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Undo revision 144861 by ArrowHead294 (talk) This is one edo where you really do need the 19-limit intervals to highlight the good ratios it does approximate.
Tag: Undo
Line 242: Line 242:


=== Selected 19-limit just intervals ===
=== Selected 19-limit just intervals ===
{{Q-odd-limit intervals|20}}
{| class="wikitable center-all"
|+Direct mapping (even if inconsistent)
|-
! Interval, complement
! Error (abs, [[Cent|¢]])
|-
| [[16/13]] '''[[13/8]]'''
| 0.5276
|-
| [[15/14]] [[28/15]]
| 0.5571
|-
| [[10/9]] [[9/5]]
| 2.4037
|-
| '''[[19/16]]''' [[32/19]]
| 2.4869
|-
| [[14/11]] [[11/7]]
| 2.4920
|-
| [[19/13]] [[26/19]]
| 3.0146
|-
| [[15/11]] [[22/15]]
| 3.0492
|-
| [[15/13]] [[26/15]]
| 7.7410
|-
| [[16/15]] [[15/8]]
| 8.2687
|-
| [[14/13]] [[13/7]]
| 8.2982
|-
| [[8/7]] '''[[7/4]]'''
| 8.8259
|-
| [[13/11]] [[22/13]]
| 10.7902
|-
| '''[[11/8]]''' [[16/11]]
| 11.3179
|-
| [[11/9]] [[18/11]]
| 12.5920
|-
| [[11/10]] [[20/11]]
| 14.9957
|-
| '''[[17/16]]''' [[32/17]]
| 15.0445
|-
| [[9/7]] [[14/9]]
| 15.0840
|-
| [[6/5]] [[5/3]]
| 15.6412
|-
| [[7/5]] [[10/7]]
| 17.4878
|-
| '''[[3/2]]''' [[4/3]]
| 18.0449
|-
| [[13/12]] [[24/13]]
| 18.5726
|-
| [[9/8]] [[16/9]]
| 23.9100
|-
| '''[[5/4]]''' [[8/5]]
| 26.3137
|-
| [[7/6]] [[12/7]]
| 26.8709
|-
| [[12/11]] [[11/6]]
| 29.36294
|}


== Chord names ==
== Chord names ==
Line 267: Line 347:
|-
|-
| 3 1 3 1 3 1 3 1 3 1
| 3 1 3 1 3 1 3 1 3 1
| Blackwood Major Decatonic [[5L_5s| (bi-equal decatonic]], according to the [[MOSNamingScheme| MOS naming scheme]])
| Blackwood Major Decatonic [[5L_5s|(bi-equal decatonic]], according to the [[MOSNamingScheme|MOS naming scheme]])
|-
|-
| 1 3 1 3 1 3 1 3 1 3
| 1 3 1 3 1 3 1 3 1 3
Line 273: Line 353:
|-
|-
| 2 1 1 2 1 1 2 1 1 2 1 1
| 2 1 1 2 1 1 2 1 1 2 1 1
| Blackwood Major Pentadecatonic (also tri-equal pentadecatonic)
|Blackwood Major Pentadecatonic (also tri-equal pentadecatonic)
|-
|-
| 1 1 2 1 1 2 1 1 2 1 1 2
|1 1 2 1 1 2 1 1 2 1 1 2
| Blackwood Diminished Pentadecatonic (also tri-equal pentadecatonic)
|Blackwood Diminished Pentadecatonic (also tri-equal pentadecatonic)
|-
|-
| 1 2 1 1 2 1 1 2 1 1 2 1
|1 2 1 1 2 1 1 2 1 1 2 1
| Blackwood Minor Pentadecatonic (also tri-equal pentadecatonic)
|Blackwood Minor Pentadecatonic (also tri-equal pentadecatonic)
|-
|-
| 2 3 2 2 2 3 2 2 2
|2 3 2 2 2 3 2 2 2
