Ploidacot: Difference between revisions

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The '''ploidacot''' system is a classification of [[rank-2 temperament|rank-2]] [[regular temperament|temperaments]] based on how a temperament can be ~~thought~~ of as a ~~union~~ of ~~copies~~ of [[~~Pythagorean tuning~~]]. It is similar to the [[pergen]], and is a canonical naming scheme for pergens of rank-2 temperaments of ~~the~~ 2.3.… [[subgroup]] in that every such pergen corresponds to a unique name in the ploidacot system.

The '''ploidacot''' system is a classification of [[rank-2 temperament|rank-2]] [[regular temperament|temperaments]] based on how a temperament divides the intervals of [[Pythagorean tuning]]. A particularly simple case is if a temperament divides its [[3/2]] interval into ''n'' steps, it can be called an ''n''-cot tuning. More generally, ploidacots are written as ''m''-ploid ''s''-sheared ''n''-cot, with ''m''- and ''n''- often replaced by greek numeral prefixes, such as mono-, di-, tri-, etc. (and ''m''-ploid omitted entirely if the [[2/1|octave]] is not split), and "''s''-sheared" replaced by a greek letter, such as alpha-, beta-, etc. (or omitted entirely if ''s'' = 0).

The "ploid" number of a temperament refers to how many equal parts, or [[period]]s the octave is divided into, and the "cot" number refers to how many [[generator]] steps of the temperament are needed to reach the third harmonic. Cots are generally presumed to reach 3/2 in a nonnegative number of generators. Temperaments where 3/2 is a whole number of ploids are written as ''acot''. However, stacking ''n'' cots sometimes doesn't reach 3/2, but instead an interval ''s'' ploids above 3/2. There are infinitely many possible values of ''s'', but for the sake of ploidacot, ''s'' takes its residue modulo ''n'' (which is the same for all possible cots), and is an integer between 0 and {{nowrap| ''n'' - 1 }} inclusive.

For example, [[meantone]] is monocot because it is does not split the octave, and is generated by the perfect fifth. [[Kleismic]] is alpha-hexacot, since it does not split the octave, but splits [[3/1]], which is one octave above 3/2, into six equal parts (~317{{c}} each). [[Pajara]] is diploid monocot, since it is generated by the fifth and splits the octave in two 600{{c}} halves. [[Shrutar]] is diploid alpha-dicot, since it splits the octave in half, and splits the interval 600{{c}} above 3/2 (~1300{{c}}) into two ~650{{c}} halves. Note that in shrutar the interval one ploid above 3/2 is ~1300{{c}} and not 3/1, since the octave is split into two 600{{c}} ploids.

It is similar to the [[pergen]], and is a canonical naming scheme for pergens of rank-2 temperaments of 2.3.(…) [[subgroup]]s in that every such pergen corresponds to a unique name in the ploidacot system.

The ploidacot system was developed by [[Praveen Venkataramana]].

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| delta

| epsilon

| digamma

| digamma/wau

| zeta

| eta

Line 52:

Line 58:

| qoppa

|-

! ~~style="white-space:~~ nowrap;" | ''n'' + 10

! {{nowrap|''n'' + 10}}

| iota-alpha

| iota-beta

Line 58:

Line 64:

| iota-delta

| iota-epsilon

| iota-digamma

| iota-digamma/iota-wau

| iota-zeta

| iota-eta

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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. Omega-based names are also not preferred when dealing with temperaments that split the octave, as they may be confusing - for instance, diploid alpha-tricot splits 4/3 in three while diploid beta-tricot splits 3/1 in three.

~~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~~.

=== 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]], than [[5/3]] and [[9/5]]).

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

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.

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

Even if 3 is included in a given temperament, 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).

Combining ploidacots and ploidasephs determines its [[5-limit]] properties; for instance, meantone can be labeled as "monocot beta-tetraseph" because four generators make up [[5/1]] while the generator represents [[3/2]], and valentine can be labeled as "enneacot pentaseph" because five generators make up [[5/4]] and nine of them make up [[3/2]].

