The Jacobins: Difference between revisions

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Quite coincidentally, [[1789edo]] supports an enormous amount of these temperaments.

== Jacobin-naiadic ==

Since 6656/6655 is the difference between a stack of three 11/8's and 13/10, it is natural to choose a rank-2 temperament that uses 11/8 as the generator to exploit the comma. Such a mapping is realized through the fractional subgroup 2.13/10.11, which produces a basis with just one comma - namely the 6656/6655. Name given because the 13/10 interval is sometimes referred to as a "naiadic", and this name separates it from the standard diatonic framework.

Subgroup: 2.13/10.11

Comma list: 6656/6655

Sval mapping: 1 2 4, 0 -3 -1

Optimal tuning (CTE): ~16/11 = 648.608

== Onzonic ==

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=== Pure onzonic ===

Pure onzonic is the temperament that was initially referred to as "jacobin" before it was pointed out that the same name would be reserved for the rank-5 temperamnet tempering out 6656/6655 alone. ~~Since 6656/6655 is the difference between a stack of three 11/8's and 13/10, it is natural to choose a rank-2 temperament that uses 11/8 as the generator to exploit the comma.~~

Pure onzonic is the temperament that was initially referred to as "jacobin" before it was pointed out that the same name would be reserved for the rank-5 temperamnet tempering out 6656/6655 alone.

[[Subgroup]]: 2.5.11.13

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 Quite coincidentally, [[1789edo]] supports an enormous amount of these temperaments.
+== Jacobin-naiadic ==
+Since 6656/6655 is the difference between a stack of three 11/8's and 13/10, it is natural to choose a rank-2 temperament that uses 11/8 as the generator to exploit the comma. Such a mapping is realized through the fractional subgroup 2.13/10.11, which produces a basis with just one comma - namely the 6656/6655. Name given because the 13/10 interval is sometimes referred to as a "naiadic", and this name separates it from the standard diatonic framework.
+Subgroup: 2.13/10.11
+Comma list: 6656/6655
+Sval mapping: 1 2 4, 0 -3 -1
+Optimal tuning (CTE): ~16/11 = 648.608
 == Onzonic ==
@@ Line 9: / Line 20: @@
 === Pure onzonic ===
-Pure onzonic is the temperament that was initially referred to as "jacobin" before it was pointed out that the same name would be reserved for the rank-5 temperamnet tempering out 6656/6655 alone. Since 6656/6655 is the difference between a stack of three 11/8's and 13/10, it is natural to choose a rank-2 temperament that uses 11/8 as the generator to exploit the comma.
+Pure onzonic is the temperament that was initially referred to as "jacobin" before it was pointed out that the same name would be reserved for the rank-5 temperamnet tempering out 6656/6655 alone.
 [[Subgroup]]: 2.5.11.13