15/8

>From: "traktus5" <kj4321@h...>
>Date: Thu Aug 19, 2004 1:58 pm
>Subject: 15/8

>Hello group. Harmonic entropy site's kind 'a deserted, so I thought
>I would post here...Does anyone know why the the main harmonic
>entropy graph does not include 15/8?

It does include 15/8 -- in fact it includes every interval between 0
and 2400 cents. If you locate the point on the horizontal axis at
about 1088 cents, and find the point on the curve directly above
that, you'll see the harmonic entropy for 15/8.

I only explicitly labeled the ratios that fell at local minima of
this graph. Other graphs, which you can find in the files folder of
this group as well as the tuning group, do show local minima at 15/8
and other ratios of such complexity. See, for example,

/harmonic_entropy/files/dyadic/margo.gif

>(15/8 is a personal favorite of mine; leading tone
>and tonic combined in one chord!

In the context of these harmonic entropy graphs, it's no more leading
tone and tonic than mediant and subdominant or any other random pair
of notes a 15/8 apart. Tonal context is not part of harmonic entropy -
- harmonic entropy only treats sounds in isolation, and the
experience of dissonance has a whole lot to do with context (such as
tonal context) too.

>..., and, to my ear, and in my choice
>of chord construction, it serves as a 'near-octave....)

Well, this near-octaveness is one reason it doesn't usually show up
as a local minima of harmonic entropy. The ratios 13/7, 15/8, 17/9,
21/10, *and* 2/1 are all competing when you hear, say, a major
seventh in 12-equal (which, I'm guessing at this point, is the tuning
you're actually using in practice).

thanks, Kelly