Marvel–breedsmic equivalence continuum: Difference between revisions
Created page with "{{Mathematical interest}} The '''marvel–breedsmic equivalence continuum''' is a continuum of 7-limit temperament families which equate a number of breedsmas (2401/2400) with a marvel comma (225/224). This continuum is theoretically interesting in that these are all 7-limit temperament families supported by septimal miracle temperament. All temperaments in the continuum satisfy {{nowrap|..." Tags: Mobile edit Mobile web edit |
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We may invert the continuum by setting ''m'' such that {{nowrap|''m'' − 1/''n'' {{=}} 1}}. This may be called the ''marvel–gamelismic equivalence continuum'', which is essentially the same thing. The just value of ''m'' is approximately 1.09352, and temperaments having ''n'' near this value tend to be the most accurate ones. | |||
{| class="wikitable center-1" | |||
|+ style="font-size: 105%;" | Temperaments with integer ''m'' | |||
|- | |||
! rowspan="2" | ''m'' | |||
! rowspan="2" | Temperament family | |||
! colspan="2" | Comma | |||
|- | |||
! Ratio | |||
! Monzo | |||
|- | |||
| −3 | |||
| [[Syntonic–31 equivalence continuum #Ampersand|Ampersand]] | |||
| [[34171875/33554432]] | |||
| {{Monzo| −25 7 6 }} | |||
|- | |||
| −2 | |||
| {{nowrap|12d & 31 & 41}} | |||
| [[1063125/1048576]] | |||
| {{Monzo| −20 5 4 1 }} | |||
|- | |||
| −1 | |||
| [[Mirwomo temperaments|Mirwomo]] | |||
| [[33075/32768]] | |||
| {{Monzo| −15 3 2 2 }} | |||
|- | |||
| 0 | |||
| [[Gamelismic clan|Gamelismic]] | |||
| [[1029/1024]] | |||
| {{Monzo| −10 1 0 3 }} | |||
|- | |||
| 1 | |||
| [[Breedsmic temperaments|Breedsmic]] | |||
| [[2401/2400]] | |||
| {{Monzo| −5 −1 −2 4 }} | |||
|- | |||
| 2 | |||
| [[Mirkwai clan|Mirkwai]] | |||
| [[16875/16807]] | |||
| {{Monzo| 0 3 4 −5 }} | |||
|- | |||
| 3 | |||
| {{nowrap|31 & 41 & 133d}} | |||
| [[3796875/3764768]] | |||
| {{Monzo| −5 5 6 −6 }} | |||
|- | |||
| 4 | |||
| {{nowrap|31 & 41 & 114d}} | |||
| [[854296875/843308032]] | |||
| {{Monzo| −10 7 8 −7 }} | |||
|- | |||
| … | |||
| … | |||
| … | |||
| … | |||
|- | |||
| ∞ | |||
| [[Marvel temperaments|Marvel]] | |||
| [[225/224]] | |||
| {{Monzo| −5 2 2 −1 }} | |||
|} | |||
[[Category:Miracle]] | [[Category:Miracle]] | ||
[[Category:Equivalence continua]] | [[Category:Equivalence continua]] | ||