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Comment by zokier | Hacker News Reader

I think you need far more basic practical examples how to play the thing, just figuring out a random major chord was a hassle and I still have no idea how to play some specific chord like for example the most basic C major chord. And if I understand it correctly, moving from e.g. major to minor chord requires transposing the right hand with the left-hand keys?

Of course the instrument having hidden state makes all this far more complicated. Would be neat if the key labels would also indicate the absolute note so I wouldn't need to do mental arithmetic here.

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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.

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[1] If you look at equal temperament as a compromise that doesn't get quite the "right" ratios.

[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.)

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?

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.

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?

> I still have no idea how to play some specific chord like for example the most basic C major chord.

The harmonic series or overtones goes:

    1   2   3   4   5   6   7   ...
    C1  C2  G2  C3  E3  G3  B♭3  ...

You could play 1,3,5 to play C1,G2,E3 but this gives notes from three different octaves. What you usually want is C3,E3,G3, and fortunately it's right there: play 4,5,6.

If you know your chord's format in just intonation, there's a (not-so-)secret converter. Type in "play_on_keyboard('4-5-6 15/2 12 10 20/3')" in the F12 console to produce fingering and play it on the keyboard. Maybe I should make this clearer by adding a text box.

EDIT: thanks to your feedback, I added a textbox below the keyboard. It will show how to play things if you can write the ratios of the notes. This may be a helpful map for turning 12 ET into just intonation:

C 16/15 D9/8 6/5 E5/4 F4/3 7/5 G3/2 8/5 A5/3 16/9 B15/8 2

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