| Balzano Nine-tone ([[2L_7s| fair mavila]], [[score9]]) <ref>[https://www.jstor.org/stable/833490?seq=1 Generalized Diatonic and Pentatonic Scales: A Group-Theoretic Approach]</ref>
| Balzano Nine-tone ([[2L_7s|fair mavila]], [[score9]]) <ref>[https://www.jstor.org/stable/833490?seq=1 Generalized Diatonic and Pentatonic Scales: A Group-Theoretic Approach]</ref>
|-
|-
| 2 2 2 2 1 2 2 2 2 2 1
|2 2 2 2 1 2 2 2 2 2 1
| Balzano Eleven-tone, Agmon Diatonic DS4, [[score11]]
|Balzano Eleven-tone, Agmon Diatonic DS4, [[score11]]
|-
|-
| 2 2 2 3 2 2 2 3 2
|2 2 2 3 2 2 2 3 2
| Balzano Nine-tone inverse (also fair mavila, score9)
|Balzano Nine-tone inverse (also fair mavila, score9)
|-
|-
| 1 2 2 2 2 2 1 2 2 2 2
|1 2 2 2 2 2 1 2 2 2 2
| Balzano Eleven-tone inverse (also score11)
|Balzano Eleven-tone inverse (also score11)
|-
|-
| 2 3 2 3 2 3 2 3
| 2 3 2 3 2 3 2 3
| Octatonic ([[4L_4s| diminished]], according to the [[MOSNamingScheme| MOS naming scheme]])
| Octatonic ([[4L_4s|diminished]], according to the [[MOSNamingScheme|MOS naming scheme]])
|-
|-
| 3 2 3 2 3 2 3 2
|3 2 3 2 3 2 3 2
| Diminished
|Diminished
|-
|-
| 2 2 1 2 2 1 2 2 1 2 2 1
|2 2 1 2 2 1 2 2 1 2 2 1
| Dodecatonic
|Dodecatonic
|-
|-
| 2 1 2 2 1 2 2 1 2 2 1 2
|2 1 2 2 1 2 2 1 2 2 1 2
| Diminished
|Diminished
|-
|-
| 1 2 2 1 2 2 1 2 2 1 2 2
|1 2 2 1 2 2 1 2 2 1 2 2
| Diminished
|Diminished
|-
|-
| 4 3 1 4 3 4 1
|4 3 1 4 3 4 1
| Twenty-tone "Major"
|Twenty-tone "Major"
|-
|-
| 4 1 3 4 1 4 3
|4 1 3 4 1 4 3
| Twenty-tone "Minor"
|Twenty-tone "Minor"
|-
|-
| 2 2 1 2 1 2 2 1 2 2 2 1
|2 2 1 2 1 2 2 1 2 2 2 1
| Twelve-tone Chromatic
|Twelve-tone Chromatic
|-
|-
| 2 2 2 2 1 2 2 2 2 1 2
|2 2 2 2 1 2 2 2 2 1 2
| Zweifel Major
|Zweifel Major
|-
|-
| 2 1 2 2 2 2 2 1 2 2 2
| 2 1 2 2 2 2 2 1 2 2 2
| Zweifel Natural Minor
| Zweifel Natural Minor
|-
|-
| 3 3 3 3 3 3 2
|3 3 3 3 3 3 2
| Major quasi-equal Heptatonic ([[6L_1s| archaeotonic or Grumpy heptatonic]])
|Major quasi-equal Heptatonic ([[6L_1s|archaeotonic or Grumpy heptatonic]])
|-
|-
| 3 2 3 3 3 3 3
|3 2 3 3 3 3 3
| Minor quasi-equal Heptatonic (also archaeotonic)
|Minor quasi-equal Heptatonic (also archaeotonic)
|-
|-
| 2 2 1 2 1 2 1 2 1 2 1 2 1
|2 2 1 2 1 2 1 2 1 2 1 2 1
| Major quasi-equal Triskaidecatonic (Grumpy triskaidecatonic)
|Major quasi-equal Triskaidecatonic (Grumpy triskaidecatonic)
|-
|-
| 2 1 2 1 2 1 2 1 2 1 2 1 2
|2 1 2 1 2 1 2 1 2 1 2 1 2
