13 limit lament

Hi there,

improvisation in David Canright's 13-limit twelve tone
scale.

1/1 13/12 9/8 7/6 5/4 4/3 11/8 3/2 13/8 5/3 7/4 11/6 2/1

Uses chord 3/2 + 13/8 + 7/4 or 1/1 13/8 7/4 as the
centre and resting point.

Piece is in the nature of a slow lament.

http://members.tripod.com/~robertinventor/tunes/improvisations.htm#13_limit_lament

Robert

Hi Jacky,

Interesting coincidence working with 13/12.

> 13/12 is the first functional semitone found in the harmonic series.

> I wonder if that's why David chose it?

I don't know.

This is what he says on the site:

"
The final, intriguing tuning goes all the way to a 13-limit (see Table). This
includes a complete eight-tone harmonic scale on the 4/3 and a seven-tone one on
1/1. Such scales sound fascinating in their variety, coherence, and newness.
However, the other tonalities (except 3/2 minor) are pretty strange.
"

So the 13/12 would be part of the eight tone harmonic scale on the 4/3

I suppose its notes would be
1/3 (2/3) 1/1 (4/3) 5/3 (2/1) 7/3 (8/3) 3/2 (10/3) 11/3 (4) 13/3 (14/3) 5/1
1 (2) 3 (4) 5 (6) 7 (8) 9 (10) 11 (12) 13 (14) 15

The 13/12 is also 3/2 below the 13/8 as well, with the 13/8 belonging to the seven note harmonic
series
on the 1/1.

1/1 (2/1) 3/1 (4/1) 5/1 (6/1) 7/1 (8/1) 9/1 (10/1) 11/1 (12/1) 13/1
1 (2) 3 (4) 5 (6) 7 (8) 9 (5) 11 (12) 13

I've edited the .mid file to make a score for the page, as best I can.

Robert

Hi Jacky,

I asked David about the 13/12 semitione.

He's talking about the bit I say about it in the 13-limit lament section of the
improvisations page...

"
BTW, your assumption on what I mean when I say "n-tone harmonic scale" is
correct -- the first n odd-number harmonics reduced to an octave scale, or
equivalently the scale from harmonic #n to harmonic #2n.
So that 12-tone scale combines the 8-tone harmonic scale:
4/3 3/2 5/3 11/6 1/1 13/12 7/6 5/4
with the 7-tone harmonic scale:
1/1 9/8 5/4 11/8 3/2 13/8 7/4
to get:
1/1 13/12 9/8 7/6 5/4 4/3 11/8 3/2 13/8 5/3 7/4 11/6
So my choice of 13/12 as the semitone really comes from its relation to 4/3
(and to 13/8); the same semitone occurs from 3/2 to 13/8.
Perhaps you can pass that along to Jacky Ligon.
"

Robert