Meantone family: Difference between revisions

Line 592:

=Sharptone=

[[~~Comma|~~Comma]]s: 21/20, 28/27

[[Comma]]s: 21/20, 28/27

Sharptone, with a wedgie <<1 4 3 4 2 -4||, is a low-accuracy temperament tempering out 21/20 and 28/27. In sharptone, a 7/4 is a major sixth, a 7/6 a whole tone, and a 7/5 a fourth. Genuinely septimal sounding harmony therefore cannot be expected, but it can be used to translate, more or less, 7-limit JI into 5-limit meantone. [[~~12edo|~~12edo]] tuning does sharptone about as well as such a thing can be done, of course not in its patent val.

Sharptone, with a wedgie <<1 4 3 4 2 -4||, is a low-accuracy temperament tempering out 21/20 and 28/27. In sharptone, a 7/4 is a major sixth, a 7/6 a whole tone, and a 7/5 a fourth. Genuinely septimal sounding harmony therefore cannot be expected, but it can be used to translate, more or less, 7-limit JI into 5-limit meantone. [[12edo]] tuning does sharptone about as well as such a thing can be done, of course not in its patent val.

[[POTE_tuning|POTE generator]]: 700.140

[[POTE_tuning|POTE generator]]: ~3/2 = 700.140

Mapping generator: ~3

Line 602:

Map: [<1 0 -4 -2|, <0 1 4 3|]

[[~~wedgie|~~Wedgie]]: <<1 4 3 4 2 -4||

[[Wedgie]]: <<1 4 3 4 2 -4||

EDOs: [[5edo|5]], [[12edo|12]]

EDOs: [[5edo|5]], [[7edo|7d]], [[12edo|12d]]

[[~~Badness|~~Badness]]: 0.0248

[[Badness]]: 0.0248

==Meanertone==

Commas: 21/20, 28/27, 33/32

POTE generator: ~3/2 = 696.615

Map: [<1 0 -4 -2 5|, <0 1 4 3 -1|]

EDOs: 5, 7d, 12de

=Meansept=

@@ Line 592: / Line 592: @@
 =Sharptone=
-[[Comma|Comma]]s: 21/20, 28/27
+[[Comma]]s: 21/20, 28/27
-Sharptone, with a wedgie &lt;&lt;1 4 3 4 2 -4||, is a low-accuracy temperament tempering out 21/20 and 28/27. In sharptone, a 7/4 is a major sixth, a 7/6 a whole tone, and a 7/5 a fourth. Genuinely septimal sounding harmony therefore cannot be expected, but it can be used to translate, more or less, 7-limit JI into 5-limit meantone. [[12edo|12edo]] tuning does sharptone about as well as such a thing can be done, of course not in its patent val.
+Sharptone, with a wedgie &lt;&lt;1 4 3 4 2 -4||, is a low-accuracy temperament tempering out 21/20 and 28/27. In sharptone, a 7/4 is a major sixth, a 7/6 a whole tone, and a 7/5 a fourth. Genuinely septimal sounding harmony therefore cannot be expected, but it can be used to translate, more or less, 7-limit JI into 5-limit meantone. [[12edo]] tuning does sharptone about as well as such a thing can be done, of course not in its patent val.
-[[POTE_tuning|POTE generator]]: 700.140
+[[POTE_tuning|POTE generator]]: ~3/2 = 700.140
 Mapping generator: ~3
@@ Line 602: / Line 602: @@
 Map: [&lt;1 0 -4 -2|, &lt;0 1 4 3|]
-[[wedgie|Wedgie]]: &lt;&lt;1 4 3 4 2 -4||
+[[Wedgie]]: &lt;&lt;1 4 3 4 2 -4||
-EDOs: [[5edo|5]], [[12edo|12]]
+EDOs: [[5edo|5]], [[7edo|7d]], [[12edo|12d]]
-[[Badness|Badness]]: 0.0248
+[[Badness]]: 0.0248
+==Meanertone==
+Commas: 21/20, 28/27, 33/32
+POTE generator: ~3/2 = 696.615
+Map: [&lt;1 0 -4 -2 5|, &lt;0 1 4 3 -1|]
+EDOs: 5, 7d, 12de
 =Meansept=