Dicot family: Difference between revisions
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The [[5-limit]] parent [[comma]] for the dicot family is 25/24, the [[chromatic semitone]]. Its [[monzo]] is {{monzo| -3 -1 2 }}, and flipping that yields {{wedgie| 2 1 -3}} for the [[wedgie]]. This tells us the generator is a third (major and minor mean the same thing), and that two thirds gives a fifth. In fact, (5/4)^2 = 3/2 * 25/24. Possible tunings for dicot are [[7edo]], [[24edo]] using the val {{val|24 38 55}} (24c) and [[31edo]] using the val {{val|31 49 71}} (31c). In a sense, what dicot is all about is using neutral thirds and pretending that's 5-limit, and like any temperament which seems to involve pretending, dicot is at the edge of what can sensibly be called a temperament at all. In other words, it is an [[exotemperament]]. | The [[5-limit]] parent [[comma]] for the dicot family is 25/24, the [[chromatic semitone]]. Its [[monzo]] is {{monzo| -3 -1 2 }}, and flipping that yields {{wedgie| 2 1 -3}} for the [[wedgie]]. This tells us the generator is a third (major and minor mean the same thing), and that two thirds gives a fifth. In fact, (5/4)^2 = 3/2 * 25/24. Possible tunings for dicot are [[7edo]], [[24edo]] using the val {{val|24 38 55}} (24c) and [[31edo]] using the val {{val|31 49 71}} (31c). In a sense, what dicot is all about is using neutral thirds and pretending that's 5-limit, and like any temperament which seems to involve pretending, dicot is at the edge of what can sensibly be called a temperament at all. In other words, it is an [[exotemperament]]. | ||
==Seven limit children== | === Seven limit children === | ||
The second comma of the [[Normal_lists|normal comma list]] defines which [[7-limit]] family member we are looking at. Septimal dicot, with wedgie {{wedgie|2 1 3 -3 -1 4}} adds 36/35, sharp with wedgie {{wedgie|2 1 6 -3 4 11}} adds 28/27, and dichotic with wedgie {{wedgie|2 1 -4 -3 -12 -12}} ads 64/63, all retaining the same period and generator. Decimal with wedgie {{wedgie|4 2 2 -6 -8 -1}} adds 49/48, sidi with wedgie {{wedgie|4 2 9 -3 6 15}} adds 245/243, and jamesbond with wedgie {{wedgie|0 0 7 0 11 16}} adds 81/80. Here decimal divides the period to 1/2 octave, and sidi uses 9/7 as a generator, with two of them making up the combined 5/3 and 8/5 neutral sixth. Jamesbond has a period of 1/7 octave, and uses an approximate 15/14 as generator. | The second comma of the [[Normal_lists|normal comma list]] defines which [[7-limit]] family member we are looking at. Septimal dicot, with wedgie {{wedgie|2 1 3 -3 -1 4}} adds 36/35, sharp with wedgie {{wedgie|2 1 6 -3 4 11}} adds 28/27, and dichotic with wedgie {{wedgie|2 1 -4 -3 -12 -12}} ads 64/63, all retaining the same period and generator. Decimal with wedgie {{wedgie|4 2 2 -6 -8 -1}} adds 49/48, sidi with wedgie {{wedgie|4 2 9 -3 6 15}} adds 245/243, and jamesbond with wedgie {{wedgie|0 0 7 0 11 16}} adds 81/80. Here decimal divides the period to 1/2 octave, and sidi uses 9/7 as a generator, with two of them making up the combined 5/3 and 8/5 neutral sixth. Jamesbond has a period of 1/7 octave, and uses an approximate 15/14 as generator. | ||
=Dicot= | == Dicot == | ||
Subgroup: 2.3.5 | Subgroup: 2.3.5 | ||
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[[Badness]]: 0.013028 | [[Badness]]: 0.013028 | ||
==7-limit== | === 7-limit === | ||
[[Comma list]]: 15/14, 25/24 | [[Comma list]]: 15/14, 25/24 | ||
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[[Badness]]: 0.019935 | [[Badness]]: 0.019935 | ||
==11-limit== | === 11-limit === | ||
[[Comma list]]: 15/14, 22/21, 25/24 | [[Comma list]]: 15/14, 22/21, 25/24 | ||
| Line 45: | Line 45: | ||
Badness: 0.019854 | Badness: 0.019854 | ||
=Eudicot= | == Eudicot == | ||
[[Comma list]]: 15/14, 25/24, 33/32 | [[Comma list]]: 15/14, 25/24, 33/32 | ||
