root" on top.
> 
> The fourth and fifth are the Western divisors of the octave, and create the Western triumvirate of I-IV-V.
> 
> Additionally, they are the only two intervals that are not recursive within one octave; i.e., when "stacked" they both produce all 12 chromatic notes; the fifth: (7 X 12 = 84) and the fourth: (5 X 12 = 60). This quality they share with no other intervals. These two "brother" intervals were made to travel outside the octave into new territory, tonally speaking.
> 
> If the fourth is "singled out" and separated from the fifth as "dissonant," just because the fourth above the root creates a tendency to reinforce another key, then this is an artificial distinction, made necessary by the instability of the major scale, with its fourth above the root.
> 
> The fourth is not "dissonant;" this is an artificial convenience of Western tonality and the harmonic deficiencies of its chosen scale, the major scale, which is designed for instability and harmonic root movement.


"Subjective hoo-hah," huh? Ha!

In fact, how sound "strikes us" and why it does so - perception and the external factors that shape it - is the thing that ultimately matters in music. Theory that doesn't take the full range of perceptual factors into consideration might as well be called "academic hoo-hah," and is of no more than curiosity value to anyone who doesn't spend his time flooding the pages of music forums with endless repetitions of his pet conceits in order to impress himself and prospective admirers with his superior understanding.

_The truly comprehensive answer to the question posed in the title of your thread is "yes and no." _ You may not like that, it may not fit with your personal slant on the subject, it may not be what you set out to prove to a doting audience, but there it is, obvious to anyone with a modicum of knowledge - or, more importantly, the ability to HEAR.

I've mentioned only one factor that determines how consonant or dissonant a perfect fourth can sound. It may be considered an esoteric or peripheral factor, but there's no rational objection to that; I assumed that others would bring up other, more obvious, factors. The elephant in the room, of course, is that in actual music - oh dear, here I go talking about _actual music_ again! - intervals assume functions which determine how we hear them, including whether we hear them as consonant or dissonant, and to what degree we do. Who knew, in 1800, that jazz would come along and turn a major seventh into a consonance? But damned if it didn't happen, and as we listen to jazz we're perfectly at peace with those sevenths - and ninths, and thirteenths, and whatever - lingering in the air, having no sense at all that we're hearing "dissonances."

The fact that a perfect fourth is the inversion of a perfect fifth and, taken out of context, "borrows" consonance from that interval, is perhaps the most obvious and least interesting thing about it. But if you've set out with the assumption that the subject should end there - that there's nothing else worth saying about the interval, and no other meaning to "consonance" or "dissonance" worth mentioning - then your entire thread is nothing but an exercise in pedantry, designed to have the rest of us seated behind our desks glassy-eyed, taking notes and preparing for the exam.

Go ahead and roll out all the "objective" numbers and ratios you want from here to eternity. But in the end, music and its elements will be, as they've always been, defined by what human beings compose, hear and feel. A perfect fourth played by an ensemble of tuning forks isn't something I need to listen to or think about. I'd rather see a purple cow.


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## mikeh375

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


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## Woodduck

mikeh375 said:


> .......................
> 
> View attachment 123023


Thanks, Mike! How now? Is that shade of purple against the green grass consonant or dissonant? Can it be expressed as a ratio? Would it matter if it were "green on top" rather than "purple on top," vertically speaking? Can we turn the cow upside down without affecting its sonance? And how much do the dark green trees, grey mountain and blue sky affect our perception? Or are such horizontal considerations mere academic distractions, hindering our intuitive grasp of the objective essence of bovine purplitude?


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## jegreenwood

I never saw a purple cow,
I never hope to see one,
But I can tell you anyhow,
I'd rather see than be one.

From the Academy of American Poets web site.


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## EdwardBast

The term dissonance applied to perfect 4ths is a common usage in the art and pedagogy of voice-leading where it is shorthand for "a tone (usually a non-chord tone) that needs to be resolved." No one believes it's an actual dissonance in the acoustic sense and no one conversant with the field gets confused about this. It's a non-issue.


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## Woodduck

^^^ Does this mean we don't need the cow?


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## mikeh375

Woodduck said:


> Thanks, Mike! How now? Is that shade of purple against the green grass consonant or dissonant? Can it be expressed as a ratio? Would it matter if it were "green on top" rather than "purple on top," vertically speaking? Can we turn the cow upside down without affecting its sonance? And how much do the dark green trees, grey mountain and blue sky affect our perception? Or are such horizontal considerations mere academic distractions, hindering our intuitive grasp of the objective essence of bovine purplitude?


It's the Milka cow. To paraphrase EdwardB, "No-one believes it's an actual cow in the physical sense and no one conversant with the field (ha ha) gets confused about this"....(sorry chaps )


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## millionrainbows

EdwardBast said:


> The term dissonance applied to perfect 4ths is a common usage in the art and pedagogy of voice-leading where it is shorthand for "a tone (usually a non-chord tone) that needs to be resolved."* No one believes it's an actual dissonance in the acoustic sense and no one conversant with the field gets confused about this. It's a non-issue.*


I'm glad to see that someone around here is man enough to admit that.

Also, since "no one believes it's an actual dissonance in the acoustic sense," then it reinforces its harmonic quality, and adds credence to my theory that "C-F" is competing as a new root (F) in a C major scale: heard as "root on top."

At the same time, it underscores that "F resolving to E" is a convention which was devised to counter this harmonic tendency.

I notice Woodduck did not disagree on your observation.


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## EdwardBast

millionrainbows said:


> I'm glad to see that someone around here is man enough to admit that.
> 
> *Also, since "no one believes it's an actual dissonance in the acoustic sense," then it reinforces its harmonic quality, and adds credence to my theory that "C-F" is competing as a new root (F) in a C major scale: heard as "root on top."
> 
> At the same time, it underscores that "F resolving to E" is a convention which was devised to counter this harmonic tendency.
> *
> I notice Woodduck did not disagree on your observation.


No. It supports none of this. It simply follows from the fact that CP music is triadically based and configurations containing fourths above the bass are not stable enough to be points of resolution in this system. They are either unstable second inversion triads, 4-3 suspensions, or other nonharmonic tones. It's simple CP grammar and voice-leading at work.



Woodduck said:


> ^^^ Does this mean we don't need the cow?


I prefer chicken with a good BBQ sauce.


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## Woodduck

millionrainbows said:


> I'm glad to see that someone around here is man enough to admit that.
> 
> Also, since "no one believes it's an actual dissonance in the acoustic sense," then it reinforces its harmonic quality, and adds credence to my theory that "C-F" is competing as a new root (F) in a C major scale: heard as "root on top."
> 
> At the same time, it underscores that "F resolving to E" is a convention which was devised to counter this harmonic tendency.
> 
> *I notice Woodduck did not disagree on your observation.*


Always looking for those "gotcha" opportunities, aren'tcha?

Of course I didn't disagree with EB. His observation is consistent with the very first sentence I wrote in this thread,_ "In brief: since "dissonance" and "consonance" have more than one definition...the answer is 'yes and no.'"_ Your response to that was "Not really."

You want to confine the use of the words "consonance" and "dissonance" to specific theoretical contexts. While accepting conventional theoretical definitions, I'm interested in ALL factors that contribute to the SENSATION of consonance or dissonance. I was specifically provoked to consider this by the claim in the Wiki article you quoted with approval: "The perfect fourth is a perfect interval like the unison, octave, and perfect fifth, and _it is a sensory consonance_ [emphasis mine]. By now I'm a little weary of having to emphasize the word "sensory" - will putting it in a bigger font and shocking pink do the trick? - but I'll dutifully repeat: I've been talking about the *SENSATION* of dissonance, using dissonance in its broad sense of "disharmony" or "clash."

EB doesn't address this, but neither does he, as you do, deny that any acoustical factors exist which can enhance the sensory effect of dissonance. I realize (belatedly) that this isn't what you wanted people to talk about in this thread, and of course I know how annoyed you get when you can't exercise dictatorial control over what others are thinking and saying on your pet subjects.