== Examples ==

* [[Meantone]] and [[~~schismic~~]] are haploid monocot

The ploidacots of most common temperaments can be intuitively derived from a basic understanding of its mapping. [[Meantone]] and [[Helmholtz (temperament)|helmholtz]] are monocot since they have a period of a whole octave and are generated by the perfect fifth. Dicot is dicot since it has a period of a whole octave and splits the perfect fifth in two. Semaphore has a period of a whole octave and splits the perfect twelfth in two. It requires one period to add to the fifth to make it a twelfth, and one is alpha. So it is alpha-dicot.

* [[Mohajira]] and [[~~Dicot family|~~dicot]] are dicot

For a more complex example, let us consider sensi and its weak extension bison. Sensi splits 6/1 in seven. It requires two periods to the fifth to reach 6/1, and two is beta. So it is beta-heptacot. Bison splits the period of sensi in two. As a result, it now requires four periods to the fifth to reach 6/1, and four is delta. So it is diploid delta-heptacot.

Below is a list of ploidacots for common temperaments

* [[Meantone]] and [[Helmholtz (temperament)|helmholtz]] are haploid monocot

* [[Mohajira]] and [[dicot]] are dicot

* [[Bug]] and [[semaphore]] are alpha-dicot

* [[Shrutar]] is diploid alpha-dicot

* [[Ennealimmal]] is enneaploid dicot

* [[Hemiennealimmal]] is octodecaploid (18-ploid) dicot

* [[Slendric]], [[~~Gamelismic clan|~~mothra]], and [[rodan]] are tricot

* [[Slendric]], [[mothra]], and [[rodan]] are tricot

* [[~~Tricot~~]] is alpha-tricot

* [[Alphatricot]] is alpha-tricot

* [[Porcupine]] is beta-tricot

* [[Hedgehog]] is diploid alpha-tricot

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* [[Sensi]] is beta-heptacot

* [[Vishnu]] is diploid epsilon-heptacot

* [[~~Tetracot family|~~Octacot]] is octacot

* [[Octacot]] is octacot

* [[~~Würschmidt family|~~Würschmidt]] is beta-octacot

* [[Würschmidt]] is beta-octacot

* [[Valentine]] is enneacot

* [[~~Sycamore family|~~Sycamore]] is hendecacot

* [[Sycamore]] is hendecacot

* [[~~High badness temperaments#Chromo|~~Chromo]] is tridecacot

* [[Chromo]] is tridecacot

* [[Pajara]] and [[~~Meantone family#Injera|~~injera]] are diploid

* [[Pajara]] and [[injera]] are diploid

* [[~~Very low accuracy temperaments#Antitonic|~~Antitonic]] is diploid acot

* [[Antitonic]] is diploid acot

* [[Augene]] is triploid

* [[Diminished]] is tetraploid

* [[Diminished (temperament)|Diminished]] is tetraploid

* [[Blackwood]] is pentaploid acot

* [[~~Whitewood family|~~Whitewood]] is heptaploid acot

* [[Whitewood]] is heptaploid acot

* [[Ennealimmal]] is enneaploid

* [[Compton]] is dodecaploid acot

== Notation ==

: ''TODO: Come up with canonical ups and downs notation systems for pergen squares''

== List of ploidacots ==

=== Acot ===

* Pentaploid acot ([[blackwood]], [[5edo]])

* Heptaploid acot ([[whitewood]], [[7edo]])

* Dodecaploid acot ([[compton]], [[12edo]])

=== Monocot ===

* [[Ploidacot/Monocot|Monocot]]

* [[Ploidacot/Diploid monocot|Diploid monocot]]

* [[Ploidacot/Triploid monocot|Triploid monocot]]

* [[Ploidacot/Tetraploid monocot|Tetraploid monocot]]

* [[Ploidacot/Pentaploid monocot|Pentaploid monocot]]

* [[Ploidacot/Hexaploid monocot|Hexaploid monocot]]

* [[Ploidacot/Heptaploid monocot|Heptaploid monocot]]

