Your first paragraph is well-stated, and I agree with it.
I can at least expect that musical taste is like multi-level regression, where human biology is one level of regression with a lot of data, a culture is a second level, people who like a particular kind of music is a different second level, and an individual is a third level. Each additional level makes our model more precise, but provides less data.
So, even if I can’t say someone’s opinion of a musical piece is wrong, I could say it is very improbable, and give my estimate of their taste some kind of entropy penalty. With enough knowledge of their opinions, I could reject the hypothesis that they belong to a particular musical affiliation group.
More importantly, there is a human level of the regression, and it provides some information. Having tastes that differ significantly from standard human tastes—it could be a result of training, so it might be “good”; but it’s also as close to “wrong” as we may be able to get.
But, none of what I just said is useful for the problem posed in my post. I think the answer is brain scans.
There is something objectively good about particular musical intervals, e.g., the octave, the 1-3-5 chord, that has to do with the ratios of their frequencies.
Therefore there is some objective truth about musical taste.
You could use that to construct some metric of each interval, and make something like a Markov model of how that metric changes over time in different musical pieces, and see if you come up with patterns. But that still wouldn’t answer the question whether a deviation from that pattern indicates something new and good, or new and bad.
I think that you’re saying that my question has no answer.
There is something objectively good about particular musical intervals, e.g., the octave, the 1-3-5 chord, that has to do with the ratios of their frequencies.
That has very, very little directly to do with the aesthetics of musical composition, however. Its implications are rather in the area of how humans interpret musical sounds: all else being equal, we tend to think of acoustically simple intervals (“consonances”) as being “more fundamental” than acoustically (more) complex intervals (“dissonances”), so that we interpret the latter in terms of the former, rather than vice-versa.
It’s a curious phenomenon that, throughout history, people have thought (i.e. written treatises as if) the key to musical composition is identifying which “atomic” musical materials “sound good” (and then stringing them together, one presumes). But that isn’t how it works at all. Musical composition operates on a higher level of abstraction; the treatment of intervals and so forth is just mechanics, like spelling words for a novelist.
(Whatever the reason is that you don’t like the Great Fugue, it isn’t because it doesn’t contain enough consonant intervals.)
The challenge of composition is, in my opinion, first establishing what the musical language or the vocabulary of the given work is, then developing an interesting narrative using that language. In common-practice tonality, the musical language is more or less a constant; modern composers, in the absence of the assumption that they are writing in common-practice tonality, have to make it clear what the language is—that is, what tonal relationships form the structure of the piece—as well as providing a coherent direction to the piece.
In a sense, in some modern idioms, the harmonicity of an interval or a chord is pretty irrelevant, once the intervallic or or chordal relationships the composer is using to create the piece are consistent and understandable. That said, harmonicity is an important part of how we hear music, so what intervals are used will of course affect the quality of the finish quality.
This is more or less the standard “party line”, and even makes a certain amount of sense on its own terms, but I think it’s actually wrong.
More specifically, I don’t think “common-practice tonality” is actually a thing, music-theoretically. The illusion that it is results in my view from two circumstances: (1) the high cultural prestige of European art music from approximately 1700-1900 (corresponding basically to an era when it happened to be dominated by Germans); and (2) the fact that more recent art music is less accessible to casual listeners due specifically to its complexity (i.e. not any difference in “musical language”, if we take that to mean the fundamental principles of musical comprehension).
I think there is a fundamental change in how Western Art Music is composed around the start of 20th century; the removal of the tonic-dominant relationship as the fundamental relationship within musical works is responisble for that. Of course, the Second Viennese School considered themselves successors to that traidition, not revolutionaries or iconoclasts, and I would be inclined to agree, but I do think that there is significant to music written before theirs and music written afterwards. I’ll readily admit this may just be down to how I’ve been taught, and I’m not a musicologist (though I do have some familiarity with different types of analysis).
