Xenharmonic Wiki

15edo: Difference between revisions

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15 EDO [[tempering_out|tempers]] out the following [[Comma|commas]]. (Note: This assumes the [[val]] {{val|15 24 35 42 52 56}}.)
15 EDO [[tempering_out|tempers]] out the following [[Comma|commas]]. (Note: This assumes the [[val]] {{val|15 24 35 42 52 56}}.)


{| class="wikitable"
{| class="wikitable center-all left-3 right-4"
|-
|-
! | [[Ratios|Ratio]]
! [[Harmonic limit|Prime<br>Limit]]
! | [[Monzo]]
! [[Ratios|Ratio]]
! | [[Cent|Cents]]
! [[Monzo]]
![[Color notation/Temperament Names|Color Names]]
! [[Cent|Cents]]
! | Name 1
! [[Color notation/Temperament Names|Color Names]]
! | Name 2
! Name 1
! | Name 3
! Name 2
! Name 3
|-
|-
| style="text-align:center;" | 256/243
| 3
| 256/243
| |<nowiki> | 8 -5 </nowiki>&gt;
| |<nowiki> | 8 -5 </nowiki>&gt;
| style="text-align:right;" | 90.22
| 90.22
| style="text-align:center;" |Sawa
| Sawa
| style="text-align:center;" | Limma
| Limma
| style="text-align:center;" | Pythagorean Minor 2nd
| Pythagorean minor 2nd
| style="text-align:center;" |  
|  
|-
|-
| style="text-align:center;" | 250/243
| 5
| 250/243
| |<nowiki> | 1 -5 3 </nowiki>&gt;
| |<nowiki> | 1 -5 3 </nowiki>&gt;
| style="text-align:right;" | 49.17
| 49.17
| style="text-align:center;" |Triyo
| Triyo
| style="text-align:center;" | Maximal Diesis
| Maximal diesis
| style="text-align:center;" | Porcupine Comma
| Porcupine comma
| style="text-align:center;" |  
|  
|-
|-
| style="text-align:center;" | 128/125
| "
| 128/125
| |<nowiki> | 7 0 -3 </nowiki>&gt;
| |<nowiki> | 7 0 -3 </nowiki>&gt;
| style="text-align:right;" | 41.06
| 41.06
| style="text-align:center;" |Trigu
| Trigu
| style="text-align:center;" | Diesis
| Diesis
| style="text-align:center;" | Augmented Comma
| Augmented comma
| style="text-align:center;" |  
|  
|-
|-
| style="text-align:center;" | 15625/15552
| "
| 15625/15552
| |<nowiki> | -6 -5 6 </nowiki>&gt;
| |<nowiki> | -6 -5 6 </nowiki>&gt;
| style="text-align:right;" | 8.11
| 8.11
| style="text-align:center;" |Tribiyo
| Tribiyo
| style="text-align:center;" | Kleisma
| Kleisma
| style="text-align:center;" | Semicomma Majeur
| semicomma majeur
| style="text-align:center;" |  
|  
|-
|-
| style="text-align:center;" | 28/27
| 7
| 28/27
| |<nowiki> | 2 -3 0 1 </nowiki>&gt;
| |<nowiki> | 2 -3 0 1 </nowiki>&gt;
| style="text-align:right;" | 62.96
| 62.96
| style="text-align:center;" |Zo
| Zo
| style="text-align:center;" | Septimal Third Tone
| Septimal third tone
| style="text-align:center;" | Small Septimal Chroma
| Small septimal chroma
| |  
|  
|-
|-
| style="text-align:center;" | 1029/1000
| "
| 1029/1000
| |<nowiki> | -3 1 -3 3 </nowiki>&gt;
| |<nowiki> | -3 1 -3 3 </nowiki>&gt;
| style="text-align:right;" | 49.49
| 49.49
| style="text-align:center;" |Trizogu
| Trizogu
| style="text-align:center;" | Keega
| Keega
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
|-
|-
| style="text-align:center;" | 49/48
| "
| 49/48
| |<nowiki> | -4 -1 0 2 </nowiki>&gt;
| |<nowiki> | -4 -1 0 2 </nowiki>&gt;
| style="text-align:right;" | 35.70
| 35.70
| style="text-align:center;" |Zozo
| Zozo
| style="text-align:center;" | Slendro Diesis
| Slendro diesis
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
|-
|-
| style="text-align:center;" | 64/63
| "
| 64/63
| |<nowiki> | 6 -2 0 -1 </nowiki>&gt;
| |<nowiki> | 6 -2 0 -1 </nowiki>&gt;
| style="text-align:right;" | 27.26
| 27.26
| style="text-align:center;" |Ru
| Ru
| style="text-align:center;" | Septimal Comma
| Septimal comma
| style="text-align:center;" | Archytas' Comma
| Archytas' comma
| style="text-align:center;" | Leipziger Komma
| Leipziger Komma
|-
|-
| style="text-align:center;" | 64827/64000
| "
| 64827/64000
| |<nowiki> | -9 3 -3 4 </nowiki>&gt;
| |<nowiki> | -9 3 -3 4 </nowiki>&gt;
| style="text-align:right;" | 22.23
| 22.23
| style="text-align:center;" |Laquadzo-atrigu
| Laquadzo-atrigu
| style="text-align:center;" | Squalentine
| Squalentine
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
|-
|-
| style="text-align:center;" | 875/864
| "
| 875/864
| |<nowiki> | -5 -3 3 1 </nowiki>&gt;
| |<nowiki> | -5 -3 3 1 </nowiki>&gt;
| style="text-align:right;" | 21.90
| 21.90
| style="text-align:center;" |Zotriyo
| Zotriyo
| style="text-align:center;" | Keema
| Keema
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
|-
|-
| style="text-align:center;" | 126/125
| "
| 126/125
| |<nowiki> | 1 2 -3 1 </nowiki>&gt;
| |<nowiki> | 1 2 -3 1 </nowiki>&gt;
| style="text-align:right;" | 13.79
| 13.79
| style="text-align:center;" |Zotrigu
| Zotrigu
| style="text-align:center;" | Septimal Semicomma
| Septimal semicomma
| style="text-align:center;" | Starling Comma
| Starling comma
| style="text-align:center;" |  
|  
|-
|-
