Dicot family: Difference between revisions

Line 1:

The '''dicot family''' of temperaments tempers out [[25/24]], the ~~classic~~ chromatic semitone. The [[generator]] is a ~~classic~~ third (major and minor mean the same thing), and two such thirds give a fifth. In fact, ~~<math>\left~~(~~\frac{~~5}{4~~}\right~~)^2 = ~~\left~~(~~\frac{~~3}{2~~}\right~~)~~\left~~(~~\frac{~~25}~~{24~~}~~\right)</math>~~.

The '''dicot family''' of temperaments tempers out [[25/24]], the classical chromatic semitone. The [[generator]] is a classical third (major and minor mean the same thing), and two such thirds give a fifth. In fact, {{nowrap|(5/4)<sup>2</sup> {{=}} (3/2)(25/24)}}.

~~As a result of tempering out 25/24~~, [[~~5/4~~]] ~~and~~ [[~~6/5~~]] ~~are equated~~, ~~as are~~ [[~~8/5~~]] and [[~~5/3~~]]~~, which eliminates~~ the ~~distinction between "minor" and "major" as most know it~~. In a sense, what dicot is all about is using neutral thirds and sixths and pretending that these are 5-limit, and like any temperament which seems to involve ~~a lot~~ of "pretending", dicot is close to the edge of what can be ~~sensibly~~ called a temperament at all. In other words, it is an [[exotemperament]].

Possible tunings for dicot are [[7edo]], [[10edo]], [[17edo]], [[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 sixths and pretending that these are 5-limit, and like any temperament which seems to involve this level of "pretending", dicot is close to the edge of what can sensibly be called a temperament at all. In other words, it is an [[exotemperament]].

== Dicot ==

@@ Line 1: / Line 1: @@
-The '''dicot family''' of temperaments tempers out [[25/24]], the classic chromatic semitone. The [[generator]] is a classic third (major and minor mean the same thing), and two such thirds give a fifth. In fact, <math>\left(\frac{5}{4}\right)^2 = \left(\frac{3}{2}\right)\left(\frac{25}{24}\right)</math>.
+The '''dicot family''' of temperaments tempers out [[25/24]], the classical chromatic semitone. The [[generator]] is a classical third (major and minor mean the same thing), and two such thirds give a fifth. In fact, {{nowrap|(5/4)<sup>2</sup> {{=}} (3/2)(25/24)}}.
-As a result of tempering out 25/24, [[5/4]] and [[6/5]] are equated, as are [[8/5]] and [[5/3]], which eliminates the distinction between "minor" and "major" as most know it. In a sense, what dicot is all about is using neutral thirds and sixths and pretending that these are 5-limit, and like any temperament which seems to involve a lot of "pretending", dicot is close to the edge of what can be sensibly called a temperament at all. In other words, it is an [[exotemperament]].
+Possible tunings for dicot are [[7edo]], [[10edo]], [[17edo]], [[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 sixths and pretending that these are 5-limit, and like any temperament which seems to involve this level of "pretending", dicot is close to the edge of what can sensibly be called a temperament at all. In other words, it is an [[exotemperament]].
 == Dicot ==