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== Theory ==
== Theory ==
The fifth harmonic is particularly wide as far as equivalences go. There are (at absolute most) ~4.8 pentaves within the human hearing range; imagine if that were the case with octaves. If one does indeed deal with pentave equivalence, this range restriction is a crucial consideration. Pentave equivalence itself may have a basis in Western music seeing as minor chords have an octave of 5 in their root (i.e. 10:12:15).
The fifth harmonic is particularly wide as far as equivalences go. There are (at absolute most) ~4.8 pentaves within the human hearing range; imagine if that were the case with octaves. If one does indeed deal with pentave equivalence, this range restriction is a crucial consideration. Pentave equivalence itself may have a basis in Western music seeing as minor chords have an octave of 5 in their root (i.e. 10:12:15).


Line 9: Line 8:
Some equal divisions of the pentave are known by alternate names or have special interest:
Some equal divisions of the pentave are known by alternate names or have special interest:


* [[3ed5]] [[orwell]] generator (with octaves)
* [[3ed5]] [[orwell]] generator
* [[4ed5]] [[meantone]] generator (with octaves)
* [[4ed5]] [[meantone]] generator
* [[5ed5]] [[2L_7s|thuja]] generator (with octaves)
* [[5ed5]] [[2L_7s|thuja]] generator
* [[6ed5]] [[Trienstonic clan #Uncle|uncle]] generator (with octaves)
* [[6ed5]] [[Trienstonic clan #Uncle|uncle]] generator
* [[8ed5]] [[mohajira]] generator
* [[Hyperpyth]] tuning (e.g. [[17ed5]])
* [[Hyperpyth]] tuning (e.g. [[17ed5]])
* [[20ed5]] Hieronymus Tuning
* [[20ed5]] Hieronymus Tuning
Line 18: Line 18:


== Individual pages for ED5s ==
== Individual pages for ED5s ==
* [[7ed5]]
* [[7ed5]]
* [[10ed5]]
* [[10ed5]]
Line 26: Line 25:
* [[15ed5]]
* [[15ed5]]
* [[17ed5]]
* [[17ed5]]
* [[19ed5]]
* [[20ed5]]
* [[20ed5]]
* [[22ed5]]
* [[22ed5]]
Line 40: Line 40:


== 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>.
{{todo|cleanup|inline=1|comment=Who please will ever read through this table? Please see: ''[[{{TALKPAGENAME}} #Spam]]''}}


{| class="wikitable"
{| class="wikitable"
Line 52: Line 51:
| | [[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.
|-
|[[8ed5]]
|
|[[Mohajira]] generator without octaves
|-
|-
| | [[9ed5]]
| | [[9ed5]]
| | [[4edo]]
| | [[4edo]]
| | Very rough correspondence, but patent vals agree through the 7-limit.
| | Very rough correspondence (~38 cent octave stretch), but patent vals agree through the 7-limit.
|-
|[[10ed5]]
|
|Every tenth note of [[43edo]], getting ~.44 cent flatter as it ascends the scale
|-
|[[11ed5]]
|
|Every fourth note of [[19edo]], getting ~.67 cent sharper as it ascends the scale
|-
|[[12ed5]]
|[[5edo]]
|Very rough correspondence, but patent 2s also agree
|-
|[[13ed5]]
|
|Every fifth note of [[28edo]], getting ~.05 cent sharper as it ascends the scale
|-
|-
| | [[14ed5]]
| | [[14ed5]]
| | [[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.
|-
|[[15ed5]]
|
|Every other note of [[13edo]], getting ~1.1 cents sharper as it ascends the scale
|-
|-
| | [[16ed5]]
| | [[16ed5]]
| | [[7edo]]
| | [[7edo]]
| | Only rough correspondence. Patent vals differ in the 7-limit.
| | Only rough correspondence (~19 cent octave stretch). Patent vals differ in the 7-limit.
|-
|[[17ed5]]
|
|This [[Hyperpyth|Hyperpyth tuning]] is every third note of [[22edo]], getting ~.26 cent sharper as it ascends the scale 
|-
|[[18ed5]]
|
|Every fourth note of [[31edo]], getting ~.04 cent flatter as it ascends the scale
|-
|[[19ed5]]
|[[8edo]]
|Very rough correspondence, but patent vals agree through the 5-limit.
|-
|[[20ed5]]
|
|[[20ed5|Hieronymus Tuning]] is every fifth note of [[43edo]], getting ~.22 cent flatter as it ascends the scale
|-
|-
| | [[21ed5]]
| | [[21ed5]]
| | [[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.
|-
|[[22ed5]]
|
|Every other note of [[19edo]], getting ~.335 cent sharper as it ascends the scale
|-
|-
| | [[23ed5]]
| | [[23ed5]]
| | [[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.
|-
|[[24ed5]]
|
|Every third note of [[31edo]], getting ~.03 cent flatter as it ascends the scale
|-
|[[25ed5]]
|
|Every fourth note of [[43edo]], getting ~.18 cent flatter as it ascends the scale
|-
|[[26ed5]]
|[[11edo]]
|Very rough correspondence, but patent vals agree through the 7-limit with the exception of 3 (which neither represents well).
|-
|[[27ed5]]
|
|Every third note of [[35edo]], getting ~.03 cent sharper as it ascends the scale
|-
|-
| | [[28ed5]]
| | [[28ed5]]
| | [[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).
|-
|[[29ed5]]
|
|Every other note of [[25edo]], getting ~.08 cent sharper as it ascends the scale
|-
|-
| | [[30ed5]]
| | [[30ed5]]
| | [[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).
|-
|[[31ed5]]
|
|Every third note of [[40edo]], getting ~.12 cent flatter as it ascends the scale
|-
|[[32ed5]]
|
|Every fourth note of [[55edo]], getting ~.2 cent flatter as it ascends the scale
|-
|[[33ed5]]
|
|Every fifth note of [[71edo]], getting ~.07 cent flatter as it ascends the scale
|-
|[[34ed5]]
|
|Every third note of [[44edo]], getting ~.13 cent sharper as it ascends the scale
|-
|-
| | [[35ed5]]
| | [[35ed5]]
| | [[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.
|-
|[[36ed5]]
|
|Every other note of [[31edo]], getting ~.02 cent flatter as it ascends the scale
|-
|-
| | [[37ed5]]
| | [[37ed5]]
| | [[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.
|-
|[[38ed5]]
|
|Every third note of [[49edo]], getting ~.145 cent flatter as it ascends the scale
|-
|[[39ed5]]
|
|Every fifth note of [[84edo]], getting ~.015 cent sharper as it ascends the scale
|-
|[[40ed5]]
|
|Every fourth note of [[69edo]], getting ~.09 cent sharper as it ascends the scale
|-
|[[41ed5]]
|
|Every third note of [[53edo]], getting ~.03 cent flatter as it ascends the scale
|-
|-
| | [[42ed5]]
| | [[42ed5]]
| | [[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.
|-
|[[43ed5]]
|
|Every other note of [[37edo]], getting ~.07 cent flatter as it ascends the scale
|-
|-
| | [[44ed5]]
| | [[44ed5]]
| | [[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.
|-
|[[45ed5]]
|
|Every fifth note of [[97edo]], getting ~.09 cent sharper as it ascends the scale
|-
|[[46ed5]]
|[[20edo]]
|Same ~11 cent octave stretch as 23ed5~10edo. Patent vals match through the 23-limit, with the exception of 13 and 17.