| style="text-align:center;" | 4000/3969
| "
| 4000/3969
| |<nowiki> | 5 -4 3 -2 </nowiki>&gt;
| |<nowiki> | 5 -4 3 -2 </nowiki>&gt;
| style="text-align:right;" | 13.47
| 13.47
| style="text-align:center;" |Rurutriyo
| Rurutriyo
| style="text-align:center;" | Octagar
| Octagar
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
|-
|-
| style="text-align:center;" | 1029/1024
| "
| 1029/1024
| |<nowiki> | -10 1 0 3 </nowiki>&gt;
| |<nowiki> | -10 1 0 3 </nowiki>&gt;
| style="text-align:right;" | 8.43
| 8.43
| style="text-align:center;" |Latrizo
| Latrizo
| style="text-align:center;" | Gamelisma
| Gamelisma
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
|-
|-
| style="text-align:center;" | 6144/6125
| "
| 6144/6125
| |<nowiki> | 11 1 -3 -2 </nowiki>&gt;
| |<nowiki> | 11 1 -3 -2 </nowiki>&gt;
| style="text-align:right;" | 5.36
| 5.36
| style="text-align:center;" |Saruru-atrigu
| Saruru-atrigu
| style="text-align:center;" | Porwell
| Porwell
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
|-
|-
| style="text-align:center;" | 250047/250000
| "
| 250047/250000
| |<nowiki> | -4 6 -6 3 </nowiki>&gt;
| |<nowiki> | -4 6 -6 3 </nowiki>&gt;
| style="text-align:right;" | 0.33
| 0.33
| style="text-align:center;" |Trizogugu
| Trizogugu
| style="text-align:center;" | Landscape Comma
| Landscape comma
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
|-
|-
| style="text-align:center;" | 100/99
| 11
| 100/99
| |<nowiki> | 2 -2 2 0 -1 </nowiki>&gt;
| |<nowiki> | 2 -2 2 0 -1 </nowiki>&gt;
| style="text-align:right;" | 17.40
| 17.40
| style="text-align:center;" |Luyoyo
| Luyoyo
| style="text-align:center;" | Ptolemisma
| Ptolemisma
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
|-
|-
| style="text-align:center;" | 121/120
| "
| 121/120
| |<nowiki> | -3 -1 -1 0 2 </nowiki>&gt;
| |<nowiki> | -3 -1 -1 0 2 </nowiki>&gt;
| style="text-align:right;" | 14.37
| 14.37
| style="text-align:center;" |Lologu
| Lologu
| style="text-align:center;" | Biyatisma
| Biyatisma
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
|-
|-
| style="text-align:center;" | 176/175
| "
| 176/175
| |<nowiki> | 4 0 -2 -1 1 </nowiki>&gt;
| |<nowiki> | 4 0 -2 -1 1 </nowiki>&gt;
| style="text-align:right;" | 9.86
| 9.86
| style="text-align:center;" |Lorugugu
| Lorugugu
| style="text-align:center;" | Valinorsma
| Valinorsma
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
|-
|-
| style="text-align:center;" | 65536/65219
| "
| 65536/65219
| |<nowiki> | 16 0 0 -2 -3 </nowiki>&gt;
| |<nowiki> | 16 0 0 -2 -3 </nowiki>&gt;
| style="text-align:right;" | 8.39
| 8.39
| style="text-align:center;" |Satrilu-aruru
| Satrilu-aruru
| style="text-align:center;" | Orgonisma
| Orgonisma
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
|-
|-
| style="text-align:center;" | 385/384
| "
| 385/384
| |<nowiki> | -7 -1 1 1 1 </nowiki>&gt;
| |<nowiki> | -7 -1 1 1 1 </nowiki>&gt;
| style="text-align:right;" | 4.50
| 4.50
| style="text-align:center;" |Lozoyo
| Lozoyo
| style="text-align:center;" | Keenanisma
| Keenanisma
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
|-
|-
| style="text-align:center;" | 441/440
| "
| 441/440
| |<nowiki> | -3 2 -1 2 -1 </nowiki>&gt;
| |<nowiki> | -3 2 -1 2 -1 </nowiki>&gt;
| style="text-align:right;" | 3.93
| 3.93
| style="text-align:center;" |Luzozogu
| Luzozogu
| style="text-align:center;" | Werckisma
| Werckisma
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
|-
|-
| style="text-align:center;" | 4000/3993
| "
| 4000/3993
| |<nowiki> | 5 -1 3 0 -3 </nowiki>&gt;
| |<nowiki> | 5 -1 3 0 -3 </nowiki>&gt;
| style="text-align:right;" | 3.03
| 3.03
| style="text-align:center;" |Triluyo
| Triluyo
| style="text-align:center;" | Wizardharry
| Wizardharry
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
|-
|-
| style="text-align:center;" | 3025/3024
| "
| 3025/3024
| |<nowiki> | -4 -3 2 -1 2 </nowiki>&gt;
| |<nowiki> | -4 -3 2 -1 2 </nowiki>&gt;
| style="text-align:right;" | 0.57
| 0.57
| style="text-align:center;" |Loloruyoyo
| Loloruyoyo
| style="text-align:center;" | Lehmerisma
| Lehmerisma
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
|-
|-
| style="text-align:center;" | 91/90
| 13
| 91/90
| |<nowiki> | -1 -2 -1 1 0 1 </nowiki>&gt;
| |<nowiki> | -1 -2 -1 1 0 1 </nowiki>&gt;
| style="text-align:right;" | 19.13
| 19.13
| style="text-align:center;" |Thozogu
| Thozogu
| style="text-align:center;" | Superleap
| Superleap
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
|-
|-
| style="text-align:center;" | 676/675
| "
| 676/675
| |<nowiki> | 2 -3 -2 0 0 2 </nowiki>&gt;
| |<nowiki> | 2 -3 -2 0 0 2 </nowiki>&gt;
| style="text-align:right;" | 2.56
| 2.56
| style="text-align:center;" |Bithogu
| Bithogu
| style="text-align:center;" | Parizeksma
| Parizeksma
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
|}
|}


