80edo: Difference between revisions

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The '''80 equal temperament''', often abbreviated 80-tET, 80-EDO, or 80-ET, is the scale derived by dividing the octave into 80 equally-sized steps. Each step represents a frequency ratio of exactly 15 [[cent|cent]]s. 80et is the first equal temperament that represents the [[19-limit]] [[tonality diamond]] [[consistent|consistently]] (it barely manages to do so).

80et [[Tempering_out|tempers out]] 176/175 and 540/539 in the [[11-limit]], 169/168, [[325/324]], [[351/350]], [[352/351]], [[364/363]] and 1001/1000 in the [[13-limit]], 136/135, 221/220, 256/255, 289/288, 561/560, 595/594, 715/714, 936/935, 1275/1274 in the [[17-limit]], 190/189, 286/285, 361/360, 400/399, 456/455, 476/475, 969/968, 1331/1330, [[1445/1444]], 1521/1520, 1540/1539 and 1729/1728 in the 19-limit, not to mention such important non-superparticular commas as [[2048/2025]], 4000/3969, 1728/1715 and 3136/3125.

80 supports a profusion of 19-limit (and lower) rank two temperaments which have mostly not been explored. We might mention:

80et provides the [[optimal patent val]] for 5-limit [[diaschismic]], for 13-limit [[srutal]], and for 7-, 11- and 13-limit [[bidia]]. It is a good tuning for various temperaments in [[canou family]], especially in higher limits.

80et supports a profusion of 19-limit (and lower) rank two temperaments which have mostly not been explored. We might mention:

31&80 <<7 6 15 27 -24 -23 -20 ... ||

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| 30

| 450

| [[13/10]], [[22/17]]

| [[35/27]], [[13/10]], [[22/17]]

|-

| 31

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[[Category:Edo]]

[[Category:19-limit]]

[[Category:Diaschismic]]

[[Category:Srutal]]

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 The '''80 equal temperament''', often abbreviated 80-tET, 80-EDO, or 80-ET, is the scale derived by dividing the octave into 80 equally-sized steps. Each step represents a frequency ratio of exactly 15 [[cent|cent]]s. 80et is the first equal temperament that represents the [[19-limit]] [[tonality diamond]] [[consistent|consistently]] (it barely manages to do so).
 et [[Tempering_out|tempers out]] 176/175 and 540/539 in the [[11-limit]], 169/168, [[325/324]], [[351/350]], [[352/351]], [[364/363]] and 1001/1000 in the [[13-limit]], 136/135, 221/220, 256/255, 289/288, 561/560, 595/594, 715/714, 936/935, 1275/1274 in the [[17-limit]], 190/189, 286/285, 361/360, 400/399, 456/455, 476/475, 969/968, 1331/1330, [[1445/1444]], 1521/1520, 1540/1539 and 1729/1728 in the 19-limit, not to mention such important non-superparticular commas as [[2048/2025]], 4000/3969, 1728/1715 and 3136/3125.
-supports a profusion of 19-limit (and lower) rank two temperaments which have mostly not been explored. We might mention:
+et provides the [[optimal patent val]] for 5-limit [[diaschismic]], for 13-limit [[srutal]], and for 7-, 11- and 13-limit [[bidia]]. It is a good tuning for various temperaments in [[canou family]], especially in higher limits.
+et supports a profusion of 19-limit (and lower) rank two temperaments which have mostly not been explored. We might mention:
 &amp;80 &lt;&lt;7 6 15 27 -24 -23 -20 ... ||
@@ Line 155: / Line 157: @@
 | 30
 | 450
-| [[13/10]], [[22/17]]
+| [[35/27]], [[13/10]], [[22/17]]
 |-
 | 31
@@ Line 205: / Line 207: @@
 [[Category:Edo]]
 [[Category:19-limit]]
+[[Category:Diaschismic]]
+[[Category:Srutal]]