# kwazy [temperament]

[Joe Monzo]

generator = ~9/7 ratio, ~163 cents
period = 600 cents
tempers 3,5-prime-space.

 sample {ET \ period \ generator} realizations { 118 \ 59 \ 16} { 494 \ 247 \ 67} { 612 \ 306 \ 83} { 730 \ 365 \ 99} {1342 \ 671 \ 182} (2 , 3 , 5) map in terms of [period, generator] ( [2, 0] , [1, 8] , [6, -5] ) [period, optimal generator] (cents) [600, 162.741892] optimum RMS error (cents) 0.017725 comma name(s) kwazy-comma comma {2 3 5}-monzo | -53 10, 16 > comma ratio ~9.01016E+15 : ~9.0072E+15 comma ~cents 0.569430491

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[adapted from Gene Ward Smith, Yahoo tuning-math, message 12030 (Tue Apr 26, 2005 10:47 pm)]

The nexus between the two divisions [494-edo and 612-edo] is of course 494&612, which is kwazy. In the 5-limit it is defined by the kwazy comma of 2,3,5-monzo |-53 10, 16 >, (approximately the ratio 9.01016E+15 : 9.0072E+15), about 4/7 of a cent in size (more precisely, ~0.569430491 cent).

This leads to a 5-limit temperament with a half-octave period and a generator which is a schisma larger than 9/7, and hence is a "quasi" 9/7. The 5-limit Graham complexity of 26 is high, as expected for a microtemperament, but much less than the 7-limit or 11-limit Graham complexity of 162. In kwazy, you get a lot of essentially just 5-limit harmony, and the "quasi" 7-limit, before eventually the 11-limit turns up.

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