Speaking of pets, I think I'll go pet that cow. If Kermit thinks it's not easy being green, imagine what it's like being purple. Might we call it "pastoral dissonance"?


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## millionrainbows

EdwardBast said:


> ...It simply follows from the fact that CP music is triadically based and configurations containing fourths above the bass are not stable enough to be points of resolution in this system.


"Triadically based" is the limiting factor, but ignores root movement. This limiter considers a second inversion F (C-F-A) as "unstable" because it does not have the root on bottom.



> They (fourths) are either unstable second inversion triads...


As an interval, harmonically, a fourth is stable, and heard as root on top.

"Fourth above the bass" must be qualified by specifying arbitrarily that "the bass must also be the root," which contradicts the harmonic gravity of the interval upwards, to root F.

A second inversion F is not "unstable" unless it is considered to be a chord in the key of C.

A _root movement to F,_ via leading tone E-F, is not "unstable."

Thus we see that the harmonic gravity of the key of C, using a C major scale, must be _artificially preserved_ by deeming certain chords, with no root in the bass, as "unstable," or by using devices such as suspensions as justification.

Again, we see that the note "F" in C major is problematic, and must be "harmonically nullified" by using arbitrary procedures and terminology; an imperfect solution to a basically flawed scale.


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## millionrainbows

Woodduck said:


> Always looking for those "gotcha" opportunities, aren'tcha?
> 
> Of course I didn't disagree with EB. His observation is consistent with the very first sentence I wrote in this thread,_ "In brief: since "dissonance" and "consonance" have more than one definition...the answer is 'yes and no.'"_ Your response to that was "Not really."


By this reply, you want to deem arbitrary procedures and conventions as "definitions," which they are not.



> You want to confine the use of the words "consonance" and "dissonance" to specific theoretical contexts. While accepting conventional theoretical definitions, I'm interested in ALL factors that contribute to the SENSATION of consonance or dissonance. I was specifically provoked to consider this by the claim in the Wiki article you quoted with approval: "The perfect fourth is a perfect interval like the unison, octave, and perfect fifth, and _it is a sensory consonance_ [emphasis mine]. By now I'm a little weary of having to emphasize the word "sensory" - will putting it in a bigger font and shocking pink do the trick? - but I'll dutifully repeat: I've been talking about the *SENSATION* of dissonance, using dissonance in its broad sense of "disharmony" or "clash."


Your "sensation" of dissonance is just that: not in any way an objective definition, but simply a "sensibility" which arose as a convention. It's only good for that limited use. It requires tacit agreement, and repeated conditioning.



> EB doesn't address this, but neither does he, as you do, deny that any acoustical factors exist which can enhance the sensory effect of dissonance.


A fourth is a fourth. It still retains all its inherent harmonic qualities as a fourth, regardless. Your "acoustic factors" are too ambiguous; there is a point at which pitch identity and intervallic qualities become obscured in the extreme upper registers of sound. So what? That's not what we're talking about. We're talking about the fourth as a clearly perceived interval, not about what happens when all pitches become indistinguishable.



> I realize (belatedly) that this isn't what you wanted people to talk about in this thread, and of course I know how annoyed you get when you can't exercise dictatorial control over what others are thinking and saying on your pet subjects.


Irrelevant twaddle. And speaking of:



> I think I'll go pet that cow. If Kermit thinks it's not easy being green, imagine what it's like being purple. Might we call it "pastoral dissonance"?


That's so funny I forgot to laugh.


----------



## Woodduck

millionrainbows said:


> By this reply, you want to deem arbitrary procedures and conventions as "definitions," which they are not.


Plain wrong. I haven't proposed any new definitions.



> Your "sensation" of dissonance is just that: not in any way an objective definition, but simply a "sensibility" which arose as a convention. It's only good for that limited use. It requires tacit agreement, and repeated conditioning.


No "conditioning" or "convention" is needed to hear the clashing overtones of a fourth played in the bass register of a piano. Deaf, are ya?



> A fourth is a fourth. It still retains all its *inherent harmonic qualities* as a fourth, regardless.


But its SENSORY qualities vary.



> Your "acoustic factors" are too ambiguous; there is a point at which pitch identity and intervallic qualities become obscured in the extreme upper registers of sound. So what? That's not what *we're* talking about.


Hey there! Yo bub! It's what _I'm_ talking about! (he said, waving his hands wildly)



> We're talking about the fourth as a _clearly perceived_ interval, not about what happens when all pitches become indistinguishable.


No, you're talking about a fourth as a _conceived_ interval, not a _perceived_ one. Perceptions don't submit to your conceptions. A "perfect fourth" is a concept. What it _sounds_ like is another matter - and it can sound more or less consonant or dissonant.



> Irrelevant twaddle.


To you, but nonetheless painfully true. You just can't bear having your pedantic lectures "derailed" by other points of view.



> That's so funny I forgot to laugh.


Not surprising.


----------



## millionrainbows

_MR said: By this reply, you want to deem arbitrary procedures and conventions as "definitions," which they are not._



Woodduck said:


> Plain wrong. I haven't proposed any new definitions.


I didn't say that you "proposed new definitions."

You simply deemed existing "definitions" as such, when they are not._ "In brief: since "dissonance" and "consonance" have more than one definition..."

_If it has more than one, that's not a definition.


----------



## amfortas

millionrainbows said:


> If it has more than one, that's not a definition.


I thought just about all words have more than one definition.


----------



## millionrainbows

amfortas said:


> I thought just about all words have more than one definition.


Then definitions don't mean anything in particular. Remember this next time you get into a discussion.


----------



## jegreenwood

millionrainbows said:


> Then definitions don't mean anything in particular. Remember this next time you get into a discussion.


From Merriam Webster on line:

Definition of definition

1a : a statement of the meaning of a word or word group or a sign or symbol
dictionary definitions

b : a statement expressing the essential nature of something

c : a product of defining

2 : the action or process of stating the meaning of a word or word group

3a : the action or the power of describing, explaining, or making definite and clear the definition of a telescope
//her comic genius is beyond definition

b(1) : clarity of visual presentation : distinctness of outline or detail
//improve the definition of an image

(2) : clarity especially of musical sound in reproduction

c : sharp demarcation of outlines or limits
//a jacket with distinct waist definition

4 : an act of determining _specifically _: the formal proclamation of a Roman Catholic dogma

Nine options. I guess you're right. The word "definition" has no um . . . definition. I will miss 3(b)(2) though.


----------



## EdwardBast

millionrainbows said:


> "Triadically based" is the limiting factor, but ignores root movement. This limiter considers a second inversion F (C-F-A) as "unstable" because it does not have the root on bottom.
> 
> As an interval, harmonically, a fourth is stable, and heard as root on top.
> 
> "Fourth above the bass" must be qualified by specifying arbitrarily that "the bass must also be the root," which contradicts the harmonic gravity of the interval upwards, to root F.
> 
> A second inversion F is not "unstable" unless it is considered to be a chord in the key of C.
> 
> A _root movement to F,_ via leading tone E-F, is not "unstable."
> 
> Thus we see that the harmonic gravity of the key of C, using a C major scale, must be _artificially preserved_ by deeming certain chords, with no root in the bass, as "unstable," or by using devices such as suspensions as justification.
> 
> *Again, we see that the note "F" in C major is problematic, and must be "harmonically nullified" by using arbitrary procedures and terminology; an imperfect solution to a basically flawed scale.*


You can't possibly be serious. Flawed scale? No, only your flawed, crackpot perspective on CP harmony, voice-leading, and the whole history of Western music and music theory.


----------



## millionrainbows

EdwardBast said:


> You can't possibly be serious. Flawed scale? No, only your flawed, crackpot perspective on CP harmony, voice-leading, and the whole history of Western music and music theory.


