Ploidacot/Omega-pentacot - Revision history

Xenllium: /* Temperament interpretations */

2026-01-10T07:29:58Z

Temperament interpretations

← Older revision		Revision as of 07:29, 10 January 2026
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	{{See also\| Schismatic family }}		{{See also\| Schismatic family }}

	In quintilischis, the generator is 18/17, three ~~generators~~ make [[19/16]], five make 4/3, and 40 make [[10/1\|10th harmonic]] in the 2.3.5.17.19 subgroup, so [[4624/4617]], [[6144/6137]], and [[6885/6859]] are tempered out. This temperament is a weak extension of [[schismic]], splitting the fourth in five. In the 2.3.5.7.17.19 subgroup, tempering out [[400/399]] (equating 20/19 and 21/20) leads to [[quintilipyth]] (12 & 253), and tempering out [[476/475]] (equating 19/17 with 28/25) leads to [[quintaschis]] (12 & 289).		In quintilischis, the generator is 18/17, three of which make [[19/16]], five make 4/3, and 40 make [[10/1\|10th harmonic]] in the 2.3.5.17.19 subgroup, so [[4624/4617]], [[6144/6137]], and [[6885/6859]] are tempered out. This temperament is a weak extension of [[schismic]], splitting the fourth in five. In the 2.3.5.7.17.19 subgroup, tempering out [[400/399]] (equating 20/19 and 21/20) leads to [[quintilipyth]] (12 & 253), and tempering out [[476/475]] (equating 19/17 with 28/25) leads to [[quintaschis]] (12 & 289).

	=== Quindromeda ===		=== Quindromeda ===
	{{Main\| Quindromeda family }}		{{Main\| Quindromeda family }}

	In [[quindromeda]], the generator is 18/17, three ~~generators~~ make 19/16, five make 4/3, and 28 make [[5/1\|5th harmonic]] in the 2.3.5.17.19 subgroup, so [[1216/1215]], [[1445/1444]], and [[6144/6137]] are tempered out. Equating 225/224 with 256/255 leads to [[quintakwai]] (12 & 193), which tempers out 400/399 (also equating 20/19 and 21/20) in the 2.3.5.7.17.19 subgroup, and 361/360 with 400/399 leads to [[quintagar]] (12 & 217), which tempers out 476/475 (also equating 19/17 with 28/25) in the 2.3.5.7.17.19 subgroup.		In [[quindromeda]], the generator is 18/17, three of which make 19/16, five make 4/3, and 28 make [[5/1\|5th harmonic]] in the 2.3.5.17.19 subgroup, so [[1216/1215]], [[1445/1444]], and [[6144/6137]] are tempered out. Equating 225/224 with 256/255 leads to [[quintakwai]] (12 & 193), which tempers out 400/399 (also equating 20/19 and 21/20) in the 2.3.5.7.17.19 subgroup, and 361/360 with 400/399 leads to [[quintagar]] (12 & 217), which tempers out 476/475 (also equating 19/17 with 28/25) in the 2.3.5.7.17.19 subgroup.

	=== Quintaleap ===		=== Quintaleap ===
	{{Main\| Quintaleap family }}		{{Main\| Quintaleap family }}

	In [[quintaleap]], the generator is 18/17, three ~~generators~~ make 19/16, five make 4/3, and 16 make [[5/2]] in the 2.3.5.17.19 subgroup, so [[256/255]], [[361/360]], and [[4624/4617]] are tempered out. In the 2.3.5.7.17.19 subgroup, tempering out 400/399 leads to [[quintupole]] (12 & 121), and tempering out 476/475 leads to [[quinticosiennic]] (12 & 145).		In [[quintaleap]], the generator is 18/17, three of which make 19/16, five make 4/3, and 16 make [[5/2]] in the 2.3.5.17.19 subgroup, so [[256/255]], [[361/360]], and [[4624/4617]] are tempered out. In the 2.3.5.7.17.19 subgroup, tempering out 400/399 leads to [[quintupole]] (12 & 121), and tempering out 476/475 leads to [[quinticosiennic]] (12 & 145).

