Xenharmonic Wiki

ED5: Difference between revisions

← Older editNewer edit →
VisualWikitext
Xenllium (talk | contribs)
autopatrolled, emailconfirmed
5,024 edits
mNo edit summary
Francium (talk | contribs)
4,816 edits
Line 40: Line 40:
* [[67ed5|67ED5]]
* [[67ed5|67ED5]]
* [[72ed5|72ED5]]
* [[72ed5|72ED5]]
* [[84ed5|84ED5]]
* [[95ed5|95ED5]]
* [[95ed5|95ED5]]
* [[256ed5|256ED5]]
*[[256ed5|256ED5]]


== ED5-EDO correspondence ==
==ED5-EDO correspondence==
Following ED5s (up to 339) contain good correspondences to EDO tunings<ref>EDO with relative error of 5th harmonic below 1/3</ref>.
Following ED5s (up to 339) contain good correspondences to EDO tunings<ref>EDO with relative error of 5th harmonic below 1/3</ref>.


Line 49: Line 50:
|-
|-
! | ED5
! | ED5
! | EDO
! |EDO
! | Comments
! | Comments
|-
|-
| | [[7ed5|7ED5]]
| |[[7ed5|7ED5]]
| | [[3edo|3EDO]]
| |[[3edo|3EDO]]
| | 7ED5 is 3EDO with ~5.9 cent compressed octaves. <br>Equivalently, 3edo is 7ED5 with pentaves stretched by ~13.7 cents. <br>Patent vals match through the 67-limit.
| | 7ED5 is 3EDO with ~5.9 cent compressed octaves. <br>Equivalently, 3edo is 7ED5 with pentaves stretched by ~13.7 cents. <br>Patent vals match through the 67-limit.
|-
|-
| | [[9ed5|9ED5]]
| |[[9ed5|9ED5]]
| | [[4edo|4EDO]]
| |[[4edo|4EDO]]
| | Very rough correspondence (~38 cent octave stretch), but patent vals agree through the 7-limit.
| |Very rough correspondence (~38 cent octave stretch), but patent vals agree through the 7-limit.
|-
|-
| | [[14ed5|14ED5]]
| |[[14ed5|14ED5]]
| | [[6edo|6EDO]]
| |[[6edo|6EDO]]
| | Same 5.9 cent octave compression as 7ED5~3EDO. Patent vals agree through the 17-limit.
| |Same 5.9 cent octave compression as 7ED5~3EDO. Patent vals agree through the 17-limit.
|-
|-
| | [[16ed5|16ED5]]
| |[[16ed5|16ED5]]
| | [[7edo|7EDO]]
| |[[7edo|7EDO]]
| | Only rough correspondence (~19 cent octave stretch). Patent vals differ in the 7-limit.
| | Only rough correspondence (~19 cent octave stretch). Patent vals differ in the 7-limit.
|-
|-
| | [[21ed5|21ED5]]
| |[[21ed5|21ED5]]
| | [[9edo|9EDO]]
| |[[9edo|9EDO]]
| | Same 5.9 cent octave compression as 7ED5~3EDO. Patent vals agree through the 59-limit.
| |Same 5.9 cent octave compression as 7ED5~3EDO. Patent vals agree through the 59-limit.
|-
|-
| | [[23ed5|23ED5]]
| |[[23ed5|23ED5]]
| | [[10edo|10EDO]]
| |[[10edo|10EDO]]
| | 23ED5 is 10EDO with ~11 cent stretched octaves. Patent vals match through the 23-limit, with the exception of 11 and 17.
| | 23ED5 is 10EDO with ~11 cent stretched octaves. Patent vals match through the 23-limit, with the exception of 11 and 17.
|-
|-
| | [[28ed5|28ED5]]
| |[[28ed5|28ED5]]
| | [[12edo|12EDO]]
| |[[12edo|12EDO]]
| | Same 5.9 cent octave compression as 7ED5~3EDO. Patent vals match through the 19-limit, with the exception of 13 (as expected).
| |Same 5.9 cent octave compression as 7ED5~3EDO. Patent vals match through the 19-limit, with the exception of 13 (as expected).
|-
|-
| | [[30ed5|30ED5]]
| |[[30ed5|30ED5]]
| | [[13edo|13EDO]]
| |[[13edo|13EDO]]
| | 30ED5 is 13EDO with ~7.4 cent stretched octaves. Patent vals match through the 19-limit, with the exception of 3 (which neither represents well).
| |30ED5 is 13EDO with ~7.4 cent stretched octaves. Patent vals match through the 19-limit, with the exception of 3 (which neither represents well).
|-
|-
| | [[35ed5|35ED5]]
| |[[35ed5|35ED5]]
| | [[15edo|15EDO]]
| |[[15edo|15EDO]]
| | Same 5.9 cent octave compression as 7ED5~3EDO. Patent vals agree through the 13-limit.
| |Same 5.9 cent octave compression as 7ED5~3EDO. Patent vals agree through the 13-limit.
|-
|-
| | [[37ed5|37ED5]]
| |[[37ed5|37ED5]]
| | [[16edo|16EDO]]
| |[[16edo|16EDO]]
| | 37ED5 is 16EDO with ~4.9 cent stretched octaves. Patent vals match through the 23-limit.