Poor deluded academic! Are you joking? Your rigid, defensive, uptight perspective does not allow you to recognize the problem of "F".


----------



## BabyGiraffe

millionrainbows said:


> Poor deluded academic! Are you joking? Your rigid, defensive, uptight perspective does not allow you to recognize the problem of "F".


What problem?
4/3 the second simplest and most consonant interval in the octave. People without ear training probably hear all intervals +/- neutral second around F as alteration of F.
Fourths saw heavy use in harmony for several centuries in medieval times (and probably in ancient music, too, but we know little about it).
The only problem is in your head and your Russel based theories.


----------



## millionrainbows

BabyGiraffe said:


> What problem?
> 4/3 the second simplest and most consonant interval in the octave. People without ear training probably hear all intervals +/- neutral second around F as alteration of F.
> Fourths saw heavy use in harmony for several centuries in medieval times (and probably in ancient music, too, but we know little about it).
> The only problem is in your head and your Russel based theories.


You have a reading comprehension problem, BabyGiraffe. I've been saying all along that the fourth is a consonance. The problem is the academic CP treatment of it as a "dissonance." Why don't you read the thread before blurting out your abuse on me!


----------



## BabyGiraffe

Sorry, my man, but CPP rules have no relevance today at all and they are based on a completely major/minor root position considered only as great sounding triadic style (with rules somewhat randomly compiled from the practices of different composers; if we focus on individual composers styles, we will find that they don't follow these type of "grammar" - there already exist academic papers on with statistical analyses of certain famous composers).

Btw, these days I am more into the figured bass opinion camp that each inversion (or even each voicing) is a unique musical entity, disregarding equivalence under inversion/permutation and octaves - they just sound different and play different "roles" in musical composition .


----------



## Bwv 1080

Fux, Haydn, Beethoven and Mozart all considered the P4 a dissonance, the quote from Gradus ad Parnassum. But the 4th is only considered a dissonance in regards to the bass, C-F-A is dissonant if C is the bass, place the root or third under it - FCFA or ACFA and the 4th is no longer a dissonance



> Unison, third, fifth, sixth, octave, and the intervals made up
> of these and the octave are consonances. Some of these are perfect
> consonances, the others imperfect. The unison, fifth, and octave are
> perfect. The sixth and third are imperfect. The remaining intervals,
> like the second, fourth,' diminished fifth, tritone, seventh, and the
> intervals made up of these and the octave, are dissonances.


the modern editor in the footnote explains


> In an earlier chapter, Fux distinguishes between the fourth obtained from the
> arithmetical division of the octave and that deriving from the harmonic
> division.
> 
> In the first case, where the lower tone of the fourth is at the same time the funda-
> mental tone - that is, in every instance when dealing with two voices - the fourth is
> considered a dissonance. In the second case its dissonant character is invalidated by
> the new fundamental tone, and it can be considered an imperfect consonance (sec
> p. 131). In classifying the fourth among the dissonances, Fux makes his decision with
> regard to what he calls "a famous and difficult question." Martini, basing his opinion
> upon that of Zarlino {lustittitioni Harinonkhe, Part III, ch. 5), goes so far as to call the fourth a perfect consonance {Esemplare, pp. xv and 172). Haydn and Beethoven
> follow Fux. Mozart {Fundamente des General-Basses, p. 4) also lists the fourth as a
> dissonance.


----------



## isorhythm

millionrainbows said:


> Poor deluded academic! Are you joking? Your rigid, defensive, uptight perspective does not allow you to recognize the problem of "F".


Million, have you considered putting aside all the various turgid theories you've put forth on these issues and just using your ears for a while? I think a lot of things will become clearer that way.


----------



## Phil loves classical

All depends on context, I can make a major triad sound dissonant. But all things equal, a perfect forth is consonant.


----------



## millionrainbows

isorhythm said:


> Million, have you considered putting aside all the various turgid theories you've put forth on these issues and just using your ears for a while? I think a lot of things will become clearer that way.


I've always thought the suspension in C sounded arbitrary, as if it could just as well resolve up to G. What about the C minor scale? It has no half-step between the Eb and F. The resolution of C-F "down" to E or Eb is totally arbitrary.


----------



## mikeh375

millionrainbows said:


> I've always thought the suspension in C sounded arbitrary, as if it could just as well resolve up to G. What about the C minor scale? It has no half-step between the Eb and F. The resolution of C-F "down" to E or Eb is totally arbitrary.


To my ears the F could retard upwards, especially if there was an E or Eb in the bass. It'd sound quite nice actually that clash in the right context and with appropriate scoring and spacing.


----------



## millionrainbows

_



In an earlier chapter, Fux distinguishes between the fourth obtained from the

Click to expand...

_


> _arithmetical division of the octave and that deriving from the harmonic _
> _division. _
> 
> _In the first case, where the lower tone of the fourth is at the same time the funda- _
> _mental tone - that is, in every instance when dealing with two voices - the fourth is _
> _considered a dissonance. _


_

_That's obvious, since C-F is normally, naturally, and harmonically considered to be "root on top." To consider it with root on bottom is counter-intuitive, and completely the result of "F" being present in the C major scale. C-F will always fight against the key of C, in favor of the key of F.
_



In the second case its dissonant character is invalidated by

Click to expand...

_


> _*the new fundamental tone,* and it can be considered an imperfect consonance. _


_

_Whatever he wants to call it, C-F establishes a new fundamental.


----------



## BabyGiraffe

"That's obvious, since C-F is normally, naturally, and harmonically considered to be "root on top.""

Nah, this phenomenon is related to the way mammalian brains processes sounds (you will find links to articles on such topics in the references of the wiki page on auditory system). 
It doesn't have any connection with the mathematical theory of acoustic or tuning, or music theory.

I don't know, if you do any kind of music production with digital technologies, but there are many "psychoacoustic" vst plugins that exploit the harmonic or spatial perception of human ear.

Btw, six four chord sounds EXCELLENT in just intonation by itself and, imo has nothing to do with dissonance of any kind (doesn't really need preparation/resolution), but can be considered unstable, because human ear cannot accept its bass note as a stable tonic of a harmonic series. That's just how our brain processes sounds - seeks and reconstructs harmonic series (and that's why even tiny speakers/headphones reproduce some form of bass in our mind - even when there is none). (12 equal major sixth is too sharp for my taste and sounds more ugly.)


----------



## millionrainbows

BabyGiraffe said:


> "That's obvious, since C-F is normally, naturally, and harmonically considered to be "root on top.""
> 
> Nah, this phenomenon is related to the way mammalian brains processes sounds (you will find links to articles on such topics in the references of the wiki page on auditory system).


I've got news for you, BabyGiraffe: you're a mammal!  :lol:


----------



## Woodduck

Phil loves classical said:


> All depends on context, I can make a major triad sound dissonant. But all things equal, a perfect forth is consonant.


Context is indeed all, all things are not equal, fourths are not _inherently_ consonant or dissonant, consonance and dissonance are not absolute states but depend on perceptual and/or stylistic context, and if the question at the head of this thread were properly asked - if context were specified - there would be no need for a discussion because the answer would be contained in the question. As asked, however, the question is a provocation to talk past each other and an opportunity for the questioner to put down any responses that don't sit within his theoretical context.

So what else is new?


----------



## Guest

Woodduck said:


> Context is indeed all, all things are not equal, fourths are not _inherently_ consonant or dissonant, consonance and dissonance are not absolute states but depend on perceptual and/or stylistic context, *and if the question at the head of this thread were properly asked - if context were specified - there would be no need for a discussion because the answer would be contained in the question*. As asked, however, the question is a provocation to talk past each other and an opportunity for the questioner to put down any responses that don't sit within his theoretical context.
> 
> So what else is new?


As Ed (Bast) said, it's a non-starter.
Thank you Woodduck.
Next.


----------



## millionrainbows

TalkingHead said:


> As Ed (Bast) said, it's a non-starter.
> Thank you Woodduck.
> Next.


