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=Individual pages for EDFs=
=Individual pages for EDFs=
[[4edf|4edf]]
*[[4edf]]
*[[5edf]]
*[[6edf]]
*[[7edf]]
*[[8edf]]
*[[Carlos_Alpha|9edf (Carlos Alpha)]]
*[[10edf]]
*[[Carlos_Beta|11edf (Carlos Beta)]]
*[[12edf]]
*[[13edf]]
*[[14edf]]
*[[15edf]]
*[[16edf]]
*[[17edf]]
*[[18edf]]
*[[19edf]]
*[[Carlos_Gamma|20edf (Carlos Gamma)]]
*[[21edf]]
*[[22edf]]
*[[23edf]]
*[[24edf]]
*[[25edf]]
*[[26edf]]
*[[27edf]]
*[[28edf]]
*[[29edf]]
*[[30edf]]
*[[31edf]]
*[[32edf]]
*[[33edf]]
*[[34edf]]
*[[35edf]]
*[[36edf]]
*[[37edf]]
*[[38edf]]
*[[39edf]]
*[[40edf]]
*[[41edf]]
*[[42edf]]
*[[43edf]]
*[[44edf]]
*[[45edf]]
*[[46edf]]
*[[47edf]]
*[[48edf]]
*[[49edf]]
*[[50edf]]
*[[51edf]]
*[[52edf]]
*[[53edf]]
*[[54edf]]
*[[55edf]]
*[[56edf]]
*[[57edf]]
*[[58edf]]
*[[59edf]]
*[[60edf]]
*[[61edf]]
*[[62edf]]
*[[63edf]]
*[[64edf]]
*[[65edf]]
*[[66edf]]
*[[67edf]]
*[[68edf]]
*[[69edf]]
*[[70edf]]
*[[71edf]]
*[[72edf]]
*[[73edf]]
*[[74edf]]
*[[75edf]]
*[[76edf]]
*[[77edf]]
*[[78edf]]
*[[79edf]]
*[[80edf]]
*[[81edf]]
*[[82edf]]
*[[83edf]]
*[[84edf]]
*[[85edf]]
*[[86edf]]
*[[87edf]]
*[[88edf]]
*[[89edf]]
*[[90edf]]
*[[91edf]]
*[[92edf]]
*[[93edf]]
*[[94edf]]
*[[95edf]]
*[[96edf]]
*[[97edf]]
*[[98edf]]
*[[99edf]]
*[[100edf]]


[[5edf|5edf]]
=EDF-EDO correspondence=
 
[[6edf|6edf]]
 
[[7edf|7edf]]
 
[[8edf|8edf]] ([[88cET|88cET]])
 
[[Carlos_Alpha|9 (Carlos Alpha)]]
 
[[10edf|10edf]]
 
[[Carlos_Beta|11 (Carlos Beta)]]
 
[[12edf|12edf]]
 
[[13edf|13edf]]
 
[[14edf|14edf]]
 
[[15edf|15edf]]
 
[[16edf|16edf]]
 
[[17edf|17edf]]
 
[[18edf|18edf]]
 
[[19edf|19edf]]
 
[[Carlos_Gamma|20 (Carlos Gamma)]]
 
[[21edf|21edf]]
 
[[22edf|22edf]]
 
[[23edf|23edf]]
 
[[24edf|24edf]]
 
[[25edf|25edf]]
 
=EDO-EDF correspondence=


{| class="wikitable"
{| class="wikitable"
|-
|-
! | EDF
! | EDO
! | EDO
! | EDF
! | Comments
! | Comments
|-
|-
| | [[7edo|7edo]]
| | [[4edf]]
| | [[4edf|4edf]]
| | [[7edo]]
| | 4edf is 7edo with 28.5 cent stretched octaves.
| | 4edf is 7edo with 28.5 cent stretched octaves.<br>Equivalently, 7edo is 4edf with 3/2s compressed by ~16 cents.<br>Patent vals match through the 5 limit. Only a rough correspondence.
 
Equivalently, 7edo is 4edf with 3/2s compressed by ~16 cents.
 
