Ploidacot - Revision history

Kili: redicect

2026-05-13T16:35:40Z

redicect

← Older revision		Revision as of 16:35, 13 May 2026
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	'''Ploidacot''' is a naming scheme for rank-2 tuning/temperament structures based on the number of periods per octave and the number of periods and independent generators per fifth, created by [[Praveen Venkataramana]].		'''Ploidacot''' is a naming scheme for rank-2 tuning/temperament structures based on the number of [[Period\|periods]] per octave and the number of periods and independent [[Generator\|generators]] per fifth, created by [[Praveen Venkataramana]].

	The general form is '''x'''-ploid '''y'''-sheared '''z'''-cot, where '''x''' is the number of periods in the octave, and where '''y''' periods ''down'' and '''z''' generators ''up'' are needed to reach ~3/2. Equivalently, '''z''' generators make 3/2 plus '''y'''/'''x''' octaves.		The general form is '''x'''-ploid '''y'''-sheared '''z'''-cot, where '''x''' is the number of periods in the octave, and where '''y''' periods ''down'' and '''z''' generators ''up'' are needed to reach ~3/2. Equivalently, '''z''' generators make 3/2 plus '''y'''/'''x''' octaves.

Inthar at 08:58, 16 April 2026

2026-04-16T08:58:03Z

← Older revision		Revision as of 08:58, 16 April 2026
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	A temperament with a ~3/2 of an exact number of periods is ''acot'' or ''0-cot''. In this situation, the shear amount tends to be left out of the ploidacot name, but it can be seen as -1 times however many periods there are in the fifth.		A temperament with a ~3/2 of an exact number of periods is ''acot'' or ''0-cot''. In this situation, the shear amount tends to be left out of the ploidacot name, but it can be seen as -1 times however many periods there are in the fifth.

			Proposed non-2/1, non-3/2 generators:
			* ''-gem'': 7/3
			* ''-seph'': 5/4
			* ''-mech'': 7/4
	== Examples ==		== Examples ==
	Blackwood has a fifth-octave period with the perfect fifth at exactly 3\5, making it a ''pentaploid (-3-sheared) acot'' temperament.		Blackwood has a fifth-octave period with the perfect fifth at exactly 3\5, making it a ''pentaploid (-3-sheared) acot'' temperament.

Inthar at 08:56, 16 April 2026

2026-04-16T08:56:41Z

← Older revision		Revision as of 08:56, 16 April 2026
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	The general form is '''x'''-ploid '''y'''-sheared '''z'''-cot, where '''x''' is the number of periods in the octave, and where '''y''' periods ''down'' and '''z''' generators ''up'' are needed to reach ~3/2. Equivalently, '''z''' generators make 3/2 plus '''y'''/'''x''' octaves.		The general form is '''x'''-ploid '''y'''-sheared '''z'''-cot, where '''x''' is the number of periods in the octave, and where '''y''' periods ''down'' and '''z''' generators ''up'' are needed to reach ~3/2. Equivalently, '''z''' generators make 3/2 plus '''y'''/'''x''' octaves.

	The numbers '''x''' and '''z''' may be expressed as numerical prefixes (e.g. mono, di, tri, tetra) instead of regular numbers, and "'''y'''-sheared" may be replaced with the number '''y''' in Greek gematria (e.g. 1 = alpha, 2 = beta, 3 = gamma, 10 = iota). Due to the unfamiliarity of Greek numerals to many people, they are heavily discouraged after epsilon. {{Adv\|This is because in the Greek numeral system, position 6 is ''wau'', not the expected ''zeta''.}} We use ''omega'' to refer to ('''z''' - 1)-shearing, corresponding to ~4/3 for single-period-octave (haploid) temperaments. When '''x''' = 1, ''haploid'' is used, not ''monoploid'', and it can optionally be omitted.		The numbers '''x''' and '''z''' may be expressed as numerical prefixes (e.g. mono, di, tri, tetra) instead of regular numbers, and "'''y'''-sheared" may be replaced with the number '''y''' in Greek gematria (e.g. 1 = alpha, 2 = beta, 3 = gamma, 10 = iota). Due to the unfamiliarity of Greek numerals to many people, on this wiki they are heavily discouraged after epsilon. {{Adv\|This is because in the Greek numeral system, position 6 is ''wau'', not the expected ''zeta''.}} We use ''omega'' to refer to ('''z''' - 1)-shearing, corresponding to ~4/3 for single-period-octave (haploid) temperaments. When '''x''' = 1, ''haploid'' is used, not ''monoploid'', and it can optionally be omitted.

	A temperament with a ~3/2 of an exact number of periods is ''acot'' or ''0-cot''. In this situation, the shear amount tends to be left out of the ploidacot name, but it can be seen as -1 times however many periods there are in the fifth.		A temperament with a ~3/2 of an exact number of periods is ''acot'' or ''0-cot''. In this situation, the shear amount tends to be left out of the ploidacot name, but it can be seen as -1 times however many periods there are in the fifth.

