
A study of musical scales (2017) - rwnspace
https://ianring.com/musictheory/scales/
======
kazinator
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.

~~~
thomasahle
When I first learned about music theory, it surprised me how common this is. I
liked the idea of scales that made certain intervals sound nice in terms of
simple fractions, and wrote a computer program to search for them. I found an
interesting scale and posted it to the music stackexchange:
[https://imgur.com/a/iBwxC4T](https://imgur.com/a/iBwxC4T)

It caused a long discussion between the people there, and I learned a lot, but
my post was eventually deleted. Somebody posted a follow-up question trying to
figure out what the terms were really supposed to mean, but it doesn't seem to
me they ever managed to agree:
[https://music.stackexchange.com/questions/66620](https://music.stackexchange.com/questions/66620)

~~~
crazynick4
I think a tuning is a set of intervals which an instrument is configured to
play. A tuning is also a temperament if it is a compromise of another tuning
in order to make the configuration technically feasible (or for other
convenience reasons). A scale is then some combination of notes within a
tuning or temperament? I don't know, it seemed like they were more concerned
with nitpicking words than answering your actual question, which was
interesting and not hard to understand.

~~~
analog31
That seems like a reasonable definition. In my view, temperaments only apply
to keyboard and electronic instruments. String instruments are tuned so the
open strings are in perfect intervals, then we just cope with it. Wind
instruments are all over the place, depending on how you blow and how loud. I
saw a viola da gamba with double frets, and the gambist told me it was so he
could manage different temperaments. An orchestra is untempered, for all
practical purposes.

I think that a scale and its temperaments are in addition to being an artistic
choice, also a _technology_. Prior to electronic music and professional
technicians, a tuning system had to be something that a musician could carry
out themselves, possibly quite frequently. The 12 tone system is the simplest
consonant system, possibly making it the easiest and quickest to tune.

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baldfat
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.

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stephenmm
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).

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z2
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
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.

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well1912
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.

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sailfast
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.

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joeminichino
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.

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squozzer
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-q...](https://spectrum.ieee.org/computing/software/the-desperate-
quest-for-genomic-compression-algorithms)

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naringas
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.

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Kagerjay
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
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
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.

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williamdclt
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

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snarfy
Really good content.

~~~
myfonj
And form.

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tfeldmann
Thank you very much, this is some fantastic content!

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adamc
Thanks, I hugely enjoyed this.

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stelfer
Thank you

