Diaschismic–gothmic equivalence continuum: Difference between revisions
add half-integer points to kleismic-tetracot continuum |
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| {{monzo| 11 -4 -2 }} | | {{monzo| 11 -4 -2 }} | ||
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All temperaments in the continuum also satisfy (15625/15552)<sup>''k''</sup> ~ 20000/19683, for a value of ''k'' defined such that 1/''r'' + 1/''k'' = 1. Varying ''k'' (for <sup>(number of)</sup> ''k''leismas) results in different temperaments listed in the table below. It converges to [[hanson]] as ''k'' approaches infinity, and is motivated by the fact that many important temperaments of 34edo follow a chain of commas connected by kleismas as discovered by [[User:Lériendil|Lériendil]]. The just value of ''k'' is 3.4117…, and temperaments near this tend to be the most accurate. | All temperaments in the continuum also satisfy (15625/15552)<sup>''k''</sup> ~ 20000/19683, for a value of ''k'' defined such that 1/''r'' + 1/''k'' = 1. Varying ''k'' (for <sup>(number of)</sup> ''k''leismas) results in different temperaments listed in the table below. It converges to [[hanson]] as ''k'' approaches infinity, and is motivated by the fact that many important temperaments of 34edo follow a chain of commas connected by kleismas as discovered by [[User:Lériendil|Lériendil]]. The just value of ''k'' is 3.4117…, and temperaments near this tend to be the most accurate. | ||
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| 17/5 | | 17/5 | ||
| [[Chlorine]] | | [[Chlorine]] | ||
| ( | | ([[Septendecima|48 digits]]; equal to ([[25/24]])<sup>17</sup> / [[2/1|2]]) | ||
| {{monzo| -52 -17 34 }} | | {{monzo| -52 -17 34 }} | ||
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! ''n'' !! ''r'' !! ''k'' !! Temperament !! Comma | ! ''n'' !! ''r'' !! ''k'' !! Temperament !! Comma | ||
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| 17/5 = 3.4|| 7/5 = 1.4 || 7/2 = 3.5 || [[Chlorine]] | | | 17/5 = 3.4|| 7/5 = 1.4 || 7/2 = 3.5 || [[Chlorine]] || {{monzo| -52 -17 34 }} | ||
|- | |- | ||
| 11/3 = 3.{{overline|6}} || 5/3 = 1.{{overline|6}} || 5/2 = 2.5 || [[Majvam]] || {{monzo| 40 7 -22 }} | | 11/3 = 3.{{overline|6}} || 5/3 = 1.{{overline|6}} || 5/2 = 2.5 || [[Majvam]] || {{monzo| 40 7 -22 }} | ||