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I started learning music recently, and another type that I would like to see, is mathematics for music genres, mathematics for music effects and mathematics for

I started learning music recently, and another type that I would like to see, is mathematics for music genres, mathematics for music effects and mathematics for music theory

peterkos 6y ago
> mathematics for music theory Oh boy now that's a fun one There's a great book called "The Oxford Handbook of Algorithmic Music"[0] that has many insights into that! Some philosophical, some really mathy. [0] https://global.oup.com/academic/product/the-oxford-handbook-of-algorithmic-music-9780190226992 https://global.oup.com/academic/product/the-oxford-handbook-...
mhh__ 6y ago
Mathematics for music effects is called digital signal processing. Proakis's book is good if you can handle analysis. Also, a word of warning/advice: Music theory is not mathematics - it's just a way of storing patterns that sound nice on western instruments. There are some musical genres that you can basically generate algorithmically, but if you want to actually learn musicianship stay well clear. Mark Levine's books are a good "textbook style" music theory book with lots of examples of actual jazz music.
- parenthesis 6y ago
  Actually, there is lots of nice maths in music theory. Yes, music theory is descriptive rather than prescriptive. But messing around (mathematically) with its ideas can help one find nice musical possibilities one might not otherwise have considered. For example, the major scale, the (ascending) melodic minor scale, and the harmonic minor scale are all seven-note scales such that all scale-wise thirds are major or minor. This is important, because people like using harmony built on stacking major and minor thirds. But are there any other seven-note scales whose thirds are all major or minor, beside the aforementioned (and their modes)? Yes, the harmonic major scale (and its modes). Not so well known, it presents lots of different, but still ultimately convential, possibilities.
  - jmiskovic 6y ago
    After digging a bit into math approach to music, I'd agree with mhh__. Music is the business of making vibrations sound good. Definition of "good" is cultural and changes with times (see Devil's interval). The standard mathematical approach to music starts from axioms that are only applicable to western music and imply no evolution. Maybe linguistic methods would serve composers better, as they deal in similar problems: how to to create meaningful whole from meaningless parts that relate to each other in complex way. Just as linguistics, music involves not only the mechanics of ear sensing, but also pattern recognition machine that likes to have just the right amount of repetition, and just the right amount of new stuff.
    - parenthesis 6y ago
      Yes, ultimately taste, or `what sounds good' decides. But mathematical approaches to all the building blocks of music can bring new materials to the ear which might sound good. For example, I love the third mode of harmonic major (Phrygian flat 4) because I like the way it sounds. But I wouldn't have discovered it if I hadn't been thinking about scales in a systematic, mathematical kind of way.
- peterkos 6y ago
  "... but if you want to actually learn musicianship stay well clear." Species counterpoint is entirely mathematical, as is (to a great extent) common-practice partwriting. Yet, I guarantee you that most people who listen to that music would think it is entirely musical, when in fact very little is more than rule-following. (And yes, this is for a lot of genres! Sonata form, pop structure, etc., etc.) Also, involving the work of David Cope, his rule-based composition systems repeatedly passed the turing test. (I'm hoping, once I get to grad school, for my master's thesis to be around this exact idea: the computational aspect of creativity, and how the idea of "musicianship" is really just a human attribute we hold on to.) I agree that music theory is mainly descriptive rather than prescriptive, but the fact that many works of genius center around patterns, well... it's hard for me to believe that we aren't heavily dependent, on some level, on math.
  - zozbot234 6y ago
    > Species counterpoint is entirely mathematical, as is (to a great extent) common-practice partwriting. It really isn't. You can try to translate the guidelines of species counterpoint into "hard" constraints and generate pieces that precisely fit these constraints - but this does not result in good or interesting music. And this is even more true for actual composition, which is developed to a level that far exceeds the guidelines of species counterpoint itself. Thinking of music patterns as being entirely "mathematical" was historically common - there is a lot of old music theory that simply involves a mathematical/numerological exploration of musically-viable ratios between frequencies - but it's not really helpful if you're trying to figure out what makes music tick.
    - peterkos 6y ago
      As a composer I agree to some extent. Like, I don't sit down and say "oh lets use some augmented sixths today", but I definitely refer back to the "rules" of music theory a lot when I get stuck or I'm looking for a way to communicate a certain mood in a piece. And this kinda device-reference approach, I believe, is mathematical. And I also think that a lot of what makes music tick is that inherent usage of the musical language we study or grow up with. Truly original music imo doesn't really exist[0]; the intentional or unintentional borrowing of ideas is why music theory is a field of study: to describe the ways in which music works. I think even modern techniques (set theory, 12-tone rows, and atonal music overall) has to look at the existing rules and say "what can we do differently" -- even as Romantic-era composers got more adventerous in their use of texture, harmony, tonality, etc. (The story of Charles Ives, who spent most of his younger life being "untrained" by his father to sing duets in overlapping keys and the like, is a good example of this.) > ... actual composition, which is developed to a level that far exceeds the guidelines of species counterpoint itself While true, I still think it's more of a spectrum than a binary "all or nothing" mathematical approach, which is why I believe that musicianship is more mathematical than not. I agree that it far exceeds the "use a forth and you're beheaded" approach but I'd be interested to hear music that is entirely free of some sort of process. [0] note: the discussion of originality in music is probably an entire essay on its own, lol

