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== 16-tone piano layout based on the mavila[7]/antidiatonic scale ==
=== Armodue theory (4-line staff) ===
[[File:16-EDO-PIano-Diagram.png|alt=16-EDO-PIano-Diagram.png|748x293px|16-EDO-PIano-Diagram.png]]
[http://www.armodue.com/ricerche.htm Armodue]: Pierpaolo Beretta's website for his "Armodue" theory for 16edo (esadekaphonic), including compositions.


This Layout places mavila[7] on the black keys and mavila[9] on the white keys. As you can see, flats are higher than naturals and sharps are lower, as per the "harmonic notation" above. Simply swap sharps with flats for "melodic notation".
For translations of parts of the Armodue pages see the [[Armodue]] on this wiki


== 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:
Important mosses include:
* [[magic]] anti-diatonic 3L4s 1414141 (5\16, 1\1)
*[[magic]] anti-diatonic 3L4s 1414141 (5\16, 1\1)
* [[magic]] superdiatonic 3L7s 1311311311 (5\16, 1\1)
*[[magic]] superdiatonic 3L7s 1311311311 (5\16, 1\1)
* Pathological [[magic]] chromatic 11121121112 3L10s (5\16, 1\1)
* Pathological [[magic]] chromatic 11121121112 3L10s (5\16, 1\1)
* [[mavila]] anti-diatonic 2L5s 2223223 (9\16, 1\1)
*[[mavila]] anti-diatonic 2L5s 2223223 (9\16, 1\1)
* [[mavila]] superdiatonic 7L2s 222212221 (9\16, 1\1)
*[[mavila]] superdiatonic 7L2s 222212221 (9\16, 1\1)
* [[gorgo]] 5L1s 333331 (3\16, 1\1)
*[[gorgo]] 5L1s 333331 (3\16, 1\1)
* [[lemba]] 4L2s 332332 (3\16, 1\2)
*[[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 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 [[1L 13s]] 3 1 1 1 1 1 1 1 1 1 1 1 1 1 (1\16, 1\1)
Line 613: Line 613:
| 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|astrology]]
|[[Lemba]], [[astrology]]
|-
|-
| 4
| 4
| 1\16
| 1\16
| [[Diminished]]/demolished
|[[Diminished]]/demolished
|-
|-
| 8
| 8
Line 654: Line 654:
| [7]:
| [7]:
| 3 2 2 3 2 2 2
| 3 2 2 3 2 2 2
| [[File:MavilaAntidiatonic16edo.mp3]]
|[[File:MavilaAntidiatonic16edo.mp3]]
|-
|-
| [9]:
| [9]:
| 1 2 2 2 1 2 2 2 2
| 1 2 2 2 1 2 2 2 2
| [[File:MavilaSuperdiatonic16edo.mp3]]
|[[File:MavilaSuperdiatonic16edo.mp3]]
|}
|}
See also [[Mavila Temperament Modal Harmony]].
See also [[Mavila Temperament Modal Harmony]].
Line 668: Line 668:
| [8]:
| [8]:
| 1 3 1 3 1 3 1 3
| 1 3 1 3 1 3 1 3
| [[File:htgt16edo.mp3]]
|[[File:htgt16edo.mp3]]
|-
|-
| [12]:
| [12]:
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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>Ratios longer than 10 digits are presented by placeholders with informative hints</ref>
![[Ratio]]<ref>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
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|-
|-
| 5
| 5
| [[648/625]]
|[[648/625]]
| {{monzo| 3 4 -4 }}
|{{monzo| 3 4 -4 }}
| 62.57
| 62.57
| Quadgu
| Quadgu
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|-
|-
| 5
| 5
| [[3125/3072]]
|[[3125/3072]]
| {{monzo| -10 -1 5 }}
|{{monzo| -10 -1 5 }}
| 29.61
| 29.61
| Laquinyo
| Laquinyo
Line 750: Line 750:
|-
|-
| 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
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|-
|-
| 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
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|-
|-
| 7
| 7
| [[3125/3087]]
|[[3125/3087]]
| {{monzo| 0 -2 5 -3 }}
|{{monzo| 0 -2 5 -3 }}
| 21.18
| 21.18
| Triru-aquinyo
| Triru-aquinyo
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|-
|-
| 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
| [[81029/1024]]
|[[81029/1024]]
| {{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
Line 827: Line 827:
|-
|-
| 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 834: Line 834:
|-
|-
| 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 841: Line 841:
|-
|-
| 11
| 11
| [[3025/3024]]
|[[3025/3024]]
| {{monzo| -4 -3 2 -1 2 }}
|{{monzo| -4 -3 2 -1 2 }}
| 0.57
| 0.57
| Loloruyoyo
| Loloruyoyo
| Lehmerisma
| Lehmerisma
|}
|}
<references/>
<references />


== Armodue theory (4-line staff) ==
== Diagrams ==
[http://www.armodue.com/ricerche.htm Armodue]: Pierpaolo Beretta's website for his "Armodue" theory for 16edo (esadekaphonic), including compositions.
[[File:16edo_wheel_01.png|alt=16edo wheel 01.png|325x325px|16edo wheel 01.png]]


For translations of parts of the Armodue pages see the [[Armodue]] on this wiki.
=== 16-tone piano layout based on the mavila[7]/antidiatonic scale ===
[[File:16-EDO-PIano-Diagram.png|alt=16-EDO-PIano-Diagram.png|748x293px|16-EDO-PIano-Diagram.png]]


== Diagrams ==
This Layout places mavila[7] on the black keys and mavila[9] on the white keys. As you can see, flats are higher than naturals and sharps are lower, as per the "harmonic notation" above. Simply swap sharps with flats for "melodic notation".
[[File:16edo_wheel_01.png|alt=16edo wheel 01.png|325x325px|16edo wheel 01.png]]


== Music ==
== Music ==
Retrieved from "https://en.xen.wiki/w/16edo"