Ploidacot - Revision history

FloraC: Linking

2026-08-08T08:44:46Z

Linking

← Older revision		Revision as of 08:44, 8 August 2026
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	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 [[octave]] is not split), and "''s''-sheared" replaced by a greek letter, such as alpha-, beta-, etc. (or omitted entirely if ''s'' = 0).		The '''ploidacot''' system is a classification of [[rank-2 temperament]]s 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 [[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 does not 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.		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 does not 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.
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	== Specification ==		== Specification ==
	=== Ploids ===		=== Ploids ===
	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.		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 ===		=== Cots ===
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	The idea of classifying temperaments by splitting a subgroup can be traced back to the introduction of the [[wedgie]], a mathematical construct that uniquely characterizes a rank-''r'' temperament by how the temperament splits each rank-''r'' subgroup of the original subgroup.		The idea of classifying temperaments by splitting a subgroup can be traced back to the introduction of the [[wedgie]], a mathematical construct that uniquely characterizes a rank-''r'' temperament by how the temperament splits each rank-''r'' subgroup of the original subgroup.

	The ploidacot system comes more directly after [[Kite Giedraitis]]' [[pergen]] system, and may be considered 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 comes more directly after [[Kite Giedraitis]]' [[pergen]] system, and may be considered a canonical naming scheme for pergens of rank-2 temperaments of 2.3.(…) subgroups in that every such pergen corresponds to a unique name in the ploidacot system.

	=== Relationship to pergens ===		=== Relationship to pergens ===

FloraC: Address prior art & various other improvements

2026-08-08T08:41:38Z

Address prior art & various other improvements

← Older revision		Revision as of 08:41, 8 August 2026
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	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 [[octave]] is not split), and "''s''-sheared" replaced by a greek letter, such as alpha-, beta-, etc. (or omitted entirely if ''s'' = 0).		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 [[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.		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 does not 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.		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]].~~

	== Specification ==		== Specification ==
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	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]].		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]].

	== Relationship to pergens ==		== Origin ==
			The ploidacot system was developed by [[Praveen Venkataramana]], based on the pattern of certain individual temperament names: ''dicot'', ''tricot'' (now ''alphatricot''), and ''tetracot''.

			The idea of classifying temperaments by splitting a subgroup can be traced back to the introduction of the [[wedgie]], a mathematical construct that uniquely characterizes a rank-''r'' temperament by how the temperament splits each rank-''r'' subgroup of the original subgroup.

			The ploidacot system comes more directly after [[Kite Giedraitis]]' [[pergen]] system, and may be considered 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.

			=== Relationship to pergens ===
	Each ploidacot has one pergen. The numbers of ploid (''p''), shear (''s''), and cot (''c'') are given, its pergen form has following features:		Each ploidacot has one pergen. The numbers of ploid (''p''), shear (''s''), and cot (''c'') are given, its pergen form has following features:
	* Every ''p''-ploid has a form of (P8/''p'', X).		* Every ''p''-ploid has a form of (P8/''p'', X).
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	\|}		\|}

	== ~~Notation~~ ==		== Relationship to notation ==
	While there are no agreed-upon notation system for many ploidacots, some of which can be notated by [[Kite's ups and downs notation~~\|ups and downs~~ notation ~~system~~]]. For example, [[~~Ploidacot~~/Tricot\|tricot]] is based on interpreting the generator as a supermajor second, allowing for an ^ or v to stand for 1/3 of a diatonic semitone, and [[Ploidacot/Tetracot\|tetracot]] is based on interpreting the generator as a submajor second, allowing for an ^ or v to stand for 1/4 of a chromatic semitone, and [[Ploidacot/Triploid monocot\|triploid monocot]] is based on interpreting the period as a submajor third, allowing for an ^ or v to stand for 1/3 of an ''inversed'' diminished second (the difference between diatonic semitone and chromatic semitone, equivalent to the [[Pythagorean comma]]). Certain ploidacots (such as [[~~Ploidacot~~/Diploid dicot\|diploid dicot]]) require another additional pair, such as lifts and drops, written / and ⧵ .		While there are no agreed-upon notation system for many ploidacots, some of which can be notated by [[Kite's ups and downs notation]] or [[Stein–Zimmermann–Gould notation]]. For example, [[ploidacot/Tricot\|tricot]] is based on interpreting the generator as a supermajor second, allowing for an ^ or v to stand for 1/3 of a diatonic semitone, and [[Ploidacot/Tetracot\|tetracot]] is based on interpreting the generator as a submajor second, allowing for an ^ or v to stand for 1/4 of a chromatic semitone, and [[Ploidacot/Triploid monocot\|triploid monocot]] is based on interpreting the period as a submajor third, allowing for an ^ or v to stand for 1/3 of an ''inversed'' diminished second (the difference between diatonic semitone and chromatic semitone, equivalent to the [[Pythagorean comma]]). Certain ploidacots (such as [[ploidacot/Diploid dicot\|diploid dicot]]) require another additional pair, such as lifts and drops, written / and ⧵ .