Patent vals match through the 5 limit. Only a rough correspondence.
|-
|-
| | [[8edo|8edo]]
| | [[5edf]]
| |
| | [[9edo]]
| |
|-
| | [[9edo|9edo]]
| | [[5edf|5edf]]
| | Very rough correspondence - patent vals disagree in the 5 limit.
| | Very rough correspondence - patent vals disagree in the 5 limit.
|-
|-
| | [[10edo|10edo]]
| | [[6edf]]
| | [[6edf|6edf]]
| | [[10edo]]
| | Also very rough.
| | Also very rough.
|-
|-
| | [[11edo|11edo]]
| | [[7edf]]
| |
| | [[12edo]]
| |
| | 7edf is 12edo with 3.4 cent stretched octaves.<br>Equivalently, 12edo is 7edf with 2.0 cent compressed 3/2s.<br>With the exception of 11 (which falls almost exactly halfway between steps in both cases), the patent vals match through the 31 limit, so the agreement is excellent.
|-
| | [[12edo|12edo]]
| | [[7edf|7edf]]
| | 7edf is 12edo with 3.4 cent stretched octaves.
 
Equivalently, 12edo is 7edf with 2.0 cent compressed 3/2s.
 
With the exception of 11 (which falls almost exactly halfway between steps in both cases),
 
the patent vals match through the 31 limit, so the agreement is excellent.
|-
| | [[13edo|13edo]]
| |
| |
|-
|-
| | [[8edf]]
| |  
| |  
| | [[8edf|8edf]]
| | Since 88cET/octacot is well known to approximate some intervals quite accurately, it would be wrong to lump this in with 14edo.
| | Since 88cET/octacot is well known to approximate some intervals quite accurately,
 
it would be wrong to lump this in with 14edo.
|-
|-
| | [[14edo|14edo]]
| | [[9edf]]
| |  
| |  
| |
|-
| | [[15edo|15edo]]
| |
| |
|-
| |
| | [[9edf|9edf]]
| | The Carlos alpha scale is neither 15edo nor 16edo.
| | The Carlos alpha scale is neither 15edo nor 16edo.
|-
|-
| | [[16edo|16edo]]
| | [[10edf]]
| |  
| | [[17edo]]
| |  
| | 10edf is 17edo with 6.6 cent compressed octaves. Patent vals match through the 13 limit, with the exception of 5 (as expected).
|-
|-
| | [[17edo|17edo]]
| | [[11edf]]
| | [[10edf|10edf]]
| | [[19edo]]
| | 10edf is 17edo with 6.6 cent compressed octaves.
| | 11edf is 19edo with 12.5 cent stretched octaves. Patent vals match through the 7 limit.<br>If you don't think Carlos beta is accurately represented by 19edo then ignore this correspondence.
 
Patent vals match through the 13 limit, with the exception of 5 (as expected).
|-
|-
| | [[18edo|18edo]]
| | [[12edf]]
| |
| |  
| |  
| | 12edf entirely misses 2/1, but nails the "double octave" 4/1, so it strongly resembles the scale with generator 2\41 of an octave.
|-
|-
| | [[19edo|19edo]]
| | [[13edf]]
| | [[11edf|11edf]]
| | 11edf is 19edo with 12.5 cent stretched octaves.
 
Patent vals match through the 7 limit.
 
If you don't think Carlos beta is accurately represented by 19edo then ignore this correspondence.
|-
| | [[20edo|20edo]]
| |
| |  
| |  
| | Perhaps surprisingly, this is not very similar to [[22edo]]. Patent vals differ in the 5 limit.
|-
|-
| |  
| | [[14edf]]
| | [[12edf|12edf]]
| | [[24edo]]
| | 12edf entirely misses 2/1, but nails the "double octave" 4/1,
| | Same 3.4 cent octave stretch as 7edf~12edo. Patent vals agree through the 19 limit.
 
so it strongly resembles the scale with generator 2\41 of an octave.
|-
|-
| | [[21edo|21edo]]
| | [[15edf]]
| |  
| | [[26edo]]
| |  
| | Fairly rough correspondence. 15edf is 26edo with ~17 cent stretched octaves. Patent vals agree through the 5 limit, but not through the 7 limit.
|-
|-
| | [[22edo|22edo]]
| | [[16edf]]
| |  
| |  
| |  
| |  
|-
|-
| |  
| | [[17edf]]
| | [[13edf|13edf]]
| | [[29edo]]
| | Perhaps surprisingly, this is not very similar to 22edo. Patent vals differ in the 5 limit.
| | 17edf is 29edo with 2.5 cent compressed octaves. Patent vals disagree in the 7 limit.
|-
|-
| | [[23edo|23edo]]
| | [[18edf]]
| |
| |  
| |  
| | Perhaps surprisingly, this is not very similar to [[31edo]]. Patent vals differ in the 5 limit.
|-
|-
| | [[24edo|24edo]]
| | [[19edf]]
| | [[14edf|14edf]]
| | 14edf is 24edo with 3.4 cent stretched octaves. Patent vals agree through the 19 limit.
|-
| | [[25edo|25edo]]
| |  
| |  
| |  
| |  
|-
|-
| | [[26edo|26edo]]
| | [[20edf]]
| | [[15edf|15edf]]
| | [[34edo]]
| | Fairly rough correspondence. 15edf is 26edo with ~17 cent stretched octaves.
| | Same 6.6 cent octave compression as 10edf~17edo. Patent vals match through the 5 limit, but not the 7 limit.<br>If you don't think Carlos gamma is accurately represented by 34edo then ignore this correspondence.
 