What do you mean by “party line”? Which part specifically is the party line? Whose party line is it? The party line of musicologists, or the party line of contemporary composers? I find it hard to imagine there’s a party line for composers, given the composers I know and the biographies of some of the bigger composers of the last century. I’m interested because these are mainly conclusions I’ve come to on my own.
I agree there is a certain amount of German-centrism in the term “common-practice tonality”, but that itself doesn’t mean it doesn’t exist. I agree contemporary music is more complex (excluding minimalism and other obvious exceptions) and that is a factor in its accessibility, but also people’s familiarity with the common-practice tonal language gives (as popular music is based on this language too) them expectations as to what music should be like; music that does not follow these conventions is difficult for them to understand.
I think there is a fundamental change in how Western Art Music is composed around the start of 20th century; the removal of the tonic-dominant relationship
Yes, this is a proposition I reject. Don’t worry, I don’t expect my claim to be obvious; explaining it would be a rather involved technical discussion. A necessary first step would be the wholesale rejection of the traditional Rameau-Riemann theory of “chord progressions” in the explanation of earlier music, in favor of the kind of approach taken by Schenker and, later, Westergaard.
What do you mean by “party line”? Which part specifically is the party line? Whose party line is it? The party line of musicologists, or the party line of contemporary composers?
All of the above; particularly those of high status.
I agree there is a certain amount of German-centrism in the term “common-practice tonality”, but that itself doesn’t mean it doesn’t exist.
It definitely exists—but only as a historical cluster of musical works, and not as a theoretical category. From a theoretical point of view (again, my theoretical point of view, which is separated by considerable inferential distance from the memes of traditional music theory), there is little use for a category which includes Bach and early Schoenberg and excludes middle and late Schoenberg.
I’m not sure I understand enough about your point of view to say whether I agree with it; I’d be interested in learning more! Have you written anything on this topic?
Westergaard sounds awesome; I’ll check him out if I get a chance (will probably be next summer—post-thesis).
There is something objectively good about particular musical intervals, e.g., the octave, the 1-3-5 chord, that has to do with the ratios of their frequencies. Therefore there is some objective truth about musical taste.
I’m not sure I agree here. I understand the point you are making about ratios of frequencies, but by that logic, equal tempered music would presumably be automatically inferior to music in just intonation, because the consonant intervals are more consonant in just intonation than E-12 tuning.
Music that is more consistently consonant is not better; all pieces composed entirely of octaves and fifths aren’t inherently better than all pieces that also have thirds (or any other less-harmonic interval you care to name). This also assumes that Western music theory is the only valid type; musical languages consisting of a non-diatonic system are not automatically inferior.
EDIT: I’d like to add that I’m inclined to think there is a degree of objective musical quality.
I understand the point you are making about ratios of frequencies, but by that logic, equal tempered music would presumably be automatically inferior to music in just intonation, because the consonant intervals are more consonant in just intonation than E-12 tuning.
Well, yeah. That’s the only reason that people still talk about just intonation—it’s considered a virtue that its intervals sound cleaner than equally tempered ones. Equal temperament is the standard because it allows transposition between keys, not because of some objection to how pure and clean just intervals are.
it’s considered a virtue that its intervals sound cleaner than equally tempered ones.
Another potential fix is to adjust timbres (i.e. sound spectra) so that they sound cleaner in equal temperament. See this example (MP3) from William Sethares’ work (ironically, the only 12-TET piece from his freely-available samples). Sounds kind of uncanny and off-key to me, but that could be due to being unfamiliar with alt. tunings. YMMV.
ETA: The Hammond organ also used 12-TET frequencies to generate its “harmonic partials”, so it was effectively just as “clean” in 12-TET as other instruments are in just intonation. On the other hand, many people would judge the effect as excessively “bland” and “indistinct”. But the sound spectrum of the Hammond organ was not very complex to begin with; applying the same fix to other instruments will probably give more appealing results.