	=== Passion ===		=== Passion ===
	{{Main\| Passion family }}		{{Main\| Passion family }}

	In [[passion]], the generator is [[16/15]], four ~~generators~~ make [[5/4]], and five make 4/3. It is best tuned with a slightly flat generator of about 98.7{{c}}, and follows that both 3 and 5 should be tuned sharp. The canonical mapping of 7 places [[7/4]] at 10 generators, and follows that the generator should be tuned flatter (about 98.1{{c}}).		In [[passion]], the generator is [[16/15]], four of which make [[5/4]], and five make 4/3. It is best tuned with a slightly flat generator of about 98.7{{c}}, and follows that both 3 and 5 should be tuned sharp. The canonical mapping of 7 places [[7/4]] at 10 generators, and follows that the generator should be tuned flatter (about 98.1{{c}}).

	=== Ripple ===		=== Ripple ===
	{{Main\| Ripple family }}		{{Main\| Ripple family }}

	In [[ripple]], the generator is [[27/25]], five ~~generators~~ make 4/3, and eight make [[8/5]]. It is best tuned with a sharp generator of about 101–102{{c}}, giving the [[11L 1s]] MOS structure (rather than 1L 11s), and follows that 3 should be tuned flat.		In [[ripple]], the generator is [[27/25]], five of which make 4/3, and eight make [[8/5]]. It is best tuned with a sharp generator of about 101–102{{c}}, giving the [[11L 1s]] MOS structure (rather than 1L 11s), and follows that 3 should be tuned flat.

	[[Category:Ploidacots\|Omega-pentacot]]		[[Category:Ploidacots\|Omega-pentacot]]

Xenllium at 09:43, 8 January 2026

2026-01-08T09:43:57Z

← Older revision		Revision as of 09:43, 8 January 2026
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	{{See also\| Schismatic family }}		{{See also\| Schismatic family }}

	In quintilischis, the generator is 18/17, three generators make [[19/16]], five make 4/3, and 40 make [[10/1\|10th harmonic]] in the 2.3.5.17.19 subgroup, so [[4624/4617]], [[6144/6137]], and [[6885/6859]] are tempered out. This temperament is a weak extension of [[schismic]], splitting the fourth in five~~, and supported by {{Optimal ET sequence\| 12, 253, 265, 277, 289, 301, 313, and 325 }} edos~~.		In quintilischis, the generator is 18/17, three generators make [[19/16]], five make 4/3, and 40 make [[10/1\|10th harmonic]] in the 2.3.5.17.19 subgroup, so [[4624/4617]], [[6144/6137]], and [[6885/6859]] are tempered out. This temperament is a weak extension of [[schismic]], splitting the fourth in five. In the 2.3.5.7.17.19 subgroup, tempering out [[400/399]] (equating 20/19 and 21/20) leads to [[quintilipyth]] (12 & 253), and tempering out [[476/475]] (equating 19/17 with 28/25) leads to [[quintaschis]] (12 & 289).

	In the 2.3.5.7.17.19 subgroup, tempering out [[400/399]] (equating 20/19 and 21/20) leads to [[quintilipyth]] (12 & 253), and tempering out [[476/475]] (equating 19/17 with 28/25) leads to [[quintaschis]] (12 & 289).

	=== Quindromeda ===		=== Quindromeda ===
	{{Main\| Quindromeda family }}		{{Main\| Quindromeda family }}

	In [[quindromeda]], the generator is 18/17, three generators make 19/16, five make 4/3, and 28 make [[5/1\|5th harmonic]] in the 2.3.5.17.19 subgroup, so [[1216/1215]], [[1445/1444]], and [[6144/6137]] are tempered out. ~~This temperament is supported by {{Optimal ET sequence\| 12, 169, 181, 193, 205, 217, 229, and 241 }} edos.~~		In [[quindromeda]], the generator is 18/17, three generators make 19/16, five make 4/3, and 28 make [[5/1\|5th harmonic]] in the 2.3.5.17.19 subgroup, so [[1216/1215]], [[1445/1444]], and [[6144/6137]] are tempered out. Equating 225/224 with 256/255 leads to [[quintakwai]] (12 & 193), which tempers out 400/399 (also equating 20/19 and 21/20) in the 2.3.5.7.17.19 subgroup, and 361/360 with 400/399 leads to [[quintagar]] (12 & 217), which tempers out 476/475 (also equating 19/17 with 28/25) in the 2.3.5.7.17.19 subgroup.