|-
|[[47ed5]]
|
|Every fourth note of [[81edo]], getting ~.02 cent sharper as it ascends the scale
|-
|[[48ed5]]
|
|Every third note of [[62edo]], getting ~.02 cent flatter as it ascends the scale
|-
|-
| | [[49ed5]]
| | [[49ed5]]
| | [[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.
|-
|[[50ed5]]
|
|Every other note of [[43edo]], getting ~.09 cent flatter as it ascends the scale
|-
|-
| | [[51ed5]]
| | [[51ed5]]
| | [[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.
|-
|[[52ed5]]
|
|Every fifth note of [[112edo]], getting ~.01 cent sharper as it ascends the scale
|-
|[[53ed5]]
|[[23edo]]
|58ed5 is 23edo with ~9.1 cent stretched octaves. Patent vals match through the 5-limit.
|-
|[[54ed5]]
|
|Every fourth note of [[93edo]], getting ~.015 cent flatter as it ascends the scale
|-
|[[55ed5]]
|
|Every third note of [[71edo]], getting ~.04 cent flatter as it ascends the scale
|-
|-
| | [[56ed5]]
| | [[56ed5]]
| | [[24edo]]
| | [[24edo]]
| | 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.
|-
|[[57ed5]]
|
|Every other note of [[49edo]], getting ~.1 cent flatter as it ascends the scale
|-
|-
| | [[58ed5]]
| | [[58ed5]]
Line 257: Line 112:
| | 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.
|-
|-
|[[59ed5]]
| | [[63ed5]]
|
| | [[27edo]]
|Every other note of [[51edo]], getting ~.17 cent sharper as it ascends the scale
| | This is a rough correspondence, but the (7n)ed5 ~ (3n)edo sequence is momentarily fixed. Patent vals match through the 13-limit.
|-
|[[60ed5]]
|[[26edo]]
|Same ~7.4 cent octave stretch as 30ed5~13edo. Patent vals match through the 29-limit.
|-
|[[61ed5]]
|
|Every fourth note of [[105edo]], getting ~.04 cent flatter as it ascends the scale
|-
|[[62ed5]]
|
|Every third note of [[80edo]], getting ~.06 cent flatter as it ascends the scale
|-
|[[63ed5]]
|[[27edo]]
|This is a rough correspondence, as the (7n)ed5 ~ (3n)edo sequence is momentarily fixed. Patent vals match through the 13-limit.
|-
|[[64ed5]]
|
|Every other note of [[55edo]], getting ~.1 cent flatter as it ascends the scale
|-
|-
| | [[65ed5]]
| | [[65ed5]]
| | [[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.
|-
|[[66ed5]]
|
|Every fifth note of [[142edo]], getting ~.04 cent flatter as it ascends the scale
|-
|[[67ed5]]
|
|Every fifth note of [[144edo]], getting ~.08 cent flatter as it ascends the scale
|-
|[[68ed5]]
|
|Every third note of [[88edo]], getting ~.07 cent sharper as it ascends the scale
|-
|[[69ed5]]
|
|Same ~11 cent octave stretch as 23ed5~10edo. Matches Mavila tuned in 30edo.
|-
|[[70ed5]]
|[[30edo]]
|This is a rough correspondence, as the (7n)ed5 ~ (3n)edo sequence begins to break down again. Patent vals match through the 11-limit, with the exception of 7.
|-
|[[71ed5]]
|
|Every other note of [[61edo]], getting ~.1 cent flatter as it ascends the scale
|-
|-
| | [[72ed5]]
| | [[72ed5]]
Line 313: Line 124:
| | 72ed5 is 31edo with ~0.34 cent compressed octaves. Patent vals match through the 31-limit.
| | 72ed5 is 31edo with ~0.34 cent compressed octaves. Patent vals match through the 31-limit.
|-
|-
|[[73ed5]]
| | [[74ed5]]
|
| | [[32edo]]
|Every other note of [[63edo]], getting ~.07 cent sharper as it ascends the scale
| | Same ~4.9 cent octave stretch as 37ed5~16edo. Patent vals match through the 13-limit with the exception of 7 and 11.
|-
|[[74ed5]]
|[[32edo]]
|Same ~4.9 cent octave stretch as 37ed5~16edo. Patent vals match through the 13-limit with the exception of 7 and 11.
|-
|[[75ed5]]
|
|Every third note of [[97edo]], getting ~.04 cent sharper as it ascends the scale
|-
|[[76ed5]]
|
|Every third note of [[98edo]], getting ~.07 cent flatter as it ascends the scale
|-
|[[77ed5]]
|[[33edo]]
|This is a rough correspondence, as the (7n)ed5 ~ (3n)edo sequence continues to break down. Patent vals match through the 7-limit.
|-
|[[78ed5]]
|
|Every other note of [[67edo]], getting ~.1 cent flatter as it ascends the scale
|-
|-
| | [[79ed5]]
| | [[79ed5]]
| | [[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).
|-
|[[80ed5]]
|
|Every other note of [[69edo]], getting ~.05 cent sharper as it ascends the scale
|-
|-
| | [[81ed5]]
| | [[81ed5]]
| | [[35edo]]
| | [[35edo]]
| | 81ed5 is 35edo with ~4.0 cent stretched octaves. Patent vals match through the 11-limit.
| | 81ed5 is 35edo with ~4.0 cent stretched octaves. Patent vals match through the 11-limit.
|-
|[[82ed5]]
|
|Every third note of [[106edo]], getting ~.02 cent sharper as it ascends the scale
|-
|[[83ed5]]
|
|Every fourth note of [[143edo]], getting ~.04 cent sharper as it ascends the scale
|-
|[[84ed5]]
|[[36edo]]
|This is a rough correspondence, as the (7n)ed5 ~ (3n)edo sequence is momentarily fixed again. Patent vals match through the 11-limit, with the exception of 7.
|-
|[[85ed5]]
|
|Every other note of [[73edo]], getting ~.1 cent flatter as it ascends the scale
|-
|-
| | [[86ed5]]
| | [[86ed5]]
| | [[37edo]]
| | [[37edo]]
| | 86ed5 is 37edo with ~1.2 cent compressed octaves. Patent vals match through the 19-limit.
| | 86ed5 is 37edo with ~1.2 cent compressed octaves. Patent vals match through the 19-limit.
|-
|[[87ed5]]
|
|Every other note of [[75edo]], getting ~.03 cent sharper as it ascends the scale
|-
|-
| | [[88ed5]]
| | [[88ed5]]
| | [[38edo]]
| | [[38edo]]
| | Same 3.2 cent octave stretch as 44ed5~19edo. Patent vals differ in the 7-limit.
| | Same 3.2 cent octave stretch as 44ed5~19edo. Patent vals differ in the 7-limit.
|-
|[[89ed5]]
|
|Every third note of [[115edo]], getting ~.0025 cent sharper as it ascends the scale
|-
|[[90ed5]]
|
|Same ~7.4 cent octave stretch as 30ed5~13edo, but really matches the tuning with generator 4\155 of an octave.
|-
|[[91ed5]]
|[[39edo]]
|This is a rough correspondence, as the (7n)ed5 ~ (3n)edo sequence begins to break down again. Patent vals match through the 7-limit.
|-
|[[92ed5]]
|
|Every fifth note of [[198edo]], getting ~.02 cent flatter as it ascends the scale
|-
|-
| | [[93ed5]]
| | [[93ed5]]
| | [[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.
