Ragismic microtemperaments - Revision history

FloraC: /* Ragitritonic */ update & fix

2026-05-20T10:42:40Z

Ragitritonic: update & fix

← Older revision		Revision as of 10:42, 20 May 2026
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	== Ragitritonic ==		== Ragitritonic ==
	: ''For the 5-limit version, see [[Schismic–Mercator equivalence continuum #Countritonic ~~(5-limit)~~]].''		: ''For the 5-limit version, see [[Schismic–Mercator equivalence continuum #Countritonic]].''

	Ragitritonic may be described as the {{nowrap\| 53 & 369 }} temperament, splitting the [[24th harmonic]] into nine tritone generators; its [[ploidacot]] is thus delta-enneacot. [[422edo]] makes for a strong tuning.		Ragitritonic may be described as the {{nowrap\| 53 & 369 }} temperament, splitting the [[24/1\|24th harmonic]] into nine tritone generators; its [[ploidacot]] is thus delta-enneacot. [[422edo]] makes for a strong tuning.

	Ragitritonic was named by [[Flora Canou]] in 2026 as a contraction of ''ragismic'' and ''tritonic''.		Ragitritonic was named by [[Flora Canou]] in 2026 as a contraction of ''ragismic'' and ''tritonic''.

FloraC: I hate this name, thanks

2026-05-20T10:41:03Z

I hate this name, thanks

← Older revision		Revision as of 10:41, 20 May 2026
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	Since {{nowrap\|(10/9)<sup>4</sup> {{=}} (4375/4374)⋅(32/21) }}, the minor tone 10/9 tends to be an interval of relatively low [[complexity]] in temperaments tempering out the ragisma, though when looking at [[microtemperament]]s the word "relatively" should be emphasized. Even so mitonic uses it as a generator, which ennealimmal and enneadecal can do also, and amity reaches it in three generators. We also have {{nowrap\| 7/6 {{=}} (4375/4374)⋅(27/25)<sup>2</sup> }}, so 27/25 also tends to relatively low complexity, with the same caveat about "relatively"; however 27/25 is the period for ennealimmal.		Since {{nowrap\|(10/9)<sup>4</sup> {{=}} (4375/4374)⋅(32/21) }}, the minor tone 10/9 tends to be an interval of relatively low [[complexity]] in temperaments tempering out the ragisma, though when looking at [[microtemperament]]s the word "relatively" should be emphasized. Even so mitonic uses it as a generator, which ennealimmal and enneadecal can do also, and amity reaches it in three generators. We also have {{nowrap\| 7/6 {{=}} (4375/4374)⋅(27/25)<sup>2</sup> }}, so 27/25 also tends to relatively low complexity, with the same caveat about "relatively"; however 27/25 is the period for ennealimmal.

	Microtemperaments considered below, sorted by [[badness]], are supermajor, enneadecal, semidimi, brahmagupta, abigail, gamera, crazy, orga, seniority, monzismic, semidimfourth, acrokleismic, quasithird, deca, keenanose, aluminium, quatracot, moulin, and palladium. Some near-microtemperaments are appended as octoid, parakleismic, counterkleismic, quincy, sfourth, and trideci. Discussed elsewhere are:		Microtemperaments considered below, sorted by [[badness]], are supermajor, enneadecal, semidimi, brahmagupta, abigail, gamera, crazy, orga, seniority, monzismic, semidimfourth, acrokleismic, quasithird, deca, keenanose, aluminium, ragitritonic, quatracot, moulin, and palladium. Some near-microtemperaments are appended as octoid, parakleismic, counterkleismic, quincy, sfourth, and trideci. Discussed elsewhere are:
	* ''[[Hystrix]]'' (+36/35) → [[Porcupine family #Hystrix\|Porcupine family]]		* ''[[Hystrix]]'' (+36/35) → [[Porcupine family #Hystrix\|Porcupine family]]
	* ''[[Rhinoceros]]'' (+49/48) → [[Unicorn family #Rhinoceros\|Unicorn family]]		* ''[[Rhinoceros]]'' (+49/48) → [[Unicorn family #Rhinoceros\|Unicorn family]]
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	Badness (Sintel): 1.18		Badness (Sintel): 1.18

	== ~~Countritonic~~ ==		== Ragitritonic ==
	: ''For the 5-limit version, see [[Schismic–Mercator equivalence continuum #Countritonic (5-limit)]].''		: ''For the 5-limit version, see [[Schismic–Mercator equivalence continuum #Countritonic (5-limit)]].''