	Equating 225/224 with 256/255 leads to [[quintakwai]] (12 & 193), which tempers out 400/399 (also equating 20/19 and 21/20) in the 2.3.5.7.17.19 subgroup, and 361/360 with 400/399 leads to [[quintagar]] (12 & 217), which tempers out 476/475 (also equating 19/17 with 28/25) in the 2.3.5.7.17.19 subgroup.

	=== Quintaleap ===		=== Quintaleap ===
	{{Main\| Quintaleap family }}		{{Main\| Quintaleap family }}

	In [[quintaleap]], the generator is 18/17, three generators make 19/16, five make 4/3, and 16 make [[5/2]] in the 2.3.5.17.19 subgroup, so [[256/255]], [[361/360]], and [[4624/4617]] are tempered out. ~~This temperament is supported by {{Optimal ET sequence\| 12, 109, 121, 133, 145, and 157 }} edos.~~		In [[quintaleap]], the generator is 18/17, three generators make 19/16, five make 4/3, and 16 make [[5/2]] in the 2.3.5.17.19 subgroup, so [[256/255]], [[361/360]], and [[4624/4617]] are tempered out. In the 2.3.5.7.17.19 subgroup, tempering out 400/399 leads to [[quintupole]] (12 & 121), and tempering out 476/475 leads to [[quinticosiennic]] (12 & 145).

	In the 2.3.5.7.17.19 subgroup, tempering out 400/399 leads to [[quintupole]] (12 & 121), and tempering out 476/475 leads to [[quinticosiennic]] (12 & 145).

	=== Passion ===		=== Passion ===
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	In [[passion]], the generator is [[16/15]], four generators make [[5/4]], and five make 4/3. It is best tuned with a slightly flat generator of about 98.7{{c}}, and follows that both 3 and 5 should be tuned sharp. The canonical mapping of 7 places [[7/4]] at 10 generators, and follows that the generator should be tuned flatter (about 98.1{{c}}).		In [[passion]], the generator is [[16/15]], four generators make [[5/4]], and five make 4/3. It is best tuned with a slightly flat generator of about 98.7{{c}}, and follows that both 3 and 5 should be tuned sharp. The canonical mapping of 7 places [[7/4]] at 10 generators, and follows that the generator should be tuned flatter (about 98.1{{c}}).

	[[Category:Ploidacots]]		=== Ripple ===
			{{Main\| Ripple family }}

			In [[ripple]], the generator is [[27/25]], five generators make 4/3, and eight make [[8/5]]. It is best tuned with a sharp generator of about 101–102{{c}}, giving the [[11L 1s]] MOS structure (rather than 1L 11s), and follows that 3 should be tuned flat.

			[[Category:Ploidacots\|Omega-pentacot]]

FloraC: Text replacement - "[[Category:Ploidacot" to "[[Category:Ploidacots"

2026-01-06T09:43:30Z

Text replacement - "[[Category:Ploidacot" to "[[Category:Ploidacots"

← Older revision		Revision as of 09:43, 6 January 2026
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	In [[passion]], the generator is [[16/15]], four generators make [[5/4]], and five make 4/3. It is best tuned with a slightly flat generator of about 98.7{{c}}, and follows that both 3 and 5 should be tuned sharp. The canonical mapping of 7 places [[7/4]] at 10 generators, and follows that the generator should be tuned flatter (about 98.1{{c}}).		In [[passion]], the generator is [[16/15]], four generators make [[5/4]], and five make 4/3. It is best tuned with a slightly flat generator of about 98.7{{c}}, and follows that both 3 and 5 should be tuned sharp. The canonical mapping of 7 places [[7/4]] at 10 generators, and follows that the generator should be tuned flatter (about 98.1{{c}}).

