3 ms·

I don't know how practical that is, but you can figure it out analytically. In equal temperament, you can find the frequency ratio of two notes in an interval

I don't know how practical that is, but you can figure it out analytically. In equal temperament, you can find the frequency ratio of two notes in an interval by raising 2 to the power of X/12, where X is the number of semitones. Once you know that, you can look for some green numbers that, when divided, would have that same ratio. So to make a chord, you figure out the ratios. Here's an example for major triads. First, some math to go from equal temperament to ratios. A major third is 4 semitones, so that's 2*(4/12), and a perfect fifth is 7 semitones, so that's 2*(7/12). Those work out to 1.2599 and 1.4983. They're really "supposed"[1] to be 1.25 and 1.5, i.e. 5/4 and 3/2. So now that you know these ratios, you can look for 3 numbers that satisfy the two ratios. If you change 3/2 into 4/6, then it becomes pretty clear that 4 and 5 will satisfy the 5/4 ratio (giving you a major third) and that 4 and 6 will satisfy the 6/4 ratio (giving you a perfect fifth). So to get a major triad, you can play 4, 5, and 6. With similar reasoning, you can figure out that 10, 12, and 15 form a minor triad. ---- [1] If you look at equal temperament as a compromise that doesn't get quite the "right" ratios.

adrianmonk 3y ago
[Too late to edit, replying to myself...] That's supposed to be 2**(4/12) and 2**(7/12) above. I forgot to escape the asterisks. (It's exponentiation, not multiplication.)
fercircularbuf 3y ago
You appear to know what you're talking about (I certainly don't), but it also seems to me that the knowledge in this post is not accessible to I would imagine the vast majority of people. Do you have any recommendations for where to start learning about this kind of thing aimed at music theory troglodytes like myself?
- sampo 3y ago
  Music theory is ... is like git. The underlying framework is pretty nice and based on only a small set of basic principles. But the user interface is badly designed and none the tutorials explain it well. Once you understand the basic principles, you're good. But no one has figured out how to explain things to a new person.
  - mtsr 3y ago
    But since you can't get much use out of music theory without going through some user interface (a particular instrument or notation), you also need to learn how it's laid out (how one maps onto the other, really). But maybe something like this keyboard could be an interesting teaching tool?

adrianmonk 3y ago

[Too late to edit, replying to myself...] That's supposed to be 2**(4/12) and 2**(7/12) above. I forgot to escape the asterisks. (It's exponentiation, not multiplication.)

fercircularbuf 3y ago

You appear to know what you're talking about (I certainly don't), but it also seems to me that the knowledge in this post is not accessible to I would imagine the vast majority of people. Do you have any recommendations for where to start learning about this kind of thing aimed at music theory troglodytes like myself?

sampo 3y ago
Music theory is ... is like git. The underlying framework is pretty nice and based on only a small set of basic principles. But the user interface is badly designed and none the tutorials explain it well. Once you understand the basic principles, you're good. But no one has figured out how to explain things to a new person.
- mtsr 3y ago
  But since you can't get much use out of music theory without going through some user interface (a particular instrument or notation), you also need to learn how it's laid out (how one maps onto the other, really). But maybe something like this keyboard could be an interesting teaching tool?