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== Intervals ==
== Intervals ==
{{Mavila}}
Inconsistent intervals are in ''italics''.


Alternatively, one can use Armodue nine-nominal notation.
{| class="wikitable center-1 right-2"
 
|-
{| class="wikitable center-all"
! rowspan="2" | #
|+ style="font-size: 105%" | Intervals of 16edo
! rowspan="2" | [[Cent]]s
! colspan="3" | Approximate ratios
|-
|-
! Degree
! 7-limit
! [[Cent]]s
! 13-limit
! Approximate ratios*
! No-3 approach*
|-
|-
| 0
| 0
| 0
| 0
| [[1/1]]
| 1/1
| 1/1
| 1/1
|-
|-
| 1
| 1
| 75
| 75
| 28/27, 27/26
| ''[[15/14]]'', [[21/20]], [[25/24]]
| [[22/21]], [[26/25]]
| [[28/27]], [[27/26]]
|-
|-
| 2
| 2
| 150
| 150
| 12/11, 35/32
| ''[[9/8]]'', ''[[16/15]]''
| [[11/10]], [[12/11]], [[13/12]], [[14/13]]
| 12/11, [[35/32]]
|-
|-
| 3
| 3
| 225
| 225
| [[8/7]], ''[[10/9]]'', [[28/25]]
| [[15/13]], [[25/22]]
| 8/7
| 8/7
|-
|-
| 4
| 4
| 300
| 300
| 19/16, 32/27
| [[6/5]], [[7/6]], [[25/21]]
| [[13/11]]
| [[19/16]], [[32/27]]
|-
|-
| 5
| 5
| 375
| 375
| [[5/4]], ''[[9/7]]''
| [[11/9]], [[16/13]], [[26/21]]
| 5/4, 16/13, 26/21
| 5/4, 16/13, 26/21
|-
|-
| 6
| 6
| 450
| 450
| 13/10, 35/27
| [[21/16]], [[32/25]]
| [[14/11]], [[13/10]]
| 13/10, [[35/27]]
|-
|-
| 7
| 7
| 525
| 525
| 19/14, 27/20, 35/26, 256/189
| [[4/3]]
| [[11/8]], ''[[18/13]]'', [[15/11]]
| [[19/14]], [[27/20]], [[35/26]]
|-
|-
| 8
| 8
| 600
| 600
| [[7/5]], [[10/7]], [[25/18]], [[36/25]]
|
| 7/5, 10/7
| 7/5, 10/7
|-
|-
| 9
| 9
| 675
| 675
| 28/19, 40/27, 52/35, 189/128
| [[3/2]]
| [[16/11]], ''[[13/9]]'', [[22/15]]
| [[28/19]], [[40/27]], [[52/35]]
|-
|-
| 10
| 10
| 750
| 750
| 20/13, 54/35
| [[25/16]], [[32/21]]
| [[11/7]], [[20/13]]
| 20/13, [[54/35]]
|-
|-
| 11
| 11
| 825
| 825
| [[8/5]], ''[[14/9]]''
| [[18/11]], [[13/8]], [[21/13]]
| 8/5, 13/8, 21/13
| 8/5, 13/8, 21/13
|-
|-
| 12
| 12
| 900
| 900
| 27/16, 32/19
| [[5/3]], [[12/7]], [[42/25]]
| [[22/13]]
| [[27/16]], [[32/19]]
|-
|-
| 13
| 13
| 975
| 975
| [[7/4]], ''[[9/5]]'', [[25/14]]
| [[26/15]], [[44/25]]
| 7/4
| 7/4
|-
|-
| 14
| 14
| 1050
| 1050
| 11/6, 64/35
| ''[[16/9]]'', ''[[15/8]]''
| [[20/11]], [[11/6]], [[24/13]], [[13/7]]
| [[11/6]], 64/35
|-
|-
| 15
| 15
| 1125
| 1125
| 27/14, 52/27
| ''[[28/15]]'', [[40/21]], [[48/25]]
| [[21/11]], [[25/13]]
| [[27/14]], [[52/27]]
|-
|-
| 16
| 16
| 1200
| 1200
| [[2/1]]
| 2/1
| 2/1
| 2/1
|}
|}


<nowiki />* Based on treating 16edo as a 2.5.7.13.19.27 subgroup temperament; other approaches are possible.
<nowiki />* Based on treating 16edo as a 2.27.5.7.13.19 subgroup temperament; other approaches are possible. Odd 27 is approximated via [[direct approximation]].
 
== Notation ==
{{Mavila}}
 
Alternatively, one can use Armodue nine-nominal notation.


{| class="wikitable center-all"
{| class="wikitable center-all"
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|}
|}


== Notation ==
16edo notation can be easy utilizing [[Goldsmith's Circle]] of keys, nominals, and respective notation{{clarify}}. The nominals for a 6 line staff can be switched for [[Erv Wilson]]'s Beta and Epsilon additions to A–G. The Armodue model uses a 4-line staff for 16edo.
16edo notation can be easy utilizing [[Goldsmith's Circle]] of keys, nominals, and respective notation{{clarify}}. The nominals for a 6 line staff can be switched for [[Erv Wilson]]'s Beta and Epsilon additions to A–G. The Armodue model uses a 4-line staff for 16edo.


Line 905: Line 943:
* [https://www.youtube.com/shorts/H-abpioYj5k ''improv in 16edo''] (2022)
* [https://www.youtube.com/shorts/H-abpioYj5k ''improv in 16edo''] (2022)
* [https://www.youtube.com/shorts/IfVvjoRqqNk ''16edo jam''] (2025)
* [https://www.youtube.com/shorts/IfVvjoRqqNk ''16edo jam''] (2025)
* [https://www.youtube.com/shorts/PXiWkZ9wDdU ''16edo waltz''] (2025)
* [https://www.youtube.com/shorts/PXiWkZ9wDdU ''16edo waltz''] (2025) &mdash; includes Lumatone view
* [https://www.youtube.com/watch?v=cUgbkkIvy0g ''Waltz in 16edo''] (2025) &mdash; this is the full version of the ''16edo waltz'' above
* [https://www.youtube.com/watch?v=cUgbkkIvy0g ''Waltz in 16edo''] (2025) &mdash; this is the full version of the ''16edo waltz'' above
* [https://www.youtube.com/shorts/UA97cjUN5eE ''Doubt by Bryan Deister (microtonal 16edo snippet)''] (2025)
* [https://www.youtube.com/shorts/UA97cjUN5eE ''Doubt by Bryan Deister (microtonal 16edo snippet)''] (2025)
Line 969: Line 1,007:
* [https://www.youtube.com/watch?v=0t7ZmlmrE0Q ''Shot Fades the Sum Of'']
* [https://www.youtube.com/watch?v=0t7ZmlmrE0Q ''Shot Fades the Sum Of'']
* [https://www.youtube.com/watch?v=2y01AlgOPvk ''When the Saints go Marching'']
* [https://www.youtube.com/watch?v=2y01AlgOPvk ''When the Saints go Marching'']
; Stephen Weigel (on 16edo keyboard) with [[Clarissa]] (vocal)
* [https://www.youtube.com/shorts/ZUBE817kwk8 Microtonal cover of ''All I Want for Christmas is You"'' by Mariah Carey] (2024)


; [[Randy Winchester]]
; [[Randy Winchester]]
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