	[[Category:~~Ploidacot~~]]		[[Category:Ploidacots]]

Xenllium at 13:39, 5 January 2026

2026-01-05T13:39:47Z

← Older revision		Revision as of 13:39, 5 January 2026
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	== Intervals and notation ==		== Intervals and notation ==
	While there is no agreed-upon notation system for omega-pentacot, the following is based on interpreting the generator as a semitone (1/5 of a fourth), allowing for an ^ or v to stand for a 1/5 of an ''inversed'' diminished second (the difference between diatonic semitone and chromatic semitone, equivalent to the [[Pythagorean comma]]), so vvvC# and ^^Db are enharmonic.		While there is no agreed-upon notation system for omega-pentacot, the following is based on interpreting the generator as a semitone (1/5 of a fourth), allowing for an ^ or v to stand for 1/5 of an ''inversed'' diminished second (the difference between diatonic semitone and chromatic semitone, equivalent to the [[Pythagorean comma]]), so vvvC# and ^^Db are enharmonic.

	{\| class="wikitable"		{\| class="wikitable"
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	Omega-pentacot temperaments are generally interpretated as quinticular temperaments; the generator is [[18/17]], five of them gives 4/3, so the [[quinticular comma]] (1419857/1417176) is tempered out.		Omega-pentacot temperaments are generally interpretated as quinticular temperaments; the generator is [[18/17]], five of them gives 4/3, so the [[quinticular comma]] (1419857/1417176) is tempered out.

			=== Quintilischis ===
			{{See also\| Schismatic family }}

			In quintilischis, the generator is 18/17, three generators make [[19/16]], five make 4/3, and 40 make [[10/1\|10th harmonic]] in the 2.3.5.17.19 subgroup, so [[4624/4617]], [[6144/6137]], and [[6885/6859]] are tempered out. This temperament is a weak extension of [[schismic]], splitting the fourth in five, and supported by {{Optimal ET sequence\| 12, 253, 265, 277, 289, 301, 313, and 325 }} edos.

			In the 2.3.5.7.17.19 subgroup, tempering out [[400/399]] (equating 20/19 and 21/20) leads to [[quintilipyth]] (12 & 253), and tempering out [[476/475]] (equating 19/17 with 28/25) leads to [[quintaschis]] (12 & 289).

	=== Quindromeda ===		=== Quindromeda ===
	{{Main\| Quindromeda family }}		{{Main\| Quindromeda family }}

	In [[quindromeda]], the generator is 18/17, three generators make [[19/16]], five make 4/3, and 28 make [[5/1\|5th harmonic]] in the 2.3.5.17.19 subgroup, so [[1216/1215]], [[1445/1444]], and [[6144/6137]] are tempered out. This temperament is supported by {{Optimal ET sequence\| 12, 169, 181, 193, 205, 217, 229, and 241 }} edos.		In [[quindromeda]], the generator is 18/17, three generators make 19/16, five make 4/3, and 28 make [[5/1\|5th harmonic]] in the 2.3.5.17.19 subgroup, so [[1216/1215]], [[1445/1444]], and [[6144/6137]] are tempered out. This temperament is supported by {{Optimal ET sequence\| 12, 169, 181, 193, 205, 217, 229, and 241 }} edos.

	Equating 225/224 with 256/255 leads to [[quintakwai]] (12 & 193), which tempers out [[400/399]] (also equating 20/19 and 21/20) in the 2.3.5.7.17.19 subgroup, and 361/360 with 400/399 leads to [[quintagar]] (12 & 217), which tempers out [[476/475]] (also equating 19/17 with 28/25) in the 2.3.5.7.17.19 subgroup.		Equating 225/224 with 256/255 leads to [[quintakwai]] (12 & 193), which tempers out 400/399 (also equating 20/19 and 21/20) in the 2.3.5.7.17.19 subgroup, and 361/360 with 400/399 leads to [[quintagar]] (12 & 217), which tempers out 476/475 (also equating 19/17 with 28/25) in the 2.3.5.7.17.19 subgroup.

	=== Quintaleap ===		=== Quintaleap ===
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	In [[quintaleap]], the generator is 18/17, three generators make 19/16, five make 4/3, and 16 make [[5/2]] in the 2.3.5.17.19 subgroup, so [[256/255]], [[361/360]], and [[4624/4617]] are tempered out. This temperament is supported by {{Optimal ET sequence\| 12, 109, 121, 133, 145, and 157 }} edos.		In [[quintaleap]], the generator is 18/17, three generators make 19/16, five make 4/3, and 16 make [[5/2]] in the 2.3.5.17.19 subgroup, so [[256/255]], [[361/360]], and [[4624/4617]] are tempered out. This temperament is supported by {{Optimal ET sequence\| 12, 109, 121, 133, 145, and 157 }} edos.