Vector at 09:15, 27 March 2026

2026-03-27T09:15:48Z

← Older revision		Revision as of 09:15, 27 March 2026
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	The general form is '''x'''-ploid '''y'''-sheared '''z'''-cot, where '''x''' is the number of periods in the octave, and where '''y''' periods ''down'' and '''z''' generators ''up'' are needed to reach ~3/2. Equivalently, '''z''' generators make 3/2 plus '''y'''/'''x''' octaves.		The general form is '''x'''-ploid '''y'''-sheared '''z'''-cot, where '''x''' is the number of periods in the octave, and where '''y''' periods ''down'' and '''z''' generators ''up'' are needed to reach ~3/2. Equivalently, '''z''' generators make 3/2 plus '''y'''/'''x''' octaves.

	The numbers '''x''' and '''z''' may be expressed as numerical prefixes (e.g. mono, di, tri, tetra) instead of regular numbers, and "'''y'''-sheared" may be replaced with the number '''y''' in Greek gematria (e.g. 1 = alpha, 2 = beta, 3 = gamma, 10 = iota). Due to the unfamiliarity of Greek numerals to many people, they are heavily discouraged after epsilon. We use ''omega'' to refer to ('''z''' - 1)-shearing, corresponding to ~4/3 for single-period-octave (haploid) temperaments. When '''x''' = 1, ''haploid'' is used, not ''monoploid'', and it can optionally be omitted.		The numbers '''x''' and '''z''' may be expressed as numerical prefixes (e.g. mono, di, tri, tetra) instead of regular numbers, and "'''y'''-sheared" may be replaced with the number '''y''' in Greek gematria (e.g. 1 = alpha, 2 = beta, 3 = gamma, 10 = iota). Due to the unfamiliarity of Greek numerals to many people, they are heavily discouraged after epsilon. {{Adv\|This is because in the Greek numeral system, position 6 is ''wau'', not the expected ''zeta''.}} We use ''omega'' to refer to ('''z''' - 1)-shearing, corresponding to ~4/3 for single-period-octave (haploid) temperaments. When '''x''' = 1, ''haploid'' is used, not ''monoploid'', and it can optionally be omitted.

	A temperament with a ~3/2 of an exact number of periods is ''acot'' or ''0-cot''. In this situation, the shear amount tends to be left out of the ploidacot name, but it can be seen as -1 times however many periods there are in the fifth.		A temperament with a ~3/2 of an exact number of periods is ''acot'' or ''0-cot''. In this situation, the shear amount tends to be left out of the ploidacot name, but it can be seen as -1 times however many periods there are in the fifth.

Vector at 07:06, 25 February 2026

2026-02-25T07:06:03Z

← Older revision		Revision as of 07:06, 25 February 2026
Line 3:		Line 3:
	The general form is '''x'''-ploid '''y'''-sheared '''z'''-cot, where '''x''' is the number of periods in the octave, and where '''y''' periods ''down'' and '''z''' generators ''up'' are needed to reach ~3/2. Equivalently, '''z''' generators make 3/2 plus '''y'''/'''x''' octaves.		The general form is '''x'''-ploid '''y'''-sheared '''z'''-cot, where '''x''' is the number of periods in the octave, and where '''y''' periods ''down'' and '''z''' generators ''up'' are needed to reach ~3/2. Equivalently, '''z''' generators make 3/2 plus '''y'''/'''x''' octaves.

	The numbers '''x''' and '''z''' may be expressed as numerical prefixes (e.g. mono, di, tri, tetra) instead of regular numbers, and "'''y'''-sheared" may be replaced with the number '''y''' in Greek gematria (e.g. 1 = alpha, 2 = beta, 3 = gamma, 10 = ~~iotaWe~~ We use ''omega'' to refer to ('''z''' - 1)-shearing, corresponding to ~4/3 for single-period-octave (haploid) temperaments. When '''x''' = 1, ''haploid'' is used, not ''monoploid'', and it can optionally be omitted.		The numbers '''x''' and '''z''' may be expressed as numerical prefixes (e.g. mono, di, tri, tetra) instead of regular numbers, and "'''y'''-sheared" may be replaced with the number '''y''' in Greek gematria (e.g. 1 = alpha, 2 = beta, 3 = gamma, 10 = iota). Due to the unfamiliarity of Greek numerals to many people, they are heavily discouraged after epsilon. We use ''omega'' to refer to ('''z''' - 1)-shearing, corresponding to ~4/3 for single-period-octave (haploid) temperaments. When '''x''' = 1, ''haploid'' is used, not ''monoploid'', and it can optionally be omitted.

