150ed6

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← 149ed6 150ed6 151ed6 →
Prime factorization 2 × 3 × 52
Step size 20.6797 ¢ 
Octave 58\150ed6 (1199.42 ¢) (→ 29\75ed6)
Twelfth 92\150ed6 (1902.53 ¢) (→ 46\75ed6)
Consistency limit 18
Distinct consistency limit 12

150 equal divisions of the 6th harmonic (abbreviated 150ed6) is a nonoctave tuning system that divides the interval of 6/1 into 150 equal parts of about 20.7 ¢ each. Each step represents a frequency ratio of 61/150, or the 150th root of 6.

Theory

150ed6 is very nearly identical to 58edo, but with the 6/1 rather than the 2/1 being just, which compresses the octave by about 0.577 cents. Like 58edo, 150ed6 is consistent to the 18-integer-limit.

Harmonics

Approximation of harmonics in 150ed6
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -0.58 +0.58 -1.15 +5.45 +0.00 +1.97 -1.73 +1.15 +4.87 +5.30 -0.58
Relative (%) -2.8 +2.8 -5.6 +26.3 +0.0 +9.5 -8.4 +5.6 +23.5 +25.6 -2.8
Steps
(reduced)
58
(58)
92
(92)
116
(116)
135
(135)
150
(0)
163
(13)
174
(24)
184
(34)
193
(43)
201
(51)
208
(58)
Approximation of harmonics in 150edt (continued)
Harmonic 13 14 15 16 17 18 19 20 21 22 23 24
Error Absolute (¢) +5.61 +1.39 +6.02 -2.31 -3.87 +0.58 -10.31 +4.29 +2.54 +4.72 -10.19 -1.15
Relative (%) +27.1 +6.7 +29.1 -11.2 -18.7 +2.8 -49.8 +20.7 +12.3 +22.8 -49.3 -5.6
Steps
(reduced)
215
(65)
221
(71)
227
(77)
232
(82)
237
(87)
242
(92)
246
(96)
251
(101)
255
(105)
259
(109)
262
(112)
266
(116)

Subsets and supersets

Since 150 factors into primes as 2 × 3 × 52, 92ed6 contains subset ed6's 2, 3, 5, 6, 10, 15, 25, 30, 50, and 75.

See also