172edo: Difference between revisions

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Using the 172c val, it tempers out the [[diaschisma]], 2048/2025 and {{monzo| 1 36 -25 }} in the 5-limit; [[4375/4374]], [[50421/50000]], and 110592/109375 in the 7-limit; [[176/175]], [[896/891]], and 1331/1323 in the 11-limit. Using the alternative 172cf val, [[196/195]], 1716/1715, [[2080/2079]], [[2197/2187]], and [[2200/2197]] are tempered out in the 13-limit. Using the alternative 172cef val, it tempers out [[441/440]], 1344/1331, and [[3388/3375]] in the 11-limit; 196/195, [[352/351]], [[832/825]], [[1001/1000]], and 2197/2187 in the 13-limit.

Using the 172b val, it tempers out the [[unicorn comma]], 1594323/1562500 and 2197265625/2147483648 in the 5-limit; [[1728/1715]], [[3645/3584]], and [[390625/388962]] in the 7-limit; [[441/440]], 1944/1925, [[4000/3993]], and 4125/4096 in the 11-limit; [[625/624]], 975/968, [[1188/1183]], [[1287/1280]], and [[1573/1568]] in the 13-limit. Using the alternative 172bdee val, it tempers out [[225/224]], 118098/117649, and 3176523/3125000 in the 7-limit; [[243/242]], 1617/1600, 2079/2048, and 117649/117128 in the 11-limit; [[351/350]], 625/624, 1188/1183, and 1573/1568 in the 13-limit.

Using the 172b val, it tempers out the [[unicorn comma]], 1594323/1562500 and 2197265625/2147483648 in the 5-limit; [[1728/1715]], [[3645/3584]], and [[390625/388962]] in the 7-limit; [[441/440]], 1944/1925, [[4000/3993]], and [[4125/4096]] in the 11-limit; [[625/624]], 975/968, [[1188/1183]], [[1287/1280]], and [[1573/1568]] in the 13-limit. Using the alternative 172bdee val, it tempers out [[225/224]], 118098/117649, and 3176523/3125000 in the 7-limit; [[243/242]], 1617/1600, 2079/2048, and 117649/117128 in the 11-limit; [[351/350]], 625/624, 1188/1183, and 1573/1568 in the 13-limit.

Using the 172f val, every 7 steps is an excellent approximation of the ninth no-2 zeta peak - associated with [[39edt]] - in the 13-limit.

=== Odd harmonics ===

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 Using the 172c val, it tempers out the [[diaschisma]], 2048/2025 and {{monzo| 1 36 -25 }} in the 5-limit; [[4375/4374]], [[50421/50000]], and 110592/109375 in the 7-limit; [[176/175]], [[896/891]], and 1331/1323 in the 11-limit. Using the alternative 172cf val, [[196/195]], 1716/1715, [[2080/2079]], [[2197/2187]], and [[2200/2197]] are tempered out in the 13-limit. Using the alternative 172cef val, it tempers out [[441/440]], 1344/1331, and [[3388/3375]] in the 11-limit; 196/195, [[352/351]], [[832/825]], [[1001/1000]], and 2197/2187 in the 13-limit.
-Using the 172b val, it tempers out the [[unicorn comma]], 1594323/1562500 and 2197265625/2147483648 in the 5-limit; [[1728/1715]], [[3645/3584]], and [[390625/388962]] in the 7-limit; [[441/440]], 1944/1925, [[4000/3993]], and 4125/4096 in the 11-limit; [[625/624]], 975/968, [[1188/1183]], [[1287/1280]], and [[1573/1568]] in the 13-limit. Using the alternative 172bdee val, it tempers out [[225/224]], 118098/117649, and 3176523/3125000 in the 7-limit; [[243/242]], 1617/1600, 2079/2048, and 117649/117128 in the 11-limit; [[351/350]], 625/624, 1188/1183, and 1573/1568 in the 13-limit.
+Using the 172b val, it tempers out the [[unicorn comma]], 1594323/1562500 and 2197265625/2147483648 in the 5-limit; [[1728/1715]], [[3645/3584]], and [[390625/388962]] in the 7-limit; [[441/440]], 1944/1925, [[4000/3993]], and [[4125/4096]] in the 11-limit; [[625/624]], 975/968, [[1188/1183]], [[1287/1280]], and [[1573/1568]] in the 13-limit. Using the alternative 172bdee val, it tempers out [[225/224]], 118098/117649, and 3176523/3125000 in the 7-limit; [[243/242]], 1617/1600, 2079/2048, and 117649/117128 in the 11-limit; [[351/350]], 625/624, 1188/1183, and 1573/1568 in the 13-limit.
+Using the 172f val, every 7 steps is an excellent approximation of the ninth no-2 zeta peak - associated with [[39edt]] - in the 13-limit.
 === Odd harmonics ===