	== List of ploidacots ==		== List of ploidacots ==
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	* [[Ploidacot/Hendecacot\|Hendecacot]]		* [[Ploidacot/Hendecacot\|Hendecacot]]
	* [[Ploidacot/Icosacot\|Icosacot]]		* [[Ploidacot/Icosacot\|Icosacot]]

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

	[[Category:Temperament naming]]		[[Category:Temperament naming]]

FloraC: - redundant examples

2026-08-08T07:42:03Z

- redundant examples

@@ Line 484: / Line 484: @@
 == Notation ==
 While there are no agreed-upon notation system for many ploidacots, some of which can be notated by [[Kite's ups and downs notation|ups and downs notation system]]. For example, [[Ploidacot/Tricot|tricot]] is based on interpreting the generator as a supermajor second, allowing for an ^ or v to stand for 1/3 of a diatonic semitone, and [[Ploidacot/Tetracot|tetracot]] is based on interpreting the generator as a submajor second, allowing for an ^ or v to stand for 1/4 of a chromatic semitone, and [[Ploidacot/Triploid monocot|triploid monocot]] is based on interpreting the period as a submajor third, allowing for an ^ or v to stand for 1/3 of an ''inversed'' diminished second (the difference between diatonic semitone and chromatic semitone, equivalent to the [[Pythagorean comma]]). Certain ploidacots (such as [[Ploidacot/Diploid dicot|diploid dicot]]) require another additional pair, such as lifts and drops, written / and ⧵ .
 == List of ploidacots ==

FloraC: Text replacement - "octave" to "octave"

2026-07-14T14:15:45Z

Text replacement - "octave" to "octave"

← Older revision		Revision as of 14:15, 14 July 2026
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	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 '''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 [[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.		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.

FloraC: /* Relationship to pergens */ cut the table down to 8, as that's where it occupies full width in the Vector skin

2026-06-06T09:26:48Z

Relationship to pergens: cut the table down to 8, as that's where it occupies full width in the Vector skin

Show changes

Xenllium: Added notation and relationship to pergens

2026-06-06T06:21:59Z

Added notation and relationship to pergens

Show changes

FloraC: Better integration of the special case

2026-05-13T07:39:36Z

Better integration of the special case

← Older revision		Revision as of 07:39, 13 May 2026
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	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]]. ~~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 '''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).

	~~To put it simply; if your temperament can divide its 3/2 interval into N steps, it can be called an N-cot tuning.~~		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.

	The "ploid" number of a temperament refers to how many equal parts, or ~~"ploids" (known as~~ [[period]]s ~~in [[regular temperament theory]]),~~ the octave is divided into, and the "cot" number refers to how many [[generator]] steps of the temperament~~, or "cots", is~~ 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 ''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.		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.

Lucius Chiaraviglio: Fix typo

2026-05-13T04:04:28Z

Fix typo

← Older revision		Revision as of 04:04, 13 May 2026
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	The "ploid" number of a temperament refers to how many equal parts, or "ploids" (known as [[period]]s in [[regular temperament theory]]), the octave is divided into, and the "cot" number refers to how many [[generator]] steps of the temperament, or "cots", is 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 ''n'' - 1 inclusive.		The "ploid" number of a temperament refers to how many equal parts, or "ploids" (known as [[period]]s in [[regular temperament theory]]), the octave is divided into, and the "cot" number refers to how many [[generator]] steps of the temperament, or "cots", is 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 ''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 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.		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.		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.

Overthink: there's no "the" subgroup

2026-05-13T03:18:18Z

there's no "the" subgroup

← Older revision		Revision as of 03:18, 13 May 2026
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	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 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.		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 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 ~~the~~ 2.3.… [[subgroup]] in that every such pergen corresponds to a unique name in the ploidacot system.		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]].		The ploidacot system was developed by [[Praveen Venkataramana]].

Pailiaq: readded the simplification - frankly i think the intro is more confusing than it was before

2026-05-13T02:04:59Z

readded the simplification - frankly i think the intro is more confusing than it was before

← Older revision		Revision as of 02:04, 13 May 2026
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	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]]. 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 '''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]]. 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).

			To put it simply; if your temperament can divide its 3/2 interval into N steps, it can be called an N-cot tuning.

	The "ploid" number of a temperament refers to how many equal parts, or "ploids" (known as [[period]]s in [[regular temperament theory]]), the octave is divided into, and the "cot" number refers to how many [[generator]] steps of the temperament, or "cots", is 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 ''n'' - 1 inclusive.		The "ploid" number of a temperament refers to how many equal parts, or "ploids" (known as [[period]]s in [[regular temperament theory]]), the octave is divided into, and the "cot" number refers to how many [[generator]] steps of the temperament, or "cots", is 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 ''n'' - 1 inclusive.