|-
|[[94ed5]]
|
|Every other note of [[81edo]], getting ~.01 cent sharper as it ascends the scale
|-
|-
| | [[95ed5]]
| | [[95ed5]]
| | [[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.
|-
|[[96ed5]]
|
|Every third note of [[124edo]], getting ~.01 cent flatter as it ascends the scale
|-
|[[97ed5]]
|
|Every fourth note of [[167edo]], getting ~.02 cent flatter as it ascends the scale
|-
|[[98ed5]]
|[[42edo]]
|This is a rough correspondence, as the (7n)ed5 ~ (3n)edo sequence momentarily stops breaking down further.
|-
|[[99ed5]]
|
|Every third note of [[128edo]], getting ~.02 cent sharper as it ascends the scale
|-
|-
| | [[100ed5]]
| | [[100ed5]]
| | [[43edo]]
| | [[43edo]]
| | 100ed5 is 43edo with ~1.9 cent compressed octaves. Patent vals match through the 37-limit.
| | 100ed5 is 43edo with ~1.9 cent compressed octaves. Patent vals match through the 37-limit.
|-
|[[101ed5]]
|
|Every other note of [[87edo]], getting ~.001 cent sharper as it ascends the scale
|-
|-
| | [[102ed5]]
| | [[102ed5]]
| | [[44edo]]
| | [[44edo]]
| | Same 1.9 cent octave stretch as 51ed5~22edo. Patent vals match through the 23-limit, with the exception of 7.
| | Same 1.9 cent octave stretch as 51ed5~22edo. Patent vals match through the 23-limit, with the exception of 7.
|-
|[[103ed5]]
|
|Every other note of [[89edo]], getting ~.009 cent sharper as it ascends the scale
|-
|[[104ed5]]
|[[45edo]]
|104ed5 is 45edo with ~5.6 cent stretched octaves. Patent vals match through the 7-limit.
|-
|[[105ed5]]
|
|This is a rough correspondence, as the (7n)ed5 ~ (3n)edo sequence begins to break down again. Patent vals match through the 5-limit, with the exception of 3.
|-
|[[106ed5]]
|
|Every third note of [[137edo]], getting ~.009 cent sharper as it ascends the scale
|-
|-
| | [[107ed5]]
| | [[107ed5]]
| | [[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.
|-
|[[108ed5]]
|
|Every other note of [[93edo]], getting ~.007 cent flatter as it ascends the scale
|-
|-
| | [[109ed5]]
| | [[109ed5]]
| | [[47edo]]
| | [[47edo]]
| | 109ed5 is 47edo with ~1.4 cent stretched octaves. Patent vals match through the 17-limit, with the exception of 11.
| | 109ed5 is 47edo with ~1.4 cent stretched octaves. Patent vals match through the 17-limit, with the exception of 11.
|-
|[[110ed5]]
|
|Every other note of [[95edo]], getting ~.67 cent sharper as it ascends the scale
|-
|[[111ed5]]
|[[48edo]]
|Same ~4.9 cent octave stretch as 37ed5~16edo. Patent vals match through the 5-limit.
|-
|[[112ed5]]
|
|This is a rough correspondence, as the (7n)ed5 ~ (3n)edo sequence is momentarily fixed again. Patent vals match through the 7-limit, with the exception of 5.
|-
|[[113ed5]]
|
|Every third note of [[146edo]], getting ~.0001 cent sharper as it ascends the scale
|-
|-
| | [[114ed5]]
| | [[114ed5]]
| | [[49edo]]
| | [[49edo]]
| | 114ed5 is 49edo with ~2.4 cent compressed octaves. Patent vals match through the 11-limit.
| | 114ed5 is 49edo with ~2.4 cent compressed octaves. Patent vals match through the 11-limit.
|-
|[[115ed5]]
|
|Every other note of [[99edo]], getting ~.001 cent flatter as it ascends the scale
|-
|-
| | [[116ed5]]
| | [[116ed5]]
| | [[50edo]]
| | [[50edo]]
| | Same 1.0 cent octave stretch as 58ed5~25edo. Patent vals agree through the 43-limit.
| | Same 1.0 cent octave stretch as 58ed5~25edo. Patent vals agree through the 43-limit.
|-
|[[117ed5]]
|
|Every other note of [[101edo]], getting ~.05 cent sharper as it ascends the scale
|-
|[[118ed5]]
|[[51edo]]
|118ed5 is 51edo with ~4.25 cent stretched octaves. Patent vals match through the 17-limit with the exception of 13.
|-
|[[119ed5]]
|
|''This is a rough correspondence, as the (7n)ed5 ~ (3n)edo sequence has finally broken down more or less altogether. Patent vals match through the 3-limit.''
|-
|[[120ed5]]
|
|Same 7.4 cent octave stretch as 30ed5~13edo, but really matches the tuning with generator 3\155 of an octave.
|-
|-
| | [[121ed5]]
| | [[121ed5]]
| | [[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).
| | 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).
|-
|[[122ed5]]
|
|Every other note of [[105edo]], getting ~.002 cent flatter as it ascends the scale
|-
|-
| | [[123ed5]]
| | [[123ed5]]
| | [[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.
|-
|[[124ed5]]
|
|Every other note of [[107edo]], getting ~.04 cent sharper as it ascends the scale
|-
|[[125ed5]]
|[[54edo]]
|125ed5 is 54edo with ~3.7 cent stretched octaves, but the correspondence is rough. Patent vals match through the 5-limit, with the exception of 3 (which neither represents well).
|-
|[[126ed5]]
|
|Same rough correspondence as 119ed5~51edo
|-
|[[127ed5]]
|
|Every third note of [[164edo]], getting ~.01 cent flatter as it ascends the scale
|-
|-
| | [[128ed5]]
| | [[128ed5]]
| | [[55edo]]
| | [[55edo]]
| | 128ed5 is 55edo with ~2.8 cent compressed octaves, but the correspondence is rough. Patent vals differ in the 7-limit.
| | 128ed5 is 55edo with ~2.8 cent compressed octaves, but the correspondence is rough. Patent vals differ in the 7-limit.
|-
|[[129ed5]]
|
|Every other note of [[111edo]], getting ~.02 cent flatter as it ascends the scale
|-
|-
| | [[130ed5]]
| | [[130ed5]]
Line 545: Line 192:
| | Same 0.26 cent octave stretch as 65ed5~28edo. Patent vals agree through the 103-limit.
| | Same 0.26 cent octave stretch as 65ed5~28edo. Patent vals agree through the 103-limit.
|-
|-
|[[131ed5]]
| | [[135ed5]]
|
| | [[58edo]]
|Every other note of [[113edo]], getting ~.03 cent sharper as it ascends the scale
| | 135ed5 is 58edo with ~2.9 cent compressed octaves. Patent vals match through the 13-limit.
|-
|[[132ed5]]
|[[57edo]]
|Same 3.2 cent octave stretch as 44ed5~19edo. Patent vals differ in the 11-limit.
|-
|[[133ed5]]
|
|''This is a rough correspondence, as the (7n)ed5 ~ (3n)edo sequence has finally broken down more or less altogether. Patent vals match through the 2-limit.''
|-
|[[134ed5]]
|
|Every third note of [[173edo]], getting ~.02 cent flatter as it ascends the scale
|-
|[[135ed5]]
|[[58edo]]
|135ed5 is 58edo with ~2.9 cent compressed octaves. Patent vals match through the 13-limit.