Patent vals agree through the 5 limit, but not through the 7 limit.
|-
|-
| | [[27edo|27edo]]
| | [[21edf]]
| |  
| | [[36edo]]
| |  
| | Same 3.4 cent octave stretch as 7edf~12edo. Patent vals differ in the 5 limit.
|-
|-
| |  
| | [[22edf]]
| | [[16edf|16edf]]
| | [[38edo]]
| |  
| | Only rough correspondence. Patent vals differ in the 5 limit.
|-
|-
| | [[28edo|28edo]]
| | [[23edf]]
| |  
| | [[39edo]]
| |  
| | Only rough correspondence. 23edf is 39edo with ~9.7 cent compressed octaves. Patent vals differ in the 7 limit.
|-
|-
| | [[29edo|29edo]]
| | [[24edf]]
| | [[17edf|17edf]]
| | [[41edo]]
| | 17edf is 29edo with 2.5 cent compressed octaves. Patent vals disagree in the 7 limit.
| | 24edf is 41edo with 0.83 cent compressed octaves. Patent vals match through the 73 limit, with the exception of 23 and 43.
|-
|-
| | [[30edo|30edo]]
| | [[25edf]]
| |  
| | [[43edo]]
| |  
| | 25edf is 43edo with 7.4 cent stretched octaves, but a rough correspondence. Patent vals differ in the 5 limit.
|-
|-
| | [[27edf]]
| | [[46edo]]
| |  
| |  
| | [[18edf|18edf]]
| | Perhaps surprisingly, this is not very similar to 31edo. Patent vals differ in the 5 limit.
|-
|-
| | [[31edo|31edo]]
| | [[28edf]]
| |  
| | [[48edo]]
| |  
| |  
|-
|-
| | [[32edo|32edo]]
| | [[31edf]]
| |  
| | [[53edo]]
| |  
| | 31edf is 53edo with 0.12 cent stretched octaves. Patent vals match through the 61 limit.
|-
|-
| |  
| | [[34edf]]
| | [[19edf|19edf]]
| | [[58edo]]
| |  
| |  
|-
|-
| | [[33edo|33edo]]
| | [[35edf]]
| | [[60edo]]
| |  
| |  
| |
|-
| | [[34edo|34edo]]
| | [[20edf|20edf]]
| | 20edf is 34edo with 6.6 cent compressed octaves.
Patent vals match through the 5 limit, but not the 7 limit.
If you don't think Carlos gamma is accurately represented by 34edo then ignore this correspondence.
|-
|-
| | [[35edo|35edo]]
| | [[38edf]]
| |  
| | [[65edo]]
| |  
| |  
|-
|-
| | [[36edo|36edo]]
| | [[41edf]]
| | [[21edf|21edf]]
| | [[70edo]]
| |  
| |  
|-
|-
| | [[37edo|37edo]]
| | [[42edf]]
| |  
| | [[72edo]]
| |  
| | This is a rough correspondence, as the (7n)edf ~ (12n)edo sequence begins to break down. Patent vals match through the 7-limit.
|-
|-
| | [[38edo|38edo]]
| | [[45edf]]
| | [[22edf|22edf]]
| | [[77edo]]
| |  
| |  
|-
|-
| | [[39edo|39edo]]
| | [[48edf]]
| | [[23edf|23edf]]
| | [[82edo]]
| |  
| |  
|-
|-
| | [[40edo|40edo]]
| | [[51edf]]
| |  
| | [[87edo]]
| |  
| |  
|-
|-
| | [[41edo|41edo]]
| | [[52edf]]
| | [[24edf|24edf]]
| | [[89edo]]
| |  
| |  
|-
|-
| | [[42edo|42edo]]
| | [[55edf]]
| |  
| | [[94edo]]
| |  
| |  
|-
|-
| | [[43edo|43edo]]
| | [[58edf]]
| | [[25edf|25edf]]
| | [[99edo]]
| |  
| |  
|}
|}
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