Misty

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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