|-
|[[136ed5]]
|
|Every other note of 117edo, getting ~.025 cent flatter as it ascends the scale
|-
|-
| | [[137ed5]]
| | [[137ed5]]
Line 573: Line 200:
| | 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.
|-
|-
|[[138ed5]]
| | [[139ed5]]
|
| | [[60edo]]
|Every other note of [[119edo]], getting ~.02 cent sharper as it ascends the scale
| | 139ed5 is 60edo with ~2.7 cent stretched octaves. Pantent vals match through the 31-limit with the exception of 11.
|-
|[[139ed5]]
|[[60edo]]
|139ed5 is 60edo with ~2.7 cent stretched octaves. Pantent vals match through the 31-limit with the exception of 11.
|-
|[[140ed5]]
|
|''Same rough correspondence as 133ed5~57edo''
|-
|[[141ed5]]
|
|Every third note of [[182edo]], getting ~.02 cent flatter as it ascends the scale
|-
|[[142ed5]]
|[[61edo]]
|142ed5 is 61edo with ~3.1 cent compressd octaves. Patent vals match through the 13-limit, with the exception of 7 and 11.
|-
|[[143ed5]]
|
|Every other note of [[123edo]], getting ~.03 cent flatter as it ascends the scale
|-
|-
| | [[144ed5]]
| | [[144ed5]]
| | [[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.
|-
|[[145ed5]]
|
|Every other note of [[125edo]], getting ~.02 cent sharper as it ascends the scale
|-
|-
| | [[146ed5]]
| | [[146ed5]]
| | [[63edo]]
| | [[63edo]]
| | 146ed5 is 63edo with ~2.3 cent stretched octaves. Patent vals match through the 13-limit.
| | 146ed5 is 63edo with ~2.3 cent stretched octaves. Patent vals match through the 13-limit.
|-
|[[147ed5]]
|
|''Same rough correspondence as 133ed5~57edo''
|-
|[[148ed5]]
|
|Same ~4.9 cent octave stretch as 37ed5~16edo, but really matches the tuning with generator 4\255 of an octave.
|-
|[[149ed5]]
|[[64edo]]
|149ed5 is 64edo with ~3.2 cent compressed octaves. Patent vals match through the 7-limit, with the exception of 3
|-
|[[150ed5]]
|
|Every other note of [[129edo]], getting ~.02 cent sharper as it ascends the scale
|-
|-
| | [[151ed5]]
| | [[151ed5]]
| | [[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).
| | 151ed5 is 65edo with ~0.59 cent compressed octaves. Patent vals match through the 53-limit, with the exception of 7 (as expected).
|-
|[[152ed5]]
|
|Every other note of [[131edo]], getting ~.001 cent sharper as it ascends the scale
|-
|-
| | [[153ed5]]
| | [[153ed5]]
| | [[66edo]]
| | [[66edo]]
| | Same 1.9 cent octave stretch as 51ed5~22edo. Patent vals match through the 13-limit, with the exception of 3.
| | Same 1.9 cent octave stretch as 51ed5~22edo. Patent vals match through the 13-limit, with the exception of 3.
|-
|[[154ed5]]
|
|Same rough correspondence as 133ed5~57edo
|-
|[[155ed5]]
|
|Every fourth note of [[267edo]], getting ~.001 cent flatter as it ascends the scale
|-
|[[156ed5]]
|[[67edo]]
|156ed5 is 67edo with ~3.3 cent compressed octaves. Patent vals match through the 11-limit, with the exception of 7
|-
|[[157ed5]]
|
|Every other note of [[135edo]], getting ~.03 cent flatter as it ascends the scale
|-
|-
| | [[158ed5]]
| | [[158ed5]]
| | [[68edo]]
| | [[68edo]]
| | Same 0.83 cent octave compression as 79ed5~34edo. Patent vals agree through the 23-limit.
| | Same 0.83 cent octave compression as 79ed5~34edo. Patent vals agree through the 23-limit.
|-
|[[159ed5]]
|
|Every other note of [[137edo]], getting ~.006 cent sharper as it ascends the scale
|-
|-
| | [[160ed5]]
| | [[160ed5]]
| | [[69edo]]
| | [[69edo]]
| | 160ed5 is 69edo with ~1.6 cent stretched octaves. Patent vals differ in the 7-limit.
| | 160ed5 is 69edo with ~1.6 cent stretched octaves. Patent vals differ in the 7-limit.
|-
|[[161ed5]]
|
|Same 11 cent octave stretch as 23ed5~10edo, but really matches the tuning with generator 3\208 of an octave.
|-
|[[162ed5]]
|
|Every third note of [[209edo]], getting ~.025 cent flatter as it ascends the scale
|-
|[[163ed5]]
|[[70edo]]
|163ed5 is 70edo with ~3.4 cent compressed octaves. Patent vals match through the 7-limit.
|-
|[[164ed5]]
|
|Every other note of [[141edo]], getting ~.03 cent flatter as it ascends the scale
|-
|-
| | [[165ed5]]
| | [[165ed5]]
| | [[71edo]]
| | [[71edo]]
| | 165ed5 is 71edo with ~1.0 cent compressed octaves. Patent vals match through the 37-limit.
| | 165ed5 is 71edo with ~1.0 cent compressed octaves. Patent vals match through the 37-limit.
|-
|[[166ed5]]
|
|Every other note of [[143edo]], getting ~.02 cent sharper as it ascends the scale
|-
|-
| | [[167ed5]]
| | [[167ed5]]
| | [[72edo]]
| | [[72edo]]
| | 167ed5 is 72edo with ~1.3 cent stretched octaves. Patent vals agree through the 19-limit.
| | 167ed5 is 72edo with ~1.3 cent stretched octaves. Patent vals agree through the 19-limit.
|-
|[[168ed5]]
|
|Same rough correspondence as 133ed5~57edo
|-
|[[169ed5]]
|
|Every third note of [[218edo]], getting ~.03 cent flatter as it ascends the scale
|-
|[[170ed5]]
|[[73edo]]
|170ed5 is 73edo with ~3.5 cent compressed octaves, but the correspondence is rough. Patent vals match through the 7-limit.
|-
|[[171ed5]]
|
|Every other note of [[147edo]], getting ~.03 cent flatter as it ascends the scale
|-
|-
| | [[172ed5]]
| | [[172ed5]]
| | [[74edo]]
| | [[74edo]]
| | Same 1.2 cent octave compression as 86ed5~37edo. Patent vals agree through the 13-limit.
| | Same 1.2 cent octave compression as 86ed5~37edo. Patent vals agree through the 13-limit.
|-
|[[173ed5]]
|
|Every other note of [[149edo]], getting ~.0015 cent flatter as it ascends the scale
|-
|-
| | [[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.
|-
|[[175ed5]]
|
|Every other note of [[151edo]], getting ~.03 cent flatter as it ascends the scale
|-
|[[176ed5]]
|[[76edo]]
|Same 3.2 cent octave stretch as 44ed5~19edo. Patent vals differ in the 11-limit.
|-
|[[177ed5]]
|
|Every fourth note of [[305edo]], getting ~.004 cent sharper as it ascends the scale
|-
|[[178ed5]]
|
|Every third note of [[230edo]], getting ~.001 cent sharper as it ascends the scale
|-
|-
| | [[179ed5]]
| | [[179ed5]]
| | [[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.
