# ennealimmal

[Joe Monzo]

A musical tuning temperament family, discovered and named by Gene Ward Smith.

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[data from Gene Ward Smith Yahoo tuning-math message 11967 (Thu Apr 14, 2005 11:47 am)]

 family name: ennealimmal, 72&99 period: 1/9 octave, or 133 & 1/3 cents. Very nearly 27/25 ratio generator: 36/35 ratio or 21/20 ratio
###### 5-limit
 name: ennealimmal comma: ennealimma = 2 / (27/25)^9 = 2,3,5-monzo |1 -27 18> = ~0.861826202 cents prime mapping: [<9 15 22|, <0 -2 -3|] period, generator 5-limit generator: 250/243 ratio poptimal generators: 68/1665-edo, 37/906-edo TOP period: 133.3322145 cents TOP generator: 49.0061286 cents TOP mapping: <1199.98993 1901.97096 2786.29033| cents MOS cardinalities: 18, 27, 45, 72, 99, 171, 270, 441, 612, 1503, 1665
###### 7-limit
 name: ennealimmal wedgie: <<18 27 18 1 -22 -34|| prime mapping: [<9 15 22 26|, <0 -2 -3 -2|] period, generator poptimal generator: 43/1053-edo, 61/1494-edo, 49/1200-edo (from the last, exactly 49 cents is a poptimal generator.) TOP period: 133.3373752 cents TOP generator: 49.0239856 cents TOP mapping: <1200.03638 1902.01266 2786.35030 3368.72378| cents TM basis: {2401/2400, 4375/4374} ratios MOS cardinalities: 18, 27, 45, 72, 99, 171, 270, 441, 612, 1053
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[Joe Monzo]

## Tonescape lattices of ennealimmal-45

Below are screen-shots of Tonescape lattices of ennealimmal-45 tuning, with the syntonic-comma and ennealimma as the two unison-vectors:

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