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User:Xenwolf/Fifthspan: Difference between revisions

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→Fifthspan examples: expanded from 1 to 99edo
Xenwolf (talk | contribs)
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Line 56: Line 56:
|-
|-
! [[4edo]]
! [[4edo]]
| N/A
| N/A (2x 2edo)
|-
|-
! [[5edo]]
! [[5edo]]
Line 71: Line 71:
|-
|-
! [[6edo]]
! [[6edo]]
| N/A
| N/A (2x 3edo)
|-
|-
! [[7edo]]
! [[7edo]]
Line 110: Line 110:
|-
|-
! [[10edo]]
! [[10edo]]
| N/A
| N/A (2x 5edo)
|-
|-
! [[11edo]]
! [[11edo]]
Line 149: Line 149:
|-
|-
! [[14edo]]
! [[14edo]]
| N/A
| N/A (2x 7edo)
|-
|-
! [[15edo]]
! [[15edo]]
| N/A
| N/A (3x 5edo)
|-
|-
! [[16edo]]
! [[16edo]]
Line 203: Line 203:
|-
|-
! [[20edo]]
! [[20edo]]
| N/A
| N/A (4x 5edo)
|-
|-
! [[21edo]]
! [[21edo]]
| N/A
| N/A (3x 7edo)
|-
|-
! [[22edo]]
! [[22edo]]
Line 233: Line 233:
|-
|-
! [[24edo]]
! [[24edo]]
| N/A
| N/A (2x 12edo)
|-
|-
! [[25edo]]
! [[25edo]]
| N/A
| N/A (5x 5edo)
|-
|-
! [[26edo]]
! [[26edo]]
Line 263: Line 263:
|-
|-
! [[28edo]]
! [[28edo]]
| N/A
| N/A (4x 7edo)
|-
|-
! [[29edo]]
! [[29edo]]
Line 278: Line 278:
|-
|-
! [[30edo]]
! [[30edo]]
| N/A
| N/A (6x 5edo)
|-
|-
! [[31edo]]
! [[31edo]]
Line 317: Line 317:
|-
|-
! [[34edo]]
! [[34edo]]
| N/A
| N/A (2x 17edo)
|-
|-
! [[35edo]]
! [[35edo]]
| N/A
| N/A (5x 7edo)
|-
|-
! [[36edo]]
! [[36edo]]
| N/A
| N/A (3x 12edo)
|-
|-
! [[37edo]]
! [[37edo]]
Line 338: Line 338:
|-
|-
! [[38edo]]
! [[38edo]]
| N/A
| N/A (2x 19edo)
|-
|-
! [[39edo]]
! [[39edo]]
Line 401: Line 401:
|-
|-
! [[44edo]]
! [[44edo]]
| N/A
| N/A (2x 22edo)
|-
|-
! [[45edo]]
! [[45edo]]
Line 440: Line 440:
|-
|-
! [[48edo]]
! [[48edo]]
| N/A
| N/A (4x 12edo)
|-
|-
! [[49edo]]
! [[49edo]]
Line 467: Line 467:
|-
|-
! [[51edo]]
! [[51edo]]
| N/A
| N/A (3x 17edo)
|-
|-
! [[52edo]]
! [[52edo]]
| N/A
| N/A (2x 26edo)
|-
|-
! [[53edo]]
! [[53edo]]
Line 485: Line 485:
|-
|-
! [[54edo]]
! [[54edo]]
| N/A
| N/A (2x 27edo)
|-
|-
! [[55edo]]
! [[55edo]]
Line 512: Line 512:
|-
|-
! [[57edo]]
! [[57edo]]
| N/A
| N/A (3x 19edo)
|-
|-
! [[58edo]]
! [[58edo]]
| N/A
| N/A (2x 29edo)
|-
|-
! [[59edo]]
! [[59edo]]
Line 530: Line 530:
|-
|-
! [[60edo]]
! [[60edo]]
| N/A
| N/A (5x 12edo)
|-
|-
! [[61edo]]
! [[61edo]]
Line 545: Line 545:
|-
|-
! [[62edo]]
! [[62edo]]
| N/A
| N/A (2x 31edo)
|-
|-
! [[63edo]]
! [[63edo]]
Line 584: Line 584:
|-
|-
! [[66edo]]
! [[66edo]]
| N/A
| N/A (3x 22edo)
|-
|-
! [[67edo]]
! [[67edo]]
Line 599: Line 599:
|-
|-
! [[68edo]]
! [[68edo]]
| N/A
| N/A (4x 17edo)
|-
|-
! [[69edo]]
! [[69edo]]
Line 638: Line 638:
|-
|-
! [[72edo]]
! [[72edo]]
| N/A
| N/A (6x 12edo)
|-
|-
! [[73edo]]
! [[73edo]]
Line 677: Line 677:
|-
|-
! [[76edo]]
! [[76edo]]
| N/A
| N/A (4x 19edo)
|-
|-
! [[77edo]]
! [[77edo]]
Line 692: Line 692:
|-
|-
! [[78edo]]
! [[78edo]]
| N/A
| N/A (2x 39edo)
|-
|-
! [[79edo]]
! [[79edo]]
Line 731: Line 731:
|-
|-
! [[82edo]]
! [[82edo]]
| N/A
| N/A (2x 41edo)
|-
|-
! [[83edo]]
! [[83edo]]
Line 746: Line 746:
|-
|-
! [[84edo]]
! [[84edo]]
| N/A
| N/A (7x 12edo)
|-
|-
! [[85edo]]
! [[85edo]]
| N/A
| N/A (5x 17edo)
|-
|-
! [[86edo]]
! [[86edo]]
| N/A
| N/A (2x 43edo)
|-
|-
! [[87edo]]
! [[87edo]]
| N/A
| N/A (3x 29edo)
|-
|-
! [[88edo]]
! [[88edo]]
Line 806: Line 806:
|-
|-
! [[92edo]]
! [[92edo]]
| N/A
| N/A (2x 46edo)
|-
|-
! [[93edo]]
! [[93edo]]
| N/A
| N/A (3x 31edo)
|-
|-
! [[94edo]]
! [[94edo]]
Line 836: Line 836:
|-
|-
! [[96edo]]
! [[96edo]]
| N/A
| N/A (8x 12edo)
|-
|-
! [[97edo]]
! [[97edo]]
Line 875: Line 875:
|}
|}