|-
|[[180ed5]]
|
|''Same 7.4 cent octave stretch as 30ed5~13edo, but really matches the tuning with generator 2\155 of an octave.''
|-
|-
| | [[181ed5]]
| | [[181ed5]]
| | [[78edo]]
| | [[78edo]]
| | 181ed5 is 78edo with ~0.73 cent stretched octaves. Patent vals match through the 59-limit, with the exception of 13.
| | 181ed5 is 78edo with ~0.73 cent stretched octaves. Patent vals match through the 59-limit, with the exception of 13.
|-
|[[182ed5]]
|
|''Same 5.9 cent octave compression as 91ed5~39edo, but really matches the tuning with generator 5\392 of an octave.''
|-
|[[183ed5]]
|[[79edo]]
|183ed5 is 79edo with ~2.8 cent compressed octaves. Patent vals match through the 11-limit, with the exception of 7
|-
|[[184ed5]]
|
|''Same 11 cent octave stretch as 23ed5~10edo, but really matches the tuning with generator 4\317 of an octave.''
|-
|[[185ed5]]
|
|''Same 4.9 cent octave stretch as 37ed5~16edo, but really matches the tuning with generator 3\239 of an octave.''
|-
|-
| | [[186ed5]]
| | [[186ed5]]
| | [[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.
|-
|[[187ed5]]
|
|Every other note of [[161edo]], getting ~.007 cent flatter as it ascends the scale
|-
|-
| | [[188ed5]]
| | [[188ed5]]
| | [[81edo]]
| | [[81edo]]
| | 188ed5 is 81edo with ~0.49 cent stretched octaves. Patent vals match through the 41-limit.
| | 188ed5 is 81edo with ~0.49 cent stretched octaves. Patent vals match through the 41-limit.
|-
|[[189ed5]]
|
|Every other note of [[163edo]], getting ~.002 cent sharper as it ascends the scale
|-
|[[190ed5]]
|[[82edo]]
|Same 2.5 cent octave stretch as 95ed5~41edo. Patent vals match through the 11-limit, with the exception of 13 and 17
|-
|[[191ed5]]
|
|Every fourth note of [[329edo]], getting ~.002 cent flatter as it ascends the scale
|-
|[[192ed5]]
|
|Every third note of [[248edo]], getting ~.01 cent flatter as it ascends the scale
|-
|-
| | [[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.
|-
|[[194ed5]]
|
|Every other note of [[167edo]], getting ~.009 cent flatter as it ascends the scale
|-
|-
| | [[195ed5]]
| | [[195ed5]]
Line 805: Line 268:
| | 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.
|-
|-
|[[196ed5]]
| | [[200ed5]]
|
| | [[86edo]]
|Every other note of 169edo, getting ~.015 cent sharper as it ascends the scale
| | Same 1.9 cent octeave compression as 100ed5~43edo. Patent vals match alternate primes through the 17-limit.
|-
|[[197ed5]]
|[[85edo]]
|197ed5 is 85edo with ~2.2 cent stretched octaves.Patent vals match alternate primes through the 17-limit.
|-
|[[198ed5]]
|
|Every fourth note of [[341edo]], getting ~.004 cent flatter as it ascends the scale
|-
|[[199ed5]]
|
|Every third note of [[257edo]], getting ~.007 cent flatter as it ascends the scale
|-
|[[200ed5]]
|[[86edo]]
|Same 1.9 cent octeave compression as 100ed5~43edo. Patent vals match alternate primes through the 17-limit.
|-
|[[201ed5]]
|
|Every other note of [[173edo]], getting ~.001 cent flatter as it ascends the scale
|-
|-
| | [[202ed5]]
| | [[202ed5]]
Line 833: Line 276:
| | 202ed5 is 87edo with ~0.05 cent stretched octaves. Patent vals match through the 71-limit.
| | 202ed5 is 87edo with ~0.05 cent stretched octaves. Patent vals match through the 71-limit.
|-
|-
|[[203ed5]]
| | [[204ed5]]
|
| | [[88edo]]
|Every other note of [[175edo]], getting ~.002 cent sharper as it ascends the scale
| | Same 1.9 cent octave stretch as 51ed5~22edo. Patent vals match through the 7-limit.
|-
|[[204ed5]]
|[[88edo]]
|Same 1.9 cent octave stretch as 51ed5~22edo. Patent vals match through the 7-limit.
|-
|[[205ed5]]
|
|Every fourth note of [[353edo]], getting ~.006 cent flatter as it ascends the scale
|-
|[[206ed5]]
|
|Every third note of [[266edo]], getting ~.008 cent flatter as it ascends the scale
|-
|[[207ed5]]
|[[89edo]]
|207ed5 is 89edo with ~2 cent compressed octaves. Patent vals match through the 23, with the exception of 13 and 19.
|-
|[[208ed5]]
|
|Every other note of [[179edo]], getting ~.01 cent flatter as it ascends the scale
|-
|-
| | [[209ed5]]
| | [[209ed5]]
| | [[90edo]]
| | [[90edo]]
| | 209ed5 is 90edo with ~0.15 cent compressed octaves. Patent vals match through the 53-limit.
| | 209ed5 is 90edo with ~0.15 cent compressed octaves. Patent vals match through the 53-limit.
|-
|[[210ed5]]
|
|Every other note of [[181edo]], getting ~.0085 cent sharper as it ascends the scale
|-
|-
| | [[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.
|-
|[[212ed5]]
|
|Every third note of [[274edo]], getting ~.004 cent sharper as it ascends the scale
|-
|[[213ed5]]
|
|Every fourth note of [[367edo]], getting ~.002 cent sharper as it ascends the scale
|-
|[[214ed5]]
|[[92edo]]
|Same 2.1 cent octave compression as 107ed5~46edo, but the correspondence is rough. Patent vals match through the 5-limit.
|-
|[[215ed5]]
|
|Every other note of [[185edo]], getting ~.13 cent flatter as it ascends the scale
|-
|-
| | [[216ed5]]
| | [[216ed5]]
| | [[93edo]]
| | [[93edo]]
| | Same 0.34 cent octave compression as 72ed5~31edo. Patent vals agree through the 31-limit.
| | Same 0.34 cent octave compression as 72ed5~31edo. Patent vals agree through the 31-limit.
|-
|[[217ed5]]
|
|Every other note of [[187edo]], getting ~.006 cent sharper as it ascends the scale
|-
|-
| | [[218ed5]]
| | [[218ed5]]
| | [[94edo]]
| | [[94edo]]
| | Same 1.4 cent octave stretch as 109ed5~47edo. Patent vals match through the 23-limit, with the exception of 13.
| | Same 1.4 cent octave stretch as 109ed5~47edo. Patent vals match through the 23-limit, with the exception of 13.
|-
|[[219ed5]]
|
|Every third note of [[286edo]], getting ~.135 cent sharper as it ascends the scale
|-
|[[220ed5]]
|
|''Same 3.2 cent octave stretch as 44ed5~19edo, but really matches the tuning with generator 3\379 of an octave.''
|-
|[[221ed5]]
|[[95edo]]
|221ed5 is 95edo with ~2.3 cent compressed octaves. Patent vals match through the 29-limit with the exception of 13 and 23
|-
|[[222edo]]
|
|Every other note of [[191edo]], getting ~.01 cent flatter as it ascends the scale
|-
|-
| | [[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.
