Misty

Misty is the regular temperament tempering out the misty comma. It equates the Pythagorean comma with the diesis, and splits this interval into three equal parts, one representing the schisma~diaschisma, and two representing the syntonic comma. Consequently, the octave is also split into three. This temperament, supported by 12et, is notably in the schismic-Pythagorean equivalence continuum, with n = 3.

In the 7-limit, the canonical extension tempers out 3136/3125 and 5120/5103. Possible tunings include 87edo, 99edo and 111edo.

See Misty family for more technical data.

Interval chain

#	Period 0		Period 1		Period 2
	Cents*	Approximate Ratios	Cents*	Approximate Ratios	Cents*	Approximate Ratios
0	0.0	1/1	400.0	63/50	800.0	100/63
1	96.9	135/128	496.9	4/3	896.9	42/25
2	193.7	28/25	593.7	45/32	993.7	16/9
3	290.6	32/27	690.6	112/75	1090.6	15/8
4	387.4	5/4	787.4	63/40	1187.4	125/63, 448/225

* in 7-limit CTE tuning

Tuning spectra

• 7-limit POTE tuning: ~3/2 = 703.0212
• 7-limit CTE tuning: ~3/2 = 703.1448

ET Generator	Eigenmonzo (Unchanged Interval)	Generator (¢)	Comments
7\12		700.000	Lower bound of 9-odd-limit diamond monotone
	4/3	701.955
65\111		702.703
	15/14	702.778
	28/27	702.849
	7/5	702.915
	9/7	702.924
	10/9	702.933	9-odd-limit minimax (error = 1.955¢)
	7/6	703.012
58\99		703.030
	36/35	703.048
	49/48	703.062
	21/20	703.107
	8/7	703.117	7-odd-limit minimax (error = 1.217¢)
	6/5	703.128	5-odd-limit minimax (error = 1.173¢)
	25/24	703.259
	5/4	703.422
51\87		703.448
	16/15	703.910
44\75		704.000
37\63		704.762	Upper bound of 9-odd-limit diamond monotone