Syntonic–rastmic equivalence continuum: Difference between revisions

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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.

Revision as of 17:42, 9 December 2021 view source FloraC (talk \| contribs) autopatrolled, Bureaucrats, Interface administrators, Sysops 18,318 edits 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)]..."		Revision as of 02:07, 11 December 2021 view source Aura (talk \| contribs) autopatrolled, emailconfirmed 5,920 edits 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. Newer edit →
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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.