Ploidacot: Difference between revisions

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== Specification ==

=== Ploids ===

Any rank-2 temperament of the 2.3.… subgroup has an octave, and it ~~must~~ split the octave into a number of parts, or [[period]]s, called '''ploids'''. The temperament's number of ploids per octave is specified by a Greek numeral prefix (di-, tri-, etc.) and -ploid. For instance, pajara divides the octave into two, so it is diploid. Temperaments that do not divide the octave are called haploid (''not'' *monoploid), which can be omitted.

Any rank-2 temperament of the 2.3.… subgroup has an octave, and it may split the octave into a number of parts, or [[period]]s, called '''ploids'''. The temperament's number of ploids per octave is specified by a Greek numeral prefix (di-, tri-, etc.) and -ploid. For instance, pajara divides the octave into two, so it is diploid. Temperaments that do not divide the octave are called haploid (''not'' *monoploid), which can be omitted.

=== Cots ===

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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.

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 ===

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== 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

* [[Blackwood]] is pentaploid acot

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

* [[Whitewood]] is heptaploid acot

* [[Ennealimmal]] is enneaploid

* [[Compton]] is dodecaploid acot

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== 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]]

=== Dicot ===

* [[Ploidacot/Dicot|Dicot]]

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

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

=== Tricot ===

* [[Ploidacot/Tricot|Tricot]]

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

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

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

=== Hexacot ===

* [[Ploidacot/Hexacot|Hexacot]]

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

=== Heptacot ===

* [[Ploidacot/Heptacot|Heptacot]]

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

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

=== Octacot ===

* [[Ploidacot/Octacot|Octacot]]

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

=== Enneacot ===

* [[Ploidacot/Enneacot|Enneacot]]

=== >10 cots ===

* [[Ploidacot/Icosacot|Icosacot]]

== See also ==

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

[[Category:Temperament naming]]

@@ Line 5: / Line 5: @@
 == Specification ==
 === Ploids ===
-Any rank-2 temperament of the 2.3.… subgroup has an octave, and it must split the octave into a number of parts, or [[period]]s, called '''ploids'''. The temperament's number of ploids per octave is specified by a Greek numeral prefix (di-, tri-, etc.) and -ploid. For instance, pajara divides the octave into two, so it is diploid. Temperaments that do not divide the octave are called haploid (''not'' *monoploid), which can be omitted.
+Any rank-2 temperament of the 2.3.… subgroup has an octave, and it may split the octave into a number of parts, or [[period]]s, called '''ploids'''. The temperament's number of ploids per octave is specified by a Greek numeral prefix (di-, tri-, etc.) and -ploid. For instance, pajara divides the octave into two, so it is diploid. Temperaments that do not divide the octave are called haploid (''not'' *monoploid), which can be omitted.
 === Cots ===
@@ Line 75: / Line 75: @@
 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.
+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 ===
@@ Line 81: / Line 81: @@
 == 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 107: @@
 * [[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
 * [[Blackwood]] is pentaploid acot
-* [[Whitewood family|Whitewood]] is heptaploid acot
+* [[Whitewood]] is heptaploid acot
 * [[Ennealimmal]] is enneaploid
 * [[Compton]] is dodecaploid acot
@@ Line 118: / Line 123: @@
 == 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]]
+=== Dicot ===
+* [[Ploidacot/Dicot|Dicot]]
+* [[Ploidacot/Alpha-dicot|Alpha-dicot]]
+* [[Ploidacot/Diploid dicot|Diploid dicot]]
+=== Tricot ===
+* [[Ploidacot/Tricot|Tricot]]
+* [[Ploidacot/Alpha-tricot|Alpha-tricot]]
+* [[Ploidacot/Diploid alpha-tricot|Diploid alpha-tricot]]
+* [[Ploidacot/Omega-tricot|Omega-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/Gamma-pentacot|Gamma-pentacot]]
+=== Hexacot ===
+* [[Ploidacot/Hexacot|Hexacot]]
+* [[Ploidacot/Alpha-hexacot|Alpha-hexacot]]
+=== Heptacot ===
+* [[Ploidacot/Heptacot|Heptacot]]
+* [[Ploidacot/Alpha-heptacot|Alpha-heptacot]]
+* [[Ploidacot/Beta-heptacot|Beta-heptacot]]
+=== Octacot ===
+* [[Ploidacot/Octacot|Octacot]]
+* [[Ploidacot/Beta-octacot|Beta-octacot]]
+=== Enneacot ===
+* [[Ploidacot/Enneacot|Enneacot]]
+=== >10 cots ===
+* [[Ploidacot/Icosacot|Icosacot]]
+== See also ==
+* [[Wedgie]] - a mathematical generalization of the concept of ploidacots that uniquely characterizes a temperament
 [[Category:Temperament naming]]