5 ms·

My problem is that whenever I've picked up a music theory textbook, the author opens with "put your hands on the keyboard... doesn't playing <foo> <bar> and <ba

My problem is that whenever I've picked up a music theory textbook, the author opens with "put your hands on the keyboard... doesn't playing <foo> <bar> and <baz> feel natural?" As someone who has had zero music training, but has considered generative music as a possible hobby, I'd like to at least start trying to understand the domain before committing to a physical instrument and working on developing muscle memory. I'd really love a rigorous music theory textbook that does not assume you already play an instrument.

zozbot234 6y ago
Music theory is based on generalizing patterns that are found in actual music. Your "muscle memory" is an integral part of understanding this generalization semi-rigorously. About the only thing that can be called loosely 'rigorous' wrt. music theory is the derivation of the diatonic scale from "stacking" fifths.
- PaulDavisThe1st 6y ago
  I don't agree with your dismal final sentence. Musical set theory [1] is an examination of scales/harmony without giving preference to western modes. The harmonic series is a physical phenomena at the root of all musical cultural behavior, and is a completely rigorous subject. The diatonic scale isn't derived by stacking fifths, since that would be tautological: a "fifth" is a concept taken from the diatonic scale. What you likely meant was "derivation of the diatonic scale by stacking key integer ratios between frequencies, particularly the ratio 3:2)" That already elides the whole concept that dissonance and consonance correspond to the presence or absence of non-integer ratios between frequencies with notable energy. It also skips over the admittedly subjective way in which introducing more dissonance by way of "odd" ratios can still be perceived as musically interesting (though almost always in culturally determined ways). [1] this isn't pure MST, but it's a great place to start even if it is limited to 12TET tuning: https://ianring.com/musictheory/scales/ https://ianring.com/musictheory/scales/
PaulDavisThe1st 6y ago
A book that I came across the other day (via a recommendation from YT-ber Adam Neely): "Harmonic Experience" by W.A. Mathieu. It's a little expensive as a first dive into this stuff, but it does look like a very natural way to lead you into and through the actual experience of western tonal harmony, often by singing along with a drone (easy to generate on today's computers). https://www.amazon.com/Harmonic-Experience-Harmony-Natural-Expression/dp/0892815604/ref=sr_1_1?dchild=1&keywords=9781620554012&linkCode=qs&qid=1607193553&s=books&sr=1-1 https://www.amazon.com/Harmonic-Experience-Harmony-Natural-E...
fenomas 6y ago
To be honest the math is super simple, but standard music theory piles a heap of messy terminology on top of it. For years I've been meaning to write a "programmer's guide to 85% of western music theory" article, but never quite gotten around to it. The core of it boils down to stuff like: * scales are arrays of note offsets: * majorScale = [0, 2, 4, 5, 7, 9, 11] * to change a scale's key, offset each note: * dMajor = cMajor.map(n => n+2) * "modes" typically means scales that are reindexed: * dorian = major.map((n,i) => major[(i+1) % 7]) and so on. Obviously knowing that stuff doesn't make the music theory any more intuitive - if a textbook says "a V/ii chord", I have no idea what that sounds like. But deriving what notes it has, or writing a function to play them, is super easy once the terminology is demystified.
- uxcolumbo 6y ago
  Would love to read more about this. Until your article is done, can you recommend other sources that go into this?
  - fenomas 6y ago
    I don't really remember finding any good dense sources, I mostly slogged through wikipedia articles and gradually decoded things. I really ought to get around to that article...
  - jim-jim-jim 6y ago
    It doesn't contain code, but "Musimathics" by Gareth Loy was way more useful to me than any vanilla theory book. I think most other musically ignorant programmers would agree.
- bambax 6y ago
  A book is lot of work, but a blog post would be a great start! Regarding modes, your presentation is excellent and true (AFAIK), but why some scales don't have the same modes as other scales; given scales with the same number of notes, they should have the same modes? Yet for example, while the modes of the major scale are Ionian then Dorian, Phrygian, Lydian, Mixolydian, Aeolian and Locrian, the modes of the double harmonic major scale are [name of the scale] then Lydian, Ultraphrygian, Hungarian, Oriental, Ionian and Locrian. Is it only a problem of nomenclature or is there a profound truth behind it?
viraptor 6y ago
If you want something practical / simpler, have a look at https://www.youtube.com/user/MusicTheoryForGuitar https://www.youtube.com/user/MusicTheoryForGuitar (it's guitar-oriented, but contains general content) - they're not in a specific order so you'll have to pick and choose your topics. It's a bit better than a book, because you'll hear the examples in most cases too. Then you could go to more advanced ones like 12tone or Adam Neely's Q&As.
abetusk 6y ago
I feel for you on this. I was in the same boat. Even talking to musicians, they couldn't explain it to me with the rigor I wanted. For me, the real insight came when I understood why the 12 note chromatic scale was chosen, why chords "sound good" and that a lot of the confusing terminology hides pretty simple concepts. I don't feel like I could make any music, generative or otherwise, that sounds passable but here's what I've learned so far: * As a good approximation of the human auditory system, frequencies are perceived on a logarithmic scale * Rhythm is tied heavily with language and the tempo of speech, word length and frequency [0] * Note combinations sound more "pleasing" when the ration of their frequencies are small as reduced fractions [1] * The 12 note chromatic scale is a good compromise of number of notes and enough pleasantly sounding note combinations * The 12 note chromatic scale is generated from a base frequency of 440Hz multiplied by the twelfth roots of 2 * The 12 note chromatic scale can be further restricted to the diatonic scales to help further restrict the note set to allow for ease of composition As far as I can tell, a lot of music theory centers around the different diatonic scales ("Ionian", "Aeolian", etc.), which are just restrictions of the chromatic 12 note scale to some notes that sound reasonable together. I have some very rough notes on it [2], though I'm not sure how readable it is. I'm also in the same boat in terms of "instrument choice", though I would much rather invest in some live coding environment, like Gibber or Sonic Pi, or some software DAW system like LMMS. I still haven't found something that gets at the right level of functionality and abstraction that I want. [0] https://github.com/abetusk/papers/blob/release/Music/patel2003.pdf https://github.com/abetusk/papers/blob/release/Music/patel20... [1] https://github.com/abetusk/papers/blob/release/Music/measures-consonances_honingh.pdf https://github.com/abetusk/papers/blob/release/Music/measure... [2] https://github.com/abetusk/dev/blob/release/notes/MusicNotes.md https://github.com/abetusk/dev/blob/release/notes/MusicNotes...