=== Dicot ===

* [[Ploidacot/Dicot|Dicot]]

* [[Ploidacot/Alpha-dicot|Alpha-dicot]]

* [[Ploidacot/Diploid dicot|Diploid dicot]]

* [[Ploidacot/Diploid alpha-dicot|Diploid alpha-dicot]]

* [[Ploidacot/Triploid dicot|Triploid dicot]]

* [[Ploidacot/Triploid alpha-dicot|Triploid alpha-dicot]]

=== Tricot ===

* [[Ploidacot/Tricot|Tricot]]

* [[Ploidacot/Alpha-tricot|Alpha-tricot]]

* [[Ploidacot/Omega-tricot|Omega-tricot]]

* [[Ploidacot/Diploid tricot|Diploid tricot]]

* [[Ploidacot/Diploid alpha-tricot|Diploid alpha-tricot]]

* [[Ploidacot/Diploid beta-tricot|Diploid beta-tricot]]

* [[Ploidacot/Triploid tricot|Triploid tricot]]

=== Tetracot ===

* [[Ploidacot/Tetracot|Tetracot]]

* [[Ploidacot/Alpha-tetracot|Alpha-tetracot]]

* [[Ploidacot/Beta-tetracot|Beta-tetracot]]

* [[Ploidacot/Omega-tetracot|Omega-tetracot]]

=== Pentacot ===

* [[Ploidacot/Pentacot|Pentacot]]

* [[Ploidacot/Alpha-pentacot|Alpha-pentacot]]

* [[Ploidacot/Beta-pentacot|Beta-pentacot]]

* [[Ploidacot/Gamma-pentacot|Gamma-pentacot]]

* [[Ploidacot/Omega-pentacot|Omega-pentacot]]

=== Hexacot ===

* [[Ploidacot/Hexacot|Hexacot]]

* [[Ploidacot/Alpha-hexacot|Alpha-hexacot]]

* [[Ploidacot/Beta-hexacot|Beta-hexacot]]

* [[Ploidacot/Gamma-hexacot|Gamma-hexacot]]

* [[Ploidacot/Delta-hexacot|Delta-hexacot]]

* [[Ploidacot/Omega-hexacot|Omega-hexacot]]

=== Heptacot ===

* [[Ploidacot/Heptacot|Heptacot]]

* [[Ploidacot/Alpha-heptacot|Alpha-heptacot]]

* [[Ploidacot/Beta-heptacot|Beta-heptacot]]

* [[Ploidacot/Gamma-heptacot|Gamma-heptacot]]

* [[Ploidacot/Delta-heptacot|Delta-heptacot]]

* [[Ploidacot/Epsilon-heptacot|Epsilon-heptacot]]

* [[Ploidacot/Omega-heptacot|Omega-heptacot]]

=== Octacot ===

* [[Ploidacot/Octacot|Octacot]]

* [[Ploidacot/Beta-octacot|Beta-octacot]]

* [[Ploidacot/Epsilon-octacot|Epsilon-octacot]]

* [[Ploidacot/Omega-octacot|Omega-octacot]]

=== Enneacot ===

* [[Ploidacot/Enneacot|Enneacot]]

* [[Ploidacot/Delta-enneacot|Delta-enneacot]]

* [[Ploidacot/Omega-enneacot|Omega-enneacot]]

=== Decacot ===

* [[Ploidacot/Decacot|Decacot]]

* [[Ploidacot/Beta-decacot|Beta-decacot]]

* [[Ploidacot/Epsilon-decacot|Epsilon-decacot]]

=== >10 cots ===

* [[Ploidacot/Hendecacot|Hendecacot]]

* [[Ploidacot/Icosacot|Icosacot]]

== See also ==

* [[Wedgie]] – a mathematical generalization of the concept of ploidacots that uniquely characterizes a temperament

[[Category:Temperament naming]]