In the context of a suspension/resolution, "dissonance" is a misuse of the term. Thank you, logic. Further?


----------



## Woodduck

millionrainbows said:


> In the context of a suspension/resolution, "dissonance" is a misuse of the term. Thank you, logic. Further?


Logic has nothing to do with it. We may not like the fact that words have, by convention, varied definitions and usages, but if we want to communicate rather than rant endlessly we'd better try to set aside our distaste for lexical diversity. "Dissonance" does not have a fixed reference to a single phenomenon, but rather a complex of related meanings. Perhaps the overarching concepts unifying that complex are "disagreement," "discordance" and "discomfort": the interval of a fourth can sound more or less agreeable, concordant and comfortable, and there are several acoustic and musical reasons for the differences in our perception. Hence "dissonance" has been, and will be, used to describe all these differing instances.


----------



## Bwv 1080

millionrainbows said:


> In the context of a suspension/resolution, "dissonance" is a misuse of the term. Thank you, logic. Further?


Tell that to every music theory textbook


----------



## millionrainbows

Bwv 1080 said:


> Tell that to every music theory textbook


I disagree with all those textbooks, because I don't think the term "dissonance" should be used in this way. A fourth is classified as a "perfect" interval, with the fifth and octave. It's only a 4:3 ratio, which is very consonant in relative terms.


----------



## millionrainbows

Woodduck said:


> "Dissonance" does not have a fixed reference to a single phenomenon, but rather a complex of related meanings.


"Dissonance" and "consonance" are relative terms, but not for those reasons. They are comparative terms, not defining terms. Unless one is comparing other interval ratios, the term is misused. In a suspension/resolution, it is a misused term to call it a 'dissonance,' because there is no comparator. It's a syntactical error; bad English.



> Perhaps the overarching concepts unifying that complex are "disagreement," "discordance" and "discomfort": the interval of a fourth can sound more or less agreeable, concordant and comfortable, and there are several acoustic and musical reasons for the differences in our perception. Hence "dissonance" has been, and will be, used to describe all these differing instances.


 Bad syntax. Awkward use of language.


----------



## Woodduck

millionrainbows said:


> Bad syntax. Awkward use of language.


I'd say you're out of gas. But maybe not...


----------



## mikeh375

millionrainbows said:


> I disagree with all those textbooks, because I don't think the term "dissonance" should be used in this way. A fourth is classified as a "perfect" interval, with the fifth and octave. It's only a 4:3 ratio, which is very consonant in relative terms.


You have to give musical context some credit here. Don't get me wrong, I love fourths and consider them consonant as I'm sure a lot of us here do too, but dismissing textbooks that use CP for their frame of reference as wrong makes your stance and definitions far too pedantic for me.

Learning how to control the 4-3 suspension and _treating it as a dissonance_ in formative years gives the young composer a feel for voice leading, sense of line and emotional efficacy. It is also important to understand preparation, dissonance and resolution for successful choral writing (obviously instrumental parts too) and so initial conservative, traditional treatment of the fourth (ie, requiring resolution or perhaps parallel movement as in 1st inversion chords) is a good introduction to learning how to create a parts natural musicality. 
If the young composer progresses away from CP, then the relaxation of what was initially defined as dissonant will naturally occur and they will be more able to handle more overt dissonance in a practical manner for their work, given the lessons learnt.


----------



## isorhythm

millionrainbows said:


> "Dissonance" and "consonance" are relative terms, but not for those reasons. They are comparative terms, not defining terms. Unless one is comparing other interval ratios, the term is misused.


Comparing interval ratios won't accurately describe the subjective experience of dissonance and consonance in music, so it's a bad approach.



millionrainbows said:


> In a suspension/resolution, it is a misused term to call it a 'dissonance,' because there is no comparator. It's a syntactical error; bad English.


Fortunately for the rest of the English-speaking world this isn't up to you.


----------



## BabyGiraffe

isorhythm said:


> Comparing interval ratios won't accurately describe the subjective experience of dissonance and consonance in music, so it's a bad approach.


Well, "true" harmony is a matter of discrete interval ratios and there is nothing subjective in them. 
Mistune an octave (the only interval that is supposedly in tune in Western music - except in extreme piano registers) and you will hear a big difference - that's the most extreme example.
Fortunately, we have great tolerance for mistunings and they are even a good musical effect (all the artificial chorus effects in electronic gear).
Btw, "musical intervals" can be found in all kinds of places, including astronomy (also, if you have been on math olympiads all these geometric problems often times involve musically useful ratios):

https://en.wikipedia.org/wiki/Orbital_resonance

(Some Renaissance architects used heavily 3 and 5-limit proportions. Simple ratios even look better...)


----------



## EdwardBast

Bwv 1080 said:


> Tell that to every music theory textbook


In a 4-3 suspension (unless harmonized with a 6-5) 4 is almost always dissonant in CP music - dissonant against 5, which makes the resolution to 3 necessary. By itself it requires resolution for reasons of voice-leading and grammar, but not dissonance in the acoustic sense. Not everything that needs to resolve is an acoustic dissonance.

Bottom line: If one defines dissonance as anything that requires a voice-leading resolution, which is the way theory books define it, the P4 above the bass is a dissonance. If one defines dissonance by acoustic criteria, it isn't. Once again, this is a non-issue for anyone who can understand that there are two definitions and who is willing to use whichever is applicable to the situation at hand.


----------



## millionrainbows

mikeh375 said:


> You have to give musical context some credit here. Don't get me wrong, I love fourths and consider them consonant as I'm sure a lot of us here do too, but dismissing textbooks that use CP for their frame of reference as wrong makes your stance and definitions far too pedantic for me.
> 
> Learning how to control the 4-3 suspension and _treating it as a dissonance_ in formative years gives the young composer a feel for voice leading, sense of line and emotional efficacy. It is also important to understand preparation, dissonance and resolution for successful choral writing (obviously instrumental parts too) and so initial conservative, traditional treatment of the fourth (ie, requiring resolution or perhaps parallel movement as in 1st inversion chords) is a good introduction to learning how to create a parts natural musicality.
> If the young composer progresses away from CP, then the relaxation of what was initially defined as dissonant will naturally occur and they will be more able to handle more overt dissonance in a practical manner for their work, given the lessons learnt.


Thanks, mike, that's a nice, balanced answer, and I appreciate your aplomb.


----------



## millionrainbows

BabyGiraffe said:


> *Well, "true" harmony is a matter of discrete interval ratios and there is nothing subjective in them. *
> Mistune an octave (the only interval that is supposedly in tune in Western music - except in extreme piano registers) and you will hear a big difference - that's the most extreme example.


At last, something we can agree on.


----------



## millionrainbows

isorhythm said:


> Comparing interval ratios won't accurately describe the subjective experience of dissonance and consonance in music, so it's a bad approach.


Sez you. Your "subjective" experience means nothing, except to pedants.


----------



## Woodduck

millionrainbows said:


> Sez you. Your "subjective" experience means nothing, except to pedants.


Pedantry and subjective experience are deadly enemies. The latter is the soul of art. The former kills it.


----------



## millionrainbows

Woodduck said:


> Pedantry and subjective experience are deadly enemies. The latter is the soul of art. The former kills it.


With intervals and dissonance, we're talking acoustics, physics, vibration, science, not "art." Welcome to the Quadrivium! Crank up the old Victrola and put on some Xenakis. :lol:

Sure, you can have your 4-3 suspensions, just don't try to tell me they represent any variety of objective "proof." Keep it separated, like Church and state, lest ye be called a demagogue.


----------



## Woodduck

millionrainbows said:


> With intervals and dissonance, we're talking acoustics, physics, vibration, science, not "art." Welcome to the Quadrivium! Crank up the old Victrola and put on some Xenakis. :lol:
> 
> Sure, *you can have your 4-3 suspensions*, just don't try to tell me they represent any variety of objective "proof." Keep it separated, like Church and state, lest ye be called a demagogue.