	A temperament with a ~3/2 of an exact number of periods is ''acot'' or ''0-cot''. In this situation, the shear amount tends to be left out of the ploidacot name, but it can be seen as -1 times however many periods there are in the fifth.		A temperament with a ~3/2 of an exact number of periods is ''acot'' or ''0-cot''. In this situation, the shear amount tends to be left out of the ploidacot name, but it can be seen as -1 times however many periods there are in the fifth.

Inthar at 03:26, 25 February 2026

2026-02-25T03:26:54Z

← Older revision		Revision as of 03:26, 25 February 2026
Line 3:		Line 3:
	The general form is '''x'''-ploid '''y'''-sheared '''z'''-cot, where '''x''' is the number of periods in the octave, and where '''y''' periods ''down'' and '''z''' generators ''up'' are needed to reach ~3/2. Equivalently, '''z''' generators make 3/2 plus '''y'''/'''x''' octaves.		The general form is '''x'''-ploid '''y'''-sheared '''z'''-cot, where '''x''' is the number of periods in the octave, and where '''y''' periods ''down'' and '''z''' generators ''up'' are needed to reach ~3/2. Equivalently, '''z''' generators make 3/2 plus '''y'''/'''x''' octaves.

	The numbers '''x''' and '''z''' may be expressed as numerical prefixes (e.g. mono, di, tri, tetra) instead of regular numbers, and "'''y'''-sheared" may be replaced with the number '''y''' in Greek gematria (e.g. 1 = alpha, 2 = beta, 3 = gamma, 10 = iotaWe We use ''omega'' to refer to (z-1)-shearing, corresponding to ~4/3 for single-period-octave (haploid) temperaments. When '''x''' = 1, ''haploid'' is used, not ''monoploid'', and it can optionally be omitted.		The numbers '''x''' and '''z''' may be expressed as numerical prefixes (e.g. mono, di, tri, tetra) instead of regular numbers, and "'''y'''-sheared" may be replaced with the number '''y''' in Greek gematria (e.g. 1 = alpha, 2 = beta, 3 = gamma, 10 = iotaWe We use ''omega'' to refer to ('''z''' - 1)-shearing, corresponding to ~4/3 for single-period-octave (haploid) temperaments. When '''x''' = 1, ''haploid'' is used, not ''monoploid'', and it can optionally be omitted.

	A temperament with a ~3/2 of an exact number of periods is ''acot'' or ''0-cot''. In this situation, the shear amount tends to be left out of the ploidacot name, but it can be seen as -1 times however many periods there are in the fifth.		A temperament with a ~3/2 of an exact number of periods is ''acot'' or ''0-cot''. In this situation, the shear amount tends to be left out of the ploidacot name, but it can be seen as -1 times however many periods there are in the fifth.

Inthar at 03:26, 25 February 2026

2026-02-25T03:26:28Z

← Older revision		Revision as of 03:26, 25 February 2026
Line 3:		Line 3:
	The general form is '''x'''-ploid '''y'''-sheared '''z'''-cot, where '''x''' is the number of periods in the octave, and where '''y''' periods ''down'' and '''z''' generators ''up'' are needed to reach ~3/2. Equivalently, '''z''' generators make 3/2 plus '''y'''/'''x''' octaves.		The general form is '''x'''-ploid '''y'''-sheared '''z'''-cot, where '''x''' is the number of periods in the octave, and where '''y''' periods ''down'' and '''z''' generators ''up'' are needed to reach ~3/2. Equivalently, '''z''' generators make 3/2 plus '''y'''/'''x''' octaves.

	The numbers '''x''' and '''z''' may be expressed as numerical prefixes (e.g. mono, di, tri, tetra) instead of regular numbers, and "'''y'''-sheared" may be replaced with the number '''y''' in Greek gematria (e.g. 1 = alpha, 2 = beta, 3 = gamma, 10 = ~~iota~~). When '''x''' = 1, ''haploid'' is used, not ''monoploid'', and it can optionally be omitted.		The numbers '''x''' and '''z''' may be expressed as numerical prefixes (e.g. mono, di, tri, tetra) instead of regular numbers, and "'''y'''-sheared" may be replaced with the number '''y''' in Greek gematria (e.g. 1 = alpha, 2 = beta, 3 = gamma, 10 = iotaWe We use ''omega'' to refer to (z-1)-shearing, corresponding to ~4/3 for single-period-octave (haploid) temperaments. When '''x''' = 1, ''haploid'' is used, not ''monoploid'', and it can optionally be omitted.

	A temperament with a ~3/2 of an exact number of periods is ''acot'' or ''0-cot''. In this situation, the shear amount tends to be left out of the ploidacot name, but it can be seen as -1 times however many periods there are in the fifth.		A temperament with a ~3/2 of an exact number of periods is ''acot'' or ''0-cot''. In this situation, the shear amount tends to be left out of the ploidacot name, but it can be seen as -1 times however many periods there are in the fifth.

