Mintaka: Difference between revisions

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'''Mintaka''' is a [[temperament]] in the 3.7.11 [[subgroup]] where [[~]][[11/7]] is a [[generator]], and the comma [[1331/1323]] is [[tempering out|tempered out]], so a stack of two generators represents [[27/11]] in addition to 121/49, and a stack of three generators, [[3/1|tritave]]-reduced, represents [[9/7]]. As 11/7 as a generator against the tritave produces a [[5L 2s (3/1-equivalent)|5L 2s]] (macrodiatonic) scale, with the generator here occupying the role of a [[4/3|perfect fourth]], it is possible to use an analogue of the [[chain-of-fifths notation]] that is standardly used for [[diatonic]] scales, with the understanding that sharps are sharper than flats (for example, A♯ is sharper than B♭), though the [[5L 7s (3/1-equivalent)|5L 7s]] macrochromatic scale is suggested for musical use due to the hardness of the macrodiatonic and the increased breadth of the tritave. [[22edt|9\22]]edt is a very good tuning for the generator, and 22edt overall excels in the 3.7.11 subgroup, but other tunings such as [[17edt|7\17]]edt and [[39edt|16\39]]edt are also useful.

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[[Mos scale]]s of reasonable tunings have cardinalities of 5 (2L 3s), 7 (5L 2s), 12 (5L 7s), or 17 (5L 12s).

~~For technical data, see ''[[No-twos subgroup temperaments#Mintaka]]''.~~

== Extensions of Mintaka ==

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+{{tdhat|No-twos subgroup temperaments#Mintaka}}
 '''Mintaka''' is a [[temperament]] in the 3.7.11 [[subgroup]] where [[~]][[11/7]] is a [[generator]], and the comma [[1331/1323]] is [[tempering out|tempered out]], so a stack of two generators represents [[27/11]] in addition to 121/49, and a stack of three generators, [[3/1|tritave]]-reduced, represents [[9/7]]. As 11/7 as a generator against the tritave produces a [[5L 2s (3/1-equivalent)|5L 2s]] (macrodiatonic) scale, with the generator here occupying the role of a [[4/3|perfect fourth]], it is possible to use an analogue of the [[chain-of-fifths notation]] that is standardly used for [[diatonic]] scales, with the understanding that sharps are sharper than flats (for example, A♯ is sharper than B♭), though the [[5L 7s (3/1-equivalent)|5L 7s]] macrochromatic scale is suggested for musical use due to the hardness of the macrodiatonic and the increased breadth of the tritave. [[22edt|9\22]]edt is a very good tuning for the generator, and 22edt overall excels in the 3.7.11 subgroup, but other tunings such as [[17edt|7\17]]edt and [[39edt|16\39]]edt are also useful.
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 [[Mos scale]]s of reasonable tunings have cardinalities of 5 (2L 3s), 7 (5L 2s), 12 (5L 7s), or 17 (5L 12s).
-For technical data, see ''[[No-twos subgroup temperaments#Mintaka]]''.
 == Extensions of Mintaka ==