== EDO information ==
== EDO information with fifthspans ==


{{Primes in edo|columns=9|title=[[5edo]] |5 }}
=== [[5edo]] ===
{{Primes in edo|columns=9|title=[[7edo]] |7 }}
{{Primes in edo_fs|columns=9|5}}
{{Primes in edo|columns=9|title=[[8edo]] |8 }}
 
{{Primes in edo|columns=9|title=[[9edo]] |9 }}
=== [[7edo]] ===
{{Primes in edo|columns=9|title=[[11edo]]|11}}
{{Primes in edo_fs|columns=9|7}}
{{Primes in edo|columns=9|title=[[12edo]]|12}}
 
{{Primes in edo|columns=9|title=[[13edo]]|13}}
=== [[8edo]] ===
{{Primes in edo|columns=9|title=[[16edo]]|16}}
{{Primes in edo_fs|columns=9|8}}
{{Primes in edo|columns=9|title=[[17edo]]|17}}
 
{{Primes in edo|columns=9|title=[[18edo]]|18}}
=== [[9edo]] ===
{{Primes in edo|columns=9|title=[[19edo]]|19}}
{{Primes in edo_fs|columns=9|9}}
{{Primes in edo|columns=9|title=[[22edo]]|22}}
 
{{Primes in edo|columns=9|title=[[23edo]]|23}}
=== [[11edo]] ===
{{Primes in edo|columns=9|title=[[26edo]]|26}}
{{Primes in edo_fs|columns=9|11}}
{{Primes in edo|columns=9|title=[[27edo]]|27}}
 
{{Primes in edo|columns=9|title=[[29edo]]|29}}
=== [[12edo]] ===
{{Primes in edo|columns=9|title=[[31edo]]|31}}
{{Primes in edo_fs|columns=9|12}}
{{Primes in edo|columns=9|title=[[39edo]]|39}}
 
{{Primes in edo|columns=9|title=[[41edo]]|41}}
=== [[13edo]] ===
{{Primes in edo|columns=9|title=[[46edo]]|46}}
{{Primes in edo_fs|columns=9|13}}
{{Primes in edo|columns=9|title=[[53edo]]|53}}
 
