Ploidacot: Difference between revisions

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

The ploidacot system, similarly to [[pergen]]s, 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]]).

The ploidacot system, similarly to [[pergen]]s, 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]], than [[5/3]] and [[9/5]]).

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.

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 === No-twos or no-threes temperaments ===
-The ploidacot system, similarly to [[pergen]]s, 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]]).
+The ploidacot system, similarly to [[pergen]]s, 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]], than [[5/3]] and [[9/5]]).
 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.