| |37ED5 is 16EDO with ~4.9 cent stretched octaves. Patent vals match through the 23-limit.
|-
|-
| | [[42ed5|42ED5]]
| |[[42ed5|42ED5]]
| | [[18edo|18EDO]]
| |[[18edo|18EDO]]
| | Same 5.9 cent octave compression as 7ED5~3EDO. Patent vals match through the 17-limit, with the exception of 11.
| |Same 5.9 cent octave compression as 7ED5~3EDO. Patent vals match through the 17-limit, with the exception of 11.
|-
|-
| | [[44ed5|44ED5]]
| |[[44ed5|44ED5]]
| | [[19edo|19EDO]]
| |[[19edo|19EDO]]
| | 44ED5 is 19EDO with ~3.2 cent stretched octaves. Patent vals match through the 13-limit.
| |44ED5 is 19EDO with ~3.2 cent stretched octaves. Patent vals match through the 13-limit.
|-
|-
| | [[49ed5|49ED5]]
| |[[49ed5|49ED5]]
| | [[21edo|21EDO]]
| |[[21edo|21EDO]]
| | Same 5.9 cent octave compression as 7ED5~3EDO. Patent vals agree through the 17-limit.
| |Same 5.9 cent octave compression as 7ED5~3EDO. Patent vals agree through the 17-limit.
|-
|-
| | [[51ed5|51ED5]]
| |[[51ed5|51ED5]]
| | [[22edo|22EDO]]
| |[[22edo|22EDO]]
| | 51ED5 is 22EDO with ~1.9 cent stretched octaves. Patent vals match through the 19-limit.
| |51ED5 is 22EDO with ~1.9 cent stretched octaves. Patent vals match through the 19-limit.
|-
|-
| | [[56ed5|56ED5]]
| | [[56ed5|56ED5]]
Line 112: Line 113:
| | This is a rough correspondence, as the (7n)ED5 ~ (3n)EDO sequence begins to break down. Patent vals match through the 13-limit, with the exception of 7.
| | This is a rough correspondence, as the (7n)ED5 ~ (3n)EDO sequence begins to break down. Patent vals match through the 13-limit, with the exception of 7.
|-
|-
| | [[58ed5|58ED5]]
| |[[58ed5|58ED5]]
| | [[25edo|25EDO]]
| |[[25edo|25EDO]]
| | 58ED5 is 25EDO with ~1.0 cent stretched octaves. Patent vals match through the 73-limit, with the exception of 13.
| |58ED5 is 25EDO with ~1.0 cent stretched octaves. Patent vals match through the 73-limit, with the exception of 13.
|-
|-
| | [[63ed5|63ED5]]
| | [[63ed5|63ED5]]
Line 120: Line 121:
| | This is a rough correspondence, but the (7n)ED5 ~ (3n)EDO sequence is momentarily fixed. Patent vals match through the 13-limit.
| | This is a rough correspondence, but the (7n)ED5 ~ (3n)EDO sequence is momentarily fixed. Patent vals match through the 13-limit.
|-
|-
| | [[65ed5|65ED5]]
| |[[65ed5|65ED5]]
| | [[28edo|28EDO]]
| |[[28edo|28EDO]]
| | 65ED5 is 28EDO with ~0.26 cent stretched octaves. Patent vals match through the 43-limit.
| |65ED5 is 28EDO with ~0.26 cent stretched octaves. Patent vals match through the 43-limit.
|-
|-
| | [[72ed5|72ED5]]
| |
| | [[31edo|31EDO]]
[[72ed5|72ED5]]
| | 72ED5 is 31EDO with ~0.34 cent compressed octaves. Patent vals match through the 31-limit.
| |
[[31edo|31EDO]]
| |72ED5 is 31EDO with ~0.34 cent compressed octaves. Patent vals match through the 31-limit.
|-
|-
| | [[74ed5|74ED5]]
| |[[74ed5|74ED5]]
| | [[32edo|32EDO]]
| |[[32edo|32EDO]]
| | Same 4.9 cent octave stretch as 37ED5~16EDO. Patent vals match through the 13-limit with the exception of 7 and 11.
| |Same 4.9 cent octave stretch as 37ED5~16EDO. Patent vals match through the 13-limit with the exception of 7 and 11.
|-
|-
| | [[79ed5|79ED5]]
| |[[79ed5|79ED5]]
| | [[34edo|34EDO]]
| |[[34edo|34EDO]]
| | 79ED5 is 34EDO with ~0.83 cent compressed octaves. Patent vals match through the 17-limit, with the exception of 7 (which neither represents well).
| |79ED5 is 34EDO with ~0.83 cent compressed octaves. Patent vals match through the 17-limit, with the exception of 7 (which neither represents well).
|-
|-
| | [[81ed5|81ED5]]
| |
| | [[35edo|35EDO]]
[[81ed5|81ED5]]
| | 81ED5 is 35EDO with ~4.0 cent stretched octaves. Patent vals match through the 11-limit.
| |[[35edo|35EDO]]
| |81ED5 is 35EDO with ~4.0 cent stretched octaves. Patent vals match through the 11-limit.
