Dicot family: Difference between revisions

The [[5-limit]] parent [[comma]] for the dicot family is [[25/24]], the classic chromatic semitone. Its [[monzo]] is {{monzo| -3 -1 2 }}, and flipping that yields {{wedgie| 2 1 -3}} for the [[wedgie]]. This tells us the generator is a third (major and minor mean the same thing), and that two thirds gives a fifth. In fact, (5/4)^2 = 3/2 * 25/24. Possible tunings for dicot are [[7edo]], [[24edo]] using the val {{val|24 38 55}} (24c) and [[31edo]] using the val {{val|31 49 71}} (31c). In a sense, what dicot is all about is using neutral thirds and pretending that's 5-limit, and like any temperament which seems to involve pretending, dicot is at the edge of what can sensibly be called a temperament at all. In other words, it is an [[exotemperament]].

* 5-odd-limit [[diamond monotone]]: ~5/4 = [300.000, 400.000] (1\4 to 1\3)

* 5-odd-limit [[diamond tradeoff]]: ~5/4 = [315.641, 386.314]

* 5-odd-limit diamond monotone and tradeoff: ~5/4 = [315.641, 386.314]

=== Seven limit children ===

The second comma of the [[Normal_lists|normal comma list]] defines which [[7-limit]] family member we are looking at. Septimal dicot, with wedgie {{wedgie|2 1 3 -3 -1 4}} adds 36/35, sharp with wedgie {{wedgie|2 1 6 -3 4 11}} adds 28/27, and dichotic with wedgie {{wedgie|2 1 -4 -3 -12 -12}} ads 64/63, all retaining the same period and generator. Decimal with wedgie {{wedgie|4 2 2 -6 -8 -1}} adds 49/48, sidi with wedgie {{wedgie|4 2 9 -3 6 15}} adds 245/243, and jamesbond with wedgie {{wedgie|0 0 7 0 11 16}} adds 81/80. Here decimal divides the period to 1/2 octave, and sidi uses 9/7 as a generator, with two of them making up the combined 5/3 and 8/5 neutral sixth. Jamesbond has a period of 1/7 octave, and uses an approximate 15/14 as generator.

 

== Septimal dicot ==

Optimal GPV sequence: {{Val list| 3de, 4e, 7 }}

Optimal GPV sequence: {{Val list| 3d, 4, 7, 18bc, 25bccd }}

Optimal GPV sequence: {{Val list| 3d, 4, 7, 25bccd, 32bccddef, 39bcccdddef }}

Optimal GPV sequence: {{Val list| 3, 4, 7d }}

Optimal GPV sequence: {{Val list| 3, 4, 7d }}

Optimal GPV sequence: {{Val list| 3de, 7d, 10, 17d, 27cde }}

Optimal GPV sequence: {{Val list| 10, 14c, 24c, 38ccd, 52cccde }}

Optimal GPV sequence: {{Val list| 4, 10e, 14c }}

Optimal GPV sequence: {{Val list| 4, 6, 10 }}

Optimal GPV sequence: {{Val list| 7, 10, 17, 27ce, 44cce }}

Optimal GPV sequence: {{Val list| 3, 7e, 10 }}

Optimal GPV sequence: {{Val list| 7, 14c }}

==== 13-limit ====

Optimal GPV sequence: {{Val list| 7, 14c }}

==== Septimal ====

Optimal GPV sequence: {{Val list| 7, 14cf }}

Optimal GPV sequence: {{Val list| 3de, 14c, 45cce, 59bcccdee }}