Dicot family: Difference between revisions
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{{Technical data page}} | {{Technical data page}} | ||
The '''dicot family''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] [[25/24]], the classical chromatic semitone. The head of this family, dicot, is [[generator|generated]] by a classical third (major and minor mean the same thing), and two such thirds give a fifth. In fact, {{nowrap|(5/4)<sup>2</sup> {{=}} (3/2)(25/24)}}. | The '''dicot family''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] [[25/24]], the classical chromatic semitone. | ||
== Dicot == | |||
The head of this family, dicot, is [[generator|generated]] by a classical third (major and minor mean the same thing), and two such thirds give a fifth. In fact, {{nowrap|(5/4)<sup>2</sup> {{=}} (3/2)(25/24)}}. | |||
Possible tunings for dicot are [[7edo]], [[10edo]], [[17edo]], [[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 sixths and pretending that these are 5-limit, and like any temperament which seems to involve a lot of "pretending", dicot is close to the edge of what can be sensibly called a temperament at all. In other words, it is an [[exotemperament]]. | Possible tunings for dicot are [[7edo]], [[10edo]], [[17edo]], [[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 sixths and pretending that these are 5-limit, and like any temperament which seems to involve a lot of "pretending", dicot is close to the edge of what can be sensibly called a temperament at all. In other words, it is an [[exotemperament]]. | ||
[[Subgroup]]: 2.3.5 | [[Subgroup]]: 2.3.5 | ||
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=== Overview to extensions === | === Overview to extensions === | ||
The second comma of the [[ | The second comma of the [[normal lists|normal comma list]] defines which [[7-limit]] family member we are looking at. Septimal dicot adds 36/35, flattie adds 21/20, sharpie adds 28/27, and dichotic adds 64/63, all retaining the same period and generator. | ||
Decimal adds 49/48, sidi adds 245/243, and jamesbond 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. | Decimal adds 49/48, sidi adds 245/243, and jamesbond 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. | ||
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Temperaments discussed elsewhere are: | Temperaments discussed elsewhere are: | ||
* ''[[Geryon]]'' → [[Very low accuracy temperaments #Geryon|Very low accuracy temperaments]] | * ''[[Geryon]]'' → [[Very low accuracy temperaments #Geryon|Very low accuracy temperaments]] | ||
* ''[[Jamesbond]]'' → [[7th-octave temperaments #Jamesbond|7th-octave temperaments]] | |||
The rest are considered below. | The rest are considered below. | ||
=== 2.3.5.11 subgroup === | === 2.3.5.11 subgroup === | ||
The 2.3.5.11-subgroup extension | The 2.3.5.11-subgroup extension maps [[11/9]]~[[27/22]] to the neutral third. As such, it is related to most of the septimal extensions. | ||
Subgroup: 2.3.5.11 | Subgroup: 2.3.5.11 | ||
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Gencom mapping: {{mapping| 1 1 2 0 2 | 0 2 1 0 5 }} | Gencom mapping: {{mapping| 1 1 2 0 2 | 0 2 1 0 5 }} | ||
Optimal tunings: | Optimal tunings: | ||
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Gencom mapping: {{mapping| 1 1 2 0 2 4 | 0 2 1 0 5 -1 }} | Gencom mapping: {{mapping| 1 1 2 0 2 4 | 0 2 1 0 5 -1 }} | ||
Optimal tunings: | Optimal tunings: | ||
* WE: ~2 = 1202.433{{c}}, ~ | * WE: ~2 = 1202.433{{c}}, ~5/4 = 351.237{{c}} | ||
* CWE: ~2 = 1200.000{{c}}, ~ | * CWE: ~2 = 1200.000{{c}}, ~5/4 = 350.978{{c}} | ||
{{Optimal ET sequence|legend=0| 3e, 7, 17 }} | {{Optimal ET sequence|legend=0| 3e, 7, 17 }} | ||
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== Flattie == | == Flattie == | ||
This temperament used to be known as | This temperament used to be known as ''flat''. Unlike septimal dicot where 7/6 is added to the neutral third, here 8/7 is added instead. | ||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
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== Sharpie == | == Sharpie == | ||
This temperament used to be known as | This temperament used to be known as ''sharp''. This is where you find 7/6 at the major second and 7/4 at the major sixth. | ||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||