Syntonic–chromatic equivalence continuum: Difference between revisions
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|+ Temperaments in the continuum | |+ Temperaments in the continuum | ||
|- | |- | ||
! rowspan="2" | ''k'' | ! rowspan="2" | ''k'' | ||
! rowspan="2" | ''n'' | ! rowspan="2" | ''n'' | ||
! rowspan="2" | Temperament | ! rowspan="2" | Temperament | ||
! colspan="2" | Comma | ! colspan="2" | Comma | ||
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| -5 | | -5 | ||
| -3 | | -3 | ||
| 7 & 64 "nadir | | 7 & 64 ("nadir"<nowiki>*</nowiki>) | ||
| [[1162261467/1048576000]] | | [[1162261467/1048576000]] | ||
| {{monzo| -23 19 -3}} | | {{monzo| -23 19 -3}} | ||
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| -3 | | -3 | ||
| -1 | | -1 | ||
| 7 & 33 ( | | 7 & 33 ("tragicomical"/"deeptone"<nowiki>*</nowiki>) | ||
| [[177147/163840]] | | [[177147/163840]] | ||
| {{monzo| -15 11 -1}} | | {{monzo| -15 11 -1}} | ||
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| {{monzo| -4 4 -1 }} | | {{monzo| -4 4 -1 }} | ||
|} | |} | ||
<nowiki>*</nowiki> not finalized. | |||
We may also invert the continuum by setting ''m'' such that 1/''m'' + 1/''n'' = 1. The just value of ''m'' is 1.2333… | We may also invert the continuum by setting ''m'' such that 1/''m'' + 1/''n'' = 1. The just value of ''m'' is 1.2333… | ||
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|} | |} | ||
{| class="wikitable" | |||
|+ Notable temperaments of fractional ''n'' | |||
|- | |||
! Temperament !! ''n'' !! ''m'' | |||
|- | |||
| [[Enipucrop]] || 3/2 = 1.5 || 3 | |||
|- | |||
| [[Seville]] || 7/3 = 2.{{overline|3}} || 7/4 = 1.75 | |||
|- | |||
| [[Sixix]] || 5/2 = 2.5 || 5/3 = 1.{{overline|6}} | |||
|- | |||
| [[Sevond]] || 7/2 = 3.5 || 7/5 = 1.4 | |||
|- | |||
| [[Artoneutral (temperament)|Artoneutral]] || 9/2 = 4.5 || 9/7 = 1.{{overline|285714}} | |||
|- | |||
| [[Brahmagupta]] || 21/4 = 5.25 || 21/17 = 1.235… | |||
|- | |||
| [[Raider]] || 37/7 = 5.{{overline|285714}} || 37/30 = 1.2{{overline|3}} | |||
|- | |||
| [[Geb]] || 16/3 = 5.{{overline|3}} || 16/13 = 1.{{overline|230769}} | |||
|- | |||
| [[Undetrita]] || 11/2 = 5.5 || 11/9 = 1.{{overline|2}} | |||
|} | |||
== Enipucrop == | == Enipucrop == | ||
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== Absurdity == | == Absurdity == | ||
{{ | {{See also| Porwell temperaments #Absurdity }} | ||
The 5-limit 7&84 temperament, so named because it truly is an absurd temperament. The generator is 81/80 and the period is 800/729, which is (10/9) / (81/80). This is also part of the syntonic-chromatic equivalence continuum, in this case where (81/80)<sup>5</sup> = 25/24. | The 5-limit 7&84 temperament, so named because it truly is an absurd temperament. The generator is 81/80 and the period is 800/729, which is (10/9) / (81/80). This is also part of the syntonic-chromatic equivalence continuum, in this case where (81/80)<sup>5</sup> = 25/24. | ||