	~~Countritonic (''co-un-tritonic'')~~ may be described as the {{nowrap\| 53 & ~~422~~ }} temperament, ~~generated by an octave-reduced 91st~~ harmonic ~~or subharmonic in the 13~~-~~limit~~. It was named by [[Flora Canou]] in ~~2023~~ as a ~~variant~~ of ~~[[countriton]]~~.		Ragitritonic may be described as the {{nowrap\| 53 & 369 }} temperament, splitting the [[24th harmonic]] into nine tritone generators; its [[ploidacot]] is thus delta-enneacot. [[422edo]] makes for a strong tuning.

			Ragitritonic was named by [[Flora Canou]] in 2026 as a contraction of ''ragismic'' and ''tritonic''.

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7

Godtone: this breaks the links

2026-05-14T22:29:16Z

this breaks the links

← Older revision		Revision as of 22:29, 14 May 2026
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	== Enneadecal ==		== Enneadecal ==
	: ''For the 5-limit version, see [[Syntonic–kleismic equivalence continuum #Enneadecal]].''		: ''For the 5-limit version, see [[Syntonic–kleismic equivalence continuum #Enneadecal (5-limit)]].''

	Enneadecal tempers out the [[enneadeca]], {{monzo\| -14 -19 19 }}, and as a consequence has a period of 1/19 octave. This is because the enneadeca is the amount by which nineteen [[6/5\|just minor thirds]] fall short of an octave. If to this we add 4375/4374 we get the 7-limit temperament we are considering here, but note should be taken of the fact that it makes for a reasonable 5-limit microtemperament also, where the generator can be ~25/24, ~27/25, ~10/9, ~5/4 or ~3/2. To this we may add possible 7-limit generators such as ~225/224, ~15/14 or ~9/7. Since enneadecal tempers out [[703125/702464]], the amount by which 81/80 falls short of three stacked 225/224, we can equate the 225/224 generator with (81/80)<sup>1/3</sup>. This is the interval needed to adjust the 1/3-comma meantone flat fifths and major thirds of [[19edo]] up to just ones.		Enneadecal tempers out the [[enneadeca]], {{monzo\| -14 -19 19 }}, and as a consequence has a period of 1/19 octave. This is because the enneadeca is the amount by which nineteen [[6/5\|just minor thirds]] fall short of an octave. If to this we add 4375/4374 we get the 7-limit temperament we are considering here, but note should be taken of the fact that it makes for a reasonable 5-limit microtemperament also, where the generator can be ~25/24, ~27/25, ~10/9, ~5/4 or ~3/2. To this we may add possible 7-limit generators such as ~225/224, ~15/14 or ~9/7. Since enneadecal tempers out [[703125/702464]], the amount by which 81/80 falls short of three stacked 225/224, we can equate the 225/224 generator with (81/80)<sup>1/3</sup>. This is the interval needed to adjust the 1/3-comma meantone flat fifths and major thirds of [[19edo]] up to just ones.
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	== Countritonic ==		== Countritonic ==
	: ''For the 5-limit version, see [[Schismic–Mercator equivalence continuum #Countritonic]].''		: ''For the 5-limit version, see [[Schismic–Mercator equivalence continuum #Countritonic (5-limit)]].''

	Countritonic (''co-un-tritonic'') may be described as the {{nowrap\| 53 & 422 }} temperament, generated by an octave-reduced 91st harmonic or subharmonic in the 13-limit. It was named by [[Flora Canou]] in 2023 as a variant of [[countriton]].		Countritonic (''co-un-tritonic'') may be described as the {{nowrap\| 53 & 422 }} temperament, generated by an octave-reduced 91st harmonic or subharmonic in the 13-limit. It was named by [[Flora Canou]] in 2023 as a variant of [[countriton]].
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	== Oviminor ==		== Oviminor ==
	: ''For the 5-limit version, see [[Syntonic–kleismic equivalence continuum #Oviminor]].''		: ''For the 5-limit version, see [[Syntonic–kleismic equivalence continuum #Oviminor (5-limit)]].''

