Porcusmine: Difference between revisions

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CellularAutomaton (talk | contribs)
fleshed out tunings section
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'''Porcusmine''' is a [[Maximum variety|max-variety-3]], [[generator-offset]] scale with step pattern 4L 3M 1s. It is equivalent to the [[porcupine]] ([[7L 1s]]) mos with 4 of the large steps made bigger and the other 3 made smaller, or to the smitonic ([[4L 3s]]) with an extra-small step added. Porcusmine is not chiral. [[19edo]] is the smallest edo to support a non-degenerate porcusmine.
'''Porcusmine''' is a [[Maximum variety|max-variety-4]] or max-variety-3, [[generator-offset]] scale with step pattern 4L 3M 1s. It is equivalent to the [[porcupine]] ([[7L 1s]]) mos with 4 of the large steps made bigger and the other 3 made smaller, or to the smitonic ([[4L 3s]]) with an extra-small step added. Porcusmine is not chiral. [[19edo]] is the smallest edo to support a non-degenerate porcusmine.


Porcusmine can be tuned as a [[5-limit]] JI scale or a tempered version thereof, where L represents [[10/9]], M represents [[27/25]], and s represents [[25/24]].
Porcusmine can be tuned as a [[5-limit]] JI scale or a tempered version thereof, where L represents [[10/9]], M represents [[27/25]], and s represents [[25/24]].
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== Tunings ==
== Tunings ==
Porcusmine is MV3 when L+s=M+M, as reflected in the table below.
{| class="wikitable sortable"
{| class="wikitable sortable"
|+Porcusmine tunings
|+Porcusmine tunings
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|3:2:1
|3:2:1
|excellent pental thirds, fairly good 3-limit
|excellent pental thirds, fairly good 3-limit
|
|MV3
|-
|-
|23edo
|23edo
|4:2:1
|4:2:1
|excellent 6/5 and 9/8, fairly good 7/5  
|excellent 6/5 and 9/8, fairly good 7/5
|
|
|-
|-
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|27edo
|27edo
|4:3:2
|4:3:2
|
|excellent 10/9, 7/6, 6/5, and 7/5; fairly good 9/7 and 3/2
|
|MV3
|-
|-
|27edo
|27edo
|5:2:1
|5:2:1
|
|excellent 5:6:7; fairly good 7/4, 11/9, and 3/2
|
|
|-
|-
|30edo
|30edo
|5:3:1
|5:3:1
|
|excellent 15/14, 9/8, 6/5, and 9/7; fairly good 15/8, 7/4, and 11/8
|
|MV3
|-
|-
|31edo
|31edo
|5:3:2
|5:3:2
|
|excellent 15/14 or 16/15, 7/6, 5/4, and 7/5; fairly good 6/5, 9/7, 3/2
|
|meantone fifths
|-
|-
|31edo
|31edo
|6:2:1
|6:2:1
|
|excellent 7/4, 7/6, 11/9, 5/4, 7/5; fairly good 6/5, 3/2, and 11/8
|
|single meantone fifth
|-
|-
|33edo
|33edo
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|5:4:2
|5:4:2
|very close to 5-limit just tuning
|very close to 5-limit just tuning
|offers slightly sharp fifths
|gentle fifths
|-
|-
|34edo
|34edo