Keemun

Keemun is an extension of the hanson temperament, and tempers out 49/48, 56/55, and 100/99 in the 11-limit. This means it uses the same simple mappings for the 7th and 11th harmonics as orgone. Unfortunately, the optimal tunings for the 3rd and 5th harmonics is substantially flatter than that for the 7th & 11th ones, requiring you to compromise one set for the other. The edos that support keemun in their patent vals are 4edo, 15edo, 19edo, and 34edo, with 49d and 64bde coming closer to balancing the errors equally.

Keemun

Subgroups	2.3.5.7
Comma basis	49/48, 126/125
Reduced mapping	⟨1; 6 5 3]
ET join	15 & 19
Generators (CWE)	~6/5 = 316.8 ¢
MOS scales	4L 3s, 4L 7s, 4L 11s, 15L 4s
Ploidacot	alpha-hexacot
Minimax error	7-odd-limit: 17.8 ¢
Target scale size	7-odd-limit: 7 notes

This temperament was originally discovered by Dave Keenan and named by Herman Miller in 2006 after the Chinese black tea.

See Kleismic family #Keemun for technical data.

Interval chain

#	Cents*	11-limit ratios	13-limit ratios
			Keemun (4 & 19)	Kema (15 & 19)	Kumbaya (4 & 15)
0	0.000	1/1
1	317.576	6/5			13/11, 16/13
2	635.151	10/7, 16/11		13/9
3	952.727	7/4, 12/7	22/13	26/15
4	70.302	21/20, 25/24, 33/32, 36/35			14/13
5	387.878	5/4, 14/11	16/13
6	705.453	3/2			20/13
7	1023.029	9/5, 20/11			24/13
8	140.605	12/11, 15/14	14/13	13/12
9	458.180	9/7, 21/16		13/10
10	775.756	25/16	20/13
11	1093.331	15/8	24/13	13/7
12	210.907	9/8			15/13
13	528.482	15/11			18/13
14	846.058	18/11	21/13	13/8
15	1163.634	27/14	25/13
16	281.209		15/13	13/11
17	598.785	45/32	18/13
18	916.360	27/16
19	33.936	81/80

* In 11-limit POTE tuning, octave reduced

Music

Chris Vaisvil

• The Fallen of Kleismic[15] – blog | play – in 53edo