	Oviminor was named by [[Eliora]] in 2022 after the facts that it takes 184 minor thirds of [[6/5]] to reach the interval class of [[4/3]], the Roman consul was Eggius in the year 184 AD, and the Latin word for egg is ovum, and with prefix ovi-. It sets a new record of complexity for a chain of nineteen 6/5's past [[egads]], though it is less accurate.		Oviminor was named by [[Eliora]] in 2022 after the facts that it takes 184 minor thirds of [[6/5]] to reach the interval class of [[4/3]], the Roman consul was Eggius in the year 184 AD, and the Latin word for egg is ovum, and with prefix ovi-. It sets a new record of complexity for a chain of nineteen 6/5's past [[egads]], though it is less accurate.
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	== Parakleismic ==		== Parakleismic ==
	{{Main\| Parakleismic }}		{{Main\| Parakleismic }}
	: ''For the 5-limit version, see [[Syntonic–kleismic equivalence continuum #Parakleismic]].''		: ''For the 5-limit version, see [[Syntonic–kleismic equivalence continuum #Parakleismic (5-limit)]].''

	In the 5-limit, parakleismic is an undoubted microtemperament, tempering out the parakleisma, {{monzo\| 8 14 -13 }}, with the [[118edo]] tuning giving errors well under a cent. It has a generator a very slightly (half a cent or less) flat [[6/5]], 13 of which give 32/3, and 14 give 64/5. While 118 no longer has better than a cent of accuracy in the 7-limit, it is a decent temperament there nonetheless, and this allows an extension adding [[3136/3125]] and 4375/4374, for which [[99edo]], 118edo, and especially [[217edo]] are accurate tunings.		In the 5-limit, parakleismic is an undoubted microtemperament, tempering out the parakleisma, {{monzo\| 8 14 -13 }}, with the [[118edo]] tuning giving errors well under a cent. It has a generator a very slightly (half a cent or less) flat [[6/5]], 13 of which give 32/3, and 14 give 64/5. While 118 no longer has better than a cent of accuracy in the 7-limit, it is a decent temperament there nonetheless, and this allows an extension adding [[3136/3125]] and 4375/4374, for which [[99edo]], 118edo, and especially [[217edo]] are accurate tunings.

Xenllium at 10:06, 14 May 2026

2026-05-14T10:06:09Z

← Older revision		Revision as of 10:06, 14 May 2026
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	== Enneadecal ==		== Enneadecal ==
	: ''For the 5-limit version, see [[Syntonic–kleismic equivalence continuum #Enneadecal ~~(5-limit)~~]].''		: ''For the 5-limit version, see [[Syntonic–kleismic equivalence continuum #Enneadecal]].''

	Enneadecal tempers out the [[enneadeca]], {{monzo\| -14 -19 19 }}, and as a consequence has a period of 1/19 octave. This is because the enneadeca is the amount by which nineteen [[6/5\|just minor thirds]] fall short of an octave. If to this we add 4375/4374 we get the 7-limit temperament we are considering here, but note should be taken of the fact that it makes for a reasonable 5-limit microtemperament also, where the generator can be ~25/24, ~27/25, ~10/9, ~5/4 or ~3/2. To this we may add possible 7-limit generators such as ~225/224, ~15/14 or ~9/7. Since enneadecal tempers out [[703125/702464]], the amount by which 81/80 falls short of three stacked 225/224, we can equate the 225/224 generator with (81/80)<sup>1/3</sup>. This is the interval needed to adjust the 1/3-comma meantone flat fifths and major thirds of [[19edo]] up to just ones.		Enneadecal tempers out the [[enneadeca]], {{monzo\| -14 -19 19 }}, and as a consequence has a period of 1/19 octave. This is because the enneadeca is the amount by which nineteen [[6/5\|just minor thirds]] fall short of an octave. If to this we add 4375/4374 we get the 7-limit temperament we are considering here, but note should be taken of the fact that it makes for a reasonable 5-limit microtemperament also, where the generator can be ~25/24, ~27/25, ~10/9, ~5/4 or ~3/2. To this we may add possible 7-limit generators such as ~225/224, ~15/14 or ~9/7. Since enneadecal tempers out [[703125/702464]], the amount by which 81/80 falls short of three stacked 225/224, we can equate the 225/224 generator with (81/80)<sup>1/3</sup>. This is the interval needed to adjust the 1/3-comma meantone flat fifths and major thirds of [[19edo]] up to just ones.
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	== Countritonic ==		== Countritonic ==
	: ''For the 5-limit version, see [[Schismic–Mercator equivalence continuum #Countritonic ~~(5-limit)~~]].''		: ''For the 5-limit version, see [[Schismic–Mercator equivalence continuum #Countritonic]].''