|-
|-
| | [[86ed5|86ED5]]
| |[[84ed5|84ED5]]
| | [[37edo|37EDO]]
| |[[36edo|36EDO]]
| | 86ED5 is 37EDO with ~1.2 cent compressed octaves. Patent vals match through the 19-limit.
| |Same 5.9 cent octave compression as 7ED5~3EDO.
|-
|-
| | [[88ed5|88ED5]]
| |[[86ed5|86ED5]]
| | [[38edo|38EDO]]
| |[[37edo|37EDO]]
| | Same 3.2 cent octave stretch as 44ED5~19EDO. Patent vals differ in the 7-limit.
| |86ED5 is 37EDO with ~1.2 cent compressed octaves. Patent vals match through the 19-limit.
|-
|-
| | [[93ed5|93ED5]]
| |[[88ed5|88ED5]]
| |[[38edo|38EDO]]
| |Same 3.2 cent octave stretch as 44ED5~19EDO. Patent vals differ in the 7-limit.
|-
| |[[93ed5|93ED5]]
| | [[40edo|40EDO]]
| | [[40edo|40EDO]]
| | 93ED5 is 40EDO with ~1.6 cent compressed octaves. Patent vals match through the 7-limit.
| |93ED5 is 40EDO with ~1.6 cent compressed octaves. Patent vals match through the 7-limit.
|-
|-
| | [[95ed5|95ED5]]
| |[[95ed5|95ED5]]
| | [[41edo|41EDO]]
| |[[41edo|41EDO]]
| | 95ED5 is 41EDO with ~2.5 cent stretched octaves. Patent vals match through the 11-limit.
| |95ED5 is 41EDO with ~2.5 cent stretched octaves. Patent vals match through the 11-limit.
|-
|-
| | [[100ed5|100ED5]]
| |
| | [[43edo|43EDO]]
[[100ed5|100ED5]]
| | 100ED5 is 43EDO with ~1.9 cent compressed octaves. Patent vals match through the 37-limit.
| |[[43edo|43EDO]]
| |100ED5 is 43EDO with ~1.9 cent compressed octaves. Patent vals match through the 37-limit.
|-
|-
| | [[102ed5|102ED5]]
| |  
| | [[44edo|44EDO]]
[[102ed5|102ED5]]
| | Same 1.9 cent octave stretch as 51ED5~22EDO. Patent vals match through the 23-limit, with the exception of 7.
| |[[44edo|44EDO]]
| |Same 1.9 cent octave stretch as 51ED5~22EDO. Patent vals match through the 23-limit, with the exception of 7.
|-
|-
| | [[107ed5|107ED5]]
| |
[[107ed5|107ED5]]
| | [[46edo|46EDO]]
| | [[46edo|46EDO]]
| | 107ED5 is 46EDO with ~2.1 cent compressed octaves. Patent vals match through the 11-limit.
| |107ED5 is 46EDO with ~2.1 cent compressed octaves. Patent vals match through the 11-limit.
|-
|-
| | [[109ed5|109ED5]]
| |  
| | [[47edo|47EDO]]
[[109ed5|109ED5]]
| | 109ED5 is 47EDO with ~1.4 cent stretched octaves. Patent vals match through the 17-limit, with the exception of 11.
| |[[47edo|47EDO]]
| |109ED5 is 47EDO with ~1.4 cent stretched octaves. Patent vals match through the 17-limit, with the exception of 11.
|-
|-
| | [[114ed5|114ED5]]
| |
| | [[49edo|49EDO]]
[[114ed5|114ED5]]
| | 114ED5 is 49EDO with ~2.4 cent compressed octaves. Patent vals match through the 11-limit.
| |[[49edo|49EDO]]
| |114ED5 is 49EDO with ~2.4 cent compressed octaves. Patent vals match through the 11-limit.
|-
|-
| | [[116ed5|116ED5]]
| |
| | [[50edo|50EDO]]
[[116ed5|116ED5]]
| | Same 1.0 cent octave stretch as 58ED5~25EDO. Patent vals agree through the 43-limit.
| |[[50edo|50EDO]]
| |Same 1.0 cent octave stretch as 58ED5~25EDO. Patent vals agree through the 43-limit.
|-
|-
| | [[121ed5|121ED5]]
| |
| | [[52edo|52EDO]]
[[121ed5|121ED5]]
| | 121ED5 is 52EDO with ~2.6 cent compressed octaves, but the correspondence is rough. Patent vals match through the 11-limit, with the exception of 3 (which neither represents well).
| |[[52edo|52EDO]]
| |121ED5 is 52EDO with ~2.6 cent compressed octaves, but the correspondence is rough. Patent vals match through the 11-limit, with the exception of 3 (which neither represents well).
|-
|-
| | [[123ed5|123ED5]]
| |
[[123ed5|123ED5]]
| | [[53edo|53EDO]]
| | [[53edo|53EDO]]
| | 123ED5 is 53EDO with ~0.61 cent stretched octaves. Patent vals match through the 29-limit.
| |123ED5 is 53EDO with ~0.61 cent stretched octaves. Patent vals match through the 29-limit.
|-
|-
| | [[128ed5|128ED5]]
| |
| | [[55edo|55EDO]]
[[128ed5|128ED5]]
| | 128ED5 is 55EDO with ~2.8 cent compressed octaves, but the correspondence is rough. Patent vals differ in the 7-limit.
