72nd-octave temperaments: Difference between revisions
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{{ | {{Infobox fractional-octave|72}} | ||
[[72edo]] is a notable tuning system due to its 17-limit consistency, being a multiple of 12, and usage in various ecclesiastical forms of chanting. | [[72edo]] is a notable tuning system due to its 17-limit consistency, being a multiple of 12, and usage in various ecclesiastical forms of chanting. | ||
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{{Optimal ET sequence|legend=1|1224, 1872def, 4320, 5544}} | {{Optimal ET sequence|legend=1|1224, 1872def, 4320, 5544}} | ||
===17-limit=== | |||
=== 17-limit === | |||
Subgroup: 2.3.5.7.11.13.17 | Subgroup: 2.3.5.7.11.13.17 | ||
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{{Optimal ET sequence|legend=1|1224, 1872def, 4320, 5544}} | {{Optimal ET sequence|legend=1|1224, 1872def, 4320, 5544}} | ||
===2.3.5.7.11.13.17.31 subgroup=== | === 2.3.5.7.11.13.17.31 subgroup === | ||
Since 4320edo and 5544edo have good 31st and 37th harmonics, addition of these subgroups is prescribed. | Since 4320edo and 5544edo have good 31st and 37th harmonics, addition of these subgroups is prescribed. | ||
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Optimal tuning (CTE): ~3/2 = 701.948 | Optimal tuning (CTE): ~3/2 = 701.948 | ||
===2.3.5.7.11.13.17.31.37 subgroup=== | === 2.3.5.7.11.13.17.31.37 subgroup === | ||
[[37/22]] is mapped to exact three-quarters of the octave. | [[37/22]] is mapped to exact three-quarters of the octave. | ||