zozbot234 6y ago

Music theory is based on generalizing patterns that are found in actual music. Your "muscle memory" is an integral part of understanding this generalization semi-rigorously. About the only thing that can be called loosely 'rigorous' wrt. music theory is the derivation of the diatonic scale from "stacking" fifths.

PaulDavisThe1st 6y ago
I don't agree with your dismal final sentence. Musical set theory [1] is an examination of scales/harmony without giving preference to western modes. The harmonic series is a physical phenomena at the root of all musical cultural behavior, and is a completely rigorous subject. The diatonic scale isn't derived by stacking fifths, since that would be tautological: a "fifth" is a concept taken from the diatonic scale. What you likely meant was "derivation of the diatonic scale by stacking key integer ratios between frequencies, particularly the ratio 3:2)" That already elides the whole concept that dissonance and consonance correspond to the presence or absence of non-integer ratios between frequencies with notable energy. It also skips over the admittedly subjective way in which introducing more dissonance by way of "odd" ratios can still be perceived as musically interesting (though almost always in culturally determined ways). [1] this isn't pure MST, but it's a great place to start even if it is limited to 12TET tuning: https://ianring.com/musictheory/scales/ https://ianring.com/musictheory/scales/

PaulDavisThe1st 6y ago

A book that I came across the other day (via a recommendation from YT-ber Adam Neely): "Harmonic Experience" by W.A. Mathieu. It's a little expensive as a first dive into this stuff, but it does look like a very natural way to lead you into and through the actual experience of western tonal harmony, often by singing along with a drone (easy to generate on today's computers). https://www.amazon.com/Harmonic-Experience-Harmony-Natural-Expression/dp/0892815604/ref=sr_1_1?dchild=1&keywords=9781620554012&linkCode=qs&qid=1607193553&s=books&sr=1-1 https://www.amazon.com/Harmonic-Experience-Harmony-Natural-E...

