Xenharmonic Wiki

20edf: Difference between revisions

VisualWikitext
Wikispaces>keenanpepper
**Imported revision 288541998 - Original comment: **
 
Carlos Gamma as we know today is non-octave, even tho it was originally intended to include the octaves
 
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
{{Infobox ET}}
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
{{ED intro}}
: This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2011-12-27 01:13:55 UTC</tt>.<br>
 
: The original revision id was <tt>288541998</tt>.<br>
== Theory ==
: The revision comment was: <tt></tt><br>
20edf corresponds to 34.1902edo. It is closely related to [[Carlos Gamma]] and the [[gammic]] temperament, which adds an independent dimension for the [[2/1|octave]] (although strictly speaking, the "canonical" optimized Carlos Gamma tuning is not exactly 20edf, with its fifth stretched by the microscopic amount of 0.016{{c}}). It very accurately represents the intervals [[5/4]], with 11 steps, and [[17/16]], with 3 steps.
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
 
<h4>Original Wikitext content:</h4>
=== Harmonics ===
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">Redirects to Carlos Gamma.</pre></div>
{{Harmonics in equal|20|3|2|columns=11}}
<h4>Original HTML content:</h4>
{{Harmonics in equal|20|3|2|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 20edf (continued)}}
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;20edf&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Redirects to Carlos Gamma.&lt;/body&gt;&lt;/html&gt;</pre></div>
 
== Intervals ==
The first steps up to two just perfect fifths should give a feeling of the granularity of this system…
{| class="wikitable mw-collapsible"
|+ Intervals of 20edf
|-
!Degrees
!3/2.5/4.17/16 interpretation
!Cents
|-
|1
|51/50
|35.1
|-
|2
|25/24
|70.2
|-
|3
|17/16
|105.29
|-
|4
|625/576, 867/800
|140.39
|-
|5
|320/289, 425/384
|175.49
|-
|6
|96/85
|210.59
|-
|7
|144/125
|245.68
|-
|8
|20/17
|280.78
|-
|9
|6/5
|315.88
|-
|10
|153/125, 125/102
|350.98
|-
|11
|5/4
|386.075
|-
|12
|51/40
|421.17
|-
|13
|125/96
|456.27
|-
|14
|85/64
|491.37
|-
|15
|576/425, 867/640
|526.47
|-
|16
|400/289, 864/625
|561.56
|-
|17
|24/17
|596.66
|-
|18
|36/25
|631.76
|-
|19
|25/17
|666.86
|-
|'''20'''
|'''3/2'''
|'''701.955'''
|-
|21
|153/100
|737.05
|-
|22
|25/16
|772.15
|-
|23
|51/32
|807.25
|-
|24
|625/384
|842.35
|-
|25
|425/256, 480/289
|877.44
|-
|26
|144/85
|912.54
|-
|27
|216/125
|947.64
|-
|28
|30/17
|982.74
|-
|29
|9/5
|1017.835
|-
|30
|125/68
|1052.93
|-
|31
|15/8
|1088.03
|-
|32
|153/80
|1123.13
|-
|33
|125/64
|1158.23
|-
|34
|255/128
|1193.32
|-
|35
|864/425
|1228.42
|-
|36
|600/289
|1263.52
|-
|37
|36/17
|1298.62
|-
|38
|54/25
|1333.715
|-
|39
|75/34
|1368.81
|-
|'''40'''
|'''9/4'''
|'''1403.91'''
|}
 
{{stub}}
Retrieved from "https://en.xen.wiki/w/20edf"