5 ms·

Yes. And the "superstition" and archaic language he is complaining about in his abstract are actually thousands of years of collective wisdom which has helped

by hashkb 10y ago

Yes. And the "superstition" and archaic language he is complaining about in his abstract are actually thousands of years of collective wisdom which has helped many musicians to create many widely acclaimed pieces of music in every genre. Any study of music that begins by discarding all of that is pretty silly IMO. > We show to be incomplete the theory of the heretofore agreed-upon authority on this subject, 19th-century Physicist Hermann Helmholtz [Helmholtz1863]: he says notes are in "concord" because the sound playing them together is "less worse" than that of some other notes. But note that, in this theory, more notes can only penalize, some merely less than others, and so the most harmonious sound should be a single note by itself(!) and harmony would not exist as a phenomenon of music at all. Hokay, buddy.

iaw 10y ago
I got the same reaction. He felt a bit dismissive from the gate, I've only thus far skimmed the paper but some of what he references is in the old music theory texts I've looked it.
drostie 10y ago
His criticism of Helmholtz is probably spot-on but I haven't encountered the folks that he has, claiming that Helmholtz is the "agreed-upon authority on this subject." A bunch of the material available in this paper is sufficiently common knowledge to appear e.g. on Wikipedia: https://en.wikipedia.org/wiki/Equal_temperament https://en.wikipedia.org/wiki/Equal_temperament . The most major novelty here appears to be an attempt to hand-wave some general aesthetic principles for what humans like, and apply these to the brain via some sort of fuzzy "computational approach" (which never, y'know, broaches the point of an actual computer program). A lot of the overarching explanation can be ignored to the benefit of the theory in many cases: for example, it is likely more helpful to a neurobiological understanding of harmony to steal his insight that the minor chord probably sounds "good but off" because it has the right intervals in the wrong order, than to couch it in the author's full explanation with computational assumptions etc.
ntumlin 10y ago
> Any study of music that begins by discarding all of that is pretty silly IMO. It's kind of fun to think that we've just discovered some local optimum for enjoyable music and that going in a completely different direction will lead to something both unrecognizable and mind-blowingly awesome. I'm not even remotely convinced that's the case, but it's fun to dream.
- rhizome 10y ago
  Harmony is fundamentally dependent on the scale and mode used. A large portion of the world (possibly a majority) listens to alternate derivations of the harmonic series which use many more notes than the 12-note Western chromatic scale.
  - uint32 10y ago
    This idea is often presented as soon as anyone mentions "harmonic series" and "Western music theory" in the same breath, and in the same hand-wavey terms. Do you have any material to support these claims?
    - zhemao 10y ago
      I don't see how this is so questionable. Frequency is continuous, so the way we subdivide into discrete notes is quite arbitrary. You don't even have to go outside of western music to find examples. Modernist classical composers of the 20th century experimented with microphones. Just look up "microtonal music" and you'll find many examples.
    - 21echoes 10y ago
      No disrespect, and I could be misreading your point, but I think it only seems hand-wavey to you because you're not familiar with the definitions of the terms being used. It's just statement of facts that is in basically no dispute by the musical community. A few definitions: > Harmony The frequency ratio of two or more pitches > Scale and mode The set of frequency ratios out of which a given piece of music can be constructed > The 12-note Western chromatic scale The modern western chromatic scale is formed out frequency ratios which are powers of the twelfth root of 2, or ~1.059. This is called the "12 note" scale, because 1.059^12 == 2, and our brains are predisposed to find pitches who are multiples of two apart similar. This is because pitch classification in humans (along with many other human senses) measures inbound signal in exponential, rather than linear, terms, and 2:1 is also the simplest ratio by which two pitches can have constructive interference. As far as why the 12-note scale is the Western scale, there's a fair amount of debate, but most are in agreement that it likely comes from the fact that 12 is a low number with a fair number of integer factors (1, 2, 3, 4, 6). Integer factors translates very directly into constructive wave interference (3:2 has less destructive interference than 101:100). So, one can easily construct many constructive interference ratios out of the (2^^(1/12)) atomic element (e.g. the "major chord", the most common set of three pitches in western music, is (1.059^7):(1.059^4):1 ~= 6:5:4). Each exponent of the twelfth root of two is very close to, respectively: 16/15, 9/8, 6/5, 5/4, 4/3, 7/5, 3/2, 8/5, 5/3, 16/9, 15/8 So! Now the only remaining question is just a question of the antropological evidence: do all other cultures also use the twelfth root of two as their simplest harmonic difference? And the answer is very clearly no: * Indian music uses the twenty second root of two -- the "shruti" https://en.wikipedia.org/wiki/Shruti_(music) https://en.wikipedia.org/wiki/Shruti_(music) * Indonesian music has many different scales, some based on the 9th root of 2 ( https://en.wikipedia.org/wiki/Pelog https://en.wikipedia.org/wiki/Pelog ), others based on the 5th root of 2 ( https://en.wikipedia.org/wiki/Slendro https://en.wikipedia.org/wiki/Slendro which is often paired with a scale based on the 17th root of 2) * Arabic music uses the twentyfourth root of two ( https://en.wikipedia.org/wiki/Arabic_maqam#Notation https://en.wikipedia.org/wiki/Arabic_maqam#Notation although to be fair, this is just the square root of the western twelfth root of two, but this conceit is largely used for notation, while actual performance uses adjustments smaller than the twenty-fourth root of two) * And plenty of other cultures besides ( https://en.wikipedia.org/wiki/Microtonal_music#Microtonal https://en.wikipedia.org/wiki/Microtonal_music#Microtonal, https://danielpaulschnee.wordpress.com/2015/05/11/microtonality-in-asian-music https://danielpaulschnee.wordpress.com/2015/05/11/microtonal... etc ) Does this constitute "A large portion of the world (possibly a majority)"? I'd probably say not a majority, but certainly more than 15%, likely at least 25%.