This is talking about music as if it isn’t inherently based on time. If anything, a large number of consonances would make music sound much worse, because “dissonance” in many ways is simply sounds that require resolution of tension. If there is no tension, there is no resolution of tension. Dissonance is commonly believed to be the thing that actually makes music interesting.
Of course there is music that uses lots of consonance, but typically they will use some other device (rhythm, rising tones) to increase tension so they have something to resolve.
This also assumes that Western music theory is the only valid type; musical languages consisting of a non-diatonic system are not automatically inferior
This isn’t an assumption. It’s an empirical fact. Almost all music around the world uses a diatonic or pentatonic scale. The pentatonic favors such intervals even more strongly. The odds against this happening, if there were even one other equally-good possible non-harmonic scale, are astronomical. QED.
Contrary to popular belief, music doesn’t “use” theoretical constructs such as the diatonic scale; listeners use them to interpret music.
In other words, the important fact about the diatonic scale is not whether it is presented explicitly in music, but that even when it isn’t, it is still the basis for a listener’s comprehension of the pitch structure.
(Also note that the pentatonic scale is a strict subset of the diatonic scale.)
This isn’t an assumption. It’s an empirical fact. Almost all music around the world uses a diatonic or pentatonic scale. The pentatonic favors such intervals even more strongly. The odds against this happening, if there were even one other equally-good possible non-harmonic scale, are astronomical. QED.
The work presented in this comment (link to audio examples) makes a convincing case that the consonance of “diatonic” scale intervals is simply an artifact of common timbres/sound spectra (which in turn are due to the physical makeup of most musical instruments), combined with familiarity. The music presented there sounds “consonant” and “harmonious” to me in a way that most atonal music simply doesn’t.
(I am linking 4hodmt’s comment here only because it’s directly relevant and I don’t expect its author to join this subthread. Any upvotes should be directed there.)
What about music that does not use those scales? And 1-3-5 chords are not present in all pentatonic systems. By what standard do you consider this music to be objectively superior? Is it something based on harmonicity?
I’m not sure I agree here. I understand the point you are making about ratios of frequencies, but by that logic, equal tempered music would presumably be automatically inferior to music in just intonation, because the consonant intervals are more consonant in just intonation than E-12 tuning.
And I suspect that is the case, but haven’t had the opportunity to test it. It would be interesting to do blind tests using computer-generated versions of the same music using both scales.
This may not work. Temperment is difficult to adjust. As equal temperment is so ubiquitous nowadays, people will often hear non-equal temperments as simply out-of-tune and dislike them on that. Our ears are very much used to equal temperments.
But composition is not that only thing that music is. There is also performance and musical interpretation, and those will drastically affect your opinions on a particular composition. Computer-generated versions will probably not help your opinion of a piece...
Your first paragraph is well-stated, and I agree with it.
I can at least expect that musical taste is like multi-level regression, where human biology is one level of regression with a lot of data, a culture is a second level, people who like a particular kind of music is a different second level, and an individual is a third level. Each additional level makes our model more precise, but provides less data.
So, even if I can’t say someone’s opinion of a musical piece is wrong, I could say it is very improbable, and give my estimate of their taste some kind of entropy penalty. With enough knowledge of their opinions, I could reject the hypothesis that they belong to a particular musical affiliation group.
More importantly, there is a human level of the regression, and it provides some information. Having tastes that differ significantly from standard human tastes—it could be a result of training, so it might be “good”; but it’s also as close to “wrong” as we may be able to get.
But, none of what I just said is useful for the problem posed in my post. I think the answer is brain scans.
There is something objectively good about particular musical intervals, e.g., the octave, the 1-3-5 chord, that has to do with the ratios of their frequencies. Therefore there is some objective truth about musical taste. You could use that to construct some metric of each interval, and make something like a Markov model of how that metric changes over time in different musical pieces, and see if you come up with patterns. But that still wouldn’t answer the question whether a deviation from that pattern indicates something new and good, or new and bad.
I think that you’re saying that my question has no answer.