|-
|[[224ed5]]
|
|Every other note of [[193edo]], getting ~.004 cent sharper as it ascends the scale
|-
|-
| | [[225ed5]]
| | [[225ed5]]
| | [[97edo]]
| | [[97edo]]
| | 225ed5 is 97edo with ~1.2 cent stretched octaves. Patent vals match through the 19-limit, with the exception of 11.
| | 225ed5 is 97edo with ~1.2 cent stretched octaves. Patent vals match through the 19-limit, with the exception of 11.
|-
|[[226edo]]
|
|Every third note of [[292edo]], getting ~.000055 cent sharper as it ascends the scale
|-
|[[227ed5]]
|
|Every fourth note of [[391edo]], getting ~.002 cent flatter as it ascends the scale
|-
|[[228ed5]]
|[[98edo]]
|Same 2.4 octave compression as 114ed5~49edo, but the correspondence is rough. Patent vals match through the 5-limit with the exception of 3.
|-
|[[229ed5]]
|
|Every other note of [[197edo]], getting ~.015 cent flatter as it ascends the scale
|-
|-
| | [[230ed5]]
| | [[230ed5]]
| | [[99edo]]
| | [[99edo]]
| | 230ed5 is 99edo with ~0.67 cent compressed octaves. Patent vals match through the 7-limit.
| | 230ed5 is 99edo with ~0.67 cent compressed octaves. Patent vals match through the 7-limit.
|-
|[[231ed5]]
|
|Every other note of [[199edo]], getting ~.002 cent sharper as it ascends the scale
|-
|-
| | [[232ed5]]
| | [[232ed5]]
| | [[100edo]]
| | [[100edo]]
| | Same 1.0 cent octave stretch as 58ed5~25edo. Patent vals match through the 13-limit.
| | Same 1.0 cent octave stretch as 58ed5~25edo. Patent vals match through the 13-limit.
|-
|[[233ed5]]
|
|Every third note of [[301edo]], getting ~.0002 cent flatter as it ascends the scale
|-
|[[234edo]]
|
|Every fourth note of [[403edo]], getting ~.003 cent flatter as it ascends the scale
|-
|[[235ed5]]
|[[101edo]]
|235ed5 is 101edo with ~2.5 cent compressed octaves. Patent vals match through the 19-limit, with the exception of 13 and 17.
|-
|[[236ed5]]
|
|''Same 4.25 cent octave compression as 118ed5~51edo, but really matches the tuning with generator 2\203 of an octave''
|-
|-
| | [[237ed5]]
| | [[237ed5]]
| | [[102edo]]
| | [[102edo]]
| | Same 0.83 cent octave compression as 79ed5~34edo. Patent vals differ in the 7-limit.
| | Same 0.83 cent octave compression as 79ed5~34edo. Patent vals differ in the 7-limit.
|-
|[[238ed5]]
|
|Every other note of [[205edo]], getting ~.0001 cent flatter as it ascends the scale
|-
|-
| | [[239ed5]]
| | [[239ed5]]
| | [[103edo]]
| | [[103edo]]
| | 239ed5 is 103edo with ~0.80 cent stretched octaves. Patent vals match through the 17-limit.
| | 239ed5 is 103edo with ~0.80 cent stretched octaves. Patent vals match through the 17-limit.
|-
|[[240ed5]]
|
|Every other note of [[207edo]], getting ~.015 cent sharper as it ascends the scale
|-
|[[241ed5]]
|[[104edo]]
|241ed5 is 104edo with ~2.4 cent stretched octaves. Patent vals match through the 17-limit, with the exception of 7 through 13
|-
|[[242ed5]]
|
|Same 2.6 cent octave compression as 121ed5~52edo, but really matches the tuning with generator 4\417 of an octave
|-
|[[243ed5]]
|
|Every third note of [[314edo]], getting ~.001 cent sharper as it ascends the scale
|-
|-
| | [[244ed5]]
| | [[244ed5]]
| | [[105edo]]
| | [[105edo]]
| | 244ed5 is 105edo with ~0.97 cent compressed octaves. Patent vals disagree in the 5-limit and higher prime limit.
| | 244ed5 is 105edo with ~0.97 cent compressed octaves. Patent vals disagree in the 5-limit and higher prime limit.
|-
|[[245ed6]]
|
|Every other note of [[211edo]], getting ~.002 cent flatter as it ascends the scale
|-
|-
| | [[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.
|-
|[[247ed5]]
|
|Every other note of [[213edo]], getting ~.01 cent sharper as it ascends the scale
|-
|[[248ed5]]
|[[107edo]]
|248ed5 is 107edo with ~2.2 cent stretched octaves. Patent vals match through the 17-limit with the exception of 11 and 13.
|-
|[[249ed5]]
|
|Every fourth note of [[429edo]], getting ~.001 cent sharper as it ascends the scale
|-
|[[250ed5]]
|
|''Same 3.7 cent octave stretch as 125ed5~54edo, but really matches the tuning with generator 3/323 of an octave''
|-
|-
| | [[251ed5]]
| | [[251ed5]]
| | [[108edo]]
| | [[108edo]]
| | 251ed5 is 108edo with ~1.1 cent compressed octaves. Patent vals match through the 13-limit.
| | 251ed5 is 108edo with ~1.1 cent compressed octaves. Patent vals match through the 13-limit.
|-
|[[252ed5]]
|
|Every other note of [[217edo]], getting ~.003 cent flatter as it ascends the scale
|-
|-
| | [[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.
|-
|[[254ed5]]
|
|Every other note of [[219edo]], getting ~.01 cent sharper as it ascends the scale
|-
|[[255ed5]]
|[[110edo]]
|Same 1.9 cent octave stretch as 51ed5~22edo. Patent vals match through the 5-limit.
|-
|[[256ed5]]
|
|''Same 2.8 cent octave compression as 128ed5~55edo, but actually matches the tuning with generator 4/441 of an octave''
|-
|[[257ed5]]
|
|Every third note of [[332edo]], getting ~.002 cent flatter as it ascends the scale
|-
|-
| | [[258ed5]]
| | [[258ed5]]
| | [[111edo]]
| | [[111edo]]
| | Same 1.2 cent octave compression as 86ed5~37edo. Patent vals agree through the 19-limit.
| | Same 1.2 cent octave compression as 86ed5~37edo. Patent vals agree through the 19-limit.
|-
|[[259ed5]]
|
|Every other note of [[223edo]], getting ~.004 cent flatter as it ascends the scale
|-
|-
| | [[260ed5]]
| | [[260ed5]]
Line 1,065: Line 344:
| | Same 0.26 cent octave stretch as 65ed5~28edo. Patent vals match through the 47-limit, with the exception of 3.
| | Same 0.26 cent octave stretch as 65ed5~28edo. Patent vals match through the 47-limit, with the exception of 3.
|-
|-
|[[261ed5]]
| | [[265ed5]]
|
| | [[114edo]]
|Every other note of [[225edo]], getting ~.009 cent sharpter as it ascends the scale
| | 265edo is 114edo with ~2.2 cent compressed octaves. Patent vals match through the 43-limit, with the exception of 11, 19 and 37.
|-
|[[262ed5]]
|[[113edo]]
|262ed5 is 113edo with ~1.7 cent stretched octaves. Patent vals match through the 13-limit with the exception of 11.
|-
|[[263ed5]]
|
|Every fourth note of [[453edo]], getting ~.002 cent flatter as it ascends the scale
|-
|[[264ed5]]
|
|''Same 3.2 cent octave stretch as 44ed5~19edo, but actually matches the tuning with generator 3/341 of an octave.''