	Countritonic (''co-un-tritonic'') may be described as the {{nowrap\| 53 & 422 }} temperament, generated by an octave-reduced 91st harmonic or subharmonic in the 13-limit. It was named by [[Flora Canou]] in 2023 as a variant of [[countriton]].		Countritonic (''co-un-tritonic'') may be described as the {{nowrap\| 53 & 422 }} temperament, generated by an octave-reduced 91st harmonic or subharmonic in the 13-limit. It was named by [[Flora Canou]] in 2023 as a variant of [[countriton]].
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	== Oviminor ==		== Oviminor ==
	: ''For the 5-limit version, see [[Syntonic–kleismic equivalence continuum #Oviminor ~~(5-limit)~~]].''		: ''For the 5-limit version, see [[Syntonic–kleismic equivalence continuum #Oviminor]].''

	Oviminor was named by [[Eliora]] in 2022 after the facts that it takes 184 minor thirds of [[6/5]] to reach the interval class of [[4/3]], the Roman consul was Eggius in the year 184 AD, and the Latin word for egg is ovum, and with prefix ovi-. It sets a new record of complexity for a chain of nineteen 6/5's past [[egads]], though it is less accurate.		Oviminor was named by [[Eliora]] in 2022 after the facts that it takes 184 minor thirds of [[6/5]] to reach the interval class of [[4/3]], the Roman consul was Eggius in the year 184 AD, and the Latin word for egg is ovum, and with prefix ovi-. It sets a new record of complexity for a chain of nineteen 6/5's past [[egads]], though it is less accurate.
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	== Parakleismic ==		== Parakleismic ==
	{{Main\| Parakleismic }}		{{Main\| Parakleismic }}
	: ''For the 5-limit version, see [[Syntonic–kleismic equivalence continuum #Parakleismic ~~(5-limit)~~]].''		: ''For the 5-limit version, see [[Syntonic–kleismic equivalence continuum #Parakleismic]].''

	In the 5-limit, parakleismic is an undoubted microtemperament, tempering out the parakleisma, {{monzo\| 8 14 -13 }}, with the [[118edo]] tuning giving errors well under a cent. It has a generator a very slightly (half a cent or less) flat [[6/5]], 13 of which give 32/3, and 14 give 64/5. While 118 no longer has better than a cent of accuracy in the 7-limit, it is a decent temperament there nonetheless, and this allows an extension adding [[3136/3125]] and 4375/4374, for which [[99edo]], 118edo, and especially [[217edo]] are accurate tunings.		In the 5-limit, parakleismic is an undoubted microtemperament, tempering out the parakleisma, {{monzo\| 8 14 -13 }}, with the [[118edo]] tuning giving errors well under a cent. It has a generator a very slightly (half a cent or less) flat [[6/5]], 13 of which give 32/3, and 14 give 64/5. While 118 no longer has better than a cent of accuracy in the 7-limit, it is a decent temperament there nonetheless, and this allows an extension adding [[3136/3125]] and 4375/4374, for which [[99edo]], 118edo, and especially [[217edo]] are accurate tunings.

