6 ms·

A study of musical scales (2017)

225 points by rwnspace 8y ago

baldfat 8y ago
WOW. As a former Music Theory 2 and Music Theory 3 student in college this is awesome. I am also very disappointed in myself for not trying to do something like this and failing earlier in my life. There is really a lot more that could be gained from this work. I am sensing someone's PhD project.
tfeldmann 8y ago
Thank you very much, this is some fantastic content!
deleted 8y ago
[deleted]
snarfy 8y ago
Really good content.
- myfonj 8y ago
  And form.
joeminichino 8y ago
Absolutely amazing. I'm a coder and a musician and I've been complaining to myself about a certain tendency to repetition in my compositions lately, this is amazing stuff to break patterns.
stelfer 8y ago
Thank you
Kagerjay 8y ago
This is fascinating! Unfortunately I don't understand even half of it, I've been wanting to learn music theory for some time I should go back and learn to play a musical instrument
- TaupeRanger 8y ago
  There's not much "music theory" here aside from the knowledge that there are 12 notes which repeat in octaves. He mentions a few modes (phrygian, etc) but that's not particularly esoteric. The rest is relating those ideas to simple mathematical constructs and seeing what comes out.
  - jm_l 8y ago
    To understand propriety/coherence (about 2/3 of the way down the page) you'll also need to have an understanding of enharmonics, and perhaps some context on why it's important to be able to know whether an interval is e.g. an augmented 3rd or a perfect fourth.
- scrozier 8y ago
  I have to agree with TaupeRanger here. This certainly has (almost) nothing to do with playing an instrument. It has little to do with music theory in the traditional sense. This is for the programmer/mathematician side of your brain, primarily. For the musician side, get a little electronic keyboard, poke around at it, and buy an introductory music theory book.
z2 8y ago
For something that puts this to action--Wolfram made a random music generator in 2005 with a ton of scales. http://tones.wolfram.com http://tones.wolfram.com
- romaniv 8y ago
  I bet this would be #1 comment if something in the process used neural networks and if it wasn't from Wolfram. Anyway, pretty cool generator.
williamdclt 8y ago
Very, very impressive. I don't have time to read everything right now, but just skimming everything this is an incredible resource, even for a non-programmer
well1912 8y ago
Nearly jumped out of my seat when I saw this! Look at how similar our approaches are: http://welliam.github.io/molts/ http://welliam.github.io/molts/ (apologies for how poorly written it is, it's been a few years!) Not that it's a super novel concept, but we both used this for the modes of limited transposition. For me it was an efficient way of generating MOLTs for any equal temperament scale.
adamc 8y ago
Thanks, I hugely enjoyed this.
stephenmm 8y ago
Nice work! If I could make one suggestion it would be to use hex instead of decimal. It would make the numbers easier to remember (shorter) and I think it would be easier to recognize patterns (Ie. whole scale is 0x333 and major scale 0xAB3).
sailfast 8y ago
It's been awhile since I've had the chance to dig into more advanced music theory but this is such an interesting framing of all of the possibilities present in both named and unnamed scales and the relationship of notes. The idea to lay it out mathematically like this and how you frame your overall thinking about scales is great. Bach would appreciate this work. Also reminds me a bit of how folks like Jacob Collier think about harmonies and new ways to arrive at different notes. The more you can internalize these kinds of mathematics, the more you can improvise in new and different ways. Well done! Really enjoyed this.
nu-world-odor 8y ago
buckethead only uses lydian...
naringas 8y ago
pretty good, this has motivated me to do an online post about my own take at similar issues. However I do not assume 12-tet, just the ocatave, so it's slightly different.
kazinator 8y ago
The problem with this is is that it accepts the twelve-tone equal temperament system as a sort of absolute frame of reference, rather than the compromise/approximation that it is. Musical scales are not just check-box menu choices out of twelve-tone equal temperament.
- crazynick4 8y ago
  Exactly. I would like to see this done using integer ratios to define the frequency intervals. You can still use the octave as a 'start' and 'end' point for the scale to make things simple (although there's no axiom anywhere that says this has to be the case, it's just a good candidate because it's the simplest and most easily recognizable interval, aside from the unison). Since you'd be dealing with a potentially infinite number of intervals, you can start with the 'simplest' 20 or so (using lowest possible integer values to create the distinct ratios). Some would argue that the simplest 40 can be considered musical although that would get you into some seriously dissonant territory, not to mention the amount of possibilities you would have available at that point.
- ibejoeb 8y ago
  That's the first thing that the author states. I'll bet you know more music than me, but maybe that puts me more into the target audience. It's a very interesting way to explore essentially the whole of western music. I did some similar "modeling" when I was learning, too, mostly because it's an effective way for me to commit things to memory. I remember struggling with using tones/scale degrees or intervals as a basis, just as the author describes. It might not be universal and suitable for high-level academic use, but I don't think there's a problem with it.
  - kazinator 8y ago
    The problem is that the twelve-tone system was designed for a very specific "use case", in the context of a certain kind of music: classical/Baroque revolving around major and minor scales, modulating around the cycle of fifths. For anything else, it is basically a misuse. Mass produced equal temperament instruments are used all over the world and basically turn the local music into shlocky pop.
squozzer 8y ago
For some reason, probably coincidence mangled with early-stage dementia, I found this article remarkably similar to https://spectrum.ieee.org/computing/software/the-desperate-quest-for-genomic-compression-algorithms https://spectrum.ieee.org/computing/software/the-desperate-q...

