172edo: Difference between revisions
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172edo is in[[consistent]] to the [[5-odd-limit]] and higher limits, with three mappings possible for the 5-limit: {{val| 172 273 399 }} ([[patent val]]), {{val| 172 '''272''' 399 }} (172b), and {{val| 172 273 '''400''' }} (172c). Using the patent val, it [[tempering out|tempers out]] the [[semicomma]], 2109375/2097152 and 1220703125/1162261467 in the 5-limit; [[245/243]], [[3125/3087]], and 2097152/2066715 in the 7-limit, [[support]]ing the 7-limit [[bohpier]] temperament; [[385/384]], [[896/891]], 1331/1323, and 9375/9317 in the 11-limit; [[169/168]], [[352/351]], [[364/363]], and [[1716/1715]] in the 13-limit, supporting the [[leapweek]] temperament. Using the 172f val, [[275/273]], [[640/637]], [[847/845]], and [[1575/1573]] are tempered out in the 13-limit. | 172edo is in[[consistent]] to the [[5-odd-limit]] and higher limits, with three mappings possible for the 5-limit: {{val| 172 273 399 }} ([[patent val]]), {{val| 172 '''272''' 399 }} (172b), and {{val| 172 273 '''400''' }} (172c). Using the patent val, it [[tempering out|tempers out]] the [[semicomma]], 2109375/2097152 and 1220703125/1162261467 in the 5-limit; [[245/243]], [[3125/3087]], and 2097152/2066715 in the 7-limit, [[support]]ing the 7-limit [[bohpier]] temperament; [[385/384]], [[896/891]], 1331/1323, and 9375/9317 in the 11-limit; [[169/168]], [[352/351]], [[364/363]], and [[1716/1715]] in the 13-limit, supporting the [[leapweek]] temperament. Using the 172f val, [[275/273]], [[640/637]], [[847/845]], and [[1575/1573]] are tempered out in the 13-limit. | ||
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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 15-limit. | |||
=== Odd harmonics === | === Odd harmonics === | ||