Table of 5-limit commas: Difference between revisions

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A [[5-limit]] comma is the amount which separates m<sub>1</sub> [[3/2|fifth]]<nowiki/>s and m<sub>2</sub> [[5/4|third]]<nowiki/>s from n [[octave]]<nowiki/>s. It is the simplest kind of comma a tuning may [[Tempering out|temper out]].
A [[5-limit]] comma is the amount which separates m<sub>1</sub> [[3/2|fifth]]<nowiki/>s and m<sub>2</sub> [[5/4|third]]<nowiki/>s from n [[octave]]<nowiki/>s.


{| class="wikitable"
{| class="wikitable"
Line 8: Line 8:
! Monzo
! Monzo
! Cents
! Cents
|-
| [[144/125|classic diminished third]]<br>[[University temperament|university comma]]
| trigubi comma
| 3g3
| 144 / 125
| {{monzo| 4 2 -3 }}
| 244.969
|-
| [[Uncle|uncle comma]]
| sagu comma
| sg3
| 4096 / 3645
| {{monzo| 12 -6 -1 }}
| 201.956
|-
|-
| [[10/9|minor whole tone]]
| [[10/9|minor whole tone]]
Line 15: Line 29:
| {{monzo| 1 -2 1 }}
| {{monzo| 1 -2 1 }}
| 182.404
| 182.404
|-
| [[Laconic|laconic comma]]
| latrigubi comma
| L3g2
| 2187 / 2000
| {{monzo| -4 7 -3 }}
| 154.744
|-
|-
| [[27/25|large limma]]<br>acute diatonic semitone<br>[[Bug family|bug comma]]
| [[27/25|large limma]]<br>acute diatonic semitone<br>[[Bug family|bug comma]]
Line 30: Line 51:
| 111.731
| 111.731
|-
|-
| [[135/128|major limma]]<br>[[Pelogic family|mavila comma]]<br>[[Pelogic family|pelogic coma]]
| [[135/128|major limma]]<br>[[Pelogic family|mavila comma]]<br>[[Pelogic family|pelogic comma]]
| layobi comma
| layobi comma
| Ly1
| Ly1
Line 36: Line 57:
| {{monzo| -7 3 1 }}
| {{monzo| -7 3 1 }}
| 92.179
| 92.179
|-
| [[Archytas clan #Quasisuper|quasisuper comma]]
| sasagu comma
| ssg3
| 8388608 / 7971615
| {{monzo| 23 -13 -1 }}
| 88.271
|-
|-
| [[25/24|chromatic semitone]]<br>[[Dicot family|dicot comma]]
| [[25/24|chromatic semitone]]<br>[[Dicot family|dicot comma]]
Line 53: Line 81:
| 12&amp;163 comma
| 12&amp;163 comma
| quadlagu comma
| quadlagu comma
| L<sup>4</sup>g-3
| 4Lg-3
| 22876792454961 / 21990232555520
| 22876792454961 / 21990232555520
| {{monzo| -42 28 -1 }}
| {{monzo| -42 28 -1 }}
| 68.426
| 68.426
|-
| [[Sensamagic clan #Leapweek|leapweek comma]]
| quadsagu comma
| 4sg4
| 4398046511104 / 4236443047215
| {{monzo| 42 -25 -1 }}
| 64.811
|-
| 12&amp;197 comma
| quinlayo comma
| 5Ly-4
| 9265100944259205 / 9007199254740992
| {{monzo| -53 32 1 }}
| 48.874
|-
|-
| [[Leapday|leapday comma]]
| [[Leapday|leapday comma]]
| trisayo comma
| trisayo comma
| s<sup>3</sup>y3
| 3sy3
| 10737418240 / 10460353203
| 10737418240 / 10460353203
| {{monzo| 31 -21 1 }}
| {{monzo| 31 -21 1 }}
| 45.259
| 45.259
|-
|-
| [[Schismic-Pythagorean equivalence continuum|double large green comma]]
| [[Schismic–Pythagorean equivalence continuum|double large green comma]]
| lalagu comma
| lalagu comma
| LLg-2
| LLg-2
Line 74: Line 116:
| [[128/125|diesis]]<br>[[Augmented family|augmented comma]]
| [[128/125|diesis]]<br>[[Augmented family|augmented comma]]
| trigu comma
| trigu comma
| g<sup>3</sup>2
| 3g2
| 128 / 125
| 128 / 125
| {{monzo| 7 0 -3 }}
| {{monzo| 7 0 -3 }}
| 41.059
| 41.059
|-
| [[Marvel temperaments #Gracecordial|gracecordial comma]]
| trilayo comma
| 3Ly-3
| 17433922005 / 17179869184
| {{monzo| -34 20 1 }}
| 25.414
|-
|-
| [[Mirkwai clan #Kwai|kwai comma]]
| [[Mirkwai clan #Kwai|kwai comma]]
| quinsayo comma
| quinsayo comma
| s<sup>5</sup>y4
| 5sy4
| 5629499534213120 / 5559060566555523
| 5629499534213120 / 5559060566555523
| {{monzo| 50 -33 1 }}
| {{monzo| 50 -33 1 }}
Line 90: Line 139:
| g1
| g1
| 81 / 80
| 81 / 80
| {{monzo| 4 -1 -1 }}
| {{monzo| -4 4 -1 }}
| 21.506
| 21.506
|-
|-
Line 99: Line 148:
| {{monzo| 11 -4 -2 }}
| {{monzo| 11 -4 -2 }}
| 19.553
| 19.553
|-
| [[vulture comma]]
| sasaquadyo comma
| ss4y2
| 10485760000 / 10460353203
| {{monzo| 24 -21 4 }}
| 4.1998
|-
|-
| [[Schisma]]
| [[Schisma]]
Line 106: Line 162:
| {{monzo| -15 8 1 }}
| {{monzo| -15 8 1 }}
| 1.9537
| 1.9537
|-
| [[Luna comma]]
| sasaquintrigu comma
| ss15g5
| 274877906944 / 274658203125
| {{monzo| 38 -2 -15 }}
| 1.3843
|-
| [[Ennealimma]]
| satritribiyo comma
| s18y-3
| 7629394531250 / 7625597484987
| {{monzo| 1 -27 18 }}
| 0.8618
|}
|}