@@ Line 1: / Line 1: @@
-The '''ploidacot''' system is a classification of [[rank-2 temperament|rank-2]] [[regular temperament|temperaments]] based on how a temperament can be thought of as a union of copies of [[Pythagorean tuning]]. It is similar to the [[pergen]], and is a canonical naming scheme for pergens of rank-2 temperaments of the 2.3.… [[subgroup]] in that every such pergen corresponds to a unique name in the ploidacot system.
+The '''ploidacot''' system is a classification of [[rank-2 temperament|rank-2]] [[regular temperament|temperaments]] based on how a temperament divides the intervals of [[Pythagorean tuning]]. A particularly simple case is if a temperament divides its [[3/2]] interval into ''n'' steps, it can be called an ''n''-cot tuning. More generally, ploidacots are written as ''m''-ploid ''s''-sheared ''n''-cot, with ''m''- and ''n''- often replaced by greek numeral prefixes, such as mono-, di-, tri-, etc. (and ''m''-ploid omitted entirely if the [[2/1|octave]] is not split), and "''s''-sheared" replaced by a greek letter, such as alpha-, beta-, etc. (or omitted entirely if ''s'' = 0).
+The "ploid" number of a temperament refers to how many equal parts, or [[period]]s the octave is divided into, and the "cot" number refers to how many [[generator]] steps of the temperament are needed to reach the third harmonic. Cots are generally presumed to reach 3/2 in a nonnegative number of generators. Temperaments where 3/2 is a whole number of ploids are written as ''acot''. However, stacking ''n'' cots sometimes doesn't reach 3/2, but instead an interval ''s'' ploids above 3/2. There are infinitely many possible values of ''s'', but for the sake of ploidacot, ''s'' takes its residue modulo ''n'' (which is the same for all possible cots), and is an integer between 0 and {{nowrap| ''n'' - 1 }} inclusive.
+For example, [[meantone]] is monocot because it is does not split the octave, and is generated by the perfect fifth. [[Kleismic]] is alpha-hexacot, since it does not split the octave, but splits [[3/1]], which is one octave above 3/2, into six equal parts (~317{{c}} each). [[Pajara]] is diploid monocot, since it is generated by the fifth and splits the octave in two 600{{c}} halves. [[Shrutar]] is diploid alpha-dicot, since it splits the octave in half, and splits the interval 600{{c}} above 3/2 (~1300{{c}}) into two ~650{{c}} halves. Note that in shrutar the interval one ploid above 3/2 is ~1300{{c}} and not 3/1, since the octave is split into two 600{{c}} ploids.
+It is similar to the [[pergen]], and is a canonical naming scheme for pergens of rank-2 temperaments of 2.3.(…) [[subgroup]]s in that every such pergen corresponds to a unique name in the ploidacot system.
 The ploidacot system was developed by [[Praveen Venkataramana]].
@@ Line 36: / Line 42: @@
 | delta
 | epsilon
-| digamma
+| digamma/wau
 | zeta
 | eta
@@ Line 52: / Line 58: @@
 | qoppa
 |-
-! style="white-space: nowrap;" | ''n'' + 10
+! {{nowrap|''n'' + 10}}
 | iota-alpha
 | iota-beta
@@ Line 58: / Line 64: @@
 | iota-delta
 | iota-epsilon
-| iota-digamma
+| iota-digamma/iota-wau
 | iota-zeta
 | iota-eta
@@ Line 73: / Line 79: @@
