16edo: Difference between revisions
m →Diagrams: todo |
→Regular temperament properties: style, comma names, misc. cleanup |
||
Line 517: | Line 517: | ||
{| class="commatable wikitable center-all left-3 right-4 left-6" | {| class="commatable wikitable center-all left-3 right-4 left-6" | ||
|- | |- | ||
![[Harmonic limit|Prime<br> | ! [[Harmonic limit|Prime<br>limit]] | ||
![[Ratio]]<ref group=note>Ratios longer than 10 digits are presented by placeholders with informative hints</ref> | ! [[Ratio]]<ref group=note>Ratios longer than 10 digits are presented by placeholders with informative hints</ref> | ||
![[Monzo]] | ! [[Monzo]] | ||
![[Cent]]s | ! [[Cent]]s | ||
![[Color name]] | ! [[Color name]] | ||
! Name | ! Name | ||
|- | |- | ||
| 5 | | 5 | ||
|[[135/128]] | | [[135/128]] | ||
|{{monzo| -7 3 1 }} | | {{monzo| -7 3 1 }} | ||
| 92.18 | | 92.18 | ||
| Layobi | | Layobi | ||
| | | Mavila comma, major chroma | ||
|- | |- | ||
| 5 | | 5 | ||
|[[648/625]] | | [[648/625]] | ||
|{{monzo| 3 4 -4 }} | | {{monzo| 3 4 -4 }} | ||
| 62.57 | | 62.57 | ||
| Quadgu | | Quadgu | ||
| | | Diminished comma, major diesis | ||
|- | |- | ||
| 5 | | 5 | ||
|[[3125/3072]] | | [[3125/3072]] | ||
|{{monzo| -10 -1 5 }} | | {{monzo| -10 -1 5 }} | ||
| 29.61 | | 29.61 | ||
| Laquinyo | | Laquinyo | ||
Line 546: | Line 546: | ||
|- | |- | ||
| 5 | | 5 | ||
|[[6115295232/6103515625|(20 digits)]] | | [[6115295232/6103515625|(20 digits)]] | ||
|{{monzo| 23 6 -14 }} | | {{monzo| 23 6 -14 }} | ||
| 3.34 | | 3.34 | ||
| Sasepbiru | | Sasepbiru | ||
|[[Vishnuzma]] | | [[Vishnuzma]] | ||
|- | |- | ||
| 7 | | 7 | ||
|[[36/35]] | | [[36/35]] | ||
|{{monzo| 2 2 -1 -1 }} | | {{monzo| 2 2 -1 -1 }} | ||
| 48.77 | | 48.77 | ||
| Rugu | | Rugu | ||
| | | Mint comma, septimal quartertone | ||
|- | |- | ||
| 7 | | 7 | ||
|[[525/512]] | | [[525/512]] | ||
|{{monzo| -9 1 2 1 }} | | {{monzo| -9 1 2 1 }} | ||
| 43.41 | | 43.41 | ||
| Lazoyoyo | | Lazoyoyo | ||
Line 567: | Line 567: | ||
|- | |- | ||
| 7 | | 7 | ||
|[[50/49]] | | [[50/49]] | ||
|{{monzo| 1 0 2 -2 }} | | {{monzo| 1 0 2 -2 }} | ||
| 34.98 | | 34.98 | ||
| Biruyo | | Biruyo | ||
Line 574: | Line 574: | ||
|- | |- | ||
| 7 | | 7 | ||
|[[64827/64000]] | | [[64827/64000]] | ||
|{{monzo| -9 3 -3 4 }} | | {{monzo| -9 3 -3 4 }} | ||
| 22.23 | | 22.23 | ||
| Laquadzo-atrigu | | Laquadzo-atrigu | ||
| Squalentine | | Squalentine comma | ||
|- | |- | ||
| 7 | | 7 | ||
|[[3125/3087]] | | [[3125/3087]] | ||
|{{monzo| 0 -2 5 -3 }} | | {{monzo| 0 -2 5 -3 }} | ||
| 21.18 | | 21.18 | ||
| Triru-aquinyo | | Triru-aquinyo | ||
| Gariboh | | Gariboh comma | ||
|- | |- | ||
| 7 | | 7 | ||
|[[126/125]] | | [[126/125]] | ||
|{{monzo| 1 2 -3 1 }} | | {{monzo| 1 2 -3 1 }} | ||
| 13.79 | | 13.79 | ||
| Zotrigu | | Zotrigu | ||
Line 595: | Line 595: | ||
|- | |- | ||
| 7 | | 7 | ||
|[[1029/1024]] | | [[1029/1024]] | ||
|{{monzo| -10 1 0 3 }} | | {{monzo| -10 1 0 3 }} | ||
| 8.43 | | 8.43 | ||
| Latrizo | | Latrizo | ||
Line 602: | Line 602: | ||
|- | |- | ||
| 7 | | 7 | ||
|[[6144/6125]] | | [[6144/6125]] | ||
|{{monzo| 11 1 -3 -2 }} | | {{monzo| 11 1 -3 -2 }} | ||
| 5.36 | | 5.36 | ||