|-
|[[265ed5]]
|[[114edo]]
|265edo is 114edo with ~2.2 cent compressed octaves. Patent vals match through the 43-limit, with the exception of 11, 19 and 37.
|-
|[[266ed5]]
|
|Every other note of [[229edo]], getting ~.0055 cent flatter as it ascends the scale
|-
|-
| | [[267ed5]]
| | [[267ed5]]
| | [[115edo]]
| | [[115edo]]
| | 267ed5 is 115edo with ~0.10 cent stretched octaves. Patent vals match through the 17-limit.
| | 267ed5 is 115edo with ~0.10 cent stretched octaves. Patent vals match through the 17-limit.
|-
|[[268ed5]]
|
|Every other note of [[231edo]], getting ~.008 cent sharper as it ascends the scale
|-
|[[269ed5]]
|[[116edo]]
|269ed5 is 116edo with ~1.5 cent stretched octaves. Patent vals match through the 17-limit with the exception of 7.
|-
|[[270ed5]]
|
|''Same 2.9 cent octave compression as 135ed5~58edo, but really matches the tuning with generator 4/465 of an octave''
|-
|[[271ed5]]
|
|Every third note of [[350edo]], getting ~.004 cent flatter as it ascends the scale
|-
|[[272ed5]]
|[[117edo]]
|272ed5 is 117edo with ~1.5 cent stretched octaves. Patent vals match through the 11-limit with the exception of 7.
|-
|[[273ed5]]
|
|Every other note of [[235edo]], getting ~.0065 cent flatter as it ascends the scale
|-
|-
| | [[274ed5]]
| | [[274ed5]]
Line 1,121: Line 356:
| | Same 0.05 cent octave compression as 137ed5~59edo. Patent vals agree through the 103-limit.
| | Same 0.05 cent octave compression as 137ed5~59edo. Patent vals agree through the 103-limit.
|-
|-
|[[275ed5]]
| | [[276ed5]]
|
| | [[119edo]]
|Every other note of [[237edo]], getting ~.0055 cent sharper as it ascends the scale
| | 276ed5 is 119edo with ~1.35 cent stretched octaves. Patent vals agree through the 23-limit with the exception of 13 and 19.
|-
|[[276ed5]]
|[[119edo]]
|276ed5 is 119edo with ~1.35 cent stretched octaves. Patent vals agree through the 23-limit with the exception of 13 and 19.
|-
|[[277ed5]]
|
|Every fourth note of [[477edo]], getting ~.004 cent flatter as it ascends the scale
|-
|[[278ed5]]
|
|Every third note of [[359edo]], getting ~.005 cent flatter as it ascends the scale
|-
|[[279ed5]]
|[[120edo]]
|279ed5 is 120edo with ~1.6 cent compressed octaves. Patent vals match through the 19-limit with the exception of 11 through 17.
|-
|[[280ed5]]
|
|Every other note of [[241edo]], getting ~.007 cent flatter as it ascends the scale
|-
|-
| | [[281ed5]]
| | [[281ed5]]
| | [[121edo]]
| | [[121edo]]
| | 281ed5 is 121edo with ~0.20 cent compressed octaves. Patent vals match through the 29-limit.
| | 281ed5 is 121edo with ~0.20 cent compressed octaves. Patent vals match through the 29-limit.
|-
|[[282ed5]]
|
|Every other note of [[243edo]], getting ~.004 cent sharper as it ascends the scale
|-
|-
| | [[283ed5]]
| | [[283ed5]]
| | [[122edo]]
| | [[122edo]]
| | 283ed5 is 122edo with ~1.2 cent stretched octaves. Patent vals match through the 13-limit.
| | 283ed5 is 122edo with ~1.2 cent stretched octaves. Patent vals match through the 13-limit.
|-
|[[284ed5]]
|
|Every third note of [[367edo]], getting ~.002 cent sharper as it ascends the scale
|-
|[[285ed5]]
|
|Same 2.5 cent octave stretch as 95ed5~41edo, but really matches the tuning with generator 4/491 of an octave.
|-
|[[286ed5]]
|[[123edo]]
|286edo is 123edo with ~1.7 cent compressed octaves. Patent vals match through the 17-limit, with the exception of 7 and 13.
|-
|[[287ed5]]
|
|Every other note of [[247edo]], getting ~.008 cent flatter as it ascends the scale
|-
|-
| | [[288ed5]]
| | [[288ed5]]
| | [[124edo]]
| | [[124edo]]
| | Same 0.34 cent octave compression as 72ed5~31edo. Patent vals agree through the 23-limit.
| | Same 0.34 cent octave compression as 72ed5~31edo. Patent vals agree through the 23-limit.
|-
|[[289ed5]]
|
|Every other note of [[249edo]], getting ~.003 cent sharper as it ascends the scale
|-
|-
| | [[290ed5]]
| | [[290ed5]]
| | [[125edo]]
| | [[125edo]]
| | Same 1 cent octave stretch as 58ed5~25edo. Patent vals match through the 37-limit, with the exception of 13.
| | Same 1 cent octave stretch as 58ed5~25edo. Patent vals match through the 37-limit, with the exception of 13.
|-
|[[291ed5]]
|
|Every third note of [[376edo]], getting ~.0004 cent sharper as it ascends the scale
|-
|[[292ed5]]
|
|Same 2.3 cent octave stretch as 146ed5~63edo, but really matches the tuning with generator 4/503 of an octave
|-
|[[293ed5]]
|[[126edo]]
|293ed5 is 126edo with ~2.2 cent compressed octaves. Patent vals match through the 7-limit.
|-
|[[294ed5]]
|
|Every other note of [[253edo]], getting ~.009 cent flatter as it ascends the scale
|-
|-
| | [[295ed5]]
| | [[295ed5]]
| | [[127edo]]
| | [[127edo]]
| | 295ed5 is 127edo with ~0.47 cent compressed octaves. Patent vals match through the 17-limit, with the exception of 11.
| | 295ed5 is 127edo with ~0.47 cent compressed octaves. Patent vals match through the 17-limit, with the exception of 11.
|-
|[[296ed5]]
|
|Every other note of [[255edo]], getting ~.0055 cent sharper as it ascends the scale
|-
|-
| | [[297ed5]]
| | [[297ed5]]
Line 1,213: Line 384:
| | 297ed5 is 128edo with ~0.84 cent stretched octaves. Patent vals match through the 7-limit.
| | 297ed5 is 128edo with ~0.84 cent stretched octaves. Patent vals match through the 7-limit.
|-
|-
|[[298ed5]]
| | [[302ed5]]
|
| | [[130edo]]
|Same 3.2 cent octave compression as 149ed5~64edo, but really matches the tuning with generator 3/385 of an octave
| | Same .59 cent octave compression as 151ed5~65edo. Patent vals match through the 41-limit with the exception of 11, 19 and 23.
|-
|[[299ed5]]
|
|Every fourth note of [[515edo]], getting ~.002 cent flatter as it ascends the scale
|-
|[[300ed5]]
|[[129edo]]
|Same 1.9 cent octeave compression as 100ed5~43edo. Patent vals match alternate primes through the 5-limit.
|-
|[[301ed5]]
|
|Every other note of [[259edo]], getting ~.01 cent flatter as it ascends the scale
|-
|[[302ed5]]
|[[130edo]]
|Same .59 cent octave compression as 151ed5~65edo. Patent vals match through the 41-limit with the exception of 11, 19 and 23.
