Xenharmonic Wiki

1ed17/16: Difference between revisions

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Create page for 1ed17/16 because music now exists for it
 
 
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| title=Approximation of harmonics in 1ed17/16 (continued)
| title=Approximation of harmonics in 1ed17/16 (continued)
}}
}}
Note that this tuning is very close to [[18edt]], although by [[patent val]] [[mapping]] 18edt maps ~[[17/16]] inconsistently to 2\18edt instead of 1\18edt, while 1ed17/16 maps its own [[equave]] even more inconsistently, to 3\1ed17/16.
Note that this tuning is fairly close to [[18edt]], although by [[patent val]] [[mapping]] 18edt maps ~[[17/16]] inconsistently to 2\18edt instead of 1\18edt, while 1ed17/16 maps its own [[equave]] even more inconsistently, to 3\1ed17/16.


== Intervals ==
== Intervals ==
{{Interval table}}
Many intervals in 1ed17/16 are mapped inconsistently (including 17/16 itself, as noted above). The table of intervals by direct approximation differs considerably from the table of intervals by [[patent val]] [[mapping]].
 
=== By direct approximation (even if inconsistent) ===
{| class="wikitable"
|-
! Steps
! Cents
! Approximate ratios
|-
| 0
| 0.0
| 1/1
|-
| 1
| 105.0
| 16/15, 17/16, 18/17
|-
| 2
| 209.9
| 9/8, 26/23, 17/15
|-
| 3
| 314.9
| 6/5
|-
| 4
| 419.8
| 14/11, 23/18
|-
| 5
| 524.8
| 19/14, 23/17, 27/20
|-
| 6
| 629.7
| 13/9, 23/16
|-
| 7
| 734.7
| 23/15, 26/17, 32/21
|-
| 8
| 839.6
| 13/8, 21/13, 34/21
|-
| 9
| 945.6
| 19/11, 26/15
|-
| 10
| 1049.6
| 11/6
|-
| 11
| 1154.5
| 35/18, 39/20
|-
| 12
| 1259.5
| 35/17, 33/16, 27/13
|}
 
=== By patent val mapping ===
{{Interval table|12ed582622237229761/281474976710656}}
(The above table is implemented as <nowiki>{{Interval table|12ed582622237229761/281474976710656}}</nowiki>, the value used being (17/16)<sup>12</sup>.)
 
== Instruments ==
 
A [[Lumatone mapping for 1ed17/16]] is available.


== Music ==
== Music ==
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== See also ==
== See also ==
* [[18edt]] &mdash; relative edt
* [[18edt]] &mdash; relative edt
[[Category:Nonoctave]]
Retrieved from "https://en.xen.wiki/w/1ed17/16"