by hashkb 10y ago

iaw 10y ago

I got the same reaction. He felt a bit dismissive from the gate, I've only thus far skimmed the paper but some of what he references is in the old music theory texts I've looked it.

drostie 10y ago

His criticism of Helmholtz is probably spot-on but I haven't encountered the folks that he has, claiming that Helmholtz is the "agreed-upon authority on this subject." A bunch of the material available in this paper is sufficiently common knowledge to appear e.g. on Wikipedia: https://en.wikipedia.org/wiki/Equal_temperament https://en.wikipedia.org/wiki/Equal_temperament . The most major novelty here appears to be an attempt to hand-wave some general aesthetic principles for what humans like, and apply these to the brain via some sort of fuzzy "computational approach" (which never, y'know, broaches the point of an actual computer program). A lot of the overarching explanation can be ignored to the benefit of the theory in many cases: for example, it is likely more helpful to a neurobiological understanding of harmony to steal his insight that the minor chord probably sounds "good but off" because it has the right intervals in the wrong order, than to couch it in the author's full explanation with computational assumptions etc.

ntumlin 10y ago

> Any study of music that begins by discarding all of that is pretty silly IMO. It's kind of fun to think that we've just discovered some local optimum for enjoyable music and that going in a completely different direction will lead to something both unrecognizable and mind-blowingly awesome. I'm not even remotely convinced that's the case, but it's fun to dream.

rhizome 10y ago
Harmony is fundamentally dependent on the scale and mode used. A large portion of the world (possibly a majority) listens to alternate derivations of the harmonic series which use many more notes than the 12-note Western chromatic scale.
- uint32 10y ago
  This idea is often presented as soon as anyone mentions "harmonic series" and "Western music theory" in the same breath, and in the same hand-wavey terms. Do you have any material to support these claims?
  - zhemao 10y ago
    I don't see how this is so questionable. Frequency is continuous, so the way we subdivide into discrete notes is quite arbitrary. You don't even have to go outside of western music to find examples. Modernist classical composers of the 20th century experimented with microphones. Just look up "microtonal music" and you'll find many examples.
  - 21echoes 10y ago
    No disrespect, and I could be misreading your point, but I think it only seems hand-wavey to you because you're not familiar with the definitions of the terms being used. It's just statement of facts that is in basically no dispute by the musical community. A few definitions: > Harmony The frequency ratio of two or more pitches > Scale and mode The set of frequency ratios out of which a given piece of music can be constructed > The 12-note Western chromatic scale The modern western chromatic scale is formed out frequency ratios which are powers of the twelfth root of 2, or ~1.059. This is called the "12 note" scale, because 1.059^12 == 2, and our brains are predisposed to find pitches who are multiples of two apart similar. This is because pitch classification in humans (along with many other human senses) measures inbound signal in exponential, rather than linear, terms, and 2:1 is also the simplest ratio by which two pitches can have constructive interference. As far as why the 12-note scale is the Western scale, there's a fair amount of debate, but most are in agreement that it likely comes from the fact that 12 is a low number with a fair number of integer factors (1, 2, 3, 4, 6). Integer factors translates very directly into constructive wave interference (3:2 has less destructive interference than 101:100). So, one can easily construct many constructive interference ratios out of the (2^^(1/12)) atomic element (e.g. the "major chord", the most common set of three pitches in western music, is (1.059^7):(1.059^4):1 ~= 6:5:4). Each exponent of the twelfth root of two is very close to, respectively: 16/15, 9/8, 6/5, 5/4, 4/3, 7/5, 3/2, 8/5, 5/3, 16/9, 15/8 So! Now the only remaining question is just a question of the antropological evidence: do all other cultures also use the twelfth root of two as their simplest harmonic difference? And the answer is very clearly no: * Indian music uses the twenty second root of two -- the "shruti" https://en.wikipedia.org/wiki/Shruti_(music) https://en.wikipedia.org/wiki/Shruti_(music) * Indonesian music has many different scales, some based on the 9th root of 2 ( https://en.wikipedia.org/wiki/Pelog https://en.wikipedia.org/wiki/Pelog ), others based on the 5th root of 2 ( https://en.wikipedia.org/wiki/Slendro https://en.wikipedia.org/wiki/Slendro which is often paired with a scale based on the 17th root of 2) * Arabic music uses the twentyfourth root of two ( https://en.wikipedia.org/wiki/Arabic_maqam#Notation https://en.wikipedia.org/wiki/Arabic_maqam#Notation although to be fair, this is just the square root of the western twelfth root of two, but this conceit is largely used for notation, while actual performance uses adjustments smaller than the twenty-fourth root of two) * And plenty of other cultures besides ( https://en.wikipedia.org/wiki/Microtonal_music#Microtonal https://en.wikipedia.org/wiki/Microtonal_music#Microtonal, https://danielpaulschnee.wordpress.com/2015/05/11/microtonality-in-asian-music https://danielpaulschnee.wordpress.com/2015/05/11/microtonal... etc ) Does this constitute "A large portion of the world (possibly a majority)"? I'd probably say not a majority, but certainly more than 15%, likely at least 25%.