|-
|[[303ed5]]
|
|Every other note of [[261edo]], getting ~.002 cent sharper as it ascends the scale
|-
|[[304ed5]]
|[[131edo]]
|304ed5 is 131edo with ~.68 cent stretched octaves. Patent vals match through the 41-limit with the exception of 13 and 23.
|-
|[[305ed5]]
|
|Every other note of [[263edo]], getting ~.01 cent sharper as it ascends the scale
|-
|[[306ed5]]
|[[132edo]]
|Same 1.9 cent octave stretch as 51ed5~22edo. Patent vals match through the 13-limit with the exception of 7 and 11.
|-
|[[307ed5]]
|
|Every fourth note of [[529edo]], getting ~.002 cent sharper as it ascends the scale
|-
|[[308ed5]]
|
|Every third note of [[398edo]], getting ~.001 cent sharper as it ascends the scale
|-
|[[309ed5]]
|[[133edo]]
|309ed5 is 133edo with ~.73 cent compressed octaves. Patent vals match through the 71-limit with the exception of 7 and 59.
|-
|[[310ed5]]
|
|Every other note of [[267edo]], getting ~.0006 cent flatter as it ascends the scale
|-
|[[311ed5]]
|[[134edo]]
|311ed5 is 134edo with ~.53 cent stretched octaves. Patent vals match through the 59-limit with the exception of 11, 19 and 53
|-
|[[312ed5]]
|
|''Same 3.3 cent octave compression as 156ed5~67edo, but really matches the tuning with generator 2/269 of an octave''
|-
|[[313ed5]]
|[[135edo]]
|313ed5 is 135edo with ~1.8 cent stretched octaves. Patent vals match through the 5-limit.
|-
|[[314ed5]]
|
|Every fourth note of [[541edo]], getting ~.001 cent sharper as it ascends the scale
|-
|[[315ed5]]
|
|Every third note of [[407edo]], getting ~.002 cent sharper as it ascends the scale
|-
|[[316ed5]]
|[[136edo]]
|Same 0.83 cent octave compression as 79ed5~34edo. Patent vals match through the 41-limit with the exception of 13 and 23.
|-
|[[317ed5]]
|
|Every other note of [[273edo]], getting ~.002 cent flatter as it ascends the scale
|-
|[[318ed5]]
|[[137edo]]
|318ed5 is 137edo with ~.39 cent stretched octaves. Patent vals match through the 71-limit with the exception of 29. 61 and 71.
|-
|[[319ed5]]
|
|Every other note of [[275edo]], getting ~.007 cent sharper as it ascends the scale
|-
|[[320ed5]]
|[[138edo]]
|Same 1.6 cent octave compression as 160ed5~69edo. Patent vals match through the 5-limit with the exception of 3.
|-
|[[321ed5]]
|
|''Same 2.1 cent octave compression as 107ed5~46edo, but really matches the tuning with generator 4\553 of an octave.''
|-
|[[322ed5]]
|
|Every third note of [[416edo]], getting ~.0007 cent flatter as it ascends the scale
|-
|[[323ed5]]
|[[139edo]]
|323ed5 is 139edo with ~.94 cent compressed compressed octaves. Patent vals match alternating primes through the 11-limit
|-
|[[324ed5]]
|
|Every other note of [[279edo]], getting ~.002 cent flatter as it ascends the scale
|-
|[[325ed5]]
|[[140edo]]
|Same 0.26 cent octave stretch as 65ed5~28edo. Patent vals match through the 73-limit, with the exception of 31 and 67.
|-
|[[326ed5]]
|
|Same ~3.4 cent octave compression 163ed5~70edo, but really matches the tuning with generator 2\281 of an octave.
|-
|[[327ed5]]
|[[141edo]]
|Same 1.4 cent octave stretch as 109ed5~47edo. Patent vals match through the 5-limit, with the exception of 3.
|-
|[[328ed5]]
|
|Every fourth note of [[565edo]], getting ~.0007 cent flatter as it ascends the scale
|-
|-
|[[329ed5]]
| | [[304ed5]]
|
| | [[131edo]]
|Every third note of [[425edo]], getting ~.0015 cent flatter as it ascends the scale
| | 304ed5 is 131edo with ~.68 cent stretched octaves. Patent vals match through the 41-limit with the exception of 13 and 23.
|-
|-
|[[330ed5]]
| | [[309ed5]]
|[[142edo]]
| | [[133edo]]
|Same ~1 cent octave compression as 165ed5~71edo. Patent vals match through the 13-limit with the exception of 11.
| | 309ed5 is 133edo with ~.73 cent compressed octaves. Patent vals match through the 71-limit with the exception of 7 and 59.
|-
|-
|[[331ed5]]
| | [[311ed5]]
|
| | [[134edo]]
|Every other note of [[285edo]], getting ~.003 cent flatter as it ascends the scale
| | 311ed5 is 134edo with ~.53 cent stretched octaves. Patent vals match through the 59-limit with the exception of 11, 19 and 53.
|-
|-
|[[332ed5]]
| | [[316ed5]]
|[[143edo]]
| | [[136edo]]
|332ed5 is 143edo with ~.13 cent stretched octaves. Patent vals match through the 29-limit with the exception of 7, 17 and 19
| | Same 0.83 cent octave compression as 79ed5~34edo. Patent vals match through the 41-limit with the exception of 13 and 23.
|-
|-
|[[333ed5]]
| | [[318ed5]]
|
| | [[137edo]]
|Every other note of [[287edo]], getting ~.005 cent sharper as it ascends the scale
| | 318ed5 is 137edo with ~.39 cent stretched octaves. Patent vals match through the 71-limit with the exception of 29. 61 and 71.
|-
|-
|[[334ed5]]
| | [[323ed5]]
|[[144edo]]
| | [[139edo]]
|Same 1.3 cent octave stretch as 167ed5~72edo. Patent vals match through the 5-limit.
| | 323ed5 is 139edo with ~.94 cent compressed compressed octaves. Patent vals match alternating primes through the 11-limit
|-
|-
|[[335ed5]]
| | [[325ed5]]
|
| | [[140edo]]
|Every fourth note of [[577edo]], getting ~.0015 cent flatter as it ascends the scale
| | Same 0.26 cent octave stretch as 65ed5~28edo. Patent vals match through the 73-limit, with the exception of 31 and 67.
|-
|-
|[[336ed5]]
| | [[330ed5]]
|
| | [[142edo]]
|Every third note of [[434edo]], getting ~.002 cent flatter as it ascends the scale
| | Same ~1 cent octave compression as 165ed5~71edo. Patent vals match through the 13-limit with the exception of 11.
|-
|-
|[[337ed5]]
| | [[332ed5]]
|[[145edo]]
| | [[143edo]]
|337edo is 145edo with ~1.1 cent compressed octaves. Patent vals match through the 17-limit with the exception of 7.
| | 332ed5 is 143edo with ~.13 cent stretched octaves. Patent vals match through the 29-limit with the exception of 7, 17 and 19
|-
|-
|[[338ed5]]
| | [[337ed5]]
|
| | [[145edo]]
|Every other note of [[291edo]], getting ~.004 cent flatter as it ascends the scale
| | 337edo is 145edo with ~1.1 cent compressed octaves. Patent vals match through the 17-limit with the exception of 7.
|-
|-
| | [[339ed5]]
| | [[339ed5]]
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