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→Keyboards: Julián Carrillo built at least one third-tone piano in 18edo, which can be heard in a few of the recordings in the music section below.
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{{Harmonics in equal|18}}
{{Harmonics in equal|18}}


== Intervals ==
[[File:18-ED2-JI-approximations-2.png|alt=18-ED2-JI-approximations-2.png|18-ED2-JI-approximations-2.png|thumb]]
{| class="wikitable center-all right-2"
! Degree
! Cents
! Nearest Ratio
! Error
! 17-Limit Ratios <ref>based on the above description of 18-EDO as a 2.9.75.21.55.39.51 subgroup temperament</ref>
|-
| 0
| 0.000
| 1/1
| 0
| 1/1
|-
| 1
| 66.667
| 27/26
| +1.329
| 26/25, 25/24
|-
| 2
| 133.333
| 27/25
| +0.096
| 55/51, 14/13
|-
| 3
| 200.000
| 9/8
| -3.910
| 9/8
|-
| 4
| 266.667
| 7/6
| -0.204
| 75/64
|-
| 5
| 333.333
| 17/14 or 40/33
| -2.796 +0.293
| 39/32
|-
| 6
| 400.000
| 5/4 or 44/35
| +13.686 +3.822
| 64/55
|-
| 7
| 466.667
| 21/16
| -4.114
| 21/16
|-
| 8
| 533.333
| 15/11
| -3.617
| 34/25
|-
| 9
| 600.000
| 17/12 or 24/17
| -3.000 +3.000
| 17/12
|-
| 10
| 666.667
| 22/15
| +3.617
| 25/17
|-
| 11
| 733.333
| 32/21
| +4.114
| 32/21
|-
| 12
| 800.000
| 8/5 or 35/22
| -13.686 -3.822
| 51/32
|-
| 13
| 866.667
| 28/17 or 33/20
| +2.796 -0.293
| 64/39
|-
| 14
| 933.333
| 12/7
| +0.204
| 55/32
|-
| 15
| 1000.000
| 16/9
| +3.910
| 16/9
|-
| 16
| 1066.667
| 50/27
| -0.096
| 13/7
|-
| 17
| 1133.333
| 52/27
| -1.329
| 25/13
|-
| 18
| 1200.000
| 2/1
| 0
| 2/1**
|}
<references />
{{Clear}}
== Notation ==
== Notation ==
=== Ups and downs notation ===
=== Ups and downs notation ===
Line 261: Line 388:


{{Sagittal chart}}
{{Sagittal chart}}
== Representations of JI intervals ==
{| class="wikitable center-all right-2"
! Degree
! Cents
! Nearest Ratio
! Error
! 17-Limit Ratios <ref>based on the above description of 18-EDO as a 2.9.75.21.55.39.51 subgroup temperament</ref>
|-
| 0
| 0.000
| 1/1
| 0
| 1/1
|-
| 1
| 66.667
| 27/26
| +1.329
| 78/75, 75/72
|-
| 2
| 133.333
| 27/25
| +0.096
| 51/55, 42/39
|-
| 3
| 200.000
| 9/8
| -3.910
| 9/8
|-
| 4
| 266.667
| 7/6
| -0.204
| 75/64
|-
| 5
| 333.333
| 17/14 or 40/33
| -2.796 +0.293
| 39/32
|-
| 6
| 400.000
| 5/4 or 44/35
| +13.686 +3.822
| 64/55
|-
| 7
| 466.667
| 21/16
| -4.114
| 21/16
|-
| 8
| 533.333
| 15/11
| -3.617
| 102/75
|-
| 9
| 600.000
| 17/12 or 24/17
| -3.000 +3.000
| 17/12
|-
| 10
| 666.667
| 22/15
| +3.617
| 75/51
|-
| 11
| 733.333
| 32/21
| +4.114
| 32/21
|-
| 12
| 800.000
| 8/5 or 35/22
| -13.686 -3.822
| 51/32
|-
| 13
| 866.667
| 28/17 or 33/20
| +2.796 -0.293
| 64/39
|-
| 14
| 933.333
| 12/7
| +0.204
| 55/32
|-
| 15
| 1000.000
| 16/9
| +3.910
| 16/9
|-
| 16
| 1066.667
| 50/27
| -0.096
| 39/21
|-
| 17
| 1133.333
| 52/27
| -1.329
| 75/39
|-
| 18
| 1200.000
| 2/1
| 0
| 2/1**
|}
<references />
[[File:18-ED2-JI-approximations-2.png|alt=18-ED2-JI-approximations-2.png|18-ED2-JI-approximations-2.png]]


== Regular temperament properties ==
== Regular temperament properties ==
Retrieved from "https://en.xen.wiki/w/18edo"