Theory of Harmony

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1. erwinhAug 2022
   A lot of the early music theory comes from discovering resonating overtones before having the full physics & mathematical model to describe it exactly scientifically. The opening chapters of Theory of Harmony by Arnold Schoenberg are a very interesting read from that perspective. In a way its the same question as for math. Do mathematicians invent new mathematical theories or do they discover structures and concepts that exist in the idea world outside of our physical reality?
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2. odyssey7Oct 2019
   An influential book for me was Arnold Schoenberg's Theory of Harmony. It's half harmonic theory and half a manifesto on art. In a lengthy footnote he advises using materials to their advantages, rather than forcing them to do something they weren't meant to do. I've seen this sentiment mentioned in other places as well.

   As a vegetarian, I've felt this was wonderfully applicable. There's so many great flavors and textures you can achieve with plants, but a lot of vegetarian cook books and pre-made food aim to mimic meat-based dishes instead of embracing more natural outcomes of these different materials.

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3. odyssey7Feb 2019
   Theory of Harmony, by Schoenberg

   The book takes music theory as its subject, but explores perception, culture, the meaning of art, innovation, and other related ideas in its lengthy footnotes and tangents. It shows a world of practical considerations that go into art, which many would assume is primarily subjective.

   Schoenberg is known as a composer for exploring atonality, and for having many students who became important composers.

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4. fdintinoJan 2012
   "The distinction between tonality and noise is mathematical form" doesn't have the same ring to it, I suppose.

   My favorite study of tonal harmony is "Theory of Harmony" by Arnold Schoenberg (sounds ironic; here's a preview on google books: <http://books.google.com/books?id=5Y5MyjbU87oC&lpg=PR3...). It was the first theory textbook that attempted to teach composition of harmony without value judgments about what is "correct" or "natural," instead taking pains at every step to justify itself on first principles. He wrote the book because he believed his students needed to understand conventional harmony before they could transcend it. In my mind Schoenberg falls into that class of visionaries whose legacies are more about their failed predictions than of their analyses and contributions (Marx shared a similar fate, his own fault of course). Schoenberg was partially right — nobody in their right mind argues that ninth chords can't be processed by our feeble minds (jazz is western canon at this point), or that the tritone will summon demons (well, maybe some people in Norway still believe that) — but classical harmony hasn't been completely replaced.

   The scientific stuff in Schoenberg's Theory of Harmony is mostly garbage though. If you're interested in reading more about the modern understanding of the physical properties of music I'd recommend "Musimathics: The Mathematical Foundations of Music," and Benson's "Music: A Mathematical Offering." For an attempt to look at musical structure in terms of its cognition, I enjoyed "The Cognition of Basic Musical Structures" by David Temperley. It's a bit speculative, but that's the current state of the field if you're trying to go beyond the simplest aspects of music.

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5. odyssey7Sep 2025
   "I am taking such pains with these things, not so much out of concern that the pupil might, if they were not explained, thoughtlessly accept and mechanically apply them, as to establish explicitly that these principles are not derived from aesthetics but from practical considerations. If what is known as aesthetics does in fact contain much that is merely practical handling of the material, and if what is known as symmetry is perhaps often not much more than an organization of the material that reveals a sensible regard for its properties, yet I consider it worthwhile to set down these observations. For the conditions of practicality can change, if we take a different view of the material and if the purpose changes. But aesthetics alleges it has discovered eternal laws."

   -- Arnold Schoenberg, Theory of Harmony

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6. odyssey7Apr 2024
   Arnold Schoenberg observed the deep connection between music, perception, and cognition; anticipated composers applying timbral control as is now commonly done with synthesizers; and apparently did not anticipate non-subtlety of the effect in EDM:

   "I think the tone becomes perceptible by virtue of tone color [timbre], of which one dimension is pitch. ... Pitch is nothing else but tone color measured in one direction. Now, if it is possible to create patterns out of tone colors that are differentiated according to pitch, patterns we call 'melodies', progressions, whose coherence evokes an effect analogous to thought processes, then it must also be possible to make such progressions out of the tone colors of the other dimension, out of that which we call simply 'tone color', progressions whose relations with one another work with a kind of logic entirely equivalent to that logic which satisfies us in the melody of pitches. That has the appearance of a futuristic fantasy and is probably just that. But it is one which, I firmly believe, will be realized.

   ...

   Tone-color melodies! How acute the senses that would be able to perceive them! How high the development of spirit that could find pleasure in such subtle things!"

   -- Arnold Schoenberg, Theory of Harmony, 1911, toward the end of chapter 22.

   Personally, I anticipate that if humanlike AGI is achieved, then it will understand the illusion of music. Not merely because music understanding is an attribute of humanlike, but because there must be something intrinsic in the process of human cognition that causes the illusion of music occur. Music understanding could be viewed as an essential waypoint on the path to AGI.

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