That has very, very little directly to do with the aesthetics of musical composition, however. Its implications are rather in the area of how humans interpret musical sounds: all else being equal, we tend to think of acoustically simple intervals (“consonances”) as being “more fundamental” than acoustically (more) complex intervals (“dissonances”), so that we interpret the latter in terms of the former, rather than vice-versa.
It’s a curious phenomenon that, throughout history, people have thought (i.e. written treatises as if) the key to musical composition is identifying which “atomic” musical materials “sound good” (and then stringing them together, one presumes). But that isn’t how it works at all. Musical composition operates on a higher level of abstraction; the treatment of intervals and so forth is just mechanics, like spelling words for a novelist.
(Whatever the reason is that you don’t like the Great Fugue, it isn’t because it doesn’t contain enough consonant intervals.)
The challenge of composition is, in my opinion, first establishing what the musical language or the vocabulary of the given work is, then developing an interesting narrative using that language. In common-practice tonality, the musical language is more or less a constant; modern composers, in the absence of the assumption that they are writing in common-practice tonality, have to make it clear what the language is—that is, what tonal relationships form the structure of the piece—as well as providing a coherent direction to the piece.
In a sense, in some modern idioms, the harmonicity of an interval or a chord is pretty irrelevant, once the intervallic or or chordal relationships the composer is using to create the piece are consistent and understandable. That said, harmonicity is an important part of how we hear music, so what intervals are used will of course affect the quality of the finish quality.
This is more or less the standard “party line”, and even makes a certain amount of sense on its own terms, but I think it’s actually wrong.
More specifically, I don’t think “common-practice tonality” is actually a thing, music-theoretically. The illusion that it is results in my view from two circumstances: (1) the high cultural prestige of European art music from approximately 1700-1900 (corresponding basically to an era when it happened to be dominated by Germans); and (2) the fact that more recent art music is less accessible to casual listeners due specifically to its complexity (i.e. not any difference in “musical language”, if we take that to mean the fundamental principles of musical comprehension).
I think there is a fundamental change in how Western Art Music is composed around the start of 20th century; the removal of the tonic-dominant relationship as the fundamental relationship within musical works is responisble for that. Of course, the Second Viennese School considered themselves successors to that traidition, not revolutionaries or iconoclasts, and I would be inclined to agree, but I do think that there is significant to music written before theirs and music written afterwards. I’ll readily admit this may just be down to how I’ve been taught, and I’m not a musicologist (though I do have some familiarity with different types of analysis).
What do you mean by “party line”? Which part specifically is the party line? Whose party line is it? The party line of musicologists, or the party line of contemporary composers? I find it hard to imagine there’s a party line for composers, given the composers I know and the biographies of some of the bigger composers of the last century. I’m interested because these are mainly conclusions I’ve come to on my own.
I agree there is a certain amount of German-centrism in the term “common-practice tonality”, but that itself doesn’t mean it doesn’t exist. I agree contemporary music is more complex (excluding minimalism and other obvious exceptions) and that is a factor in its accessibility, but also people’s familiarity with the common-practice tonal language gives (as popular music is based on this language too) them expectations as to what music should be like; music that does not follow these conventions is difficult for them to understand.
Yes, this is a proposition I reject. Don’t worry, I don’t expect my claim to be obvious; explaining it would be a rather involved technical discussion. A necessary first step would be the wholesale rejection of the traditional Rameau-Riemann theory of “chord progressions” in the explanation of earlier music, in favor of the kind of approach taken by Schenker and, later, Westergaard.
All of the above; particularly those of high status.
It definitely exists—but only as a historical cluster of musical works, and not as a theoretical category. From a theoretical point of view (again, my theoretical point of view, which is separated by considerable inferential distance from the memes of traditional music theory), there is little use for a category which includes Bach and early Schoenberg and excludes middle and late Schoenberg.
Cheers for clarifying that!
I’m not sure I understand enough about your point of view to say whether I agree with it; I’d be interested in learning more! Have you written anything on this topic?
