11edt

← 10edt

11edt

12edt →

Prime factorization	11 (prime)
Step size	172.905¢
Octave	7\11edt (1210.34¢) (semiconvergent)
Consistency limit	5
Distinct consistency limit	4

11edt means the division of 3, the tritave, into 11 equal parts of 175.905 cents each, corresponding to 6.940 edo. It can therefore be seen as a very stretched version of 7edo, with octaves sharpened by ten and a third cents. The octave stretching makes the fifth in better tune, and of course the twelfth is the pure 3/1 tritave.

From a no-two point of view, it tempers out 49/45 and 15625/15309 in the 7-limit and 35/33 and 77/75 in the 11-limit.

Intervals

#	Cents	Hekts	Approximate ratios	Arcturus nonatonic notation (J = 1/1)
0			1/1	J
1	172.9	118.1	11/10, 10/9	J#, Kb
2	345.8	236.2	11/9	K
3	518.7	354.3	4/3, 27/20	L
4	691.6	472.4	3/2, 40/27	M
5	864.5	590.5	5/3, 28/17, 105/64	N
6	1037.4	708.6	29/16, 20/11, 64/35	N#, Ob
7	1210.3	826.7	2/1	O
8	1383.2	944.8		P
9	1556.1	1062.9		Q
10	1729	1181		R
11	1902	1300		J

Prime harmonics

Approximation of prime harmonics in 11edt

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	absolute (¢)	+10.3	+0.0	-19.8	-83.6	-1.6	+55.0	-63.6	-83.3	-68.2	+49.2	-66.3
	relative (%)	+6	+0	-11	-48	-1	+32	-37	-48	-39	+28	-38
Steps (reduced)		7 (7)	11 (0)	16 (5)	19 (8)	24 (2)	26 (4)	28 (6)	29 (7)	31 (9)	34 (1)	34 (1)

Scala file

Tuning in scala format is as follows:

! E:\cakewalk\scales\11_of_tritave.scl

!

11 in tritave

!

172.90500

345.81000

518.71500

691.62000

864.52500

1037.43000

1210.33500

1383.24000

1556.14500

1729.05000

3/1

Pieces

Mozart's sonata #11 in A Major K331 in 11 EDT (using a 11 => 12 key mapping so octaves become tritaves)

Frozen Time Occupies Wall Street by Chris Vaisvil =>information about the piece

Molly's Playground by Chris Vaisvil => information about the piece