51edo: Difference between revisions
Cmloegcmluin (talk | contribs) add Notation section, and Sagittal notation |
+rank-2 temps table |
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== Notation == | == Notation == | ||
=== Sagittal notation === | |||
In the following diagrams, a sagittal symbol followed by an equals sign (=) means that the following comma is the symbol's [[Sagittal notation#Primary comma|primary comma]] (the comma it ''exactly'' represents in JI), while an approximately equals sign (≈) means it is a secondary comma (a comma it ''approximately'' represents in JI). In both cases the symbol exactly represents the tempered version of the comma in this edo. | |||
==== Evo flavor ==== | |||
====Evo flavor==== | |||
<imagemap> | <imagemap> | ||
File:51-EDO_Evo_Sagittal.svg | File:51-EDO_Evo_Sagittal.svg | ||
| Line 353: | Line 352: | ||
</imagemap> | </imagemap> | ||
====Revo flavor==== | ==== Revo flavor ==== | ||
<imagemap> | <imagemap> | ||
File:51-EDO_Revo_Sagittal.svg | File:51-EDO_Revo_Sagittal.svg | ||
| Line 366: | Line 364: | ||
</imagemap> | </imagemap> | ||
====Evo-SZ flavor==== | ==== Evo-SZ flavor ==== | ||
<imagemap> | <imagemap> | ||
File:51-EDO_Evo-SZ_Sagittal.svg | File:51-EDO_Evo-SZ_Sagittal.svg | ||
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default [[File:51-EDO_Evo-SZ_Sagittal.svg]] | default [[File:51-EDO_Evo-SZ_Sagittal.svg]] | ||
</imagemap> | </imagemap> | ||
== Regular temperament properties == | |||
{| class="wikitable center-4 center-5 center-6" | |||
|- | |||
! rowspan="2" | [[Subgroup]] | |||
! rowspan="2" | [[Comma list]] | |||
! rowspan="2" | [[Mapping]] | |||
! rowspan="2" | Optimal<br>8ve stretch (¢) | |||
! colspan="2" | Tuning error | |||
|- | |||
! [[TE error|Absolute]] (¢) | |||
! [[TE simple badness|Relative]] (%) | |||
|- | |||
| 2.3.7 | |||
| 1029/1024, {{monzo| 17 -16 3 }} | |||
| {{Mapping| 51 81 143 }} | |||
| -0.339 | |||
| 1.63 | |||
| 6.92 | |||
|- style="border-top: double;" | |||
| 2.3.5 | |||
| 128/125, {{monzo| -13 17 -6 }} | |||
| {{Mapping| 51 81 119 }} (51c) | |||
| -2.789 | |||
| 2.41 | |||
| 10.3 | |||
|- style="border-top: double;" | |||
| 2.3.5 | |||
| 250/243, 34171875/33554432 | |||
| {{Mapping| 51 81 118 }} (51) | |||
| +0.581 | |||
| 2.77 | |||
| 11.8 | |||
|} | |||
=== Rank-2 temperaments === | |||
{| class="wikitable center-all left-5" | |||
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | |||
|- | |||
! Periods<br>per 8ve | |||
! Generator* | |||
! Cents* | |||
! Associated<br>ratio* | |||
! Temperament | |||
|- | |||
| 1 | |||
| 5\51 | |||
| 117.6 | |||
| 15/14 | |||
| [[Miracle]] (51e, out of tune) / oracle (51) | |||
|- | |||
| 1 | |||
| 7\51 | |||
| 164.7 | |||
| 11/10 | |||
| [[Porky]] (51) | |||
|- | |||
| 1 | |||
| 10\51 | |||
| 235.3 | |||
| 8/7 | |||
| [[Rodan]] (51cf…, out of tune) / aerodino (51ce) | |||
|- | |||
| 1 | |||
| 5\51 | |||
| 541.2 | |||
| 15/11 | |||
| [[Necromanteion]] (51ce) | |||
|- | |||
| 3 | |||
| 19\51<br>(2\51) | |||
| 447.1<br>(47.1) | |||
| 9/7<br>(36/35) | |||
| [[Hemiaug]] (51ce) | |||
|- | |||
| 3 | |||
| 21\51<br>(4\51) | |||
| 494.1<br>(94.1) | |||
| 4/3<br>(16/15) | |||
| [[Augmented]] (51c) | |||
|} | |||
<nowiki/>* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[normal lists|minimal form]] in parentheses if distinct | |||
== Scales == | == Scales == | ||
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== Instruments == | == Instruments == | ||
; Lumatone | |||
: See [[Lumatone mapping for 51edo]]. | |||
See [[Lumatone mapping for 51edo]] | |||
== Music == | == Music == | ||
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[[Category:Listen]] | [[Category:Listen]] | ||