| Minor quasi-equal Triskaidecatonic A
|Minor quasi-equal Triskaidecatonic A
|-
|-
| 1 2 1 2 1 2 1 2 1 2 1 2 2
|1 2 1 2 1 2 1 2 1 2 1 2 2
| Minor quasi-equal Triskaidecatonic B
|Minor quasi-equal Triskaidecatonic B
|-
|-
| 2 1 2 1 2 1 2 1 2 1 2 2 1  
|2 1 2 1 2 1 2 1 2 1 2 2 1  
| Minor quasi-equal Triskaidecatonic C
|Minor quasi-equal Triskaidecatonic C
|-
|-
| 3 2 2 2 2 3 2 2 2
|3 2 2 2 2 3 2 2 2
| Rothenberg Generalized Diatonic (also [[2L 7s| balzano]] or [[score9]])
|Rothenberg Generalized Diatonic (also [[2L 7s|balzano]] or [[score9]])
|-
|-
| 3 4 1 4 3 3 2
| 3 4 1 4 3 3 2
| Stearns Major
|Stearns Major
|-
|-
| 7 2 7 2 2
|7 2 7 2 2
| [[score5]] [[2L_3s| pentic, classic pentatonic]]
|[[score5]] [[2L_3s|pentic, classic pentatonic]]
|-
|-
| 5 2 2 5 2 2 2
|5 2 2 5 2 2 2
| [[score7]] ([[2L_5s| mavila, anti-diatonic]])
|[[score7]] ([[2L_5s|mavila, anti-diatonic]])
|}
|}
<references />
<references />
Line 364: Line 444:
{| class="commatable wikitable center-all left-3 right-4 left-6"
{| class="commatable wikitable center-all left-3 right-4 left-6"
|-
|-
![[Harmonic limit| Prime<br>Limit]]
![[Harmonic limit|Prime<br>Limit]]
![[Ratio]]<ref>Ratios longer than 10 digits are presented by placeholders with informative hints</ref>
![[Ratio]]<ref>Ratios longer than 10 digits are presented by placeholders with informative hints</ref>
![[Monzo]]
![[Monzo]]
Line 371: Line 451:
! Name(s)
! Name(s)
|-
|-
| 3
|3
| [[256/243]]
|[[256/243]]
| {{monzo| 8 -5 }}
|{{monzo| 8 -5 }}
| 90.22
|90.22
| Sawa
|Sawa
| [[Limma]], Pythagorean Minor 2nd
|[[Limma]], Pythagorean Minor 2nd
|-
|-
| 5
|5
| [[16875/16384]]
|[[16875/16384]]
| {{monzo|-14 3 4 }}
|{{monzo| -14 3 4 }}
| 51.12
| 51.12
| Laquadyo
|Laquadyo
| Negri Comma, Double Augmentation Diesis
|Negri Comma, Double Augmentation Diesis
|-
|-
| 5
| 5
| [[34171875/33554432| (16 digits)]]
|[[34171875/33554432|(16 digits)]]
| {{monzo|-25 7 6 }}
|{{monzo| -25 7 6 }}
| 31.57
|31.57
| Lala-tribiyo
|Lala-tribiyo
| [[Ampersand]], Ampersand's Comma
|[[Ampersand]], Ampersand's Comma
|-
|-
| 5
| 5
| [[2048/2025]]
| [[2048/2025]]
|  
|
{{monzo| 11 -4 -2 }}
{{monzo| 11 -4 -2 }}
| 19.55
|19.55
| Sagugu
|Sagugu
| Diaschisma
|Diaschisma
|-
|-
| 7
|7
| [[525/512]]
|[[525/512]]
| {{monzo|-9 1 2 1 }}
|{{monzo| -9 1 2 1 }}
| 43.41
|43.41
| Lazoyoyo
|Lazoyoyo
| Avicennma, Avicenna's Enharmonic Diesis
|Avicennma, Avicenna's Enharmonic Diesis
|-
