Porcusmine: Difference between revisions
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'''Porcusmine''' is a [[Maximum variety|max-variety- | '''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 | ||
| Line 83: | Line 84: | ||
|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 | ||
| | | | ||
|- | |- | ||
| Line 97: | Line 98: | ||
|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 | ||
| | |gentle fifths | ||
|- | |- | ||
|34edo | |34edo | ||