Diaschismic family: Difference between revisions
m →Srutal archagall: typo |
m →Echidna: commentary |
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=== 11-limit === | === 11-limit === | ||
In the 11-limit the generator of echidna can be interpreted as 11/10, the period complement of 9/7, as a stack of 11/10 and 9/7 makes [[99/70]] which is extremely close to 600{{cent}} and is equal to it if we temper [[9801/9800|S99]]. Three 11/10's then make a 4/3 (tempering [[4000/3993|S10/S11]] thus making 10/9 and 12/11 equidistant from 11/10), implying a flat 4/3. | |||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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=== 13-limit === | === 13-limit === | ||
A surprisingly natural extension to the 13-limit is possible by observing that since we temper [[176/175]], tempering [[351/350]] and [[352/351]] (which sum to 176/175) is very elegant. This is notable as this mapping of 13 is supported by patent val by the three main echidna EDOs of 80, 58 and 22 (the trivial tuning), of which all except 22 are consistent in the [[17-odd-limit]]; see the 17-limit for more details. | |||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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=== 17-limit === | === 17-limit === | ||
In the 17-limit we can equate the half-octave with 17/12 and 24/17 and we can take advantage of the sharp fifth by combining echidna with [[srutal archagall]], leading to a particularly beautiful temperament. [[58edo]] and [[80edo]] are both interesting tunings with different advantages and both are consistent in the 17-limit. | |||
Subgroup: 2.3.5.7.11.13.17 | Subgroup: 2.3.5.7.11.13.17 | ||