I started learning music recently, and another type that I would like to see, is mathematics for music genres, mathematics for music effects and mathematics for music theory

peterkos 6y ago

> mathematics for music theory Oh boy now that's a fun one There's a great book called "The Oxford Handbook of Algorithmic Music"[0] that has many insights into that! Some philosophical, some really mathy. [0] https://global.oup.com/academic/product/the-oxford-handbook-of-algorithmic-music-9780190226992 https://global.oup.com/academic/product/the-oxford-handbook-...

mhh__ 6y ago

Mathematics for music effects is called digital signal processing. Proakis's book is good if you can handle analysis. Also, a word of warning/advice: Music theory is not mathematics - it's just a way of storing patterns that sound nice on western instruments. There are some musical genres that you can basically generate algorithmically, but if you want to actually learn musicianship stay well clear. Mark Levine's books are a good "textbook style" music theory book with lots of examples of actual jazz music.

parenthesis 6y ago
Actually, there is lots of nice maths in music theory. Yes, music theory is descriptive rather than prescriptive. But messing around (mathematically) with its ideas can help one find nice musical possibilities one might not otherwise have considered. For example, the major scale, the (ascending) melodic minor scale, and the harmonic minor scale are all seven-note scales such that all scale-wise thirds are major or minor. This is important, because people like using harmony built on stacking major and minor thirds. But are there any other seven-note scales whose thirds are all major or minor, beside the aforementioned (and their modes)? Yes, the harmonic major scale (and its modes). Not so well known, it presents lots of different, but still ultimately convential, possibilities.
- jmiskovic 6y ago
  After digging a bit into math approach to music, I'd agree with mhh__. Music is the business of making vibrations sound good. Definition of "good" is cultural and changes with times (see Devil's interval). The standard mathematical approach to music starts from axioms that are only applicable to western music and imply no evolution. Maybe linguistic methods would serve composers better, as they deal in similar problems: how to to create meaningful whole from meaningless parts that relate to each other in complex way. Just as linguistics, music involves not only the mechanics of ear sensing, but also pattern recognition machine that likes to have just the right amount of repetition, and just the right amount of new stuff.
  - parenthesis 6y ago
    Yes, ultimately taste, or `what sounds good' decides. But mathematical approaches to all the building blocks of music can bring new materials to the ear which might sound good. For example, I love the third mode of harmonic major (Phrygian flat 4) because I like the way it sounds. But I wouldn't have discovered it if I hadn't been thinking about scales in a systematic, mathematical kind of way.
peterkos 6y ago
"... but if you want to actually learn musicianship stay well clear." Species counterpoint is entirely mathematical, as is (to a great extent) common-practice partwriting. Yet, I guarantee you that most people who listen to that music would think it is entirely musical, when in fact very little is more than rule-following. (And yes, this is for a lot of genres! Sonata form, pop structure, etc., etc.) Also, involving the work of David Cope, his rule-based composition systems repeatedly passed the turing test. (I'm hoping, once I get to grad school, for my master's thesis to be around this exact idea: the computational aspect of creativity, and how the idea of "musicianship" is really just a human attribute we hold on to.) I agree that music theory is mainly descriptive rather than prescriptive, but the fact that many works of genius center around patterns, well... it's hard for me to believe that we aren't heavily dependent, on some level, on math.
- zozbot234 6y ago
  > Species counterpoint is entirely mathematical, as is (to a great extent) common-practice partwriting. It really isn't. You can try to translate the guidelines of species counterpoint into "hard" constraints and generate pieces that precisely fit these constraints - but this does not result in good or interesting music. And this is even more true for actual composition, which is developed to a level that far exceeds the guidelines of species counterpoint itself. Thinking of music patterns as being entirely "mathematical" was historically common - there is a lot of old music theory that simply involves a mathematical/numerological exploration of musically-viable ratios between frequencies - but it's not really helpful if you're trying to figure out what makes music tick.
  - peterkos 6y ago
    As a composer I agree to some extent. Like, I don't sit down and say "oh lets use some augmented sixths today", but I definitely refer back to the "rules" of music theory a lot when I get stuck or I'm looking for a way to communicate a certain mood in a piece. And this kinda device-reference approach, I believe, is mathematical. And I also think that a lot of what makes music tick is that inherent usage of the musical language we study or grow up with. Truly original music imo doesn't really exist[0]; the intentional or unintentional borrowing of ideas is why music theory is a field of study: to describe the ways in which music works. I think even modern techniques (set theory, 12-tone rows, and atonal music overall) has to look at the existing rules and say "what can we do differently" -- even as Romantic-era composers got more adventerous in their use of texture, harmony, tonality, etc. (The story of Charles Ives, who spent most of his younger life being "untrained" by his father to sing duets in overlapping keys and the like, is a good example of this.) > ... actual composition, which is developed to a level that far exceeds the guidelines of species counterpoint itself While true, I still think it's more of a spectrum than a binary "all or nothing" mathematical approach, which is why I believe that musicianship is more mathematical than not. I agree that it far exceeds the "use a forth and you're beheaded" approach but I'd be interested to hear music that is entirely free of some sort of process. [0] note: the discussion of originality in music is probably an entire essay on its own, lol