3L 2s (3/2-equivalent): Difference between revisions
Undo revision 68917 by Moremajorthanmajor (talk) Tag: Undo |
rename MOS pattern to uranian and add temperaments; semiwolf is now a temperament |
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| Pattern = LLsLs | | Pattern = LLsLs | ||
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'''3L 2s<3/2>''' (sometimes called ''' | '''3L 2s<3/2>''' (sometimes called '''uranian'''), is a fifth-repeating MOS scale. The notation "<3/2>" means the period of the MOS is 3/2, disambiguating it from octave-repeating [[3L 2s]]. | ||
Because semiwolf is a fifth-repeating scale, each tone has a 3/2 perfect fifth above it. The scale has three major chords and two minor chords, all voiced so that the third of the triad is an octave higher, a tenth. Semiwolf also has two harmonic 7th chords. | Because semiwolf is a fifth-repeating scale, each tone has a 3/2 perfect fifth above it. The scale has three major chords and two minor chords, all voiced so that the third of the triad is an octave higher, a tenth. Semiwolf also has two harmonic 7th chords. | ||
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[[Step ratio|Basic]] semiwolf is in [[8edf]], which is a very good fifth-based equal temperament similar to [[88cET]]. | [[Step ratio|Basic]] semiwolf is in [[8edf]], which is a very good fifth-based equal temperament similar to [[88cET]]. | ||
== Temperaments == | |||
The most basic rank-2 temperament interpretation of uranian is semiwolf, which has 4:7:10 chords spelled <code>root-(p+1g)-(3p-2g)</code> (p = 3/2, g = the approximate 7/6). The name "semiwolf" comes from two [[7/6]] generators approximating a [[27/20]] wolf fourth. | |||
=== Semiwolf === | |||
[[Subgroup]]: 3/2.7/4.5/2 | |||
[[Comma]] list: [[245/243]] | |||
[[POL2]] generator: ~7/6 = 262.1728 | |||
[[Mapping]]: [{{val|1 1 3}}, {{val|0 1 -2}}] | |||
[[Vals]]: {{val list|8edf, 11edf, 13edf}} | |||
==== Semilupine ==== | |||
[[Subgroup]]: 3/2.7/4.5/2.11/4 | |||
[[Comma]] list: [[245/243]], [[100/99]] | |||
[[POL2]] generator: ~7/6 = 264.3771 | |||
[[Mapping]]: [{{val|1 1 3 4}}, {{val|0 1 -2 -4}}] | |||
[[Vals]]: {{val list|8edf, 13edf}} | |||
==== Hemilycan ==== | |||
[[Subgroup]]: 3/2.7/4.5/2.11/4 | |||
[[Comma]] list: [[245/243]], [[441/440]] | |||
[[POL2]] generator: ~7/6 = 261.5939 | |||
[[Mapping]]: [{{val|1 1 3 1}}, {{val|0 1 -2 4}}] | |||
[[Vals]]: {{val list|8edf, 11edf}} | |||
[[Category:Scales]] | [[Category:Scales]] | ||
[[Category:Abstract MOS patterns]] | [[Category:Abstract MOS patterns]] | ||
[[Category:Nonoctave]] | [[Category:Nonoctave]] | ||
Revision as of 19:00, 1 May 2021
| ↖ 2L 1s⟨3/2⟩ | ↑ 3L 1s⟨3/2⟩ | 4L 1s⟨3/2⟩ ↗ |
| ← 2L 2s⟨3/2⟩ | 3L 2s (3/2-equivalent) | 4L 2s⟨3/2⟩ → |
| ↙ 2L 3s⟨3/2⟩ | ↓ 3L 3s⟨3/2⟩ | 4L 3s⟨3/2⟩ ↘ |
┌╥╥┬╥┬┐ │║║│║││ │││││││ └┴┴┴┴┴┘
sLsLL
3L 2s<3/2> (sometimes called uranian), is a fifth-repeating MOS scale. The notation "<3/2>" means the period of the MOS is 3/2, disambiguating it from octave-repeating 3L 2s.
Because semiwolf is a fifth-repeating scale, each tone has a 3/2 perfect fifth above it. The scale has three major chords and two minor chords, all voiced so that the third of the triad is an octave higher, a tenth. Semiwolf also has two harmonic 7th chords.
Basic semiwolf is in 8edf, which is a very good fifth-based equal temperament similar to 88cET.
Temperaments
The most basic rank-2 temperament interpretation of uranian is semiwolf, which has 4:7:10 chords spelled root-(p+1g)-(3p-2g) (p = 3/2, g = the approximate 7/6). The name "semiwolf" comes from two 7/6 generators approximating a 27/20 wolf fourth.
Semiwolf
Subgroup: 3/2.7/4.5/2
POL2 generator: ~7/6 = 262.1728
Mapping: [⟨1 1 3], ⟨0 1 -2]]
Semilupine
Subgroup: 3/2.7/4.5/2.11/4
POL2 generator: ~7/6 = 264.3771
Mapping: [⟨1 1 3 4], ⟨0 1 -2 -4]]
Hemilycan
Subgroup: 3/2.7/4.5/2.11/4
POL2 generator: ~7/6 = 261.5939
Mapping: [⟨1 1 3 1], ⟨0 1 -2 4]]