understanding 15 EDO

(If anyone wants to comment to this that's fine. Please try to be as
simple as possible.)

Is it common to alter 15 EDO to make it fifths significatly less than 720
cents?
I was considering creating a wolf fifth starting at the note that is
640 cents up.
(Some kind person wrote to me earlier in the month with several
variations of
15 EDO. I unfortunately lost the information and name.)

Also, since a comma is about 25 cents, and the fifths are about 20 cents
sharp,
are these 2 things related? What are "vanishing commas"? Does 12 EDO
have them
and why? Does 15 EDO have them and why?

Thanks,
Stephen Szpak

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--- In tuning@yahoogroups.com, "Stephen Szpak" <stephen_szpak@h...>
wrote:
>
> (If anyone wants to comment to this that's fine. Please try to be
as
> simple as possible.)
>
>
> Is it common to alter 15 EDO to make it fifths significatly less
than 720
> cents?

I wouldn't call anything involving 15 common, but I have proposed 15
out of 27-et, or tripletone[15], as a scale.

> Also, since a comma is about 25 cents, and the fifths are about
20 cents
> sharp,
> are these 2 things related? What are "vanishing commas"? Does
12 EDO
> have them
> and why? Does 15 EDO have them and why?

Any equal temperament has them. Both 12 and 15 have 400 cent major
thirds, so they share 128/125 as a vanishing comma.

--- In tuning@yahoogroups.com, "Stephen Szpak" <stephen_szpak@h...>
wrote:
>
> (If anyone wants to comment to this that's fine. Please try to be
as
> simple as possible.)
>
>
> Is it common to alter 15 EDO to make it fifths significatly less
than 720
> cents?

You can view it as altering 15-equal, or perhaps better is to view 15-
equal as the alteration of such scales. Gene gave you a couple of
great examples. Another important one, at least for 5-limit, would be
Kleismic-15:

0
68.319
180.44
248.76
317.08
385.4
497.52
565.84
634.16
702.48
814.6
882.92
951.24
1019.6
1131.7

Lots of quite pure major and minor triads here.

> are these 2 things related? What are "vanishing commas"? Does
>12 EDO
> have them
> and why? Does 15 EDO have them and why?

I'm glad you finally (and pretty quickly) understood Gene's comment
on this. More could be said. See my reply to Mark, which I hope
you'll read and try to follow. In that post I brought up the 'maximal
diesis', which can be expressed as 250;243 -- it vanishes in 15-equal
but not in 12-equal. This implies certain 'porcupine' scale
formations and chord progressions which work in 15-equal but not in
12-equal -- Herman Miller has explored these in his music. Meanwhile,
perhaps the most important comma of all, the 'syntonic comma' or
simply 'the comma' or 81;80, vanishes in 12-equal but not in 15-
equal; thus most conventional common-practice triadic diatonic music
will work in 12-equal but not in 15-equal.