	In the 2.3.5.7.17.19 subgroup, tempering out 400/399 ~~(equating 20/19 and 21/20)~~ leads to [[quintupole]] (12 & 121), and tempering out 476/475 ~~(equating 19/17 with 28/25)~~ leads to [[quinticosiennic]] (12 & 145).		In the 2.3.5.7.17.19 subgroup, tempering out 400/399 leads to [[quintupole]] (12 & 121), and tempering out 476/475 leads to [[quinticosiennic]] (12 & 145).

	=== Passion ===		=== Passion ===

Xenllium at 14:58, 4 January 2026

2026-01-04T14:58:07Z

← Older revision		Revision as of 14:58, 4 January 2026
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	{{Breadcrumb}}{{Infobox ploidacot\|Ploids=1\|Shears=4\|Cots=5\|Pergen=[P8, P4/5]\|Forms=12, 13, 25, 37\|Title=Omega-pentacot\|Wedgie=5}}		{{Breadcrumb}}{{Infobox ploidacot\|Ploids=1\|Shears=4\|Cots=5\|Pergen=[P8, P4/5]\|Forms=12, 13, 25, 37\|Title=Omega-pentacot (delta-pentacot)\|Wedgie=5}}
	'''Omega-pentacot''' is a temperament archetype where the generator is a semitone, five of which stack to form a perfect fourth of [[4/3]], and the period is a [[2/1]] octave. Omega-pentacot temperaments usually generate the [[1L 11s]] and [[12L 1s]] MOS structures. Regular temperaments of omega-pentacot are [[Cluster MOS\|cluster temperaments]] with 12 clusters of notes in an octave.		'''Omega-pentacot''' is a temperament archetype where the generator is a semitone, five of which stack to form a perfect fourth of [[4/3]], and the period is a [[2/1]] octave. Omega-pentacot temperaments usually generate the [[1L 11s]] and [[12L 1s]] MOS structures. Regular temperaments of omega-pentacot are [[Cluster MOS\|cluster temperaments]] with 12 clusters of notes in an octave.

	== Intervals and notation ==		== Intervals and notation ==
	While there is no agreed-upon notation system for omega-pentacot, the following is based on interpreting the generator as a semitone (1/5 of a fourth), allowing for an ^ or v to stand for a 1/5 of an ''inversed'' diminished second (equivalent to the [[Pythagorean comma]]), so vvvC# and ^^Db are enharmonic.		While there is no agreed-upon notation system for omega-pentacot, the following is based on interpreting the generator as a semitone (1/5 of a fourth), allowing for an ^ or v to stand for a 1/5 of an ''inversed'' diminished second (the difference between diatonic semitone and chromatic semitone, equivalent to the [[Pythagorean comma]]), so vvvC# and ^^Db are enharmonic.

	{\| class="wikitable"		{\| class="wikitable"

Xenllium: /* Temperament interpretations */

2026-01-04T06:20:42Z

Temperament interpretations

← Older revision		Revision as of 06:20, 4 January 2026
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	In [[passion]], the generator is [[16/15]], four generators make [[5/4]], and five make 4/3. It is best tuned with a slightly flat generator of about 98.7{{c}}, and follows that both 3 and 5 should be tuned sharp. The canonical mapping of 7 places [[7/4]] at 10 generators, and follows that the generator should be tuned flatter (about 98.1{{c}}).		In [[passion]], the generator is [[16/15]], four generators make [[5/4]], and five make 4/3. It is best tuned with a slightly flat generator of about 98.7{{c}}, and follows that both 3 and 5 should be tuned sharp. The canonical mapping of 7 places [[7/4]] at 10 generators, and follows that the generator should be tuned flatter (about 98.1{{c}}).