I wish I could claim ownership of those 4-3 suspensions, but they belong to the ages.

4-3 suspensions are objectively dissonant in their contexts. "Contextual" is not a synonym for "subjective."


----------



## mikeh375

Woodduck said:


> Pedantry and subjective experience are deadly enemies. The latter is the soul of art. The former kills it.


Brilliant motto Wooduck, absolutely spot on...I'll purloin that for conversation but wont give you the credit......oh all right then, maybe I'll say "somebody once said", especially if I'm talking to friends who know me as I probably wouldn't get away with it anyway.


----------



## Woodduck

mikeh375 said:


> Brilliant motto Wooduck, absolutely spot on...I'll purloin that for conversation but wont give you the credit......oh all right then, maybe I'll say "somebody once said", especially if I'm talking to friends who know me as I probably wouldn't get away with it anyway.


Well, better to be somebody than nobody.


----------



## millionrainbows

mikeh375 said:


> Brilliant motto Wooduck, absolutely spot on...I'll purloin that for conversation but wont give you the credit......oh all right then, maybe I'll say "somebody once said", especially if I'm talking to friends who know me as I probably wouldn't get away with it anyway.


We can have it put on T-shirts, and then we can walk through the mall together, holding hands.


----------



## millionrainbows

What's really happening in a "4/3 suspension" in the key of C?

What is really happening is a change of roots: IV-I, C-F being the IV (root on top, F) going to C-G, a fifth, (root on bottom).

The F really has no need to "resolve" to E, melodically, since it is a _harmonic_ entity, _not_ a result of voice-leading.

The F has another possible function, as the b7 of a V chord G7.

How a C-F "resolves" as a "melodic" entity is not an issue; what _root movement_ is involved is more important. A 'C-F' suspension's only harmonic meanings as a chord are as an F chord (C-F-A), or as the b7 of a G7.

C-F should not be considered as a frozen 'melodic' movement of counterpoint resolving to E (in a C triad), trying to make this a melodic counterpoint problem,with "harmonic dissonance and resolution" thrown in.

The C-F _must be considered as a harmonic entity_, not as a passing note, if you want to use the terms "suspension", "dissonance," and "resolution."


----------



## Woodduck

^^^ Isn't that unnecessarily abstruse?

What's "really happening," simply, is that the note F is held over from some chord (any of several possibilities) into the tonic C chord, against which it's dissonant and needs to be resolved, normally down to E in common practice.

What else is really happening that we need to understand?


----------



## isorhythm

Right, the F in a 4-3 suspension is never perceived as a "root on top." Use your ears!


----------



## millionrainbows

isorhythm said:


> Right, the F in a 4-3 suspension is never perceived as a "root on top." Use your ears!


Use your brain! I never said that. The fourth, as an interval by itself, is heard as root on top; so even in a different context, it will assert its gravity.


----------



## millionrainbows

Woodduck said:


> ^^^ Isn't that unnecessarily abstruse?
> 
> What's "really happening," simply, is that the note F is held over from some chord (any of several possibilities) into the tonic C chord, against which it's dissonant and needs to be resolved, normally down to E in common practice.
> 
> What else is really happening that we need to understand?


It _could_ resolve up to G.

The fact that "F" needs to be resolved in C proves again that the note does not belong in a C major scale, and makes it unstable.


----------



## isorhythm

^Any non-chord tone needs to be resolved in common practice, so not sure what your point is.


----------



## Woodduck

millionrainbows said:


> It _could_ resolve up to G.
> 
> The fact that "F" needs to be resolved in C proves again that the note does not belong in a C major scale, and makes it unstable.


Yes it could.

No it doesn't.

The note F against a C chord is dissonant and normally calls for resolution. There's no dissonance in a scale; nothing needs to be resolved. Resolution is a musical function. A scale is not music until it's made a part of a musical composition.


----------



## Bwv 1080

Why is the 4-3 different from other suspensions, 2-3, 9-8, etc?


----------



## millionrainbows

Woodduck said:


> The note F against a C chord is dissonant and normally calls for resolution.





> *There's no dissonance in a scale; *nothing needs to be resolved. Resolution is a musical function. A scale is not music until it's made a part of a musical composition.


Yes there is. There is inherent dissonance insofar as the scale members reinforce the key (its starting note).

This makes a scale "consonant" with the key. The Lydian scale is more consonant than the major scale, because it reinforces the key more.

A perfect fourth is ideally a 3:4 ratio, and a major third is a 4:5 ratio, so the M3 is more dissonant and complex. The ET system favors fifths, only 2 cents off, and the fourth is its inverse.

The major third is neglected in ET, a full 14 cents sharp, thus the need for "mean tone" schemes of the 19th century.

F-E in C cannot be convincingly be called a "resolution of a dissonance" because it resolves to a major third, which increases the dissonance.

The major third is classed as an* imperfect consonance* and is considered one of the most consonant intervals* after the unison, octave, perfect fifth, and perfect fourth.*

This meaning of the term 'dissonance' will always be present, and at odds with your 'procedural' definition.

But academics can accept contradictions like this, because of their "that's just the way it is" axiomatic mindset.


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## millionrainbows

isorhythm said:


> ^Any non-chord tone needs to be resolved in common practice, so not sure what your point is.


You don't get it because you are thinking in "a non-chord tone resolving", and that's counterpoint, and has nothing to do with harmonic dissonance.

You need to think in terms of the perfect fourth as an interval, with its own gravity, which fights against "C" as the key. The only way to reinforce "C" is to replace the fourth C-F with a fifth, C-G.

E, the third, is already part of a C triad. What we need is the fifth, C-G.


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## anahit

why do you talk about perfect fourth c-f in c-maj chord, but you don't realise that there is dissonance f-g or f-e.
the perfect fourth is a perfect interval from the acoustical perspective. it is found totally consonant in c-e-*g-c* c-maj chord.


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## millionrainbows

anahit said:


> why do you talk about perfect fourth c-f in c-maj chord, but you don't realise that there is dissonance f-g or f-e.
> the perfect fourth is a perfect interval from the acoustical perspective. it is found totally consonant in c-e-*g-c* c-maj chord.


It's a long story.


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## isorhythm

millionrainbows said:


> You don't get it because you are thinking in "a non-chord tone resolving", and that's counterpoint, and has nothing to do with harmonic dissonance.
> 
> You need to think in terms of the perfect fourth as an interval, with its own gravity, which fights against "C" as the key. The only way to reinforce "C" is to replace the fourth C-F with a fifth, C-G.
> 
> E, the third, is already part of a C triad. What we need is the fifth, C-G.


You're still conflating two senses of the word "dissonance."

The thing about English and many other languages is that the same word can be used to mean different things depending on context, and both meanings are correct. It seems you personally don't like this for some reason, but that doesn't matter.


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## Woodduck

millionrainbows said:


> Yes there is. There is inherent dissonance insofar as the scale members reinforce the key (its starting note).
> 
> This makes a scale "consonant" with the key. The Lydian scale is more consonant than the major scale, because it reinforces the key more.


Your attempt to turn scales into music serves no purpose. Scales are not "keys." A "key" is a musical concept; it consists of a central tonal area _and its related tonal areas,_ which reinforce the tonic more or less strongly. Their exact relationship to the tonic, and how strongly they reinforce it, depends on how they're used.

For example, a piece of music in C Major which used only C and G chords until its final bar and then abruptly concluded on an F Major chord would strongly reinforce the key of C by seeming to abandon it for no reason; we would be left thinking that the piece was not finished, and would normally expect a return to C (unless it had decisively cadenced in C before modulating, creating in effect two separate pieces).

The Lydian mode has no subdominant. In a piece in Lydian, the fourth scale degree, making a tritone with the tonic note, doesn't reinforce the tonic the way the subdominant does in a major key, and that's simply because it has no necessary tonal relationship to the tonic note. Where there's no relationship, it's absurd to speak of "reinforcement."