Inthar: /* Relationship to pergens */

2026-02-25T03:25:48Z

Relationship to pergens

← Older revision		Revision as of 03:25, 25 February 2026
Line 17:		Line 17:

	== Relationship to pergens ==		== Relationship to pergens ==
	[[Pergen]]s are an alternative notation system to ploidacot which notates 3-limit intervals in terms of diatonic scale degrees, created by [[Kite Giedraitis]]. While ploidacot describes ''how'' to get to ~3/2, pergens describe what 3-limit interval is divided into how many parts to get the generator. To use an above example, Harry, which is a ''diploid delta-hexacot'' temperament, would have the pergen ''(P8/2, P19/6)'', which simplifies to ''(P8/2, P4/6)''. Note the use of the perfect fourth~~. We use ''omega'' to refer to -1-shearing, corresponding to ~4/3 for single-period-octave (haploid) temperaments~~.		[[Pergen]]s are an alternative notation system to ploidacot which notates 3-limit intervals in terms of diatonic scale degrees, created by [[Kite Giedraitis]]. While ploidacot describes ''how'' to get to ~3/2, pergens describe what 3-limit interval is divided into how many parts to get the generator. To use an above example, Harry, which is a ''diploid delta-hexacot'' temperament, would have the pergen ''(P8/2, P19/6)'', which simplifies to ''(P8/2, P4/6)''. Note the use of the perfect fourth.

Inthar: /* Relationship to pergens */

2026-02-25T03:25:21Z

Relationship to pergens

← Older revision		Revision as of 03:25, 25 February 2026
Line 17:		Line 17:

	== Relationship to pergens ==		== Relationship to pergens ==
	~~''TODO: present omega as official''~~		[[Pergen]]s are an alternative notation system to ploidacot which notates 3-limit intervals in terms of diatonic scale degrees, created by [[Kite Giedraitis]]. While ploidacot describes ''how'' to get to ~3/2, pergens describe what 3-limit interval is divided into how many parts to get the generator. To use an above example, Harry, which is a ''diploid delta-hexacot'' temperament, would have the pergen ''(P8/2, P19/6)'', which simplifies to ''(P8/2, P4/6)''. Note the use of the perfect fourth. We use ''omega'' to refer to -1-shearing, corresponding to ~4/3 for single-period-octave (haploid) temperaments.

	[[Pergen]]s are an alternative notation system to ploidacot which notates 3-limit intervals in terms of diatonic scale degrees, created by [[Kite Giedraitis]]. While ploidacot describes ''how'' to get to ~3/2, pergens describe what 3-limit interval is divided into how many parts to get the generator. To use an above example, Harry, which is a ''diploid delta-hexacot'' temperament, would have the pergen ''(P8/2, P19/6)'', which simplifies to ''(P8/2, P4/6)''. Note the use of the perfect fourth. ~~This does not appear to be in the "official" ploidacot standard, although [[Osmium]] has proposed the~~ use of ''omega'' to refer to -1-shearing, corresponding to ~4/3 for single-period-octave (haploid) temperaments.

Inthar: /* Relationship to pergens */

2026-02-23T03:33:29Z

Relationship to pergens

← Older revision		Revision as of 03:33, 23 February 2026
Line 19:		Line 19:
	''TODO: present omega as official''		''TODO: present omega as official''

	[[Pergen]]s are an alternative notation system to ploidacot which notates 3-limit intervals in terms of diatonic scale degrees, created by [[Kite Giedraitis]]. While ploidacot describes ''how'' to get to ~3/2, pergens describe what 3-limit interval is divided into how many parts to get the generator. To use an above example, Harry, which is a ''diploid delta-hexacot'' temperament, would have the pergen ''(P8/2, P19/6)'', which simplifies to ''(P8/2, P4/6)''. Note the use of the perfect fourth. This does not appear to be in the "official" ploidacot standard, although [[Osmium]] has proposed the use of ''omega'' to refer to -1-shearing, corresponding to ~4/3 for single-period-octave (~~monoploid~~) temperaments.		[[Pergen]]s are an alternative notation system to ploidacot which notates 3-limit intervals in terms of diatonic scale degrees, created by [[Kite Giedraitis]]. While ploidacot describes ''how'' to get to ~3/2, pergens describe what 3-limit interval is divided into how many parts to get the generator. To use an above example, Harry, which is a ''diploid delta-hexacot'' temperament, would have the pergen ''(P8/2, P19/6)'', which simplifies to ''(P8/2, P4/6)''. Note the use of the perfect fourth. This does not appear to be in the "official" ploidacot standard, although [[Osmium]] has proposed the use of ''omega'' to refer to -1-shearing, corresponding to ~4/3 for single-period-octave (haploid) temperaments.