Ploidacot: Difference between revisions

Line 69:

== Properties ==

* For ''n''-cot systems there are exactly ''n'' settings of shear, or number of ploids to add to the step that represents the interval class of 3. ~~These~~ are 0-, 1-, 2-, …, {{nowrap|(''n'' - 1)}}~~-sheared ''n''-cot~~. For example, the tricot systems are tricot (0-sheared), alpha-tricot (1-sheared), and beta-tricot (2-sheared). There is not a *gamma-tricot since that would be equivalent to tricot.

* For ''n''-cot systems there are exactly ''n'' settings of shear, or number of ploids to add to the step that represents the interval class of 3. The possible values of shear are 0, 1, 2, …, {{nowrap|(''n'' − 1)}}. For example, the tricot systems are tricot (0-sheared), alpha-tricot (1-sheared), and beta-tricot (2-sheared). There is not a *gamma-tricot since that would be equivalent to tricot.

== Extensions ==

=== Omega extension ===

The Greek letter omega, proposed by [[User:Godtone|Godtone]], is used for −1. This simplifies the classification of certain temperaments, e.g. porcupine, which instead of beta-tricot can be omega-tricot, as splitting the interval 4/3 into three is arguably more intuitive than splitting the interval 6. This effectively shifts the possible values of shear to -1, 0, 1, …, {{nowrap|(''n'' − 2)}} if ''n'' ≥ 3.

Note that omega should only be used with ''n'' ≥ 3. When ''n'' = 1, there is only monocot. When ''n'' = 2, alpha-dicot is preferred over omega-dicot.

=== Non-octave temperaments ===

== Examples ==

@@ Line 69: / Line 69: @@
 == Properties ==
-* For ''n''-cot systems there are exactly ''n'' settings of shear, or number of ploids to add to the step that represents the interval class of 3. These are 0-, 1-, 2-, …, {{nowrap|(''n'' - 1)}}-sheared ''n''-cot. For example, the tricot systems are tricot (0-sheared), alpha-tricot (1-sheared), and beta-tricot (2-sheared). There is not a *gamma-tricot since that would be equivalent to tricot.
+* For ''n''-cot systems there are exactly ''n'' settings of shear, or number of ploids to add to the step that represents the interval class of 3. The possible values of shear are 0, 1, 2, …, {{nowrap|(''n'' − 1)}}. For example, the tricot systems are tricot (0-sheared), alpha-tricot (1-sheared), and beta-tricot (2-sheared). There is not a *gamma-tricot since that would be equivalent to tricot.
+== Extensions ==
+=== Omega extension ===
+The Greek letter omega, proposed by [[User:Godtone|Godtone]], is used for −1. This simplifies the classification of certain temperaments, e.g. porcupine, which instead of beta-tricot can be omega-tricot, as splitting the interval 4/3 into three is arguably more intuitive than splitting the interval 6. This effectively shifts the possible values of shear to -1, 0, 1, …, {{nowrap|(''n'' − 2)}} if ''n'' ≥ 3.
+Note that omega should only be used with ''n'' ≥ 3. When ''n'' = 1, there is only monocot. When ''n'' = 2, alpha-dicot is preferred over omega-dicot.
+=== Non-octave temperaments ===
+{{Todo|inline=1| expand }}
 == Examples ==