Xenharmonic Wiki

20edf: Difference between revisions

← Older edit
VisualWikitext
-irrelevant shit
Carlos Gamma as we know today is non-octave, even tho it was originally intended to include the octaves
 
(7 intermediate revisions by 2 users not shown)
Line 1: Line 1:
{{Infobox ET}}
{{Infobox ET}}
==Intervals==
{{ED intro}}
 
== Theory ==
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.
 
=== Harmonics ===
{{Harmonics in equal|20|3|2|columns=11}}
{{Harmonics in equal|20|3|2|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 20edf (continued)}}
 
== Intervals ==
The first steps up to two just perfect fifths should give a feeling of the granularity of this system…
The first steps up to two just perfect fifths should give a feeling of the granularity of this system…
{| class="wikitable"
{| class="wikitable mw-collapsible"
|+ Intervals of 20edf
|-
!Degrees
!Degrees
!
!3/2.5/4.17/16 interpretation
!Cents
|-
|-
|1
|1
|51/50
|35.1
|35.1
|-
|-
| |2
|2
| |70.2
|25/24
|70.2
|-
|-
| |3
|3
| |105.29
|17/16
|105.29
|-
|-
| |4
|4
| |140.39
|625/576, 867/800
|140.39
|-
|-
| |5
|5
| |175.49
|320/289, 425/384
|175.49
|-
|-
| |6
|6
| |210.59
|96/85
|210.59
|-
|-
| |7
|7
| |245.68
|144/125
|245.68
|-
|-
| |8
|8
| |280.78
|20/17
|280.78
|-
|-
| |9
|9
| |315.88
|6/5
|315.88
|-
|-
| |10
|10
| |350.98
|153/125, 125/102
|350.98
|-
|-
| |11
|11
| |386.075
|5/4
|386.075
|-
|-
| |12
|12
| |421.17
|51/40
|421.17
|-
|-
| |13
|13
| |456.27
|125/96
|456.27
|-
|-
| |14
|14
| |491.37
|85/64
|491.37
|-
|-
| |15
|15
| |526.47
|576/425, 867/640
|526.47
|-
|-
| |16
|16
| |561.56
|400/289, 864/625
|561.56
|-
|-
| |17
|17
| |596.66
|24/17
|596.66
|-
|-
| |18
|18
| |631.76
|36/25
|631.76
|-
|-
| |19
|19
| |666.86
|25/17
|666.86
|-
|-
| |20
|'''20'''
| |701.955
|'''3/2'''
|'''701.955'''
|-
|-
|21
|21
|153/100
|737.05
|737.05
|-
|-
|22
|22
|25/16
|772.15
|772.15
|-
|-
|23
|23
|51/32
|807.25
|807.25
|-
|-
|24
|24
|625/384
|842.35
|842.35
|-
|-
|25
|25
|425/256, 480/289
|877.44
|877.44
|-
|-
|26
|26
|144/85
|912.54
|912.54
|-
|-
|27
|27
|216/125
|947.64
|947.64
|-
|-
|28
|28
|30/17
|982.74
|982.74
|-
|-
|29
|29
|9/5
|1017.835
|1017.835
|-
|-
|30
|30
|125/68
|1052.93
|1052.93
|-
|-
|31
|31
|15/8
|1088.03
|1088.03
|-
|-
|32
|32
|153/80
|1123.13
|1123.13
|-
|-
|33
|33
|125/64
|1158.23
|1158.23
|-
|-
|34
|34
|255/128
|1193.32
|1193.32
|-
|-
|35
|35
|864/425
|1228.42
|1228.42
|-
|-
|36
|36
|600/289
|1263.52
|1263.52
|-
|-
|37
|37
|36/17
|1298.62
|1298.62
|-
|-
|38
|38
|54/25
|1333.715
|1333.715
|-
|-
|39
|39
|75/34
|1368.81
|1368.81
|-
|-
|40
|'''40'''
|1403.91
|'''9/4'''
|'''1403.91'''
|}
|}
{{stub}}
Retrieved from "https://en.xen.wiki/w/20edf"