From Xenharmonic Wiki
Jump to: navigation, search


All discussion below is archived from the Wikispaces export in its original unaltered form.
Please do not add any new discussion to this archive page.
All new discussion should go on Talk:EDF.

Can't understand this temperament

Okay, I've been trying to figure this out because it sounds weird and interesting, but it's not making sense.

I'm going off of this:

"...the 8:9:10:(12) chord as exactly analogous to the 4:5:6:(8) chord in meantone..."

Now, in meantone, the "third" 5/4 and the "fifth" 3/2 are related in this way: (3/2)^4/((5/4)*(2/1)^2) = 81/80 -> 1/1.

If you're telling me that 8:9:10 chords should do the "exactly analogous" thing, that makes me think that (5/4)^4/((9/8)*(3/2)^2) should be the comma that is tempered out. That's 625/648, the same comma as diminished.

This is all well and good and makes sense as a 5-limit temperament with 3/2 as the period (and either 6/5 or 5/4 as a generator). However, the MOS series of this temperament goes:

2edf, 3edf, 5edf, 7edf, 12edf, 19edf, 26edf, 33edf...

So your 9+11=20 scale doesn't pop out of the temperament I found at all. There must be some mistake somewhere?

What is the comma tempered out of your scale?

- keenanpepper December 26, 2011, 09:10:33 PM UTC-0800

Just going by the MOS numbers (9,11,20) it seems like you might be talking about the temperament with the comma 15625/15552 (period 3/2, generator 6/5 or 5/4), but I have no idea how to interpret the "exactly analogous" statement.

- keenanpepper December 26, 2011, 10:35:42 PM UTC-0800

Ha! My fault, it isn't "exactly". I wasn't thinking of how many 5/4 tempered flat end up with 9/8 just that they do. Sorry!

Good stuff with the edf/edo correspondences.

- Kosmorsky December 27, 2011, 01:14:37 AM UTC-0800

Oh, ok. So you meant that 5/4 is the generator and a bunch of them (not necessarily 4), reduced by 3/2, gives you 9/8.

So this is equivalent to the 15625/15552 temperament then, right?

(And the 648/625 temperament is something different I just accidentally discovered...)

- keenanpepper December 27, 2011, 06:58:19 AM UTC-0800

15625/15552 it is, indeed. Should be 6 of them instead of 4.

- Kosmorsky December 27, 2011, 11:49:02 AM UTC-0800

That's cool man. Totally different musical perspective on what's mathematically "the same" as hanson temperament.

- keenanpepper December 27, 2011, 09:14:44 PM UTC-0800