Ploidacot - Revision history

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
Line 1:		Line 1:
	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
Line 5:		Line 5:
	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
Line 7:		Line 7:
	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
Line 1:		Line 1:
	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.

Overthink: mention acot; paragraphing

2026-05-13T01:39:46Z

mention acot; paragraphing

← Older revision		Revision as of 01:39, 13 May 2026
Line 1:		Line 1:
	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 "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. However, stacking ''n'' cots ~~often~~ 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'', and is an integer between 0 and ''n'' - 1 inclusive.		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 "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 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.

Overthink: make more correct

2026-05-13T01:36:19Z

make more correct

← Older revision		Revision as of 01:36, 13 May 2026
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~~]].		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 "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. However, stacking ''n'' cots often 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'', and is an integer between 0 and ''n'' - 1 inclusive.

	~~The simplest~~ and ~~most straightforward way to conceptualize this concept~~ is ~~simply; if your temperament can divide its~~ [[~~3/2~~]] ~~interval into N steps~~, ~~it can be called an N-cot tuning.~~		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;~~ since [[~~34edo~~]]'s 3/2 ~~maps to 20\34~~, ~~and 20~~ is ~~divisible~~ by ~~both 4~~ and 5, so it ~~can be called tetracot~~ (~~4-cot) or pentacot (5-cot~~).

	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 the 2.3.… [[subgroup]] in that every such pergen corresponds to a unique name in the ploidacot system.

Pailiaq at 00:41, 13 May 2026

2026-05-13T00:41:00Z

← Older revision		Revision as of 00:41, 13 May 2026
Line 4:		Line 4:

	For example; since [[34edo]]'s 3/2 maps to 20\34, and 20 is divisible by both 4 and 5, so it can be called tetracot (4-cot) or pentacot (5-cot).		For example; since [[34edo]]'s 3/2 maps to 20\34, and 20 is divisible by both 4 and 5, so it can be called tetracot (4-cot) or pentacot (5-cot).


	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 the 2.3.… [[subgroup]] in that every such pergen corresponds to a unique name in the ploidacot system.

Pailiaq: added a straightforward explanation to the intro of this article

2026-05-13T00:40:40Z

added a straightforward explanation to the intro of this article

← Older revision		Revision as of 00:40, 13 May 2026
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 can be thought of as a union of copies of [[Pythagorean tuning]].

			The simplest and most straightforward way to conceptualize this concept is simply; if your temperament can divide its [[3/2]] interval into N steps, it can be called an N-cot tuning.

			For example; since [[34edo]]'s 3/2 maps to 20\34, and 20 is divisible by both 4 and 5, so it can be called tetracot (4-cot) or pentacot (5-cot).


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