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Another 13-limit hole scale

🔗Gene Ward Smith <gwsmith@svpal.org>

3/26/2005 3:18:41 PM

The hole of radius sqrt(7)/2 around [1/2,1/4,1/4,1/4,1/4] contains 10
notes and is wrapped in the following ball scales:

Shell 1 radius sqrt(7)/2
[3, 5, 7, 9, 11, 13, 15, 21, 33, 39]

Scale 10 notes
[1, 13/12, 7/6, 5/4, 11/8, 3/2, 13/8, 5/3, 7/4, 11/6]

Shell 2 radius sqrt(15)/2
[1, 5/3, 7/3, 11/3, 13/3, 35/3, 55/3, 65/3, 77/3, 27, 91/3, 35, 45,
143/3, 55, 63, 65, 77, 91, 99, 117, 143]

Scale 32 notes
[1, 33/32, 77/72, 13/12, 10/9, 9/8, 55/48, 7/6, 39/32, 11/9, 5/4,
91/72, 21/16, 4/3, 65/48, 11/8, 13/9, 35/24, 143/96, 3/2, 55/36, 14/9,
77/48, 13/8, 5/3, 7/4, 65/36, 11/6, 15/8, 91/48, 35/18, 143/72]

Shell 3 radius sqrt(23)/2
[15/13, 15/11, 21/13, 21/11, 15/7, 33/13, 35/13, 35/11, 45/13, 39/11,
35/9, 45/11, 21/5, 55/13, 33/7, 63/13, 39/7, 63/11, 65/11, 77/13,
55/9, 45/7, 33/5, 65/9, 99/13, 39/5, 55/7, 105/13, 91/11, 77/9, 65/7,
105/11, 91/9, 117/11, 63/5, 165/13, 99/7, 77/5, 143/9, 117/7, 195/11,
231/13, 91/5, 99/5, 143/7, 117/5, 165/7, 273/11, 195/7, 143/5, 231/5,
273/5, 429/7, 429/5, 105, 165, 195, 231, 273, 429]

Scale 92 notes
[1, 65/64, 55/54, 33/32, 91/88, 21/20, 55/52, 35/33, 77/72, 15/14,
14/13, 13/12, 35/32, 11/10, 10/9, 143/128, 9/8, 91/80, 55/48, 15/13,
65/56, 7/6, 33/28, 13/11, 143/120, 77/64, 65/54, 39/32, 11/9, 5/4,
91/72, 33/26, 14/11, 143/112, 77/60, 35/27, 13/10, 55/42, 21/16,
143/108, 4/3, 35/26, 65/48, 15/11, 11/8, 91/66, 39/28, 7/5, 55/39,
91/64, 77/54, 10/7, 13/9, 35/24, 65/44, 77/52,143/96, 3/2, 91/60,
55/36, 20/13, 65/42, 14/9, 11/7, 35/22, 77/48, 21/13, 13/8, 33/20,
5/3, 91/54, 22/13, 143/84, 55/32, 7/4, 39/22, 143/80, 70/39, 65/36,
20/11, 11/6, 13/7, 15/8, 91/48, 21/11, 77/40, 35/18, 39/20, 55/28,
65/33, 77/39, 143/72]

Once again, Harry or 130-equal might be considered for a tempering.