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Badness: 0.027114 | Badness: 0.027114 | ||
==13-limit== | === 13-limit === | ||
[[Comma list]]: 15/14, 25/24, 33/32, 40/39 | [[Comma list]]: 15/14, 25/24, 33/32, 40/39 | ||
| Line 67: | Line 67: | ||
Badness: 0.023828 | Badness: 0.023828 | ||
=Flat= | == Flat == | ||
[[Comma list]]: 21/20, 25/24 | [[Comma list]]: 21/20, 25/24 | ||
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[[Badness]]: 0.025381 | [[Badness]]: 0.025381 | ||
==11-limit== | === 11-limit === | ||
Comma list: 21/20, 25/24, 33/32 | Comma list: 21/20, 25/24, 33/32 | ||
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Badness: 0.024988 | Badness: 0.024988 | ||
==13-limit== | === 13-limit === | ||
Comma list: 14/13, 21/20, 25/24, 33/32 | Comma list: 14/13, 21/20, 25/24, 33/32 | ||
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Badness: 0.023420 | Badness: 0.023420 | ||
=Sharp= | == Sharp == | ||
[[Comma list]]: 25/24, 28/27 | [[Comma list]]: 25/24, 28/27 | ||
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[[Badness]]: 0.028942 | [[Badness]]: 0.028942 | ||
==11-limit== | === 11-limit === | ||
Comma list: 25/24, 28/27, 35/33 | Comma list: 25/24, 28/27, 35/33 | ||
| Line 126: | Line 126: | ||
Badness: 0.022366 | Badness: 0.022366 | ||
=Decimal= | == Decimal == | ||
[[Comma list]]: 25/24, 49/48 | [[Comma list]]: 25/24, 49/48 | ||
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[[Badness]]: 0.028334 | [[Badness]]: 0.028334 | ||
==11-limit== | === 11-limit === | ||
Comma list: 25/24, 45/44, 49/48 | Comma list: 25/24, 45/44, 49/48 | ||
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Badness: 0.026712 | Badness: 0.026712 | ||
==Decimated== | === Decimated === | ||
Comma list: 25/24, 33/32, 49/48 | Comma list: 25/24, 33/32, 49/48 | ||
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Badness: 0.031456 | Badness: 0.031456 | ||
==Decibel== | === Decibel === | ||
Comma list: 25/24, 35/33, 49/48 | Comma list: 25/24, 35/33, 49/48 | ||
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Badness: 0.032385 | Badness: 0.032385 | ||
=Dichotic= | == Dichotic == | ||
[[Comma list]]: 25/24, 64/63 | [[Comma list]]: 25/24, 64/63 | ||
| Line 185: | Line 185: | ||
[[Badness]]: 0.037565 | [[Badness]]: 0.037565 | ||
==11-limit== | === 11-limit === | ||
Comma list: 25/24, 45/44, 64/63 | Comma list: 25/24, 45/44, 64/63 | ||
| Line 196: | Line 196: | ||
Badness: 0.030680 | Badness: 0.030680 | ||
==Dichosis== | === Dichosis === | ||
Comma list: 25/24, 35/33, 64/63 | Comma list: 25/24, 35/33, 64/63 | ||
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Badness: 0.041361 | Badness: 0.041361 | ||
=Jamesbond= | == Jamesbond == | ||
[[Comma list]]: 25/24, 81/80 | [[Comma list]]: 25/24, 81/80 | ||
| Line 220: | Line 220: | ||
[[Badness]]: 0.041714 | [[Badness]]: 0.041714 | ||
==11-limit== | === 11-limit === | ||
Comma list: 25/24, 33/32, 45/44 | Comma list: 25/24, 33/32, 45/44 | ||
| Line 231: | Line 231: | ||
Badness: 0.023524 | Badness: 0.023524 | ||
==13-limit== | === 13-limit === | ||
Comma list: 25/24, 27/26, 33/32, 40/39 | Comma list: 25/24, 27/26, 33/32, 40/39 | ||
| Line 242: | Line 242: | ||
Badness: 0.023003 | Badness: 0.023003 | ||
==Septimal== | === Septimal === | ||
Comma list: 25/24, 33/32, 45/44, 65/63 | Comma list: 25/24, 33/32, 45/44, 65/63 | ||
| Line 253: | Line 253: | ||
Badness: 0.022569 | Badness: 0.022569 | ||
=Sidi= | == Sidi == | ||
[[Comma list]]: 25/24, 245/243 | [[Comma list]]: 25/24, 245/243 | ||
| Line 266: | Line 266: | ||
[[Badness]]: 0.056586 | [[Badness]]: 0.056586 | ||
==11-limit== | === 11-limit === | ||
Comma list: 25/24, 45/44, 99/98 | Comma list: 25/24, 45/44, 99/98 | ||
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Badness: 0.032957 | Badness: 0.032957 | ||
=Quad= | == Quad == | ||
[[Comma list]]: 9/8, 25/24 | [[Comma list]]: 9/8, 25/24 | ||