> F-E in C cannot be convincingly be called a "resolution of a dissonance" because it resolves to a major third, which increases the dissonance.


That's insane. The whole history of music contradicts it. Where did you leave your ears?


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## isorhythm

Another thing...even if you only want to talk about acoustics, the third is part of the overtone series of a root while the fourth is not. Maybe that will help you accept that a third over a root can sound more consonant than a fourth?


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## Larkenfield

Without the F in the C-major scale (rather than F# like in the Lydian) there is no dominant G7 chord that seeks to dissolve to the C chord. That's why the F and not F# is there. Try writing anything without the dominant seventh F, especially if F is in the melody, as it often is. The F is necessary and the F# is a passing or auxiliary tone, under normal circumstances in standard progressions. The perfect F is not dissonant to the C: To seek resolution is not a dissonance. With C as the root the F naturally seeks to _resolve_ to the E. The dissonant arrangement between two notes is harsh and goes beyond the simple need for one chord to resolve to another, depending upon the make up of the chords, of course. Chordal _instability_ that seeks resolution to a consonant chord is not necessarily a dissonance because of how absolutely natural and inevitable that sequence sounds. The clash of a C against the C-sharp would be obvious dissonance.


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## anahit

isorhythm said:


> Another thing...even if you only want to talk about acoustics, the third is part of the overtone series of a root while the fourth is not. Maybe that will help you accept that a third over a root can sound more consonant than a fourth?


I don't think that this is a valid argument.
Than, by that logic, the minor and major seconds, minor and major septimes, tritone, ...actually all intervalls are more consonant than the perfect fourth, since they are coming in the overtone series BEFORE the perfect fourth.

Anyone who knows how the string instruments are tuned (particularly high strings, such as the violin) knows that the perfect fifth is tuned when the "oscillations disappear"; what happens, theoretically speaking, it is about the difference tones that help violinists to tune the string.
- In the perfect unison, the oscillation 0Hz - there isn't the difference tone.
- In the perfect octave the oscillation is the lower tone, the difference tone is the ground tone of the octave interval. That is why it is pretty hard for a violinist to play "in octaves".
- In the perfect fifth, the difference tone is also the bottom tone, but one octave lower. So if you tune a-e strings, than the difference tone is A. So the difference tone supports "clearness" of the intervall.
- In the perfect fourth, the difference tone is the upper tone, two octaves down. So c3-f3 gives f1 tone.

That is why P1, P8, P5 and P4 are the consonant intervalls since the difference tones confirm the intervall, and any, even slight detuning results in discrepancy, and that it why it is very hard for violinists to play these intervalls (particularly in parallel motion). We call 1, 8, 5 and 4 PERFECT, since there is only one possible tuning of them.


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## millionrainbows

Woodduck said:


> Your attempt to turn scales into music serves no purpose. Scales are not "keys."


I didn't say that "scales were keys;" I simply pointed out that C major was less harmonically congruent with "C" than the Lydian is.



> The Lydian mode has no subdominant.


Scales do not have "subdominants;" they have a fourth scale degree. When the fourth scale degree note "F" is used as a chord root, then it has a "function." Some of your own literal argumentation back atcha!



> In a piece in Lydian, the fourth scale degree, making a tritone with the tonic note, doesn't reinforce the tonic the way the subdominant does in a major key, and that's simply because it has no necessary tonal relationship to the tonic note. Where there's no relationship, it's absurd to speak of "reinforcement."


"Functions" from one scale can't be applied literally to any scale; _each scale is going to have its own unique set of functions.

_Your comparison comes from C major., and belongs there. Abandon talk of "functions" in C major, and talk about "harmonic congruity."

The "subdominant" function idea does not come from the scale; it comes from creating a root station, _building triads on a scale step_. In a major scale the subdominant function exists _not exclusively because F is in the scale, _but also because of the _interval of a fourth, C-G,_ reinforcing this new root, F.

In comparing the Lydian scale, this is irrelevant, since Lydian does not accommodate a "subdominant function on F," which is not in the scale.

_Internally_, the Lydian reinforces a more closely related key, G.

_Be fair:_ 
If you wanted to subject the major scale to the same test, you could say "the fourth scale degree of a C major scale doesn't reinforce the _dominant_ the way the F# leading tone does in Lydian, and that's simply because "F" has no necessary tonal relationship to the dominant chord. Rather, the_ interval_ C-F reinforces a lesser function, F, which, as an interval of a fourth, is heard as "root on top" (F).

You appear to have lost the ability to think logically. This transfer of functions from C major to Lydian is like trying to "stuff a horse into a suitcase."

If you DO want to create "functions" in other scales, _each scale is going to have its own unique set of functions,_ which is more like how a jazz composer would think.

You're so stuck in C major thinking that your "comparisons of function" between different scales are absurd, bordering on the insane.


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## millionrainbows

isorhythm said:


> Another thing...even if you only want to talk about acoustics, the third is part of the overtone series of a root while the fourth is not. Maybe that will help you accept that a third over a root can sound more consonant than a fourth?


The fifth is an inversion of a fourth, and the fourth is actually a more primary interval, if we discard inversions: m2, M2, m3, M3, 4th, tritone: only six basic intervals.

Ask BabyGiraffe about fourths.

If you want to speak acoustically, the fourth only "properly" exists in a C major scale as G-C, the inversion of C-G. The C-F fourth is not the "proper" fourth, but is a glitch.

In Lydian the fourth is G-C, and has no interference from another fourth.


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## millionrainbows

Larkenfield said:


> Without the F in the C-major scale (rather than F# like in the Lydian) there is no dominant G7 chord that seeks to dissolve to the C chord. That's why the F and not F# is there.


You're talking about seventh chords now; muddying the water of basic triads and basic functions.



> Try writing anything without the dominant seventh F, especially if F is in the melody, as it often is. The F is necessary and the F# is a passing or auxiliary tone, under normal circumstances in standard progressions. The perfect F is not dissonant to the C: To seek resolution is not a dissonance. With C as the root the F naturally seeks to _resolve_ to the E.


The G as a root of a new key, and as a simple triad, need not primarily or exclusively be seen as a b7, as a "dominant" using F as a b7.

It's the most closely-related key to C, and can be seen that way, not exclusively as a "dominant function," _if you're going to compare it to C Lydian._

_Be fair: _If I apply your same criteria to a Lydian scale, I could say _"Without the F# in the C-Lydian scale (rather than F like in the major) there is no G chord strongly established by leading tone, and we don't get a G major seventh chord G-B-D-F# which functions as a strong new tonic G major seventh (I) chord." _
That's why the F# and not F is there.

C major's "G" function is therefore weaker, and its "F" function is stronger from the leading tone to "F", E-F.

The C major establishes a _strong subdominant_ F (a lesser related chord than G), and a weaker connection to G (Lydian has F#, stronger leading tone), made more unstable by "F" which turns G major into a b7th chord which "cries out" for "resolution".

Not only does the C major scale (with its E-F) establish a _weaker, more distantly-related key of F, _but _it weakens the more closely-related G by turning it into a b7 chord, which is unstable on its own and needs "resolution."

_Of course, I see all this as intentional: the C major diatonic system is designed around travel to new roots, not harmonic stability. Yet, you academics seem offended by this observation! :lol:


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## Woodduck

millionrainbows said:


> _Internally_, the Lydian reinforces a more closely related key, G.


The Lydian mode doesn't "reinforce" any keys. Neither does the major mode. They're just scales - repositories of potentialities.



> If you wanted to subject the major scale to the same test,


I don't want to subject scales to tests.



> you could say "the fourth scale degree of a C major scale doesn't reinforce the _dominant_ the way the F# leading tone does in Lydian..."


