Ploidacot: Difference between revisions

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== 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.

The Greek letter omega, proposed by [[User:Godtone|Godtone]], is used for −1. ("Contra" has also been used in place of omega.) 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 {{nowrap| ''n'' ≥ 3 }}. When {{nowrap| ''n'' {{=}} 1 }}, there is only monocot. When {{nowrap| ''n'' {{=}} 2 }}, alpha-dicot is preferred over omega-dicot.

=== ~~Non~~-~~octave~~ temperaments ===

=== No-twos or no-threes temperaments ===

~~{{Todo~~|~~inline=~~1~~| expand }}~~

The ploidacot system, similarly to [[pergens]], relies on the presence of a [[3-limit]], i.e. 2.3 subgroup, spine, but its defining principles can be easily applied to a 2.5, 3.5, 3.7, etc. spine instead, and in the case of ploidacot, the "cot" suffix is simply replaced with a different suffix indicating the family of intervals being cloven. The existing extensions are "seph" for [[5/4]] with octave equivalence, and "gem" for [[7/3]] with tritave equivalence (note that 3.7 is preferred over 3.5 since [[9/7]] and 7/3 generate a much more commonly used structure in tritave systems, i.e. [[4L 5s (3/1-equivalent)|Lambda]]).

For instance, in the 2.5.7 subgroup, [[didacus]] can be labeled as "diseph", because its generator divides 5/4 in two, and [[llywelyn]] can be labeled as "alpha-heptaseph" because seven generators make up [[5/2]]. In the tritave world, [[BPS]] (3.5.7) is "monogem" as its generator is 9/7, while [[mintaka]] (3.7.11) is alpha-trigem as its generator (of ~[[21/11]]) splits [[7/1]] in three.

Even if 3 is included, the ploidaseph framework may occasionally be more useful than the ploidacot framework, in cases where the mapping of 3 is very complex and the structure of the temperament therefore deprioritizes prime 3. [[Hemiwürschmidt]], a [[strong extension]] of the aforementioned didacus, has a ploidacot of beta-hexadecacot as it divides 6/1 into sixteen generators; while [[trismegistus]] has a ploidacot of epsilon-pentadecacot as it maps [[96/1]] to fifteen generators. Each of these has a more intuitizable expression in terms of 2.5 intervals, which are much simpler in the respective temperaments: hemiwürschmidt is diseph and trismegistus is alpha-triseph (one-third 5/2).

== Examples ==

@@ Line 73: / Line 73: @@
 == 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.
+The Greek letter omega, proposed by [[User:Godtone|Godtone]], is used for −1. ("Contra" has also been used in place of omega.) 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 {{nowrap| ''n'' ≥ 3 }}. When {{nowrap| ''n'' {{=}} 1 }}, there is only monocot. When {{nowrap| ''n'' {{=}} 2 }}, alpha-dicot is preferred over omega-dicot.
-=== Non-octave temperaments ===
+=== No-twos or no-threes temperaments ===
-{{Todo|inline=1| expand }}
+The ploidacot system, similarly to [[pergens]], relies on the presence of a [[3-limit]], i.e. 2.3 subgroup, spine, but its defining principles can be easily applied to a 2.5, 3.5, 3.7, etc. spine instead, and in the case of ploidacot, the "cot" suffix is simply replaced with a different suffix indicating the family of intervals being cloven. The existing extensions are "seph" for [[5/4]] with octave equivalence, and "gem" for [[7/3]] with tritave equivalence (note that 3.7 is preferred over 3.5 since [[9/7]] and 7/3 generate a much more commonly used structure in tritave systems, i.e. [[4L 5s (3/1-equivalent)|Lambda]]).
+For instance, in the 2.5.7 subgroup, [[didacus]] can be labeled as "diseph", because its generator divides 5/4 in two, and [[llywelyn]] can be labeled as "alpha-heptaseph" because seven generators make up [[5/2]]. In the tritave world, [[BPS]] (3.5.7) is "monogem" as its generator is 9/7, while [[mintaka]] (3.7.11) is alpha-trigem as its generator (of ~[[21/11]]) splits [[7/1]] in three.
+Even if 3 is included, the ploidaseph framework may occasionally be more useful than the ploidacot framework, in cases where the mapping of 3 is very complex and the structure of the temperament therefore deprioritizes prime 3. [[Hemiwürschmidt]], a [[strong extension]] of the aforementioned didacus, has a ploidacot of beta-hexadecacot as it divides 6/1 into sixteen generators; while [[trismegistus]] has a ploidacot of epsilon-pentadecacot as it maps [[96/1]] to fifteen generators. Each of these has a more intuitizable expression in terms of 2.5 intervals, which are much simpler in the respective temperaments: hemiwürschmidt is diseph and trismegistus is alpha-triseph (one-third 5/2).
 == Examples ==