140edo: Difference between revisions

Line 1:

The 140 equal ~~division~~ divides the octave into 140 parts of 8.~~571 cents~~ each. In the 5-limit, it tempers out 15625/15552, making it a kleismic system, and the kwazy comma, |-53 10 16>. It is most notable, however, in the 7-limit, where it tempers out 2401/2400, 5120/5103, 10976/10935 and 65625/65536. It supports the 7-limit rank-two temperaments tertiaseptal, hemififths, countercata and bisupermajor, and is a good tuning recommendation for countercata, the 53&140 temperament tempering out 15625/15552 and 5120/5103, and provides the optimal patent val for 13-limit countercata. In the 11-limit it tempers out 1331/1323, 385/384, 1375/1372, 6250/6237, 5632/5625 and 9801/9800, and in the 13-limit 325/324, 352/351, 847/845, 625/624, 676/675, 1001/1000, 1716/1715 and 2080/2079.

The '''140 equal divisions of the octave''' divides the [[octave]] into 140 parts of 8.57 [[cent]]s each.

If we use the val ~~<~~140 223 325 394| we obtain a tuning for [[~~Porcupine_family|~~porcupine ~~temperament~~]]; the generator 19\140 is 0.023 cents flat of the [[~~POTE_tuning|~~POTE generator]].

In the 5-limit, it tempers out [[15625/15552]], making it a kleismic system, and the kwazy comma, {{monzo| -53 10 16 }}. It is most notable, however, in the 7-limit, where it tempers out [[2401/2400]], [[5120/5103]], [[10976/10935]] and [[65625/65536]]. It supports the 7-limit rank-2 temperaments [[tertiaseptal]], [[hemififths]], [[countercata]] and [[bisupermajor]], and is a good tuning recommendation for countercata, the 53&140 temperament tempering out 15625/15552 and 5120/5103, and provides the [[optimal patent val]] for 13-limit countercata. In the 11-limit it tempers out [[385/384]], [[1331/1323]], [[1375/1372]], [[5632/5625]], [[6250/6237]] and [[9801/9800]], and in the 13-limit [[325/324]], [[352/351]], [[625/624]], [[676/675]], [[847/845]], [[1001/1000]], [[1716/1715]] and [[2080/2079]].

If we use the [[val]] {{val| 140 223 325 394 }} (140bbd) we obtain a tuning for [[porcupine]] temperament; the generator 19\140 is 0.023 cents flat of the [[POTE generator]].

[[Category:Equal divisions of the octave]]

[[Category:Countercata]]

@@ Line 1: / Line 1: @@
-The 140 equal division divides the octave into 140 parts of 8.571 cents each. In the 5-limit, it tempers out 15625/15552, making it a kleismic system, and the kwazy comma, |-53 10 16&gt;. It is most notable, however, in the 7-limit, where it tempers out 2401/2400, 5120/5103, 10976/10935 and 65625/65536. It supports the 7-limit rank-two temperaments tertiaseptal, hemififths, countercata and bisupermajor, and is a good tuning recommendation for countercata, the 53&amp;140 temperament tempering out 15625/15552 and 5120/5103, and provides the optimal patent val for 13-limit countercata. In the 11-limit it tempers out 1331/1323, 385/384, 1375/1372, 6250/6237, 5632/5625 and 9801/9800, and in the 13-limit 325/324, 352/351, 847/845, 625/624, 676/675, 1001/1000, 1716/1715 and 2080/2079.
+The '''140 equal divisions of the octave''' divides the [[octave]] into 140 parts of 8.57 [[cent]]s each.
-If we use the val &lt;140 223 325 394| we obtain a tuning for [[Porcupine_family|porcupine temperament]]; the generator 19\140 is 0.023 cents flat of the [[POTE_tuning|POTE generator]].
+In the 5-limit, it tempers out [[15625/15552]], making it a kleismic system, and the kwazy comma, {{monzo| -53 10 16 }}. It is most notable, however, in the 7-limit, where it tempers out [[2401/2400]], [[5120/5103]], [[10976/10935]] and [[65625/65536]]. It supports the 7-limit rank-2 temperaments [[tertiaseptal]], [[hemififths]], [[countercata]] and [[bisupermajor]], and is a good tuning recommendation for countercata, the 53&amp;140 temperament tempering out 15625/15552 and 5120/5103, and provides the [[optimal patent val]] for 13-limit countercata. In the 11-limit it tempers out [[385/384]], [[1331/1323]], [[1375/1372]], [[5632/5625]], [[6250/6237]] and [[9801/9800]], and in the 13-limit [[325/324]], [[352/351]], [[625/624]], [[676/675]], [[847/845]], [[1001/1000]], [[1716/1715]] and [[2080/2079]].
+If we use the [[val]] {{val| 140 223 325 394 }} (140bbd) we obtain a tuning for [[porcupine]] temperament; the generator 19\140 is 0.023 cents flat of the [[POTE generator]].
+[[Category:Equal divisions of the octave]]
+[[Category:Countercata]]