my lattice metric

As promised, an 'octave'-specific table of some ratios ranked
according to complexity by my lattice metric formula:

2/1 2.0
3/2 4.8
7/6 5.9
6/5 6.2
7/4 6.7
4/3 6.8
5/4 7.6
11/9 8.0
9/5 8.1
9/7 8.4
11/5 8.6
13/9 9.4
9/4 9.7
11/10 10.6
11/6 10.9
15/8 11.2
10/7 11.4
13/6 11.4
9/8 11.6
7/5 12.0
13/12 12.1
24/13 13.1
40/27 14.7
25/16 15.3
13/8 15.9
27/16 16.4
11/8 16.9
45/32 17.4
99/80 22.1
81/64 23.2
225/128 24.3

(BTW, on my last table I made the error of calling 225/128
225/224)

One big problem I see is that 5:4, 6:5, and 7:6 are ranked
in this order with *decreasing* complexity, the opposite of
what it seems it should be. In fact, even 7:4 is ranked
as simpler than 5:4! This will not do.

There was some discussion here a few weeks ago about
the possibility of 13:8 being more consonant or less complex
than 11:8. It is interesting that my 'octave'-specific metric
computes them that way too.

Also, 11:6 shows up as being just a little less complex than
15:8, which is encouraging to me, as I like it to use 11:6 as
a pseudo-'major 7th'.

-monz

Joseph L. Monzo monz@juno.com
http://www.ixpres.com/interval/monzo/homepage.html
|"...I had broken thru the lattice barrier..."|
| - Erv Wilson |
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