5L 2s (3/1-equivalent): Difference between revisions

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=== Temperament interpretations ===

It is possible to construct no-twos [[rank-2 temperament]] interpretations of this scale, although most of these do not fit neatly into the 3.5.7 [[subgroup]] used for [[Bohlen-Pierce]]. Two intervals that can serve as macrodiatonic ~~generators~~ are ~[[17/9]], which is just near [[19edt]] in the soft range, and ~[[21/11]] which is just near [[17edt]] in the hard range.

It is possible to construct no-twos [[rank-2 temperament]] interpretations of this scale, although most of these do not fit neatly into the 3.5.7 [[subgroup]] used for [[Bohlen-Pierce]]. Two intervals that can serve as macrodiatonic "fifths" are ~[[17/9]], which is just near [[19edt]] in the soft range, and ~[[21/11]] which is just near [[17edt]] in the hard range.

Very soft scales (in the range between [[26edt]] and [[45edt]], serving as a macro-[[flattone]]) can be interpreted in the 3.5.7.17 subgroup as [[no-twos subgroup temperaments#Mizar|Mizar]], in which the generator of a flattened ~17/9 stacks twice and tritave-reduces to [[25/21]], which generates [[Sirius]] temperament. Scales close to basic have an interpretation in the 3.13.17 subgroup, documented as [[no-twos subgroup temperaments#Sadalmelik|Sadalmelik]] in which the generator (the stretched counterpart of the fifth) is also ~17/9 and a stack of 4 generators tritave-reduced (equivalent to the major third) is ~[[13/9]]; see also the page for [[12edt]]. Harder scales can be interpreted in [[Mintaka]] temperament in the 3.7.11 subgroup, which tempers out [[1331/1323]] so that the dark generator (the stretched counterpart of the fourth) is ~[[11/7]], a stack of 2 generators (equivalent to the minor seventh) is ~[[27/11]], and a stack of three generators (equivalent to the minor third) is ~[[9/7]].

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 === Temperament interpretations ===
-It is possible to construct no-twos [[rank-2 temperament]] interpretations of this scale, although most of these do not fit neatly into the 3.5.7 [[subgroup]] used for [[Bohlen-Pierce]]. Two intervals that can serve as macrodiatonic generators are ~[[17/9]], which is just near [[19edt]] in the soft range, and ~[[21/11]] which is just near [[17edt]] in the hard range.
+It is possible to construct no-twos [[rank-2 temperament]] interpretations of this scale, although most of these do not fit neatly into the 3.5.7 [[subgroup]] used for [[Bohlen-Pierce]]. Two intervals that can serve as macrodiatonic "fifths" are ~[[17/9]], which is just near [[19edt]] in the soft range, and ~[[21/11]] which is just near [[17edt]] in the hard range.
 Very soft scales (in the range between [[26edt]] and [[45edt]], serving as a macro-[[flattone]]) can be interpreted in the 3.5.7.17 subgroup as [[no-twos subgroup temperaments#Mizar|Mizar]], in which the generator of a flattened ~17/9 stacks twice and tritave-reduces to [[25/21]], which generates [[Sirius]] temperament. Scales close to basic have an interpretation in the 3.13.17 subgroup, documented as [[no-twos subgroup temperaments#Sadalmelik|Sadalmelik]] in which the generator (the stretched counterpart of the fifth) is also ~17/9 and a stack of 4 generators tritave-reduced (equivalent to the major third) is ~[[13/9]]; see also the page for [[12edt]]. Harder scales can be interpreted in [[Mintaka]] temperament in the 3.7.11 subgroup, which tempers out [[1331/1323]] so that the dark generator (the stretched counterpart of the fourth) is ~[[11/7]], a stack of 2 generators (equivalent to the minor seventh) is ~[[27/11]], and a stack of three generators (equivalent to the minor third) is ~[[9/7]].