fenomas 6y ago

To be honest the math is super simple, but standard music theory piles a heap of messy terminology on top of it. For years I've been meaning to write a "programmer's guide to 85% of western music theory" article, but never quite gotten around to it. The core of it boils down to stuff like: * scales are arrays of note offsets: * majorScale = [0, 2, 4, 5, 7, 9, 11] * to change a scale's key, offset each note: * dMajor = cMajor.map(n => n+2) * "modes" typically means scales that are reindexed: * dorian = major.map((n,i) => major[(i+1) % 7]) and so on. Obviously knowing that stuff doesn't make the music theory any more intuitive - if a textbook says "a V/ii chord", I have no idea what that sounds like. But deriving what notes it has, or writing a function to play them, is super easy once the terminology is demystified.

uxcolumbo 6y ago
Would love to read more about this. Until your article is done, can you recommend other sources that go into this?
- fenomas 6y ago
  I don't really remember finding any good dense sources, I mostly slogged through wikipedia articles and gradually decoded things. I really ought to get around to that article...
- jim-jim-jim 6y ago
  It doesn't contain code, but "Musimathics" by Gareth Loy was way more useful to me than any vanilla theory book. I think most other musically ignorant programmers would agree.
bambax 6y ago
A book is lot of work, but a blog post would be a great start! Regarding modes, your presentation is excellent and true (AFAIK), but why some scales don't have the same modes as other scales; given scales with the same number of notes, they should have the same modes? Yet for example, while the modes of the major scale are Ionian then Dorian, Phrygian, Lydian, Mixolydian, Aeolian and Locrian, the modes of the double harmonic major scale are [name of the scale] then Lydian, Ultraphrygian, Hungarian, Oriental, Ionian and Locrian. Is it only a problem of nomenclature or is there a profound truth behind it?

viraptor 6y ago

If you want something practical / simpler, have a look at https://www.youtube.com/user/MusicTheoryForGuitar https://www.youtube.com/user/MusicTheoryForGuitar (it's guitar-oriented, but contains general content) - they're not in a specific order so you'll have to pick and choose your topics. It's a bit better than a book, because you'll hear the examples in most cases too. Then you could go to more advanced ones like 12tone or Adam Neely's Q&As.

abetusk 6y ago

I feel for you on this. I was in the same boat. Even talking to musicians, they couldn't explain it to me with the rigor I wanted. For me, the real insight came when I understood why the 12 note chromatic scale was chosen, why chords "sound good" and that a lot of the confusing terminology hides pretty simple concepts. I don't feel like I could make any music, generative or otherwise, that sounds passable but here's what I've learned so far: * As a good approximation of the human auditory system, frequencies are perceived on a logarithmic scale * Rhythm is tied heavily with language and the tempo of speech, word length and frequency [0] * Note combinations sound more "pleasing" when the ration of their frequencies are small as reduced fractions [1] * The 12 note chromatic scale is a good compromise of number of notes and enough pleasantly sounding note combinations * The 12 note chromatic scale is generated from a base frequency of 440Hz multiplied by the twelfth roots of 2 * The 12 note chromatic scale can be further restricted to the diatonic scales to help further restrict the note set to allow for ease of composition As far as I can tell, a lot of music theory centers around the different diatonic scales ("Ionian", "Aeolian", etc.), which are just restrictions of the chromatic 12 note scale to some notes that sound reasonable together. I have some very rough notes on it [2], though I'm not sure how readable it is. I'm also in the same boat in terms of "instrument choice", though I would much rather invest in some live coding environment, like Gibber or Sonic Pi, or some software DAW system like LMMS. I still haven't found something that gets at the right level of functionality and abstraction that I want. [0] https://github.com/abetusk/papers/blob/release/Music/patel2003.pdf https://github.com/abetusk/papers/blob/release/Music/patel20... [1] https://github.com/abetusk/papers/blob/release/Music/measures-consonances_honingh.pdf https://github.com/abetusk/papers/blob/release/Music/measure... [2] https://github.com/abetusk/dev/blob/release/notes/MusicNotes.md https://github.com/abetusk/dev/blob/release/notes/MusicNotes...