| Sarurutrigu | | Sarurutrigu | ||
Line 609: | Line 609: | ||
|- | |- | ||
| 11 | | 11 | ||
|[[121/120]] | | [[121/120]] | ||
|{{monzo| -3 -1 -1 0 2 }} | | {{monzo| -3 -1 -1 0 2 }} | ||
| 14.37 | | 14.37 | ||
| Lologu | | Lologu | ||
Line 616: | Line 616: | ||
|- | |- | ||
| 11 | | 11 | ||
|[[176/175]] | | [[176/175]] | ||
|{{monzo| 4 0 -2 -1 1 }} | | {{monzo| 4 0 -2 -1 1 }} | ||
| 9.86 | | 9.86 | ||
| Lorugugu | | Lorugugu | ||
Line 623: | Line 623: | ||
|- | |- | ||
| 11 | | 11 | ||
|[[385/384]] | | [[385/384]] | ||
|{{monzo| -7 -1 1 1 1 }} | | {{monzo| -7 -1 1 1 1 }} | ||
| 4.50 | | 4.50 | ||
| Lozoyo | | Lozoyo | ||
Line 630: | Line 630: | ||
|- | |- | ||
| 11 | | 11 | ||
|[[441/440]] | | [[441/440]] | ||
|{{monzo| -3 2 -1 2 -1 }} | | {{monzo| -3 2 -1 2 -1 }} | ||
| 3.93 | | 3.93 | ||
| Luzozogu | | Luzozogu | ||
Line 637: | Line 637: | ||
|- | |- | ||
| 11 | | 11 | ||
|[[3025/3024]] | | [[3025/3024]] | ||
|{{monzo| -4 -3 2 -1 2 }} | | {{monzo| -4 -3 2 -1 2 }} | ||
| 0.57 | | 0.57 | ||
| Loloruyoyo | | Loloruyoyo | ||
Line 645: | Line 645: | ||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
*[[List of 16et rank two temperaments by badness]] | * [[List of 16et rank two temperaments by badness]] | ||
Temperaments listed by generator size: | Temperaments listed by generator size: | ||
Line 664: | Line 651: | ||
{| class="wikitable center-1 center-2" | {| class="wikitable center-1 center-2" | ||
|- | |- | ||
! Periods<br>per | ! Periods<br>per 8ve | ||
! Generator | ! Generator | ||
! Temperaments | ! Temperaments | ||
Line 670: | Line 657: | ||
| 1 | | 1 | ||
| 1\16 | | 1\16 | ||
|[[Valentine]], [[slurpee]] | | [[Valentine]], [[slurpee]] | ||
|- | |- | ||
| 1 | | 1 | ||
| 3\16 | | 3\16 | ||
|[[Gorgo]] | | [[Gorgo]] | ||
|- | |- | ||
| 1 | | 1 | ||
| 5\16 | | 5\16 | ||
|[[magic]]/muggles | | [[magic]]/[[muggles]] | ||
|- | |- | ||
| 1 | | 1 | ||
| 7\16 | | 7\16 | ||
|[[Mavila]]/armodue | | [[Mavila]]/[[armodue]] | ||
|- | |- | ||
| 2 | | 2 | ||
| 1\16 | | 1\16 | ||
|[[Bipelog]] | | [[Bipelog]] | ||
|- | |- | ||
| 2 | | 2 | ||
| 3\16 | | 3\16 | ||
|[[Lemba]], [[astrology]] | | [[Lemba]], [[astrology]] | ||
|- | |- | ||
| 4 | | 4 | ||
| 1\16 | | 1\16 | ||
|[[Diminished]]/demolished | | [[Diminished (temperament)|Diminished]]/[[demolished]] | ||
|- | |- | ||
| 8 | | 8 | ||
| 1\16 | | 1\16 | ||
| | | [[Semidim]] | ||
|} | |} | ||
== Scales == | |||
Important mosses include: | |||
* [[magic]] anti-diatonic 3L4s 1414141 (5\16, 1\1) | |||
* [[magic]] superdiatonic 3L7s 1311311311 (5\16, 1\1) | |||
* Pathological [[magic]] chromatic 11121121112 3L10s (5\16, 1\1) | |||
* [[mavila]] anti-diatonic 2L5s 2223223 (9\16, 1\1) | |||
* [[mavila]] superdiatonic 7L2s 222212221 (9\16, 1\1) | |||
* [[gorgo]] 5L1s 333331 (3\16, 1\1) | |||
* [[lemba]] 4L2s 332332 (3\16, 1\2) | |||
* Pathological [[1L 12s]] 4 1 1 1 1 1 1 1 1 1 1 1 (1\16, 1\1) | |||
* Pathological [[1L 13s]] 3 1 1 1 1 1 1 1 1 1 1 1 1 1 (1\16, 1\1) | |||
* Pathological [[2L 12s]] 2 1 1 1 1 1 1 2 1 1 1 1 1 1 (1\16, 1\2) | |||
* Pathological [[1L 14s]] 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 (1\16, 1\1) | |||
'''Mavila''' | '''Mavila''' |