| |[[55edo|55EDO]]
| |128ED5 is 55EDO with ~2.8 cent compressed octaves, but the correspondence is rough. Patent vals differ in the 7-limit.
|-
|-
| | [[130ed5|130ED5]]
| |
| | [[56edo|56EDO]]
[[130ed5|130ED5]]
| | Same 0.26 cent octave stretch as 65ED5~28EDO. Patent vals agree through the 103-limit.
| |[[56edo|56EDO]]
| |Same 0.26 cent octave stretch as 65ED5~28EDO. Patent vals agree through the 103-limit.
|-
|-
| | [[135ed5|135ED5]]
| |
| | [[58edo|58EDO]]
[[135ed5|135ED5]]
| | 135ED5 is 58EDO with ~2.9 cent compressed octaves. Patent vals match through the 13-limit.
| |[[58edo|58EDO]]
| |135ED5 is 58EDO with ~2.9 cent compressed octaves. Patent vals match through the 13-limit.
|-
|-
| | [[137ed5|137ED5]]
| |
| | [[59edo|59EDO]]
[[137ed5|137ED5]]
| |[[59edo|59EDO]]
| | 137ED5 is 59EDO with ~0.05 cent compressed octaves. Patent vals match through the 179-limit.
| | 137ED5 is 59EDO with ~0.05 cent compressed octaves. Patent vals match through the 179-limit.
|-
|-
| | [[139ed5|139ED5]]
| |
| | [[60edo|60EDO]]
[[139ed5|139ED5]]
| |[[60edo|60EDO]]
| | 139ED5 is 60EDO with ~2.7 cent stretched octaves. Pantent vals match through the 31-limit with the exception of 11.
| | 139ED5 is 60EDO with ~2.7 cent stretched octaves. Pantent vals match through the 31-limit with the exception of 11.
|-
|-
| | [[144ed5|144ED5]]
| |
[[144ed5|144ED5]]
| | [[62edo|62EDO]]
| | [[62edo|62EDO]]
| | Same 0.34 cent octave compression as 72ED5~31EDO. Patent vals match through the 19-limit, with the exception of 11.
| |Same 0.34 cent octave compression as 72ED5~31EDO. Patent vals match through the 19-limit, with the exception of 11.
|-
|-
| | [[146ed5|146ED5]]
| |
| | [[63edo|63EDO]]
[[146ed5|146ED5]]
| | 146ED5 is 63EDO with ~2.3 cent stretched octaves. Patent vals match through the 13-limit.
| |[[63edo|63EDO]]
| |146ED5 is 63EDO with ~2.3 cent stretched octaves. Patent vals match through the 13-limit.
|-
|-
| | [[151ed5|151ED5]]
| |
| | [[65edo|65EDO]]
[[151ed5|151ED5]]
| | 151ED5 is 65EDO with ~0.59 cent compressed octaves. Patent vals match through the 53-limit, with the exception of 7 (as expected).
| |[[65edo|65EDO]]
| |151ED5 is 65EDO with ~0.59 cent compressed octaves. Patent vals match through the 53-limit, with the exception of 7 (as expected).
|-
|-
| | [[153ed5|153ED5]]
| |
| | [[66edo|66EDO]]
[[153ed5|153ED5]]
| | Same 1.9 cent octave stretch as 51ED5~22EDO. Patent vals match through the 13-limit, with the exception of 3.
| |[[66edo|66EDO]]
| |Same 1.9 cent octave stretch as 51ED5~22EDO. Patent vals match through the 13-limit, with the exception of 3.
|-
|-
| | [[158ed5|158ED5]]
| |
| | [[68edo|68EDO]]
[[158ed5|158ED5]]
| | Same 0.83 cent octave compression as 79ED5~34EDO. Patent vals agree through the 23-limit.
| |[[68edo|68EDO]]
| |Same 0.83 cent octave compression as 79ED5~34EDO. Patent vals agree through the 23-limit.
|-
|-
| | [[160ed5|160ED5]]
| |
| | [[69edo|69EDO]]
[[160ed5|160ED5]]
| | 160ED5 is 69EDO with ~1.6 cent stretched octaves. Patent vals differ in the 7-limit.
| |[[69edo|69EDO]]
| |160ED5 is 69EDO with ~1.6 cent stretched octaves. Patent vals differ in the 7-limit.
|-
|-
| | [[165ed5|165ED5]]
| |
| | [[71edo|71EDO]]
[[165ed5|165ED5]]
| | 165ED5 is 71EDO with ~1.0 cent compressed octaves. Patent vals match through the 37-limit.
| |[[71edo|71EDO]]
| |165ED5 is 71EDO with ~1.0 cent compressed octaves. Patent vals match through the 37-limit.
|-
|-
| | [[167ed5|167ED5]]
| |
| | [[72edo|72EDO]]
[[167ed5|167ED5]]
| | 167ED5 is 72EDO with ~1.3 cent stretched octaves. Patent vals agree through the 19-limit.
| |[[72edo|72EDO]]
| |167ED5 is 72EDO with ~1.3 cent stretched octaves. Patent vals agree through the 19-limit.
|-
|-
| | [[172ed5|172ED5]]
| |  
| | [[74edo|74EDO]]
[[172ed5|172ED5]]
| | Same 1.2 cent octave compression as 86ED5~37EDO. Patent vals agree through the 13-limit.