The fourth scale degree in the common practice Major _tonality_ - not in the Ionian _scale_ - reinforces the tonic, because the Major tonality is a system of which the subdominant is a functioning part. The fourth scale degree in a Lydian tonality doesn't reinforce "the dominant" because there is no tonal system implicit in the Lydian mode which must include a dominant function. A sharped fourth degree implying a dominant function is intrinsic to a _Major_ tonality, not a Lydian, unless a composer chooses to utilize such a function.

We're back to musical context, not acoustical predestination, as the determinant of the functions of tones.



> You appear to have lost the ability to think logically.


You appear _n[_I]ever to have had[/I] the ability to address people without describing them to themselves. I keep telling you this but it never sinks in. Anyway, you might hope to live long enough to think as logically, or write as coherently, as some people here, so kindly keep your mud-pie-throwing impulses in check.



> If you DO want to create "functions" in other scales, _each scale is going to have its own unique set of functions,_ which is more like how a jazz composer would think.


I _don't_ want to create "functions in scales." There ARE no functions in scales. There are only functions in musical systems that utilize scales.



> You're so stuck in C major thinking that your "comparisons of function" between different scales are absurd, bordering on the insane.


Again, I haven't compared functions in scales. There are none. There are functions only in musical systems, which can utilize scales in different ways.



> F-E in C cannot be convincingly be called a "resolution of a dissonance" because it resolves to a major third, which increases the dissonance.


Obviously, by "in C" you're not referring to a C Major tonality, in which F is dissonant with a tonic chord while E is consonant. It's only in a Major tonality, not in an Ionian scale, that it it even makes sense to speak of "resolving" anything, and in C Major the 4-3 movement is normally a resolution of a dissonance.


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## millionrainbows

Woodduck said:


> The Lydian mode doesn't "reinforce" any keys. Neither does the major mode. They're just scales - repositories of potentialities.


...and one of those "potentialities" of a scale is how well it "reinforces" the starting "key" note. It's very simple. 
I didn't say that "scales were keys;" I simply pointed out that the C major scale was less harmonically congruent with the key of "C" than the Lydian scale is.



> The fourth scale degree in the common practice Major _tonality_ - not in the Ionian _scale_ - reinforces the tonic, because the Major tonality is a system of which the subdominant is a functioning part.


I didn't say that "scales were keys;" I simply pointed out that C major was less harmonically congruent with "C" than the Lydian is. 
You're talking about the CP system of tonality _exclusively,_ not as a general problem of harmonic congruity. Therefore, the Lydian scale is not to be discussed, only the major.



> The fourth scale degree in a Lydian tonality doesn't reinforce "the dominant" because there is no tonal system implicit in the Lydian mode which must include a dominant function.


That's true; your proper notion of recognized "functions" is exclusive to the CP major/minor system of tonality.

I should have said _"the fourth scale degree of a C major scale doesn't reinforce G as a new root__ the way the F# leading tone does in Lydian..."
_
I didn't say that "scales were keys;" I simply pointed out that C major was less harmonically congruent with "C" than the Lydian is.



> A sharped fourth degree implying a dominant function is intrinsic to a _Major_ tonality, not a Lydian, unless a composer chooses to utilize such a function.


I'll not speak in terms of "function" as it's established in CP tonality.



> I _don't_ want to create "functions in scales."


I do, and jazz players do this. It's a reasonable concept, since all scale members have an hierarchical relationship to the key note of a scale. It's easy to create new "functions" out of this, which are different from CP functions, but do share similarities on a heuristic level.



> There ARE no functions in scales. There are only functions in musical systems that utilize scales.


That's misleading. "Functions" are created by building triads on scale-steps, so you can't create "function" without scales. Additionally, since all scale members of any scale have an hierarchical relationship to the key note of that scale, it's easy to create new "functions" out of this.



> Again, I haven't compared functions in scales. There are none. There are functions only in musical systems, which can utilize scales in different ways.


Literally true, but misleading. "Functions" are created by building triads on scale-steps, so you can't create "function" without scales. Additionally, since all scale members of any scale have an hierarchical relationship to the key note of that scale, it's easy to create new "functions" out of this.

Your thinking is very literal and restricted.


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## millionrainbows

The C major establishes a _strong subdominant F_ (a lesser related chord than G), and _a weaker connection to G_ (Lydian has F#, stronger leading tone), made more unstable by "F" which turns G major into a b7th chord which "cries out" for "resolution".

Not only does the C major scale (with its E-F) establish a weaker, more distantly-related key of F, but it weakens the more closely-related G by turning it into a b7 chord, which is unstable on its own and needs "resolution."

Of course, I see all this as intentional: the C major diatonic system is designed around travel to new roots, not harmonic stability. Yet, you academics seem offended by this observation! _:lol:_


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## Larkenfield

Of course, no one bothers with why C to F is called a perfect fourth interval to begin with - because it's an entirely custom an interval - and the subject ends up becoming a perfect muddle. It's called the perfect fourth because it doesn't have to be resolved if F is considered to be the tonic. C below the F is simply an inverted F chord with the inverted fifth in the bass. In the key of C the F would naturally seek to resolve to E, which is not possible using the C Lydian scale with the F sharp. Using the F sharp there's no subdominant or dominant chords to resolve to C and the key of C is less defined not more more defined. Using the C Lydian scale, the fourth degree of the scale has to be altered from an F sharp to an F in order to get the sub dominant and dominant chords that lead to C.

"The perfect fourth may be derived from the harmonic series as the interval between the third and fourth harmonics. The term perfect identifies this interval as belonging to the group of perfect intervals, so called because they are neither major nor minor (unlike thirds, which are either minor or major) but perfect.

"When the fourth is considered a dissonance: The perfect fourth is a perfect interval like the unison, octave, and perfect fifth, and it is a sensory consonance. In common practice harmony, however, it is sometimes considered a stylistic dissonance in certain contexts, namely in two-voice textures and whenever it appears above the bass. If the bass note also happens to be the chord's root, the interval's upper note almost always temporarily displaces the third of any chord, and, in the terminology used in popular music, is then called a suspended fourth." I personally do not consider a suspended fourth a dissonance because there's no real clashing but just need to resolve the fourth down to the third. What's the third is not present the F has nothing to clash with as a decimal and interval that's why the third is suspended as the F. But some here the suspended out as a dissonance and some don't. I do not hear the displacement of the third as a dissonance but only as an interval that seeks to be resolved to the third. There is no clashing but simply a delay of the resolution, which is why it's called a suspended fourth. The suspended fourth is not clashing with anything but it's creating a _tension_ because of the delay that seeks to be resolved to the third in whatever key it's in. A perfect fourth is an interval that one can end on depending on the key.


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## anahit

Larkenfield said:


> It's called the perfect fourth because it doesn't have to be resolved if F is considered to be the tonic.
> ...because they are neither major nor minor (unlike thirds, which are either minor or major) but perfect.


Yes, perhaps above all, because there is only one possible tuning for the P4. Please refer to my post: 
Is the Perfect Fourth a Dissonance? If So, Why?

Acoustically, you can tune P4 only perfectly. As it is with P1, P8 and P5.

On the contrary, you can tune 3, 6, 2, 7 and tritone differently.


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## anahit

Larkenfield said:


> It's called the perfect fourth because it doesn't have to be resolved if F is considered to be the tonic.
> ...because they are neither major nor minor (unlike thirds, which are either minor or major) but perfect.


Yes, but not only, perhaps - above all - because there is only one possible tuning for the P4. Please refer to my post: 
Is the Perfect Fourth a Dissonance? If So, Why?

Acoustically, you can tune P4 only perfectly. As it is with P1, P8 and P5.

On the contrary, you can tune 3, 6, 2, 7 and tritone differently.


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## BabyGiraffe

anahit said:


> Yes, but not only, perhaps - above all - because there is only one possible tuning for the P4. Please refer to my post:
> Is the Perfect Fourth a Dissonance? If So, Why?
> 
> Acoustically, you can tune P4 only perfectly. As it is with P1, P8 and P5.
> 
> On the contrary, you can tune 3, 6, 2, 7 and tritone differently.