Westergaard sounds awesome; I’ll check him out if I get a chance (will probably be next summer—post-thesis).
Look, there’s a bug in the website—it fails to switch background colors when reaching the 10th level of nested comments!
I’m not sure I agree here. I understand the point you are making about ratios of frequencies, but by that logic, equal tempered music would presumably be automatically inferior to music in just intonation, because the consonant intervals are more consonant in just intonation than E-12 tuning.
Music that is more consistently consonant is not better; all pieces composed entirely of octaves and fifths aren’t inherently better than all pieces that also have thirds (or any other less-harmonic interval you care to name). This also assumes that Western music theory is the only valid type; musical languages consisting of a non-diatonic system are not automatically inferior.
EDIT: I’d like to add that I’m inclined to think there is a degree of objective musical quality.
Well, yeah. That’s the only reason that people still talk about just intonation—it’s considered a virtue that its intervals sound cleaner than equally tempered ones. Equal temperament is the standard because it allows transposition between keys, not because of some objection to how pure and clean just intervals are.
Another potential fix is to adjust timbres (i.e. sound spectra) so that they sound cleaner in equal temperament. See this example (MP3) from William Sethares’ work (ironically, the only 12-TET piece from his freely-available samples). Sounds kind of uncanny and off-key to me, but that could be due to being unfamiliar with alt. tunings. YMMV.
ETA: The Hammond organ also used 12-TET frequencies to generate its “harmonic partials”, so it was effectively just as “clean” in 12-TET as other instruments are in just intonation. On the other hand, many people would judge the effect as excessively “bland” and “indistinct”. But the sound spectrum of the Hammond organ was not very complex to begin with; applying the same fix to other instruments will probably give more appealing results.
Yes, I understand that. What I’m arguing here is that a musical system with greater harmonicity is not neccessarily objectively better.
This is talking about music as if it isn’t inherently based on time. If anything, a large number of consonances would make music sound much worse, because “dissonance” in many ways is simply sounds that require resolution of tension. If there is no tension, there is no resolution of tension. Dissonance is commonly believed to be the thing that actually makes music interesting.
Of course there is music that uses lots of consonance, but typically they will use some other device (rhythm, rising tones) to increase tension so they have something to resolve.
This isn’t an assumption. It’s an empirical fact. Almost all music around the world uses a diatonic or pentatonic scale. The pentatonic favors such intervals even more strongly. The odds against this happening, if there were even one other equally-good possible non-harmonic scale, are astronomical. QED.
Contrary to popular belief, music doesn’t “use” theoretical constructs such as the diatonic scale; listeners use them to interpret music.
In other words, the important fact about the diatonic scale is not whether it is presented explicitly in music, but that even when it isn’t, it is still the basis for a listener’s comprehension of the pitch structure.
(Also note that the pentatonic scale is a strict subset of the diatonic scale.)
The work presented in this comment (link to audio examples) makes a convincing case that the consonance of “diatonic” scale intervals is simply an artifact of common timbres/sound spectra (which in turn are due to the physical makeup of most musical instruments), combined with familiarity. The music presented there sounds “consonant” and “harmonious” to me in a way that most atonal music simply doesn’t.
(I am linking 4hodmt’s comment here only because it’s directly relevant and I don’t expect its author to join this subthread. Any upvotes should be directed there.)
What about music that does not use those scales? And 1-3-5 chords are not present in all pentatonic systems. By what standard do you consider this music to be objectively superior? Is it something based on harmonicity?
And I suspect that is the case, but haven’t had the opportunity to test it. It would be interesting to do blind tests using computer-generated versions of the same music using both scales.
This may not work. Temperment is difficult to adjust. As equal temperment is so ubiquitous nowadays, people will often hear non-equal temperments as simply out-of-tune and dislike them on that. Our ears are very much used to equal temperments.
But composition is not that only thing that music is. There is also performance and musical interpretation, and those will drastically affect your opinions on a particular composition. Computer-generated versions will probably not help your opinion of a piece...