| |[[74edo|74EDO]]
| |Same 1.2 cent octave compression as 86ED5~37EDO. Patent vals agree through the 13-limit.
|-
|-
| | [[174ed5|174ED5]]
| |
| | [[75edo|75EDO]]
[[174ed5|174ED5]]
| |[[75edo|75EDO]]
| | Same 1.0 cent octave stretch as 58ED5~25EDO. Patent vals differ in the 7-limit.
| | Same 1.0 cent octave stretch as 58ED5~25EDO. Patent vals differ in the 7-limit.
|-
|-
| | [[179ed5|179ED5]]
| |  
[[179ed5|179ED5]]
| | [[77edo|77EDO]]
| | [[77edo|77EDO]]
| | 179ED5 is 77EDO with ~1.4 cent compressed octaves. Patent vals match through the 19-limit, with the exception of 11.
| |179ED5 is 77EDO with ~1.4 cent compressed octaves. Patent vals match through the 19-limit, with the exception of 11.
|-
|-
| | [[181ed5|181ED5]]
| |
| | [[78edo|78EDO]]
[[181ed5|181ED5]]
| | 181ED5 is 78EDO with ~0.73 cent stretched octaves. Patent vals match through the 59-limit, with the exception of 13.
| |[[78edo|78EDO]]
| |181ED5 is 78EDO with ~0.73 cent stretched octaves. Patent vals match through the 59-limit, with the exception of 13.
|-
|-
| | [[186ed5|186ED5]]
| |
[[186ed5|186ED5]]
| | [[80edo|80EDO]]
| | [[80edo|80EDO]]
| | Same 1.6 cent octave compression as 93ED5~40EDO. Patent vals agree through the 29-limit.
| |Same 1.6 cent octave compression as 93ED5~40EDO. Patent vals agree through the 29-limit.
|-
|-
| | [[188ed5|188ED5]]
| |
| | [[81edo|81EDO]]
[[188ed5|188ED5]]
| | 188ED5 is 81EDO with ~0.49 cent stretched octaves. Patent vals match through the 41-limit.
| |[[81edo|81EDO]]
| |188ED5 is 81EDO with ~0.49 cent stretched octaves. Patent vals match through the 41-limit.
|-
|-
| | [[193ed5|193ED5]]
| |
| | [[83edo|83EDO]]
[[193ed5|193ED5]]
| |
[[83edo|83EDO]]
| | 193ED5 is 83EDO with ~1.7 cent compressed octaves. Patent vals match through the 7-limit.
| | 193ED5 is 83EDO with ~1.7 cent compressed octaves. Patent vals match through the 7-limit.
|-
|-
| | [[195ed5|195ED5]]
| |
| | [[84edo|84EDO]]
[[195ed5|195ED5]]
| |[[84edo|84EDO]]
| | Same 0.26 cent octave stretch as 65ED5~28EDO. Patent vals agree through the 31-limit.
| | Same 0.26 cent octave stretch as 65ED5~28EDO. Patent vals agree through the 31-limit.
|-
|-
| | [[200ed5|200ED5]]
| |
| | [[86edo|86EDO]]
[[200ed5|200ED5]]
| |[[86edo|86EDO]]
| | Same 1.9 cent octeave compression as 100ED5~43EDO. Patent vals match alternate primes through the 17-limit.
| | Same 1.9 cent octeave compression as 100ED5~43EDO. Patent vals match alternate primes through the 17-limit.
|-
|-
| | [[202ed5|202ED5]]
| |
| | [[87edo|87EDO]]
[[202ed5|202ED5]]
| | 202ED5 is 87EDO with ~0.05 cent stretched octaves. Patent vals match through the 71-limit.
| |[[87edo|87EDO]]
| |202ED5 is 87EDO with ~0.05 cent stretched octaves. Patent vals match through the 71-limit.
|-
|-
| | [[204ed5|204ED5]]
| |
| | [[88edo|88EDO]]
[[204ed5|204ED5]]
| | Same 1.9 cent octave stretch as 51ED5~22EDO. Patent vals match through the 7-limit.
| |[[88edo|88EDO]]
| |Same 1.9 cent octave stretch as 51ED5~22EDO. Patent vals match through the 7-limit.
|-
|-
| | [[209ed5|209ED5]]
| |
| | [[90edo|90EDO]]
[[209ed5|209ED5]]
| | 209ED5 is 90EDO with ~0.15 cent compressed octaves. Patent vals match through the 53-limit.
| |[[90edo|90EDO]]
| |209ED5 is 90EDO with ~0.15 cent compressed octaves. Patent vals match through the 53-limit.
|-
|-
| | [[211ed5|211ED5]]
| |
| | [[91edo|91EDO]]
[[211ed5|211ED5]]
| |[[91edo|91EDO]]
| | 211ED5 is 91EDO with ~1.7 cent stretched octaves. Patent vals match through the 7-limit.
| | 211ED5 is 91EDO with ~1.7 cent stretched octaves. Patent vals match through the 7-limit.
|-
|-
| | [[216ed5|216ED5]]
| |
| | [[93edo|93EDO]]
[[216ed5|216ED5]]
| | Same 0.34 cent octave compression as 72ED5~31EDO. Patent vals agree through the 31-limit.
