User:Overthink/Frameshift–Mercator equivalence continuum: Difference between revisions
Created page with "The '''Frameshift-Mercator equivalence continuum''' is the set of all temperaments which equate a number ''n'' of frameshift commas to mercator's comma. When extended to include fractional and infinite ''n'', it represents the set of all 2.3.11 temperaments supported by 159edo. Unfortunately, many of these temperaments are quite complex. {| class="wikitable center-1" |+ style="font-size: 105%;" | Temperaments in the co..." |
Started nexus-mercator equivalence continuum section |
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The ''' | The '''Frameshift–Mercator equivalence continuum''' is the set of all temperaments which equate a number ''n'' of [[Frameshift comma|frameshift commas]] to [[mercator's comma]]. When extended to include fractional and infinite ''n'', it represents the set of all [[Alpharabian tuning|2.3.11]] temperaments supported by [[159edo]]. Unfortunately, many of these temperaments are quite complex. | ||
{| class="wikitable center-1" | {| class="wikitable center-1" | ||
| Line 42: | Line 42: | ||
|- | |- | ||
| ∞ | | ∞ | ||
| Rank-2 [[Frameshift]] | |||
| [[22876792454961/22866405883904]] | |||
| {{Monzo| -34 28 0 0 -3}} | |||
|} | |||
One may want to look a version of this continuum that can be called the Nexus–Mercator equivalence continuum, which equates ''m'' nexus commas with the mercator's comma. This makes sense as the nexus comma is much simpler than the frameshift comma. (section incomplete) | |||
{| class="wikitable center-1" | |||
|+ style="font-size: 105%;" | Nexus–Mercator equivalence continuum | |||
|- | |||
! rowspan="2" | ''m'' | |||
! rowspan="2" | ''n'' | |||
! rowspan="2" | Temperament | |||
! colspan="2" | Comma | |||
|- | |||
! Ratio | |||
! Monzo | |||
|- | |||
| −1 | |||
| ? | |||
| 12e & 159 | |||
| <abbr title="443426488243037769948249630619149892803/442300615597430756708741799308284657664">[very long]</abbr> | |||
| {{Monzo| -118 81 0 0 -3 }} | |||
|- | |||
| 0 | |||
| 0 | |||
| 2.3.11 [[Mercator]] | |||
| <abbr title="19383245667680019896796723/19342813113834066795298816">[very long]</abbr> | |||
| {{Monzo| -84 53 }} | |||
|- | |||
| 1 | |||
| ? | |||
| 29 & 36 | |||
| <abbr title="1127741139168633/1125899906842624">[very long]</abbr> | |||
| {{Monzo| -50 25 0 0 3 }} | |||
|- | |||
| 2 | |||
| ? | |||
| [[Tribilo]] (Rank-2 [[nexus]]) | |||
| [[1771561/1769472]] | |||
| {{Monzo| -16 -3 0 0 6 }} | |||
|- | |||
| 3 | |||
| ? | |||
| 17 & 142 | |||
| [[618121839509504/617673396283947]] | |||
| {{Monzo| 18 -31 0 0 9 }} | |||
|- | |||
| … | |||
| … | |||
| … | |||
| | |||
|- | |||
| ∞ | |||
| 2 | |||
| Rank-2 [[Frameshift]] | | Rank-2 [[Frameshift]] | ||
| [[22876792454961/22866405883904]] | | [[22876792454961/22866405883904]] | ||
| {{Monzo| -34 28 0 0 -3}} | | {{Monzo| -34 28 0 0 -3}} | ||
|} | |} | ||