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'''[[Edt|Division of the third harmonic]] into 43 equal parts''' (43EDT) is related to [[27edo|27 EDO]], but with the 3/1 rather than the 2/1 being just. The octave is about 5.7492 cents compressed and the step size is about 44.2315 cents. It is consistent to the [[9-odd-limit|10-integer-limit]]. | '''[[Edt|Division of the third harmonic]] into 43 equal parts''' (43EDT) is related to [[27edo|27 EDO]], but with the 3/1 rather than the 2/1 being just. The octave is about 5.7492 cents compressed and the step size is about 44.2315 cents. It is consistent to the [[9-odd-limit|10-integer-limit]]. | ||
= | =Properties= | ||
This tuning is related to 27EDO having ~5.7 cent octave compression, a small but significant deviation. This is particularly relevant because 27EDO is a "sharp tending" system, and flattening its octaves has been suggested before as an improvement (I think by no less than Ivor Darreg, but I'll have to check that). | This tuning is related to 27EDO having ~5.7 cent octave compression, a small but significant deviation. This is particularly relevant because 27EDO is a "sharp tending" system, and flattening its octaves has been suggested before as an improvement (I think by no less than Ivor Darreg, but I'll have to check that). | ||
| Line 171: | Line 171: | ||
| | 40 | | | 40 | ||
| | 1769.261 | | | 1769.261 | ||
| | [[25/9]] | | | [[25/18|25/9]] | ||
|- | |- | ||
| | 41 | | | 41 | ||
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| | '''exact [[3/1]]''' | | | '''exact [[3/1]]''' | ||
|} | |} | ||
=43EDT as a regular temperament= | |||
43EDT tempers out a no-twos comma of |0 63 -43>, leading the regular temperament supported by [[27edo|27]], [[190edo|190]], and [[217edo|217]] EDOs. | |||
==27&190 temperament== | |||
===5-limit=== | |||
Comma: |0 63 -43> | |||
POTE generator: ~|0 -41 28> = 44.2294 | |||
Map: [<1 0 0|, <0 43 63|] | |||
EDOs: 27, 190, 217, 407, 597, 624, 841 | |||
===7-limit=== | |||
Commas: 4375/4374, 40353607/40000000 | |||
POTE generator: ~1029/1000 = 44.2288 | |||
Map: [<1 0 0 1|, <0 43 63 49|] | |||
EDOs: 27, 190, 217 | |||
==217&407 temperament== | |||
===7-limit=== | |||
Commas: 134217728/133984375, 512557306947/512000000000 | |||
POTE generator: ~525/512 = 44.2320 | |||
Map: [<1 0 0 9|, <0 43 63 -168|] | |||
EDOs: 217, 407, 624, 841, 1058, 1465 | |||
===11-limit=== | |||
Commas: 46656/46585, 131072/130977, 234375/234256 | |||
POTE generator: ~525/512 = 44.2312 | |||
Map: [<1 0 0 9 -1|, <0 43 63 -168 121|] | |||
EDOs: 217, 407, 624 | |||
===13-limit=== | |||
Commas: 2080/2079, 4096/4095, 39366/39325, 109512/109375 | |||
POTE generator: ~40/39 = 44.2312 | |||
Map: [<1 0 0 9 -1 3|, <0 43 63 -168 121 19|] | |||
EDOs: 217, 407, 624 | |||
[[Category:Edt]] | [[Category:Edt]] | ||
[[Category:Edonoi]] | [[Category:Edonoi]] | ||