3edf: Difference between revisions

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'''3EDF''', if the attempt is made to use it as an actual scale, would divide the [[just perfect fifth]] into three equal parts, each of size 233.985 cents, which is to say (3/2)^(1/3) as a frequency ratio. It corresponds to 5.1285 [[edo]]. If we want to consider it to be a temperament, it tempers out [[16/15]], [[21/20]], [[28/27]], [[81/80]], and [[256/243]] as well as [[5edo]].
{{Infobox ET}}
'''3edf''', if the attempt is made to use it as an actual scale, would divide the [[just perfect fifth]] into three equal parts, each of size 233.985 cents, which is to say (3/2)<sup>1/3</sup> as a frequency ratio. It corresponds to 5.1285 [[edo]]. If we want to consider it to be a temperament, it tempers out [[16/15]], [[21/20]], [[28/27]], [[81/80]], and [[256/243]] as well as [[5edo]].


==Factoids about 3EDF==
== Factoids about 3edf ==
3EDF is related to the [[Gamelismic clan|gamelismic temperaments]], which temper out 1029/1024 in the 7-limit.
3edf's step size is close to the [[slendric]] temperament, which tempers out 1029/1024 in the 2.3.7 subgroup. It can be used as a slendric tuning. It also works well as a tuning for [[Extraclassical tonality|arto and tendo chords.]]


== Intervals ==
== Intervals ==
{| class="wikitable"
{| class="wikitable center-all"
|+
! #
! rowspan="2" |
! Cents
! rowspan="2" |''ed233\420-5¢''
!Approximate JI Ratios
! rowspan="2" |ed31\54
! rowspan="2" |ed121/81 (~ed11\19)
! rowspan="2" |ed696¢
! rowspan="2" |ed32\55
! rowspan="2" |ed700¢=''r¢''
! rowspan="2" |ed3/2
! colspan="2" |Pyrite
! rowspan="2" |ed708¢
! rowspan="2" |ed122/81 (~ed13\22)
! rowspan="2" |ed34\57
! rowspan="2" |''ed37\60+5¢''
|-
|-
!(~ed17\29)
| 1
!(~ed10\17)
| 233.99
|8/7
|-
|-
|1
| 2
|''220.238-221.905''
| 467.97
|229.63
|55/42
|231.605
|232
|232.727
|''233.333''
|233.985
|234.545
|235.285
|236
|236.355
|238.597
|''246.667-248.333''
|-
|-
|2
| 3
|''440.476-443.8095''
| 701.96
|259.259
|exact 3/2
|463.211
|464
|465.4545
|''466.667''
|467.97
|469.091
|470.57
|472
|472.71
|477.193
|''493.333-496.667''
|-
|3
|''660.714-665.714''
|688.888
|694.816
|696
|698.182
|''700''
|701.955
|703.636
|705.8885
|708
|709.065
|715.7895
|''740-745''
|-
|4
|''880.952-887.619''
|918.5185
|926.421
|928
|930.909
|''933.333''
|935.94
|938.181
|941.141
|944
|945.42
|954.386
|''986.667-993.333''
|-
|5
|''1101.1905-1109.524''
|1148.148
|1158.0265
|1160
|1163.636
|''1166.667''
|1169.925
|1172.727
|1176.426
|1180
|1181.775
|1192.9825
|''1233.333-1241.667''
|-
|6
|''1321.429-1331.429''
|1377.778
|1389.632
|1392
|1396.364
|''1400''
|1403.91
|1407.272
|1411.711
|1416
|1418.13
|1431.579
|''1480-1490''
|}
|}
[[Category:Edf]]
 
[[Category:Edonoi]]
== Music ==
* [https://www.youtube.com/watch?v=0ecvufTJowE Sequences & Chaos] by Bazil Müzik
 
[[Category:Listen]]

Latest revision as of 19:22, 1 August 2025

← 2edf 3edf 4edf →
Prime factorization 3 (prime)
Step size 233.985 ¢ 
Octave 5\3edf (1169.93 ¢)
(convergent)
Twelfth 8\3edf (1871.88 ¢)
(convergent)
Consistency limit 10
Distinct consistency limit 4

3edf, if the attempt is made to use it as an actual scale, would divide the just perfect fifth into three equal parts, each of size 233.985 cents, which is to say (3/2)1/3 as a frequency ratio. It corresponds to 5.1285 edo. If we want to consider it to be a temperament, it tempers out 16/15, 21/20, 28/27, 81/80, and 256/243 as well as 5edo.

Factoids about 3edf

3edf's step size is close to the slendric temperament, which tempers out 1029/1024 in the 2.3.7 subgroup. It can be used as a slendric tuning. It also works well as a tuning for arto and tendo chords.

Intervals

# Cents Approximate JI Ratios
1 233.99 8/7
2 467.97 55/42
3 701.96 exact 3/2

Music

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