 == 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. Omega-based names are also not preferred when dealing with temperaments that split the octave, as they may be confusing - for instance, diploid alpha-tricot splits 4/3 in three while diploid beta-tricot splits 3/1 in three.
-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.
+=== 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]], than [[5/3]] and [[9/5]]).
-=== Non-octave temperaments ===
+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.
-{{Todo|inline=1| expand }}
+Even if 3 is included in a given temperament, 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).
+Combining ploidacots and ploidasephs determines its [[5-limit]] properties; for instance, meantone can be labeled as "monocot beta-tetraseph" because four generators make up [[5/1]] while the generator represents [[3/2]], and valentine can be labeled as "enneacot pentaseph" because five generators make up [[5/4]] and nine of them make up [[3/2]].
 == Examples ==
-* [[Meantone]] and [[schismic]] are haploid monocot
+The ploidacots of most common temperaments can be intuitively derived from a basic understanding of its mapping. [[Meantone]] and [[Helmholtz (temperament)|helmholtz]] are monocot since they have a period of a whole octave and are generated by the perfect fifth. Dicot is dicot since it has a period of a whole octave and splits the perfect fifth in two. Semaphore has a period of a whole octave and splits the perfect twelfth in two. It requires one period to add to the fifth to make it a twelfth, and one is alpha. So it is alpha-dicot.
-* [[Mohajira]] and [[Dicot family|dicot]] are dicot
+For a more complex example, let us consider sensi and its weak extension bison. Sensi splits 6/1 in seven. It requires two periods to the fifth to reach 6/1, and two is beta. So it is beta-heptacot. Bison splits the period of sensi in two. As a result, it now requires four periods to the fifth to reach 6/1, and four is delta. So it is diploid delta-heptacot.
+Below is a list of ploidacots for common temperaments
+* [[Meantone]] and [[Helmholtz (temperament)|helmholtz]] are haploid monocot
+* [[Mohajira]] and [[dicot]] are dicot
 * [[Bug]] and [[semaphore]] are alpha-dicot
 * [[Shrutar]] is diploid alpha-dicot
 * [[Ennealimmal]] is enneaploid dicot
 * [[Hemiennealimmal]] is octodecaploid (18-ploid) dicot
-* [[Slendric]], [[Gamelismic clan|mothra]], and [[rodan]] are tricot
+* [[Slendric]], [[mothra]], and [[rodan]] are tricot
-* [[Tricot]] is alpha-tricot
+* [[Alphatricot]] is alpha-tricot
 * [[Porcupine]] is beta-tricot
 * [[Hedgehog]] is diploid alpha-tricot
@@ Line 102: / Line 119: @@
 * [[Sensi]] is beta-heptacot
 * [[Vishnu]] is diploid epsilon-heptacot
-* [[Tetracot family|Octacot]] is octacot
+* [[Octacot]] is octacot
-* [[Würschmidt family|Würschmidt]] is beta-octacot
+* [[Würschmidt]] is beta-octacot
 * [[Valentine]] is enneacot
-* [[Sycamore family|Sycamore]] is hendecacot
+* [[Sycamore]] is hendecacot
-* [[High badness temperaments#Chromo|Chromo]] is tridecacot
+* [[Chromo]] is tridecacot
-* [[Pajara]] and [[Meantone family#Injera|injera]] are diploid
+* [[Pajara]] and [[injera]] are diploid
-* [[Very low accuracy temperaments#Antitonic|Antitonic]] is diploid acot
+* [[Antitonic]] is diploid acot
 * [[Augene]] is triploid
-* [[Diminished]] is tetraploid
+* [[Diminished (temperament)|Diminished]] is tetraploid
