16edo: Difference between revisions

BudjarnLambeth (talk | contribs)
m Diagrams: todo
Regular temperament properties: style, comma names, misc. cleanup
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{| 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>Limit]]
! [[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
| Major chroma
| Mavila comma, major chroma
|-
|-
| 5
| 5
|[[648/625]]
| [[648/625]]
|{{monzo| 3 4 -4 }}
| {{monzo| 3 4 -4 }}
| 62.57
| 62.57
| Quadgu
| Quadgu
| Major diesis
| Diminished comma, major diesis
|-
|-
| 5
| 5
|[[3125/3072]]
| [[3125/3072]]
|{{monzo| -10 -1 5 }}
| {{monzo| -10 -1 5 }}
| 29.61
| 29.61
| Laquinyo
| Laquinyo
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|-
|-
| 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
| Septimal quartertone
| 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
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|-
|-
| 7
| 7
|[[50/49]]
| [[50/49]]
|{{monzo| 1 0 2 -2 }}
| {{monzo| 1 0 2 -2 }}
| 34.98
| 34.98
| Biruyo
| Biruyo
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|-
|-
| 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
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|-
|-
| 7
| 7
|[[1029/1024]]
| [[1029/1024]]
|{{monzo| -10 1 0 3 }}
| {{monzo| -10 1 0 3 }}
| 8.43
| 8.43
| Latrizo
| Latrizo
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|-
|-
| 7
| 7
|[[6144/6125]]
| [[6144/6125]]
|{{monzo| 11 1 -3 -2 }}
| {{monzo| 11 1 -3 -2 }}
| 5.36
| 5.36
| Sarurutrigu
| Sarurutrigu
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|-
|-
| 11
| 11
|[[121/120]]
| [[121/120]]
|{{monzo| -3 -1 -1 0 2 }}
| {{monzo| -3 -1 -1 0 2 }}
| 14.37
| 14.37
| Lologu
| Lologu
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|-
|-
| 11
| 11
|[[176/175]]
| [[176/175]]
|{{monzo| 4 0 -2 -1 1 }}
| {{monzo| 4 0 -2 -1 1 }}
| 9.86
| 9.86
| Lorugugu
| Lorugugu
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|-
|-
| 11
| 11
|[[385/384]]
| [[385/384]]
|{{monzo| -7 -1 1 1 1 }}
| {{monzo| -7 -1 1 1 1 }}
| 4.50
| 4.50
| Lozoyo
| Lozoyo
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|-
|-
| 11
| 11
|[[441/440]]
| [[441/440]]
|{{monzo| -3 2 -1 2 -1 }}
| {{monzo| -3 2 -1 2 -1 }}
| 3.93
| 3.93
| Luzozogu
| Luzozogu
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|-
|-
| 11
| 11
|[[3025/3024]]
| [[3025/3024]]
|{{monzo| -4 -3 2 -1 2 }}
| {{monzo| -4 -3 2 -1 2 }}
| 0.57
| 0.57
| Loloruyoyo
| Loloruyoyo
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=== Rank-2 temperaments ===
=== Rank-2 temperaments ===
*[[List of 16et rank two temperaments by badness]]
* [[List of 16et rank two temperaments by badness]]
 
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)


Temperaments listed by generator size:
Temperaments listed by generator size:
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{| class="wikitable center-1 center-2"
{| class="wikitable center-1 center-2"
|-
|-
! Periods<br>per octave
! Periods<br>per 8ve
! Generator
! Generator
! Temperaments
! Temperaments
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| 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'''