|-
| 7
|7
| [[49/48]]
|[[49/48]]
| {{monzo|-4 -1 0 2 }}
|{{monzo| -4 -1 0 2 }}
| 35.70
|35.70
| Zozo
|Zozo
| Slendro Diesis
|Slendro Diesis
|-
|-
| 7
|7
| [[50/49]]
|[[50/49]]
| {{monzo| 1 0 2 -2 }}
|{{monzo| 1 0 2 -2 }}
| 34.98
|34.98
| Biruyo
|Biruyo
| Tritonic Diesis, Jubilisma
|Tritonic Diesis, Jubilisma
|-
|-
| 7
|7
| [[686/675]]
|[[686/675]]
| {{monzo| 1 -3 -2 3 }}
|{{monzo| 1 -3 -2 3 }}
| 27.99
|27.99
| Trizo-agugu
|Trizo-agugu
| Senga
|Senga
|-
|-
| 7
| 7
| [[64/63]]
|[[64/63]]
| {{monzo| 6 -2 0 -1 }}
|{{monzo| 6 -2 0 -1 }}
| 27.26
|27.26
| Ru
|Ru
| Septimal Comma, Archytas' Comma, Leipziger Komma
|Septimal Comma, Archytas' Comma, Leipziger Komma
|-
|-
| 7
|7
| <abbr title="854296875/843308032">(18 digits)</abbr>
|<abbr title="854296875/843308032">(18 digits)</abbr>
| {{monzo|-10 7 8 -7 }}
| {{monzo| -10 7 8 -7 }}
| 22.41
|22.41
| Lasepru-aquadbiyo
|Lasepru-aquadbiyo
| [[Blackjackisma]]
|[[Blackjackisma]]
|-
|-
| 7
|7
| [[1029/1024]]
|[[1029/1024]]
| {{monzo|-10 1 0 3 }}
|{{monzo| -10 1 0 3 }}
| 8.43
|8.43
| Latrizo
|Latrizo
| Gamelisma
|Gamelisma
|-
|-
| 7
|7
| [[225/224]]
|[[225/224]]
| {{monzo|-5 2 2 -1 }}
|{{monzo| -5 2 2 -1 }}
| 7.71
|7.71
| Ruyoyo
|Ruyoyo
| Septimal Kleisma, Marvel Comma
|Septimal Kleisma, Marvel Comma
|-
|-
| 7
|7
| [[16875/16807]]
|[[16875/16807]]
| {{monzo| 0 3 4 -5 }}
|{{monzo| 0 3 4 -5 }}
| 6.99
| 6.99
| Quinru-aquadyo
|Quinru-aquadyo
| Mirkwai
|Mirkwai
|-
|-
| 7
|7
| <abbr title="578509309952/576650390625">(24 digits)</abbr>
| <abbr title="578509309952/576650390625">(24 digits)</abbr>
| {{monzo| 11 -10 -10 10 }}
|{{monzo| 11 -10 -10 10 }}
| 5.57
|5.57
| Saquinbizogu
|Saquinbizogu
| [[Linus comma| Linus]]
|[[Linus comma|Linus]]
|-
|-
| 7
| 7
| [[2401/2400]]
|[[2401/2400]]
| {{monzo|-5 -1 -2 4 }}
|{{monzo| -5 -1 -2 4 }}
| 0.72
|0.72
| Bizozogu
|Bizozogu
| Breedsma
|Breedsma
|-
|-
| 11
|11
| [[121/120]]
|[[121/120]]
| {{monzo|-3 -1 -1 0 2 }}
|{{monzo| -3 -1 -1 0 2 }}
| 14.37
| 14.37
| Lologu
| Lologu
| Biyatisma
|Biyatisma
|-
|-
| 13
|13
| [[91/90]]
|[[91/90]]
| {{monzo|-1 -2 -1 1 0 1 }}
|{{monzo| -1 -2 -1 1 0 1 }}
| 19.13
| 19.13
| Thozogu
|Thozogu
| Superleap
|Superleap
|-
|-
| 13
|13
| [[676/675]]
|[[676/675]]
| {{monzo| 2 -3 -2 0 0 2 }}
|{{monzo| 2 -3 -2 0 0 2 }}
| 2.56
|2.56
| Bithogu
|Bithogu
| Parizeksma
|Parizeksma
|}
|}
<references />
<references />
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