That's not true - commatic variations are necessary in other systems for modulations and harmony. Cultures without harmony like Indian and African also use commatic variants, but in the melody for expressive purposes - usually they use vocal ornaments around a comma (check any youtube tutorial series on Indian vocal techniques for demonstration).
Another remark: Just because you think in terms of heptatonic scale degrees, doesn't make them the same thing.

Example: 5/4 and 6/5 (major and minor thirds and their inversions ) are DIFFERENT ratios. 
Same can be said about seconds/sevenths.
(These - sixths/thirds, seconds/sevenths are equilized in 7 equal, there is also no tritone there.)
Anyway, modern university level music theory uses integers mod 12, so you should actually think in terms of 12-tone system degrees, not 7. (Standard heptatonic music theory has no explanatory power for music after galant period ((and is completely based on meantone temperament)) - roughly after 12 equal was adopted).


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## anahit

BabyGiraffe said:


> That's not true - commatic variations are necessary in other systems for modulations and harmony. *Cultures without harmony* like Indian and African also use commatic variants, but in the melody for expressive purposes - usually they use vocal ornaments around a comma (check any youtube tutorial series on Indian vocal techniques for demonstration).
> Another remark: Just because you think in terms of heptatonic scale degrees, doesn't make them the same thing.


This is not a valid argument either. Here we talk about the classical music, not Indian, Byzantine, Chinese, etc. otherwise you cannot apply reference "consonance" or "dissonance", some of these music have many other types of intervals.

Simply said, the difference tones are the strongest force that defines the tuning as we have it, and consolidations of intervals as we have. Yes, there are different tuning systems, and yes, piano is not tuned well.


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## BabyGiraffe

anahit said:


> This is not a valid argument either. Here we talk about the classical music, not Indian, Byzantine, Chinese, etc. otherwise you cannot apply reference "consonance" or "dissonance", some of these music have many other types of intervals.
> 
> Simply said, the difference tones are the strongest force that defines the tuning as we have it, and consolidations of intervals as we have. Yes, there are different tuning systems, and yes, piano is not tuned well.


Dude, all the various combination tones and other related nonlinear psychoacoustic phenomena have very minor influence in perception of harmony.
Anyway, acoustic facts work regardless of what you take for "theory and practice" (and there is a big gap in actual practice and theory - not only in Western music; there are many academic articles in the recent years with measurements of intervals of actually performed maqams/ ragas).
Still, there is no reason not to call 6/5, 5/4, 5/3 or whatever just as "perfect" interval by itself without thinking in diatonic/heptatonic 5-limit framework (and 12 equal supports way more musical resources than diatonic sub-collection, which can explain only a fraction even of Western music).


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## millionrainbows

BabyGiraffe said:


> Dude, all the various combination tones and other related nonlinear psychoacoustic phenomena have very minor influence in perception of harmony.


I disagree. Organ builders knew quite a bit about undertones.



> Anyway, acoustic facts work regardless of what you take for "theory and practice" (and there is a big gap in actual practice and theory - not only in Western music; there are many academic articles in the recent years with measurements of intervals of actually performed maqams/ ragas).


Why don't you think about what you're saying before you reel off these condescending, inaccurate generalities.



> Still, there is no reason not to call 6/5, 5/4, 5/3 or whatever just as (a) "perfect" interval by itself without thinking in diatonic/heptatonic 5-limit framework (and 12 equal supports way more musical resources than diatonic sub-collection, which can explain only a fraction even of Western music).


Fourths and fifths (and minor seconds) are non-recursive within the octave. Also, they are the only intervals which, when projected, generate all 12 notes.


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## isorhythm

millionrainbows said:


> Also, they are the only intervals which, when projected, generate all 12 notes.


This is not true at all - you can get a 12 note scale from all kinds of combinations of various just intervals. Of course none of them will give you a 12 equal scale, but neither will fifths.


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## BabyGiraffe

The actual intervals of 12 equal are closer to 17 or 19-limit interpretation than to 3-limit pythagorean (supposedly medieval) or 5-limit meantone(which would be the classical/renaissance harmony). (Someone posted a dissertation on combination tones of 12 equal and their harmonic implications some months ago on reddit; maybe 12 equal fanatics would find it interesting.)

Anyway, I suspect that even in medieval times singers were not using the correct theoretical intervals in practice (sharp pythagorean major thirds are way harder to sing)...



"Fourths and fifths (and minor seconds) are non-recursive within the octave. Also, they are the only intervals which, when projected, generate all 12 notes. "

Too bad that there are other bazillion methods of coming with 12 pitches gamut...


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## millionrainbows

isorhythm said:


> This is not true at all - you can get a 12 note scale from all kinds of combinations of various just intervals. Of course none of them will give you a 12 equal scale, but neither will fifths.


This is totally false in the context of the Equal tempered scale that we all use, not some esoteric microtonal data which only serves to muddy the waters.

I don't think it's worth the trouble to prove it to you, but here it is:

Fifth: C-G-D-A-E-B-F#-C#-G#-D#-E#(F)
Fourth: C-F-Bb-Eb-Ab-Db-Gb-Cb(B)-E-A-D-G
minor second: C-C#-C-D#-E-F-F#-G-G#-A-A#-B

Major second: C-D-E-F#-G# A#...repeats at B#(C)
Minor third: C-Eb-Gb-A...repeats at C...etc.

All of this microtonal bulls--t is out of context with the thread, and is a big distraction to anyone who is talking about the Western ET scale.


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## isorhythm

Stacking perfect fifths doesn't produce an equal tempered scale. But you already know that, right?

We've gone pretty far afield from the original topic here.


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## millionrainbows

isorhythm said:


> Stacking perfect fifths doesn't produce an equal tempered scale. But you already know that, right?


Yes. Stacking fifths, then "closing the octave" DOES give us 12 notes, and the fifths are only 2 cents flat, so the 12-note ET system favors fifths, but you already know that, right?

Quit harping on "just" intervals and get with the generalizations of ET, please. A fifth is a fifth, 7 semitones, period.


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## Guest

I'm a Perfect Wife and I'm not a dissonance.


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## BabyGiraffe

millionrainbows said:


> All of this microtonal bulls--t is out of context with the thread, and is a big distraction to anyone who is talking about the Western ET scale.


Idiotic comment; the core of Western music is microtonal; there were various systems - pythagorean, many different meantone and irregular "well-temperaments" in use; 12 equal being in vogue is a recent phenomena (England was probably the last country that adopted 12 equal, maybe because of provincialism); historically informed recordings are also microtonal. 
You should be ashamed for falsifying well known facts.


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## millionrainbows

BabyGiraffe said:


> Idiotic comment; the core of Western music is microtonal; there were various systems - pythagorean, many different meantone and irregular "well-temperaments" in use; 12 equal being in vogue is a recent phenomena (England was probably the last country that adopted 12 equal, maybe because of provincialism); historically informed recordings are also microtonal.
> You should be ashamed for falsifying well known facts.


You should be ashamed for making such personal comments. Historically, everything has led up to 12-note Equal Temperament.
Microtonalty is for fringe outsiders like you and Harry Partch.


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## BabyGiraffe

millionrainbows said:


> You should be ashamed for making such personal comments. Historically, everything has led up to 12-note Equal Temperament.
> Microtonalty is for fringe outsiders like you and Harry Partch.


Microtonality is the future (and the past), my friend. Many modernist/contemporary composers, including atonal/avantgarde type you adore, have used it or have employed it occasionally in unsystematic fashion. It is also becoming more popular in electronic music in the last 20 years (idm/ambient).
12 equal is good for what it is - a mixture of meantone/augmented/diminished temperaments; in other division of octaves we have different options. There is no need to overrate 12 equal.


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## millionrainbows

I'm not overrating ET; it is simply the topic here. It is the context this thread is supposed to be based on. You are not my audience. You are a distraction.


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