 * [[Blackwood]] is pentaploid acot
-* [[Whitewood family|Whitewood]] is heptaploid acot
+* [[Whitewood]] is heptaploid acot
-* [[Ennealimmal]] is enneaploid
 * [[Compton]] is dodecaploid acot
 == Notation ==
 : ''TODO: Come up with canonical ups and downs notation systems for pergen squares''
+== List of ploidacots ==
+=== Acot ===
+* Pentaploid acot ([[blackwood]], [[5edo]])
+* Heptaploid acot ([[whitewood]], [[7edo]])
+* Dodecaploid acot ([[compton]], [[12edo]])
+=== Monocot ===
+* [[Ploidacot/Monocot|Monocot]]
+* [[Ploidacot/Diploid monocot|Diploid monocot]]
+* [[Ploidacot/Triploid monocot|Triploid monocot]]
+* [[Ploidacot/Tetraploid monocot|Tetraploid monocot]]
+* [[Ploidacot/Pentaploid monocot|Pentaploid monocot]]
+* [[Ploidacot/Hexaploid monocot|Hexaploid monocot]]
+* [[Ploidacot/Heptaploid monocot|Heptaploid monocot]]
+=== Dicot ===
+* [[Ploidacot/Dicot|Dicot]]
+* [[Ploidacot/Alpha-dicot|Alpha-dicot]]
+* [[Ploidacot/Diploid dicot|Diploid dicot]]
+* [[Ploidacot/Diploid alpha-dicot|Diploid alpha-dicot]]
+* [[Ploidacot/Triploid dicot|Triploid dicot]]
+* [[Ploidacot/Triploid alpha-dicot|Triploid alpha-dicot]]
+=== Tricot ===
+* [[Ploidacot/Tricot|Tricot]]
+* [[Ploidacot/Alpha-tricot|Alpha-tricot]]
+* [[Ploidacot/Omega-tricot|Omega-tricot]]
+* [[Ploidacot/Diploid tricot|Diploid tricot]]
+* [[Ploidacot/Diploid alpha-tricot|Diploid alpha-tricot]]
+* [[Ploidacot/Diploid beta-tricot|Diploid beta-tricot]]
+* [[Ploidacot/Triploid tricot|Triploid tricot]]
+=== Tetracot ===
+* [[Ploidacot/Tetracot|Tetracot]]
+* [[Ploidacot/Alpha-tetracot|Alpha-tetracot]]
+* [[Ploidacot/Beta-tetracot|Beta-tetracot]]
+* [[Ploidacot/Omega-tetracot|Omega-tetracot]]
+=== Pentacot ===
+* [[Ploidacot/Pentacot|Pentacot]]
+* [[Ploidacot/Alpha-pentacot|Alpha-pentacot]]
+* [[Ploidacot/Beta-pentacot|Beta-pentacot]]
+* [[Ploidacot/Gamma-pentacot|Gamma-pentacot]]
+* [[Ploidacot/Omega-pentacot|Omega-pentacot]]
+=== Hexacot ===
+* [[Ploidacot/Hexacot|Hexacot]]
+* [[Ploidacot/Alpha-hexacot|Alpha-hexacot]]
+* [[Ploidacot/Beta-hexacot|Beta-hexacot]]
+* [[Ploidacot/Gamma-hexacot|Gamma-hexacot]]
+* [[Ploidacot/Delta-hexacot|Delta-hexacot]]
+* [[Ploidacot/Omega-hexacot|Omega-hexacot]]
+=== Heptacot ===
+* [[Ploidacot/Heptacot|Heptacot]]
+* [[Ploidacot/Alpha-heptacot|Alpha-heptacot]]
+* [[Ploidacot/Beta-heptacot|Beta-heptacot]]
+* [[Ploidacot/Gamma-heptacot|Gamma-heptacot]]
+* [[Ploidacot/Delta-heptacot|Delta-heptacot]]
+* [[Ploidacot/Epsilon-heptacot|Epsilon-heptacot]]
+* [[Ploidacot/Omega-heptacot|Omega-heptacot]]
+=== Octacot ===
+* [[Ploidacot/Octacot|Octacot]]
+* [[Ploidacot/Beta-octacot|Beta-octacot]]
+* [[Ploidacot/Epsilon-octacot|Epsilon-octacot]]
+* [[Ploidacot/Omega-octacot|Omega-octacot]]
+=== Enneacot ===
+* [[Ploidacot/Enneacot|Enneacot]]
+* [[Ploidacot/Delta-enneacot|Delta-enneacot]]
+* [[Ploidacot/Omega-enneacot|Omega-enneacot]]
+=== Decacot ===
+* [[Ploidacot/Decacot|Decacot]]
+* [[Ploidacot/Beta-decacot|Beta-decacot]]
+* [[Ploidacot/Epsilon-decacot|Epsilon-decacot]]
+=== >10 cots ===
+* [[Ploidacot/Hendecacot|Hendecacot]]
+* [[Ploidacot/Icosacot|Icosacot]]
+== See also ==
+* [[Wedgie]] – a mathematical generalization of the concept of ploidacots that uniquely characterizes a temperament
 [[Category:Temperament naming]]