Dicot family: Difference between revisions

Revision as of 12:57, 6 June 2021

The 5-limit parent comma for the dicot family is 25/24, the chromatic semitone. Its monzo is [-3 -1 2⟩, and flipping that yields ⟨⟨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 7 EDO, 24 EDO using the val ⟨24 38 55] (24c) and 31 EDO using the 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

The second comma of the normal comma list defines which 7-limit family member we are looking at. Septimal dicot, with wedgie ⟨⟨2 1 3 -3 -1 4]] adds 36/35, sharp with wedgie ⟨⟨2 1 6 -3 4 11]] adds 28/27, and dichotic with wedgie ⟨⟨2 1 -4 -3 -12 -12]] ads 64/63, all retaining the same period and generator. Decimal with wedgie ⟨⟨4 2 2 -6 -8 -1]] adds 49/48, sidi with wedgie ⟨⟨4 2 9 -3 6 15]] adds 245/243, and jamesbond with 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

Subgroup: 2.3.5

Comma list: 25/24

Mapping: [⟨1 1 2], ⟨0 2 1]]

POTE generator: ~5/4 = 348.594

Tuning ranges:

Diamond monotone range: ~5/4 = [300.000, 400.000] (1\4 to 1\3)
Diamond tradeoff range: ~5/4 = [315.641, 386.314]
Diamond monotone and tradeoff: ~5/4 = [315.641, 386.314]

Template:Val list

Badness: 0.013028

7-limit

Subgroup: 2.3.5.7

Comma list: 15/14, 25/24

Mapping: [⟨1 1 2 2], ⟨0 2 1 3]]

Wedgie: ⟨⟨2 1 3 -3 -1 4]]

POTE generator: ~5/4 = 336.381

Template:Val list

Badness: 0.019935

11-limit

Subgroup: 2.3.5.7.11

Comma list: 15/14, 22/21, 25/24

Mapping: [⟨1 1 2 2 2], ⟨0 2 1 3 5]]

POTE generator: ~5/4 = 342.125

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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\|7EDO~~]], [[~~24edo\|24EDO~~]] using the val {{val\|24 38 55}} (24c) and [[~~31edo\|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 [[7 EDO]], [[24 EDO]] using the val {{val\|24 38 55}} (24c) and [[31 EDO]] 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 ===

Dicot family: Difference between revisions

Revision as of 12:57, 6 June 2021

Seven limit children

Dicot

7-limit

11-limit

Eudicot

13-limit

Flat

11-limit

13-limit

Sharp

11-limit

Decimal

11-limit

Decimated

Decibel

Dichotic

11-limit

Dichosis

Jamesbond

11-limit

13-limit

Septimal

Sidi

11-limit

Quad

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