=== [[16edo]] ===
{{Primes in edo_fs|columns=9|16}}
 
=== [[17edo]] ===
{{Primes in edo_fs|columns=9|17}}
 
=== [[18edo]] ===
{{Primes in edo_fs|columns=9|18}}
 
=== [[19edo]] ===
{{Primes in edo_fs|columns=9|19}}
 
=== [[22edo]] ===
{{Primes in edo_fs|columns=9|22}}
 
=== [[23edo]] ===
{{Primes in edo_fs|columns=9|23}}
 
=== [[26edo]] ===
{{Primes in edo_fs|columns=9|26}}
 
=== [[27edo]] ===
{{Primes in edo_fs|columns=9|27}}
 
=== [[29edo]] ===
{{Primes in edo_fs|columns=9|29}}
 
=== [[31edo]] ===
{{Primes in edo_fs|columns=9|31}}
 
=== [[39edo]] ===
{{Primes in edo_fs|columns=9|39}}
 
=== [[41edo]] ===
{{Primes in edo_fs|columns=9|41}}
 
=== [[46edo]] ===
{{Primes in edo_fs|columns=9|46}}
 
=== [[53edo]] ===
{{Primes in edo_fs|columns=9|53}}


== Separate mod steps ==
== Separate mod steps ==
Line 916: Line 957:
! prime 19
! prime 19
! prime 23
! prime 23
|-
|- class="thick-border" style="border-top: 2px solid #777"
! rowspan="2" | Error
! rowspan="2" | Error
! absolute ([[cent|¢]])
! absolute ([[cent|¢]])
Line 939: Line 980:
| -21
| -21
| +10
| +10
|-
|- class="thick-border" style="border-top: 2px solid #777"
! rowspan="2" | [[nearest edomapping|Mapping]]
! rowspan="2" | [[patent val|Mapping]]
! [[patent val]]
! value
| '''17'''
| '''17'''
| 27
| 27
Line 962: Line 1,003:
| 4
| 4
| 9
| 9
|-
|- class="thick-border" style="border-top: 2px solid #777"
! colspan="2" | [[fifthspan]] (steps)
! colspan="2" | [[Fifthspan]] (in steps)
| 0
| 0
| '''1'''
| '''1'''
Line 973: Line 1,014:
| 14
| 14
| 6
| 6
|}
{| class="wikitable center-all"
|-
|-
! rowspan="2" colspan="2" | fifthspan explained
|+ Approximation of prime intervals in 12 EDO
| rowspan="2" | -
| 10= '''1''' *10 %17
| 5= '''9''' *10 %17
| 14= '''15''' *10 %17
| 8= '''11''' *10 %17
| 12= '''8''' *10 %17
| 1= '''12''' *10 %17
| 4= '''14''' *10 %17
| 9= '''6''' *10 %17
|-
|-
| 1= 10 *12 %17
! colspan="2" | Prime interval
| 9= 5 *12 %17
! style="min-width: 3em" | 2
| 15= 14 *12 %17
! style="min-width: 3em" | 3
| 11= 8 *12  %17
! style="min-width: 3em" | 5
| 8= 12 *12 %17
! style="min-width: 3em" | 7
| 12= 1 *12 %17
! style="min-width: 3em" | 11
| 14= 4 *12 %17
! style="min-width: 3em" | 13
| 6= 9 *12 %17
! style="min-width: 3em" | 17
! style="min-width: 3em" | 19
|-
! rowspan="2" | Error
! absolute ([[cent|¢]])
| 0.0
| -2.0
| +13.7
| +31.2
| +48.7
| -40.5
| -5.0
| +2.5
|-
! [[Relative error|relative]] (%)
| 0
| -2
| +14
| +31
| +49
| -41
| -5
| +2
|-
! rowspan="2" | Mapping
! [[patent val]] ''v''
| 12
| 19
| 28
| 34
| 42
| 44
| 49
| 51
|-
! [[Octave reduction|''v'' mod 12]]
| 0
| 7
| 4
| 10
| 6
| 8
| 1
| 3
|}
 
----
{| class="wikitable center-all"
|-
|+ Approximation of prime intervals in 17 EDO
|-
! colspan="2" | Prime number
! 2
! 3
! 5
! 7
! 11
! 13
! 17
! 19
|-
! rowspan="2" | Error
! absolute ([[cent|¢]])
| +0.0
| +3.9
| −33.4
| +19.4
| +13.4
| +6.5
| −34.4
| −15.2
|-
! [[Relative error|relative]] (%)
| +0
| +6
| −47
| +27
| +19
| +9
| −49
| −21
|-
! rowspan="2" | Mapping
! [[patent val]] ''v''
| 17
| 27
| 39
| 48
| 59
| 63
| 69
| 72
|-
! ''v'' ([[octave-reduced|mod 17]])
| 0
| 10
| 5
| 14
| 8
| 12
| 1
| 4
|}
{| class="wikitable center-all"
|-
|+ Approximation of prime intervals in 17 EDO
|-
! colspan="2" | Prime number
! 2
! 3
! 5
! 7
! 11
! 13
! 17
! 19
|- class="thick-border" style="border-top: 2px solid #aaa"
! rowspan="2" | Error
! absolute ([[cent|¢]])
| +0.0
| +3.9
| −33.4
| +19.4
| +13.4
| +6.5
| −34.4
| −15.2
|-
! [[Relative error|relative]] (%)
| +0
| +6
| −47
| +27
| +19
| +9
| −49
| −21
|- class="thick-border" style="border-top: 2px solid #aaa"
! rowspan="2" | Mapping
! [[patent val]] ''v''
| 17
| 27
| 39
| 48
| 59
| 63
| 69
| 72
|-
! ''v'' ([[octave-reduced|mod 17]])
| 0
| 10
| 5
| 14
| 8
| 12
| 1
| 4
|- class="thick-border" style="border-top: 2px solid #aaa"
! colspan="2" | [[Fifthspan]]
| 0
| 1
| −8
| −2
| −6
| 8
| −5
| −3
|}
|}


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