> How would that be better?

It would be better because a fifteenth is a double octave, but eight times two is not fifteenth.

> Again, how module arithmetic is simpler than a simple deduction from 9?

Because you'd be able to base both concepts on octaves (well, renamed to sevenths) being seven steps on the scale.

I still don't see it being much better in practice. It's pretty rare to use ordinals to refer to intervals greater than 2 octaves. There is really virtually no cognitive load required to hear "major tenth" and realize that it's a major 3rd plus an octave.

There's virtually no cognitive load if you already know music theory. That's a very important distinction - music theory in its current state is completely undiscoverable for no good reason.

How undiscoverable? I grew up in a fairly music-oriented family and played a lot of instruments as a kid, but didn't formally study music theory. It wasn't until I read parent that I realized "fifth", "third", etc. are 1-indexed ordinals, and not some inscrutable scheme involving fractions. Everything suddenly makes way more sense.

I feel fairly confident that sane terminology would greatly ease this problem.

> That's a very important distinction - music theory in its current state is completely undiscoverable for no good reason.

I don't doubt that it could be improved, but I don't think it's all that bad, considering how many people do learn music theory.

Pretty irrelevant but that reminded me of this scene from Cannibal the Musical [0]. The whole video is worth watching, especially if you've seen the rest of the movie but I only linked to the music theory argument. The movie is one of Trey Parker's earlier works and is quite entertaining [1].

Coming from a family of musicians and artists, it's all pretty foreign to me. And I used to take lessons, and occasionally sit and work my way through a beginner guitar book. I've always heard music theory to be pretty obtuse and challenging. I'm sure if I put in some hours to understand the fundamentals it'd make a lot more sense, and read it at home with a little dedication it'd be a bit easier. It's truly interesting.

[0] - https://www.youtube.com/watch?v=pF8oIKLlBsI#t=132 [1] - http://www.imdb.com/title/tt0115819/?ref_=fn_al_tt_1

> There is really virtually no cognitive load required to hear "major tenth" and realize that it's a major 3rd plus an octave.

Maybe not for you, but it certainly took me a moment to convince myself that that is true.

Just use modulo-seven arithmetic...

Er, yes, I believe that's the point the grandparent was making (and the parent was disagreeing with)

I was just trying to show that changing the indexing from zero- to one-based makes no difference in this case. The same-octave interval will always be the multi-octave interval mod 7, regardless of whether you call the tonic 0 or 1.

Granted, but I was replying to a post stating that "it" is not better in practice, where "it" is using 0 base, mod 7 arithmetic.

Anyway, yes, you've shown correctly that mod 7 arithmetic is useful, proving half the great-great-somethingth-parent's point. Now, the remaining interesting cases are the inversion case and the multiplication case, where 0 based is simpler (for me) than 1 based.

Also, the idea of using the word "octave" for "mod 7" is already pretty broken, and is what caused me my initial hesitation.

There is some cognitive load, but it is certainly no more than it would be to hear "Major 9th" and realize that it's a Major 2nd plus an octave, as it would be in the zero-indexed case.

It's really no more than a matter of semantics, Any interval mod-7 gives you the number of the scale degree on which the interval lands within the current octave. This doesn't change if with zero-indexing.

A Major 10th mod-7 is a Major 3rd regardless of zero or one-based indexing, the only difference is which notes in the current key you're actually talking about (in the key of C it would be E or D for one-based and zero-based indexing respectively)

I don't know that it's any easier to remember "the tonic is 0" than it is to remember "the tonic is 1"

>It would be better because a fifteenth is a double octave, but eight times two is not fifteenth.

If you are concerned about that, then wouldn't calling an octave "a seventh" (your proposed fix) be equally concerning? Eight (octave) is not seven.

You seem to be missing the point. An octave is a difference of seven scale steps, just like a second is a difference of one scale step, and a unison (a "first") is a difference of no scale steps.

The fact that this interval of seven notes is called an "octave", named after the number 8, is entirely because of our 1-based system that double-counts the note you start on.

If we had a 0-based system, it wouldn't be called an "octave". It would be named after the number 7. Let's call it a 7-interval, to avoid confusion with actual music terms.

In a 0-based system, you could say, for example, that two 2-intervals make a 4-interval because 2 * 2 = 4.

In the 1-based system we really have, you have to say "two thirds make a fifth", and the mathematical connection is not obvious.

> How would that be better? The 7th, 14th, 21st, etc would all be octaves of the root. Currently it's the 8th, the 15th, 23rd, which is much less intuitive.

Minor nitpick: 22nd would be an octave not 23rd... mod-7 still works, its just that you get a 1 back because the root is currently defined as scale degree 1

You're right, good catch.