Re: an 11 and 13 flavour 7 note scale

Hi there,

Following on from 7-tet with its near 11/9s,
here is a piece in a scale with pure 11/9s.

As usual:
http://tunesmithy.netfirms.com/tunes/tunes.htm

scale is
1/1 12/11 11/9 4/3 3/2 13/8 11/6 2/1

I find the 11/9s kind of very beautiful,
but a little kind of cold beauty somehow.
While 13/8 I find very warm. So adding that
in helps to make a balanced scale I think.

The 11/9 is very close to mid point between
1/1 and 3/2 as 11/9 * 11/8 = 121/81.
This is the 243/242 comma.

So this scale has the 11/9 "diminished seventh"
as 1/1 11/9 3/2 11/6.

Ratio from 13/8 to 12/11 is also close to 3/2
- this time, by the 144/143 comma.

13/8 is fairly close to 5/3 (ratio 39/40), so the
interval from 4/3 to 13/8 is fairly close to 5/4.

After composing in 7-tet, kind of refreshing to have
a go at a scale with pure 3/2s and 4/3s in it!
Especially as it also has the pure 11/9s too.

Here is the Scala listing for the intervals of the scale:

Interval class, Number of incidences, Size:
1: 1 13/12 138.573 cents tridecimal 2/3-tone
1: 3 12/11 150.637 cents 3/4-tone, undecimal neutral second
1: 1 121/108 196.771 cents
1: 1 9/8 203.910 cents major whole tone
1: 1 44/39 208.835 cents
2: 1 144/121 301.274 cents two (3/4-tone, undecimal neutral second)
2: 1 39/32 342.483 cents 39th harmonic
2: 3 11/9 347.408 cents undecimal neutral third
2: 1 27/22 354.547 cents neutral third, Zalzal's wosta
2: 1 16/13 359.472 cents tridecimal neutral third
3: 1 117/88 493.120 cents
3: 3 4/3 498.045 cents perfect fourth
3: 1 192/143 510.109 cents
3: 2 11/8 551.318 cents undecimal semi-augmented fourth
4: 2 16/11 648.682 cents undecimal semi-diminished fifth
4: 1 143/96 689.891 cents
4: 3 3/2 701.955 cents perfect fifth
4: 1 176/117 706.880 cents
5: 1 13/8 840.528 cents tridecimal neutral sixth
5: 1 44/27 845.453 cents neutral sixth
5: 3 18/11 852.592 cents undecimal neutral sixth
5: 1 64/39 857.517 cents 39th subharmonic
5: 1 121/72 898.726 cents
6: 1 39/22 991.165 cents
6: 1 16/9 996.090 cents Pythagorean minor seventh
6: 1 216/121 1003.229 cents
6: 3 11/6 1049.363 cents 21/4-tone, undecimal neutral seventh
6: 1 24/13 1061.427 cents
Highest number of different intervals for one interval class: 5

Robert