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)}}. Its [[ploidacot]] is the same as its name, dicot. | |||
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 | Decimal adds [[49/48]], sidi adds [[245/243]], and jamesbond adds [[16/15]]. Here decimal divides the [[period]] to a [[sqrt(2)|semi-octave]], and sidi uses 14/9 as a generator, with two of them making up the combined 5/2~12/5 neutral tenth. Jamesbond has a period of 1/7 octave, and uses an approximate 15/14 as generator. | ||
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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== Septimal dicot == | == Septimal dicot == | ||
Septimal dicot is the extension where 7/6 and 9/7 are also conflated into 5/4~6/5. Although 5/4~6/5 | Septimal dicot is the extension where [[7/6]] and [[9/7]] are also conflated into 5/4~6/5. Although 5/4~6/5 covers a giant block of pitches already, 7/6 and 9/7 are often considered as thirds too. On that account one could argue for the canonicity of this extension, despite the relatively poor accuracy. | ||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
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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 | ||
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{{Main| Decimal }} | {{Main| Decimal }} | ||
{{See also| Jubilismic clan }} | {{See also| Jubilismic clan }} | ||
Decimal tempers out 49/48 and [[50/49]], and has a semi-octave period for 7/5~10/7 and a hemitwelfth generator for 7/4~12/7. Its ploidacot is diploid dicot. [[10edo]] makes for a good tuning, from which it derives its name. [[14edo]] in the 14c val and [[24edo]] in the 24c val are also among the possibilities. | |||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
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== Sidi == | == Sidi == | ||
Sidi tempers out 245/243, and splits 5/2~12/5 in two. Its ploidacot is beta-tetracot. This relates it to [[squares]], to which it can be used as a simpler alternative. 14edo in the 14c val can be used as a tuning, in which case it is identical to squares, however. | |||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||