	~~{{Todo\| unify precision }}~~		[[Category:Ploidacot]]

Xenllium at 23:37, 2 January 2026

2026-01-02T23:37:15Z

Show changes

Xenllium at 23:19, 31 December 2025

2025-12-31T23:19:20Z

Show changes

Xenllium: Created page with "{{Breadcrumb}}{{Infobox ploidacot|Ploids=1|Shears=4|Cots=5|Pergen=[P8, P4/5]|Forms=12, 13, 25, 37|Title=Omega-pentacot|Wedgie=5}} '''Omega-pentacot''' is a temperament archetype where the generator is a semitone, five of which stack to form a perfect fourth of 4/3, and the period is a 2/1 octave. Omega-pentacot temperaments usually generate the 1L 11s and 12L 1s MOS structures. Regular temperaments of omega-pentacot are Cluster MOS|cluster tem..."

2025-12-30T14:53:08Z

Created page with "{{Breadcrumb}}{{Infobox ploidacot|Ploids=1|Shears=4|Cots=5|Pergen=[P8, P4/5]|Forms=12, 13, 25, 37|Title=Omega-pentacot|Wedgie=5}} '''Omega-pentacot''' is a temperament archetype where the generator is a semitone, five of which stack to form a perfect fourth of 4/3, and the period is a 2/1 octave. Omega-pentacot temperaments usually generate the 1L 11s and 12L 1s MOS structures. Regular temperaments of omega-pentacot are Cluster MOS|cluster tem..."

New page

{{Breadcrumb}}{{Infobox ploidacot|Ploids=1|Shears=4|Cots=5|Pergen=[P8, P4/5]|Forms=12, 13, 25, 37|Title=Omega-pentacot|Wedgie=5}}
'''Omega-pentacot''' is a temperament archetype where the generator is a semitone, five of which stack to form a perfect fourth of [[4/3]], and the period is a [[2/1]] octave. Omega-pentacot temperaments usually generate the [[1L 11s]] and [[12L 1s]] MOS structures. Regular temperaments of omega-pentacot are [[Cluster MOS|cluster temperaments]] with 12 clusters of notes in an octave.

== Temperament interpretations ==
=== Quinticular ===
{{See also| Quinticular comma }}

Omega-pentacot temperaments are generally interpretated as quinticular temperaments; the generator is [[18/17]], five of them gives 4/3, so the [[quinticular comma]] (1419857/1417176) is tempered out.

=== Quindromeda ===
{{Main| Quindromeda family }}

In [[quindromeda]], the generator is 18/17, three generators make [[19/16]], five make 4/3, and 28 make [[5/1|5th harmonic]] in the 2.3.5.17.19 subgroup, so [[1216/1215]], [[1445/1444]], and [[6144/6137]] are tempered out. This temperament is supported by {{Optimal ET sequence| 12, 169, 181, 193, 205, 217, 229, and 241 }} edos.

Equating 225/224 with 256/255 leads to [[quintakwai]] (12 & 193), which tempers out [[400/399]] (also equating 20/19 and 21/20) in the 2.3.5.7.17.19 subgroup, and 361/360 with 400/399 leads to [[quintagar]] (12 & 217), which tempers out [[476/475]] (also equating 19/17 with 28/25) in the 2.3.5.7.17.19 subgroup.

=== Quintaleap ===
{{Main| Quintaleap family }}

In [[quintaleap]], the generator is 18/17, three generators make 19/16, five make 4/3, and 16 make [[5/2]] in the 2.3.5.17.19 subgroup, so [[256/255]], [[361/360]], and [[4624/4617]] are tempered out. This temperament is supported by {{Optimal ET sequence| 12, 109, 121, 133, 145, and 157 }} edos.

In the 2.3.5.7.17.19 subgroup, tempering out 400/399 (equating 20/19 and 21/20) leads to [[quintupole]] (12 & 121), and tempering out 476/475 (equating 19/17 with 28/25) leads to [[quinticosiennic]] (12 & 145).

=== Passion ===
{{Main| Passion family }}

In [[passion]], the generator is [[16/15]], four generators make [[5/4]], and five make 4/3. It is best tuned with a slightly flat generator of about 98.7{{c}}, and follows that both 3 and 5 should be tuned sharp. The canonical mapping of 7 places [[7/4]] at 10 generators, and follows that the generator should be tuned flatter (about 98.1{{c}}).

{{Todo| unify precision }}