User:Overthink/Sandbox

Scratchwork

The following tables show how 15-odd-limit intervals are represented in 5edo. Prime harmonics are in bold; inconsistent intervals are in italics.

15-odd-limit intervals in 5edo (direct approximation, even if inconsistent)

Interval and complement	Error (abs, ¢)	Error (rel, %)
1/1, 2/1	0.000	0.0
15/13, 26/15	7.741	3.2
7/4, 8/7	8.826	3.7
3/2, 4/3	18.045	7.5
13/10, 20/13	25.786	10.7
7/6, 12/7	26.871	11.2
9/8, 16/9	36.090	15.0
9/7, 14/9	44.916	18.7
13/11, 22/13	49.210	20.5
15/11, 22/15	56.951	23.7
9/5, 10/9	57.596	24.0
11/7, 14/11	62.492	26.0
11/8, 16/11	71.318	29.7
11/10, 20/11	74.996	31.2
5/3, 6/5	75.641	31.5
13/9, 18/13	83.382	34.7
11/6, 12/11	89.363	37.2
5/4, 8/5	93.686	39.0
13/12, 24/13	101.427	42.3
7/5, 10/7	102.512	42.7
11/9, 18/11	107.408	44.8
13/7, 14/13	111.702	46.5
15/8, 16/15	111.731	46.6
15/14, 28/15	119.443	49.8
13/8, 16/13	119.472	49.8

15-odd-limit intervals in 5edo (patent val mapping)

Interval and complement	Error (abs, ¢)	Error (rel, %)
1/1, 2/1	0.000	0.0
15/13, 26/15	7.741	3.2
7/4, 8/7	8.826	3.7
3/2, 4/3	18.045	7.5
13/10, 20/13	25.786	10.7
7/6, 12/7	26.871	11.2
9/8, 16/9	36.090	15.0
9/7, 14/9	44.916	18.7
9/5, 10/9	57.596	24.0
11/7, 14/11	62.492	26.0
11/8, 16/11	71.318	29.7
5/3, 6/5	75.641	31.5
13/9, 18/13	83.382	34.7
11/6, 12/11	89.363	37.2
5/4, 8/5	93.686	39.0
13/12, 24/13	101.427	42.3
7/5, 10/7	102.512	42.7
11/9, 18/11	107.408	44.8
15/8, 16/15	111.731	46.6
13/8, 16/13	119.472	49.8
15/14, 28/15	120.557	50.2
13/7, 14/13	128.298	53.5
11/10, 20/11	165.004	68.8
15/11, 22/15	183.049	76.3
13/11, 22/13	190.790	79.5

Whatever

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25 September 2026

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24 September 2026

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