| |[[93edo|93EDO]]
| |Same 0.34 cent octave compression as 72ED5~31EDO. Patent vals agree through the 31-limit.
|-
|-
| | [[218ed5|218ED5]]
| |
| | [[94edo|94EDO]]
[[218ed5|218ED5]]
| | Same 1.4 cent octave stretch as 109ED5~47EDO. Patent vals match through the 23-limit, with the exception of 13.
| |[[94edo|94EDO]]
| |Same 1.4 cent octave stretch as 109ED5~47EDO. Patent vals match through the 23-limit, with the exception of 13.
|-
|-
| | [[223ed5|223ED5]]
| |
| | [[96edo|96EDO]]
[[223ed5|223ED5]]
| |[[96edo|96EDO]]
| | 223ED5 is 96EDO with ~0.51 cent compressed octaves. Patent vals match through the 13-limit.
| | 223ED5 is 96EDO with ~0.51 cent compressed octaves. Patent vals match through the 13-limit.
|-
|-
| | [[225ed5|225ED5]]
| |
| | [[97edo|97EDO]]
[[225ed5|225ED5]]
| | 225ED5 is 97EDO with ~1.2 cent stretched octaves. Patent vals match through the 19-limit, with the exception of 11.
| |[[97edo|97EDO]]
| |225ED5 is 97EDO with ~1.2 cent stretched octaves. Patent vals match through the 19-limit, with the exception of 11.
|-
|-
| | [[230ed5|230ED5]]
| |
| | [[99edo|99EDO]]
[[230ed5|230ED5]]
| | 230ED5 is 99EDO with ~0.67 cent compressed octaves. Patent vals match through the 7-limit.
| |[[99edo|99EDO]]
| |230ED5 is 99EDO with ~0.67 cent compressed octaves. Patent vals match through the 7-limit.
|-
|-
| | [[232ed5|232ED5]]
| |
| | [[100edo|100EDO]]
[[232ed5|232ED5]]
| | Same 1.0 cent octave stretch as 58ED5~25EDO. Patent vals match through the 13-limit.
| |
[[100edo|100EDO]]
| |Same 1.0 cent octave stretch as 58ED5~25EDO. Patent vals match through the 13-limit.
|-
|-
| | [[237ed5|237ED5]]
| |
| | [[102edo|102EDO]]
[[237ed5|237ED5]]
| | Same 0.83 cent octave compression as 79ED5~34EDO. Patent vals differ in the 7-limit.
| |
[[102edo|102EDO]]
| |Same 0.83 cent octave compression as 79ED5~34EDO. Patent vals differ in the 7-limit.
|-
|-
| | [[239ed5|239ED5]]
| |
| | [[103edo|103EDO]]
[[239ed5|239ED5]]
| | 239ED5 is 103EDO with ~0.80 cent stretched octaves. Patent vals match through the 17-limit.
| |
[[103edo|103EDO]]
| |239ED5 is 103EDO with ~0.80 cent stretched octaves. Patent vals match through the 17-limit.
|-
|-
| | [[244ed5|244ED5]]
| |
| | [[105edo|105EDO]]
[[244ed5|244ED5]]
| | 244ED5 is 105EDO with ~0.97 cent compressed octaves. Patent vals disagree in the 5-limit and higher prime limit.
| |
[[105edo|105EDO]]
| |244ED5 is 105EDO with ~0.97 cent compressed octaves. Patent vals disagree in the 5-limit and higher prime limit.
|-
|-
| | [[246ed5|246ED5]]
| |  
| | [[106edo|106EDO]]
[[246ed5|246ED5]]
| |  
[[106edo|106EDO]]
| | Same 0.61 cent octave stretch as 123ED5~53EDO. Patent vals match through the 43-limit, with the exception of 7.
| | Same 0.61 cent octave stretch as 123ED5~53EDO. Patent vals match through the 43-limit, with the exception of 7.
|-
|-
| | [[251ed5|251ED5]]
| |
| | [[108edo|108EDO]]
[[251ed5|251ED5]]
| | 251ED5 is 108EDO with ~1.1 cent compressed octaves. Patent vals match through the 13-limit.
| |
[[108edo|108EDO]]
| |251ED5 is 108EDO with ~1.1 cent compressed octaves. Patent vals match through the 13-limit.
|-
|-
| | [[253ed5|253ED5]]
| |  
| | [[109edo|109EDO]]
[[253ed5|253ED5]]
| |  
[[109edo|109EDO]]
| | 253ED5 is 109EDO with ~0.43 cent stretched octaves. Patent vals match through the 13-limit.
| | 253ED5 is 109EDO with ~0.43 cent stretched octaves. Patent vals match through the 13-limit.
|-
|-
| | [[258ed5|258ED5]]
| |
| | [[111edo|111EDO]]
[[258ed5|258ED5]]
| | Same 1.2 cent octave compression as 86ED5~37EDO. Patent vals agree through the 19-limit.
| |
[[111edo|111EDO]]
| |Same 1.2 cent octave compression as 86ED5~37EDO. Patent vals agree through the 19-limit.
|-
|-
| | [[260ed5|260ED5]]
| |
| | [[112edo|112EDO]]
[[260ed5|260ED5]]
| | Same 0.26 cent octave stretch as 65ED5~28EDO. Patent vals match through the 47-limit, with the exception of 3.
