3 ms·

I've mentioned this before, but for me, the definitive work on this vast subject is "The Harmonic Experience" by W.A. Mathieu. He really gets into low prime rat

I've mentioned this before, but for me, the definitive work on this vast subject is "The Harmonic Experience" by W.A. Mathieu. He really gets into low prime ratios, why they sound good to us, and also why the building blocks of modern western harmony are approximations of those ratios, rather than the real thing. A fascinating read for anyone interested in the subject.

soundwave106 10y ago
Seconded. The one law I think you can say about harmony and melody, is that there seems to be a universal preference towards low frequency ratio combinations. EG: in all of world music, it seems octaves (2/1) fifths (3/2), fourths (4/3), and thirds (5/4) occur quite often and are the fundamental driving force of so many styles. They are seen as more "pure sounding" to the ear. Regarding the linked paper, the low ratio concept has been known for a while, and linking it to the harmonic series is fine. But there's more to music than simple pure ratios. Even many simple pop songs often offers transitions between "purity" and "impurity" (the simple dominant seven to tonic resolutions is enough to show this.) This is where the linked paper fell short... way short. It seemed to imply in 4.3 that there is no room for dissonance (or, to describe it without using Western terms, stepping away from the pure ratios, perhaps to resolve to purity... or perhaps not...) whatsoever in music, which is very laughable to anyone who's actually composed. 4.2.1 also almost seemed to apply a certain sense of Western cultural superiority... even though I would argue that Western culture actually is a case against his ideas. (As in... equal temperament decreases the "purity" by detuning some of the ratios, particularly the thirds. But a greater freedom is allowed for key modulation, and I agree with Mathieu that the ambiguity 12TET opens up is a feature in itself. Let's not go into the large amount of dissonance in some art such as 20th century classical, jazz, even some pop particularly in the alternative realm). I'm currently in the middle of Mathieu's book. The main disadvantage of his style is that it is a bit "flowery" which may not appeal to those who like reading their math more exactly. But one big advantage of W.A. Mathieu is that he seems well versed in three very different backgrounds (Indian classical music, jazz and Western classical music, although definitely heavier on the first two). For those familiar with neo-Riemannian theory, I consider his book a good tie-off with that side of music theory, not completely the same, but tangentially related. Unlike some neo-Riemannian books, because of Mathieu's background, I believe it avoids both some of the cultural mistakes that other music theory books seem to make and also avoids the mistake of trying to be the "one theory to rule them all".
- pcsanwald 10y ago
  I love the nature of his prose, but it's definitely not for everyone. One of the best things about the book for me was his emphasis on understanding the concepts through experience (singing against a drone), but of course this isn't everyone's goal. Still, for me, it continues to be a life-changing read which fundamentally altered the way I think about and hear music, and I've worked as a professional musician for more than 20 years.

soundwave106 10y ago

Seconded. The one law I think you can say about harmony and melody, is that there seems to be a universal preference towards low frequency ratio combinations. EG: in all of world music, it seems octaves (2/1) fifths (3/2), fourths (4/3), and thirds (5/4) occur quite often and are the fundamental driving force of so many styles. They are seen as more "pure sounding" to the ear. Regarding the linked paper, the low ratio concept has been known for a while, and linking it to the harmonic series is fine. But there's more to music than simple pure ratios. Even many simple pop songs often offers transitions between "purity" and "impurity" (the simple dominant seven to tonic resolutions is enough to show this.) This is where the linked paper fell short... way short. It seemed to imply in 4.3 that there is no room for dissonance (or, to describe it without using Western terms, stepping away from the pure ratios, perhaps to resolve to purity... or perhaps not...) whatsoever in music, which is very laughable to anyone who's actually composed. 4.2.1 also almost seemed to apply a certain sense of Western cultural superiority... even though I would argue that Western culture actually is a case against his ideas. (As in... equal temperament decreases the "purity" by detuning some of the ratios, particularly the thirds. But a greater freedom is allowed for key modulation, and I agree with Mathieu that the ambiguity 12TET opens up is a feature in itself. Let's not go into the large amount of dissonance in some art such as 20th century classical, jazz, even some pop particularly in the alternative realm). I'm currently in the middle of Mathieu's book. The main disadvantage of his style is that it is a bit "flowery" which may not appeal to those who like reading their math more exactly. But one big advantage of W.A. Mathieu is that he seems well versed in three very different backgrounds (Indian classical music, jazz and Western classical music, although definitely heavier on the first two). For those familiar with neo-Riemannian theory, I consider his book a good tie-off with that side of music theory, not completely the same, but tangentially related. Unlike some neo-Riemannian books, because of Mathieu's background, I believe it avoids both some of the cultural mistakes that other music theory books seem to make and also avoids the mistake of trying to be the "one theory to rule them all".

pcsanwald 10y ago
I love the nature of his prose, but it's definitely not for everyone. One of the best things about the book for me was his emphasis on understanding the concepts through experience (singing against a drone), but of course this isn't everyone's goal. Still, for me, it continues to be a life-changing read which fundamentally altered the way I think about and hear music, and I've worked as a professional musician for more than 20 years.