Syntonic–rastmic equivalence continuum - Revision history

Xenllium at 00:24, 31 January 2026

2026-01-31T00:24:30Z

← Older revision		Revision as of 00:24, 31 January 2026
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	\|-		\|-
	! Ratio		! Ratio
	! ~~Monzo~~		! 2.3.5.11 monzo
			\|-
			\| −1
			\| Antiprotomere
			\| [[19683/19360]]
			\| {{monzo\| -5 9 -1 -2 }}
	\|-		\|-
	\| 0		\| 0

Xenllium at 23:40, 30 January 2026

2026-01-30T23:40:15Z

← Older revision		Revision as of 23:40, 30 January 2026
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	\|+ style="font-size: 105%;" \| Temperaments in the continuum		\|+ style="font-size: 105%;" \| Temperaments in the continuum
	\|-		\|-
	! rowspan="2" ~~\| {{nowrap~~\|''n'' ~~{{=}} ''k'' + 2}}~~		! rowspan="2" \| ''n''
	! rowspan="2" \| Temperament		! rowspan="2" \| Temperament
	! colspan="2" \| Comma		! colspan="2" \| Comma
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	\| {{monzo\| -1 -11 -1 6 }}		\| {{monzo\| -1 -11 -1 6 }}
	\|-		\|-
			\| …
	\| …		\| …
	\| …		\| …

ArrowHead294 at 02:10, 4 January 2025

2025-01-04T02:10:31Z

← Older revision		Revision as of 02:10, 4 January 2025
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	The '''~~syntonic-rastmic~~ equivalence continuum''' is a continuum of temperaments which equate a number of [[243/242\|rastmas (243/242)]] with the [[81/80\|syntonic comma (81/80)]].		The '''syntonic–rastmic equivalence continuum''' is a [[equivalence continuum\|continuum]] of temperaments which equate a number of [[243/242\|rastmas (243/242)]] with the [[81/80\|syntonic comma (81/80)]].

	All temperaments in the continuum satisfy 81/80 ~ (243/242)<sup>''n''</sup>. Varying ''n'' results in different temperaments listed in the table below. It converges to the 2.3.5.11 subgroup temperament of {243/242} as ''n'' approaches infinity. If we allow non-integer and infinite ''n'', the continuum describes the set of all 2.3.5.11 subgroup temperaments supported by [[mohaha]] due to it being the unique temperament that tempers out both commas and thus tempers out all combinations of them. The just value of ''n'' is 3.~~0125…~~, and temperaments near this tend to be the most accurate ones.		All temperaments in the continuum satisfy {{nowrap\|81/80 ~ (243/242)<sup>''n''</sup>}}. Varying ''n'' results in different temperaments listed in the table below. It converges to the 2.3.5.11 subgroup temperament of {243/242} as ''n'' approaches infinity. If we allow non-integer and infinite ''n'', the continuum describes the set of all 2.3.5.11 subgroup temperaments supported by [[mohaha]] due to it being the unique temperament that tempers out both commas and thus tempers out all combinations of them. The just value of ''n'' is 3.0125, and temperaments near this tend to be the most accurate ones.

	The continuum is very significant for the [[~~syntonic-rastmic~~ subchroma notation]], as each member of it entails a distinct way of notation.		The continuum is very significant for the [[syntonic–rastmic subchroma notation]], as each member of it entails a distinct way of notation.

	{\| class="wikitable center-1"		{\| class="wikitable center-1"
	\|+ Temperaments in the continuum		\|+ style="font-size: 105%;" \| Temperaments in the continuum
	\|-		\|-
	! rowspan="2" \| ''n'' = ''k'' + 2		! rowspan="2" \| {{nowrap\|''n'' {{=}} ''k'' + 2}}
	! rowspan="2" \| Temperament		! rowspan="2" \| Temperament
	! colspan="2" \| Comma		! colspan="2" \| Comma

ArrowHead294: ArrowHead294 moved page Syntonic-rastmic equivalence continuum to Syntonic–rastmic equivalence continuum

2025-01-04T02:09:24Z

ArrowHead294 moved page Syntonic-rastmic equivalence continuum to Syntonic–rastmic equivalence continuum

← Older revision	Revision as of 02:09, 4 January 2025
(No difference)

Fredg999 category edits: Removing from Category:Regular temperament theory using Cat-a-lot

2022-03-02T22:13:09Z

Removing from Category:Regular temperament theory using Cat-a-lot

← Older revision		Revision as of 22:13, 2 March 2022
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	[[Category:Mohaha]]		[[Category:Mohaha]]
	~~[[Category:Regular temperament theory]]~~
	[[Category:Equivalence continua]]		[[Category:Equivalence continua]]

Fredg999 category edits: Removing from Category:Temperament collections using Cat-a-lot

2022-02-28T20:08:22Z

Removing from Category:Temperament collections using Cat-a-lot

← Older revision		Revision as of 20:08, 28 February 2022
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	[[Category:Mohaha]]		[[Category:Mohaha]]
	[[Category:Regular temperament theory]]		[[Category:Regular temperament theory]]
	~~[[Category:Temperament collections]]~~
	[[Category:Equivalence continua]]		[[Category:Equivalence continua]]