FloraC: Status update

2026-04-15T17:58:58Z

Status update

← Older revision		Revision as of 17:58, 15 April 2026
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	* ''[[Rhinoceros]]'' (+49/48) → [[Unicorn family #Rhinoceros\|Unicorn family]]		* ''[[Rhinoceros]]'' (+49/48) → [[Unicorn family #Rhinoceros\|Unicorn family]]
	* ''[[Crepuscular]]'' (+50/49) → [[Fifive family #Crepuscular\|Fifive family]]		* ''[[Crepuscular]]'' (+50/49) → [[Fifive family #Crepuscular\|Fifive family]]
	* ''[[Modus]]'' (+64/63) → [[Tetracot family #Modus\|Tetracot family]]		* [[Modus]] (+64/63) → [[Tetracot family #Modus\|Tetracot family]]
	* ''[[Flattone]]'' (+81/80) → [[Meantone family #Flattone\|Meantone family]]		* [[Flattone]] (+81/80) → [[Meantone family #Flattone\|Meantone family]]
	* [[Sensi]] (+126/125 or 245/243) → [[Sensipent family #Sensi\|Sensipent family]]		* [[Sensi]] (+126/125 or 245/243) → [[Sensipent family #Sensi\|Sensipent family]]
	* [[Catakleismic]] (+225/224) → [[Kleismic family #Catakleismic\|Kleismic family]]		* [[Catakleismic]] (+225/224) → [[Kleismic family #Catakleismic\|Kleismic family]]

Xenllium: /* Octoid */

2026-04-05T10:28:03Z

Octoid

← Older revision		Revision as of 10:28, 5 April 2026
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	== Octoid ==		== Octoid ==
			: {{Main\| Octoid }}
	: ''For the 5-limit version, see [[8th-octave temperaments #Octoid]].''		: ''For the 5-limit version, see [[8th-octave temperaments #Octoid]].''

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	[[Badness]] (Sintel): 1.08		[[Badness]] (Sintel): 1.08

	~~Scales: [[octoid72]], [[octoid80]]~~

	=== 11-limit ===		=== 11-limit ===
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	Badness (Sintel): 0.466		Badness (Sintel): 0.466

	~~Scales: [[octoid72]], [[octoid80]]~~

	==== 13-limit ====		==== 13-limit ====
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	Badness (Sintel): 0.631		Badness (Sintel): 0.631

	~~Scales: [[octoid72]], [[octoid80]]~~

	~~; Music~~
	* ''Dreyfus'' (archived 2010) by [[Gene Ward Smith]] – [https://soundcloud.com/genewardsmith/genewardsmith-dreyfus SoundCloud] \| [https://www.archive.org/details/Dreyfus details] \| [https://www.archive.org/download/Dreyfus/Genewardsmith-Dreyfus.mp3 play] – Octoid[72] in 224edo tuning

	===== 17-limit =====		===== 17-limit =====

FloraC: + intros

2026-04-04T13:22:44Z

+ intros

Show changes

FloraC: Switch to Sintel's badness, WE & CWE tunings (11/11)

2026-04-03T15:43:44Z

Switch to Sintel's badness, WE & CWE tunings (11/11)

Show changes

FloraC: Switch to Sintel's badness, WE & CWE tunings (10/)

2026-04-03T15:13:30Z

Switch to Sintel's badness, WE & CWE tunings (10/)

Show changes

FloraC: Switch to Sintel's badness, WE & CWE tunings (9/)

2026-04-03T14:08:53Z

Switch to Sintel's badness, WE & CWE tunings (9/)

Show changes

← Older revision		Revision as of 17:58, 15 April 2026
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	* ''[[Rhinoceros]]'' (+49/48) → [[Unicorn family #Rhinoceros\|Unicorn family]]		* ''[[Rhinoceros]]'' (+49/48) → [[Unicorn family #Rhinoceros\|Unicorn family]]
	* ''[[Crepuscular]]'' (+50/49) → [[Fifive family #Crepuscular\|Fifive family]]		* ''[[Crepuscular]]'' (+50/49) → [[Fifive family #Crepuscular\|Fifive family]]
	* ''[[Modus]]'' (+64/63) → [[Tetracot family #Modus\|Tetracot family]]		* [[Modus]] (+64/63) → [[Tetracot family #Modus\|Tetracot family]]
	* ''[[Flattone]]'' (+81/80) → [[Meantone family #Flattone\|Meantone family]]		* [[Flattone]] (+81/80) → [[Meantone family #Flattone\|Meantone family]]
	* [[Sensi]] (+126/125 or 245/243) → [[Sensipent family #Sensi\|Sensipent family]]		* [[Sensi]] (+126/125 or 245/243) → [[Sensipent family #Sensi\|Sensipent family]]
	* [[Catakleismic]] (+225/224) → [[Kleismic family #Catakleismic\|Kleismic family]]		* [[Catakleismic]] (+225/224) → [[Kleismic family #Catakleismic\|Kleismic family]]