| |
[[112edo|112EDO]]
| |Same 0.26 cent octave stretch as 65ED5~28EDO. Patent vals match through the 47-limit, with the exception of 3.
|-
|-
| | [[265ed5|265ED5]]
| |
| | [[114edo|114EDO]]
[[265ed5|265ED5]]
| | 265ED5 is 114EDO with ~2.2 cent compressed octaves. Patent vals match through the 43-limit, with the exception of 11, 19 and 37.
| |
[[114edo|114EDO]]
| |265ED5 is 114EDO with ~2.2 cent compressed octaves. Patent vals match through the 43-limit, with the exception of 11, 19 and 37.
|-
|-
| | [[267ed5|267ED5]]
| |
| | [[115edo|115EDO]]
[[267ed5|267ED5]]
| | 267ED5 is 115EDO with ~0.10 cent stretched octaves. Patent vals match through the 17-limit.
| |
[[115edo|115EDO]]
| |267ED5 is 115EDO with ~0.10 cent stretched octaves. Patent vals match through the 17-limit.
|-
|-
| | [[274ed5|274ED5]]
| |
| | [[118edo|118EDO]]
[[274ed5|274ED5]]
| | Same 0.05 cent octave compression as 137ED5~59EDO. Patent vals agree through the 103-limit.
| |
[[118edo|118EDO]]
| |Same 0.05 cent octave compression as 137ED5~59EDO. Patent vals agree through the 103-limit.
|-
|-
| | [[276ed5|276ED5]]
| |
| | [[119edo|119EDO]]
[[276ed5|276ED5]]
| | 276ED5 is 119EDO with ~1.35 cent stretched octaves. Patent vals match through the 23-limit with the exception of 13 and 19.
| |
[[119edo|119EDO]]
| |276ED5 is 119EDO with ~1.35 cent stretched octaves. Patent vals match through the 23-limit with the exception of 13 and 19.
|-
|-
| | [[281ed5|281ED5]]
| |
| | [[121edo|121EDO]]
[[281ed5|281ED5]]
| | 281ED5 is 121EDO with ~0.20 cent compressed octaves. Patent vals match through the 29-limit.
| |
[[121edo|121EDO]]
| |281ED5 is 121EDO with ~0.20 cent compressed octaves. Patent vals match through the 29-limit.
|-
|-
| | [[283ed5|283ED5]]
| |
| | [[122edo|122EDO]]
[[283ed5|283ED5]]
| | 283ED5 is 122EDO with ~1.2 cent stretched octaves. Patent vals match through the 13-limit.
| |
[[122edo|122EDO]]
| |283ED5 is 122EDO with ~1.2 cent stretched octaves. Patent vals match through the 13-limit.
|-
|-
| | [[288ed5|288ED5]]
| |
| | [[124edo|124EDO]]
[[288ed5|288ED5]]
| | Same 0.34 cent octave compression as 72ED5~31EDO. Patent vals agree through the 23-limit.
| |
[[124edo|124EDO]]
| |Same 0.34 cent octave compression as 72ED5~31EDO. Patent vals agree through the 23-limit.
|-
|-
| | [[290ed5|290ED5]]
| |
| | [[125edo|125EDO]]
[[290ed5|290ED5]]
| | Same 1.0 cent octave stretch as 58ED5~25EDO. Patent vals match through the 37-limit, with the exception of 13.
| |
[[125edo|125EDO]]
| |Same 1.0 cent octave stretch as 58ED5~25EDO. Patent vals match through the 37-limit, with the exception of 13.
|-
|-
| | [[295ed5|295ED5]]
| |
| | [[127edo|127EDO]]
[[295ed5|295ED5]]
| | 295ED5 is 127EDO with ~0.47 cent compressed octaves. Patent vals match through the 17-limit, with the exception of 11.
| |
[[127edo|127EDO]]
| |295ED5 is 127EDO with ~0.47 cent compressed octaves. Patent vals match through the 17-limit, with the exception of 11.
|-
|-
| | [[297ed5|297ED5]]
| |  
| | [[128edo|128EDO]]
[[297ed5|297ED5]]
| | 297ED5 is 128EDO with ~0.84 cent stretched octaves. Patent vals match through the 7-limit.
| |
[[128edo|128EDO]]
| |297ED5 is 128EDO with ~0.84 cent stretched octaves. Patent vals match through the 7-limit.
|-
|-
| | [[302ed5|302ED5]]
| |
| | [[130edo|130EDO]]
[[302ed5|302ED5]]
| | Same 0.59 cent octave compression as 151ED5~65EDO. Patent vals match through the 41-limit, with the exception of 11, 19 and 23.
| |
[[130edo|130EDO]]
| |Same 0.59 cent octave compression as 151ED5~65EDO. Patent vals match through the 41-limit, with the exception of 11, 19 and 23.
|-
|-
| | [[304ed5|304ED5]]
| |
| | [[131edo|131EDO]]
[[304ed5|304ED5]]
| | 304ED5 is 131EDO with ~0.68 cent stretched octaves. Patent vals match through the 41-limit, with the exception of 13 and 23.