== Books ==
== Books ==
=== Theory ===
=== Theory ===
* [http://tonalsoft.com/sonic-arts/darreg/dar35.htm The 15-Tone Scale System] by [[Ivor_Darreg|Ivor Darreg]] (Mirrored at http://www.webcitation.org/5xZyzKBEW. Originally at [http://sonic-arts.org/darreg/dar35.htm], now broken)
* [http://tonalsoft.com/sonic-arts/darreg/dar35.htm The 15-Tone Scale System] by [[Ivor Darreg]] (Mirrored at http://www.webcitation.org/5xZyzKBEW. Originally at [http://sonic-arts.org/darreg/dar35.htm], now broken)
* [https://web.archive.org/web/20110713044141/http://www.inteas.com/Penta01.htm The Pentadecaphonic System] (Originally at [http://www.inteas.com/Penta01.htm], now broken)
* [https://web.archive.org/web/20110713044141/http://www.inteas.com/Penta01.htm The Pentadecaphonic System] (Originally at [http://www.inteas.com/Penta01.htm], now broken)
* [http://www.webcitation.org/5xeJYBsDg 15-EDO Tutorial] by [[Brent_Carson|Brent Carson]] (Originally at [http://home.comcast.net/%7Ebrentishere/15noteequaltempermenttutorial.html], now broken)
* [http://www.webcitation.org/5xeJYBsDg 15-EDO Tutorial] by [[Brent Carson]] (Originally at [http://home.comcast.net/%7Ebrentishere/15noteequaltempermenttutorial.html], now broken)


=== Guitar ===
=== Guitar ===
Retrieved from "https://en.xen.wiki/w/15edo"