225 points by rwnspace 8y ago

WOW. As a former Music Theory 2 and Music Theory 3 student in college this is awesome. I am also very disappointed in myself for not trying to do something like this and failing earlier in my life. There is really a lot more that could be gained from this work. I am sensing someone's PhD project.

tfeldmann 8y ago

Thank you very much, this is some fantastic content!

deleted 8y ago

[deleted]

snarfy 8y ago

Really good content.

myfonj 8y ago
And form.

joeminichino 8y ago

Absolutely amazing. I'm a coder and a musician and I've been complaining to myself about a certain tendency to repetition in my compositions lately, this is amazing stuff to break patterns.

stelfer 8y ago

Thank you

Kagerjay 8y ago

This is fascinating! Unfortunately I don't understand even half of it, I've been wanting to learn music theory for some time I should go back and learn to play a musical instrument

TaupeRanger 8y ago
There's not much "music theory" here aside from the knowledge that there are 12 notes which repeat in octaves. He mentions a few modes (phrygian, etc) but that's not particularly esoteric. The rest is relating those ideas to simple mathematical constructs and seeing what comes out.
- jm_l 8y ago
  To understand propriety/coherence (about 2/3 of the way down the page) you'll also need to have an understanding of enharmonics, and perhaps some context on why it's important to be able to know whether an interval is e.g. an augmented 3rd or a perfect fourth.
scrozier 8y ago
I have to agree with TaupeRanger here. This certainly has (almost) nothing to do with playing an instrument. It has little to do with music theory in the traditional sense. This is for the programmer/mathematician side of your brain, primarily. For the musician side, get a little electronic keyboard, poke around at it, and buy an introductory music theory book.

z2 8y ago

For something that puts this to action--Wolfram made a random music generator in 2005 with a ton of scales. http://tones.wolfram.com http://tones.wolfram.com

romaniv 8y ago
I bet this would be #1 comment if something in the process used neural networks and if it wasn't from Wolfram. Anyway, pretty cool generator.

williamdclt 8y ago

Very, very impressive. I don't have time to read everything right now, but just skimming everything this is an incredible resource, even for a non-programmer

well1912 8y ago

Nearly jumped out of my seat when I saw this! Look at how similar our approaches are: http://welliam.github.io/molts/ http://welliam.github.io/molts/ (apologies for how poorly written it is, it's been a few years!) Not that it's a super novel concept, but we both used this for the modes of limited transposition. For me it was an efficient way of generating MOLTs for any equal temperament scale.

adamc 8y ago

Thanks, I hugely enjoyed this.

stephenmm 8y ago

Nice work! If I could make one suggestion it would be to use hex instead of decimal. It would make the numbers easier to remember (shorter) and I think it would be easier to recognize patterns (Ie. whole scale is 0x333 and major scale 0xAB3).

sailfast 8y ago

It's been awhile since I've had the chance to dig into more advanced music theory but this is such an interesting framing of all of the possibilities present in both named and unnamed scales and the relationship of notes. The idea to lay it out mathematically like this and how you frame your overall thinking about scales is great. Bach would appreciate this work. Also reminds me a bit of how folks like Jacob Collier think about harmonies and new ways to arrive at different notes. The more you can internalize these kinds of mathematics, the more you can improvise in new and different ways. Well done! Really enjoyed this.

nu-world-odor 8y ago

buckethead only uses lydian...

naringas 8y ago

pretty good, this has motivated me to do an online post about my own take at similar issues. However I do not assume 12-tet, just the ocatave, so it's slightly different.

kazinator 8y ago

The problem with this is is that it accepts the twelve-tone equal temperament system as a sort of absolute frame of reference, rather than the compromise/approximation that it is. Musical scales are not just check-box menu choices out of twelve-tone equal temperament.

crazynick4 8y ago
Exactly. I would like to see this done using integer ratios to define the frequency intervals. You can still use the octave as a 'start' and 'end' point for the scale to make things simple (although there's no axiom anywhere that says this has to be the case, it's just a good candidate because it's the simplest and most easily recognizable interval, aside from the unison). Since you'd be dealing with a potentially infinite number of intervals, you can start with the 'simplest' 20 or so (using lowest possible integer values to create the distinct ratios). Some would argue that the simplest 40 can be considered musical although that would get you into some seriously dissonant territory, not to mention the amount of possibilities you would have available at that point.
ibejoeb 8y ago
That's the first thing that the author states. I'll bet you know more music than me, but maybe that puts me more into the target audience. It's a very interesting way to explore essentially the whole of western music. I did some similar "modeling" when I was learning, too, mostly because it's an effective way for me to commit things to memory. I remember struggling with using tones/scale degrees or intervals as a basis, just as the author describes. It might not be universal and suitable for high-level academic use, but I don't think there's a problem with it.
- kazinator 8y ago
  The problem is that the twelve-tone system was designed for a very specific "use case", in the context of a certain kind of music: classical/Baroque revolving around major and minor scales, modulating around the cycle of fifths. For anything else, it is basically a misuse. Mass produced equal temperament instruments are used all over the world and basically turn the local music into shlocky pop.

squozzer 8y ago

For some reason, probably coincidence mangled with early-stage dementia, I found this article remarkably similar to https://spectrum.ieee.org/computing/software/the-desperate-quest-for-genomic-compression-algorithms https://spectrum.ieee.org/computing/software/the-desperate-q...