| |
[[131edo|131EDO]]
| |304ED5 is 131EDO with ~0.68 cent stretched octaves. Patent vals match through the 41-limit, with the exception of 13 and 23.
|-
|-
| | [[309ed5|309ED5]]
| |
| | [[133edo|133EDO]]
[[309ed5|309ED5]]
| | 309ED5 is 133EDO with ~0.73 cent compressed octaves. Patent vals match through the 71-limit, with the exception of 7 and 59.
| |
[[133edo|133EDO]]
| |309ED5 is 133EDO with ~0.73 cent compressed octaves. Patent vals match through the 71-limit, with the exception of 7 and 59.
|-
|-
| | [[311ed5|311ED5]]
| |
| | [[134edo|134EDO]]
[[311ed5|311ED5]]
| | 311ED5 is 134EDO with ~0.53 cent stretched octaves. Patent vals match through the 59-limit, with the exception of 11, 19 and 53.
| |
[[134edo|134EDO]]
| |311ED5 is 134EDO with ~0.53 cent stretched octaves. Patent vals match through the 59-limit, with the exception of 11, 19 and 53.
|-
|-
| | [[316ed5|316ED5]]
| |
| | [[136edo|136EDO]]
[[316ed5|316ED5]]
| | Same 0.83 cent octave compression as 79ED5~34EDO. Patent vals match through the 41-limit, with the exception of 13 and 23.
| |
[[136edo|136EDO]]
| |Same 0.83 cent octave compression as 79ED5~34EDO. Patent vals match through the 41-limit, with the exception of 13 and 23.
|-
|-
| | [[318ed5|318ED5]]
| |
| | [[137edo|137EDO]]
[[318ed5|318ED5]]
| | 318ED5 is 137EDO with ~0.39 cent stretched octaves. Patent vals match through the 23-limit, with the exception of 7.
| |
[[137edo|137EDO]]
| |318ED5 is 137EDO with ~0.39 cent stretched octaves. Patent vals match through the 23-limit, with the exception of 7.
|-
|-
| | [[323ed5|323ED5]]
| |
| | [[139edo|139EDO]]
[[323ed5|323ED5]]
| | 323ED5 is 139EDO with ~0.94 cent compressed compressed octaves. Patent vals match alternating primes through the 11-limit.
| |
[[139edo|139EDO]]
| |323ED5 is 139EDO with ~0.94 cent compressed compressed octaves. Patent vals match alternating primes through the 11-limit.
|-
|-
| | [[325ed5|325ED5]]
| |
| | [[140edo|140EDO]]
[[325ed5|325ED5]]
| |  
[[140edo|140EDO]]
| | Same 0.26 cent octave stretch as 65ED5~28EDO. Patent vals match through the 73-limit, with the exception of 31 and 67.
| | Same 0.26 cent octave stretch as 65ED5~28EDO. Patent vals match through the 73-limit, with the exception of 31 and 67.
|-
|-
| | [[330ed5|330ED5]]
| |
| | [[142edo|142EDO]]
[[330ed5|330ED5]]
| | Same 1.0 cent octave compression as 165ED5~71EDO. Patent vals match through the 13-limit, with the exception of 11.
| |
[[142edo|142EDO]]
| |Same 1.0 cent octave compression as 165ED5~71EDO. Patent vals match through the 13-limit, with the exception of 11.
|-
|-
| | [[332ed5|332ED5]]
| |  
| | [[143edo|143EDO]]
[[332ed5|332ED5]]
| |  
[[143edo|143EDO]]
| | 332ED5 is 143EDO with ~0.13 cent stretched octaves. Patent vals match through the 29-limit, with the exception of 7, 17 and 19.
| | 332ED5 is 143EDO with ~0.13 cent stretched octaves. Patent vals match through the 29-limit, with the exception of 7, 17 and 19.
|-
|-
| | [[337ed5|337ED5]]
| |
| | [[145edo|145EDO]]
[[337ed5|337ED5]]
| | 337ED5 is 145EDO with ~1.1 cent compressed octaves. Patent vals match through the 17-limit, with the exception of 7.
| |
[[145edo|145EDO]]
| |337ED5 is 145EDO with ~1.1 cent compressed octaves. Patent vals match through the 17-limit, with the exception of 7.
|-
|-
| | [[339ed5|339ED5]]
| |[[339ed5|339ED5]]
| | [[146edo|146EDO]]
| |[[146edo|146EDO]]
| | 339ED5 is practically identical to 146EDO, with a slight octave stretch (~0.0053 cents). Patent vals match through the 827-limit.
| |339ED5 is practically identical to 146EDO, with a slight octave stretch (~0.0053 cents). Patent vals match through the 827-limit.
|}
|}
<references/>
<references />


== See also ==
==See also==
* [[Pentave Reduced Harmonics]]
*[[Pentave Reduced Harmonics]]
* [[Pentave Reduced Subharmonics]]
*[[Pentave Reduced Subharmonics]]
* [[Relative errors of small ED5s]]
*[[Relative errors of small ED5s]]
* http://www.nonoctave.com/tuning/fifth_harmonic.html
*http://www.nonoctave.com/tuning/fifth_harmonic.html


[[Category:Equal-step tuning]]
[[Category:Equal-step tuning]]
Retrieved from "https://en.xen.wiki/w/ED5"