Fredg999 category edits: Moving from Category:Temperament collection to Category:Temperament collections using Cat-a-lot

2022-02-28T17:08:53Z

Moving from Category:Temperament collection to Category:Temperament collections using Cat-a-lot

← Older revision		Revision as of 17:08, 28 February 2022
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	[[Category:Mohaha]]		[[Category:Mohaha]]
	[[Category:Regular temperament theory]]		[[Category:Regular temperament theory]]
	[[Category:Temperament ~~collection~~]]		[[Category:Temperament collections]]
	[[Category:Equivalence continua]]		[[Category:Equivalence continua]]

Aura: Okay, I had to fix the initial sentence... Given that this continuum is about equating a certain number of rastmas with the syntonic comma, I'm wondering if we need to rename both this page and syntonic-rastmic subchroma notation to better fit with this reality.

2021-12-11T02:07:59Z

Okay, I had to fix the initial sentence... Given that this continuum is about equating a certain number of rastmas with the syntonic comma, I'm wondering if we need to rename both this page and syntonic-rastmic subchroma notation to better fit with this reality.

← Older revision		Revision as of 02:07, 11 December 2021
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	The '''syntonic-rastmic equivalence continuum''' is a continuum of temperaments which equate a number of [[81/80\|~~syntonic commas~~ (81/80)]] with the [[~~243~~/~~242~~\|~~rastma~~ (~~243~~/~~242~~)]].		The '''syntonic-rastmic equivalence continuum''' is a continuum of temperaments which equate a number of [[243/242\|rastmas (243/242)]] with the [[81/80\|syntonic comma (81/80)]].

	All temperaments in the continuum satisfy 81/80 ~ (243/242)<sup>''n''</sup>. Varying ''n'' results in different temperaments listed in the table below. It converges to the 2.3.5.11 subgroup temperament of {243/242} as ''n'' approaches infinity. If we allow non-integer and infinite ''n'', the continuum describes the set of all 2.3.5.11 subgroup temperaments supported by [[mohaha]] due to it being the unique temperament that tempers out both commas and thus tempers out all combinations of them. The just value of ''n'' is 3.0125…, and temperaments near this tend to be the most accurate ones.		All temperaments in the continuum satisfy 81/80 ~ (243/242)<sup>''n''</sup>. Varying ''n'' results in different temperaments listed in the table below. It converges to the 2.3.5.11 subgroup temperament of {243/242} as ''n'' approaches infinity. If we allow non-integer and infinite ''n'', the continuum describes the set of all 2.3.5.11 subgroup temperaments supported by [[mohaha]] due to it being the unique temperament that tempers out both commas and thus tempers out all combinations of them. The just value of ''n'' is 3.0125…, and temperaments near this tend to be the most accurate ones.

FloraC: Created page with "The '''syntonic-rastmic equivalence continuum''' is a continuum of temperaments which equate a number of syntonic commas (81/80) with the [[243/242|rastma (243/242)]..."

2021-12-09T17:42:50Z

Created page with "The '''syntonic-rastmic equivalence continuum''' is a continuum of temperaments which equate a number of syntonic commas (81/80) with the [[243/242|rastma (243/242)]..."

New page

The '''syntonic-rastmic equivalence continuum''' is a continuum of temperaments which equate a number of [[81/80|syntonic commas (81/80)]] with the [[243/242|rastma (243/242)]].

All temperaments in the continuum satisfy 81/80 ~ (243/242)<sup>''n''</sup>. Varying ''n'' results in different temperaments listed in the table below. It converges to the 2.3.5.11 subgroup temperament of {243/242} as ''n'' approaches infinity. If we allow non-integer and infinite ''n'', the continuum describes the set of all 2.3.5.11 subgroup temperaments supported by [[mohaha]] due to it being the unique temperament that tempers out both commas and thus tempers out all combinations of them. The just value of ''n'' is 3.0125…, and temperaments near this tend to be the most accurate ones.

The continuum is very significant for the [[syntonic-rastmic subchroma notation]], as each member of it entails a distinct way of notation.

{| class="wikitable center-1"
|+ Temperaments in the continuum
|-
! rowspan="2" | ''n'' = ''k'' + 2
! rowspan="2" | Temperament
! colspan="2" | Comma
|-
! Ratio
! Monzo
|-
| 0
| Meantone expansion
| [[81/80]]
| {{monzo| -4 4 -1 }}
|-
| 1
| [[Protomere]]
| [[121/120]]
| {{monzo| -3 -1 -1 2 }}
|-
| 2
| [[Deuteromere]]
| [[14641/14580]]
| {{monzo| -2 -6 -1 4 }}
|-
| 3
| [[Tritomere]]
| [[1771561/1771470]]
| {{monzo| -1 -11 -1 6 }}
|-
| …
| …
| …
|-
| ∞
| Neutral expansion
| [[243/242]]
| {{monzo| -1 5 0 -2 }}
|}

This series of temperament names derives from Greek ordinal prefixes + [[Wiktionary: -mere #English|-mere]], which derives from ancient Greek ''meros'', meaning "part".

[[Category:Mohaha]]
[[Category:Regular temperament theory]]
[[Category:Temperament collection]]
[[Category:Equivalence continua]]