Xenharmonic Wiki

7edf: Difference between revisions

← Older edit
VisualWikitext
No edit summary
ArrowHead294 (talk | contribs)
14,512 edits
 
(25 intermediate revisions by 9 users not shown)
Line 1: Line 1:
'''[[EDF|Division of the just perfect fifth]] into 7 equal parts''' (7EDF) is related to [[12edo|12 edo]], but with the 3/2 rather than the 2/1 being just. The octave is about 3.3514 cents stretched and the step size is about 100.2793 cents. The patent val has a generally sharp tendency for harmonics up to 21, with the exception for 11 and 13.
{{Infobox ET}}
{{ED intro}}


Lookalikes: [[12edo]], [[19ED3|19ed3]], [[31ed6]]
== Theory ==
==Intervals==
7edf is related to [[12edo]], but with the 3/2 rather than the 2/1 being just, which stretches the octave by 3.3514{{c}}. The patent val has a generally sharp tendency for harmonics up to 21, with the exception for 11 and 13. It forms as a decent approximation to stretched-octave tuning on pianos, since pianos' strings have overtones that tend slightly sharp and are thus often tuned with stretched octaves.
{| class="wikitable"
 
|+
=== Harmonics ===
! rowspan="2" |
{{Harmonics in equal|7|3|2|prec=2|columns=15}}
! rowspan="2" |ed31\54
 
! rowspan="2" |ed121/81 (~ed11\19)
=== Subsets and supersets ===
! rowspan="2" |ed3/2
7edf is the 4th [[prime equal division|prime edf]], after [[5edf]] and before [[11edf]].
! colspan="2" |Pyrite
 
! rowspan="2" |ed122/81 (~ed13\22)
== Intervals ==
! rowspan="2" |ed34\57
{| class="wikitable center-1 right-2 center-3"
|-
|-
!(~ed17\29)
! #
!(~ed10\17)
! Cents
! Approximate ratios
! 12edo notation
|-
|-
|1
| 0
|98.4127
| 0
|99.2594
| exact 1/1
|100.2793
| C
|100.5194
|100.8365
|101.295
|102.2556
|-
|-
|2
| 1
|196.8254
| 100.3
|198.5188
| 18/17, 17/16
|200.5586
| C#, Db
|201.0389
|201.673
|202.5899
|204.5113
|-
|-
|3
| 2
|295.238
| 200.6
|297.7782
| 9/8
|300.8379
| D
|301.5583
|302.5095
|303.8849
|306.7669
|-
|-
|4
| 3
|393.6508
| 300.8
|397.03765
| 19/16, 44/37
|401.1171
| D#, Eb
|402.0777
|403.346
|405.1799
|409.0226
|-
|-
|5
| 4
|492.0635
| 401.1
|496.2971
| 63/50
|501.3964
| E
|502.5972
|504.1825
|506.4749
|511.2781
|-
|-
|6
| 5
|590.476
| 501.4
|595.5565
|4/3
|601.6757
| F
|603.1166
|605.019
|607.7698
|613.5338
|-
|-
|7
| 6
|688.8889
| 601.7
|694.8158
| 64/45
|701.955
| F#, Gb
|703.636
|705.85545
|709.0648
|715.7895
|-
|-
|8
| 7
|787.3016
| 702.0
|794.0753
| exact 3/2
|802.2343
| G
|804.1555
|806.6919
|810.3598
|818.0451
|-
|-
|9
| 8
|885.7143
| 802.2
|893.3347
| 100/63
|902.5136
| G#, Ab
|904.6749
|907.5284
|911.6547
|920.30075
|-
|-
|10
| 9
|984.127
| 902.5
|992.5941
| 27/16
|1002.7929
| A
|1005.1943
|1008.3649
|1012.9497
|1022.5564
|-
|-
|11
| 10
|1082.5397
| 1002.8
|1091.8535
| 16/9
|1103.0721
| A#, Bb
|1105.7138
|1109.2014
|1114.2447
|1124.812
|-
|-
|12
| 11
|1180.9524
| 1103.1
|1191.1129
| 17/9
|1203.3514
| B
|1206.2332
|1210.0379
|1215.5397
|1227.0677
|-
|-
|13
| 12
|1279.3651
| 1203.4
|1290.37235
| 2/1
|1303.6307
| C
|1306.7526
|1310.8744
|1316.8346
|1329.3233
|-
|-
|14
| 13
|1377.7778
| 1303.6
|1389.6318
| 17/8
|1403.91
| C#, Db
|1407.2721
|-
|1411.7109
| 14
|1418.1296
| 1403.9
|1431.57895
| exact 9/4
| D
|}
|}
[[Category:Edf]]
 
[[Category:Edonoi]]
== See also ==
[[Category:todo:improve synopsis]]
* [[12edo]] – relative edo
* [[19edt]] – relative edt
* [[28ed5]] – relative ed5
* [[31ed6]] – relative ed6
* [[34ed7]] – relative ed7
* [[40ed10]] – relative ed10
* [[43ed12]] – relative ed12
* [[76ed80]] – close to the zeta-optimized tuning for 12edo
* [[1ed18/17|AS18/17]] – relative [[AS|ambitonal sequence]]
 
{{Todo|expand}}
 
[[Category:12edo]]
Retrieved from "https://en.xen.wiki/w/7edf"