[[Category:5-limit]]
[[Category:5-limit]]
[[Category:Comma]]
[[Category:Lists of commas]]

Latest revision as of 23:13, 3 May 2025

A 5-limit comma is the amount which separates m1 fifths and m2 thirds from n octaves.

Name(s) Color Name Ratio Monzo Cents
classic diminished third
university comma 		trigubi comma 3g3 144 / 125 [4 2 -3⟩ 244.969
uncle comma sagu comma sg3 4096 / 3645 [12 -6 -1⟩ 201.956
minor whole tone yo comma y2 10 / 9 [1 -2 1⟩ 182.404
laconic comma latrigubi comma L3g2 2187 / 2000 [-4 7 -3⟩ 154.744
large limma
acute diatonic semitone
bug comma 		gugu comma gg2 27 / 25 [0 3 -2⟩ 133.238
diatonic semitone
father comma 		gubi comma g2 16 / 15 [4 -1 -1⟩ 111.731
major limma
mavila comma
pelogic comma 		layobi comma Ly1 135 / 128 [-7 3 1⟩ 92.179
quasisuper comma sasagu comma ssg3 8388608 / 7971615 [23 -13 -1⟩ 88.271
chromatic semitone
dicot comma 		yoyo comma yy1 25 / 24 [-3 -1 2⟩ 70.672
superpyth comma sayo comma sy2 20480 / 19683 [12 -9 1⟩ 68.719
12&163 comma quadlagu comma 4Lg-3 22876792454961 / 21990232555520 [-42 28 -1⟩ 68.426
leapweek comma quadsagu comma 4sg4 4398046511104 / 4236443047215 [42 -25 -1⟩ 64.811
12&197 comma quinlayo comma 5Ly-4 9265100944259205 / 9007199254740992 [-53 32 1⟩ 48.874
leapday comma trisayo comma 3sy3 10737418240 / 10460353203 [31 -21 1⟩ 45.259
double large green comma lalagu comma LLg-2 43046721 / 41943040 [-23 16 -1⟩ 44.966
diesis
augmented comma 		trigu comma 3g2 128 / 125 [7 0 -3⟩ 41.059
gracecordial comma trilayo comma 3Ly-3 17433922005 / 17179869184 [-34 20 1⟩ 25.414
kwai comma quinsayo comma 5sy4 5629499534213120 / 5559060566555523 [50 -33 1⟩ 21.799
syntonic comma
meantone comma
didymus comma 		gu comma g1 81 / 80 [-4 4 -1⟩ 21.506
Diaschisma sagugu comma sgg2 2048 / 2025 [11 -4 -2⟩ 19.553
vulture comma sasaquadyo comma ss4y2 10485760000 / 10460353203 [24 -21 4⟩ 4.1998
Schisma layo comma Ly-2 32805 / 32768 [-15 8 1⟩ 1.9537
Luna comma sasaquintrigu comma ss15g5 274877906944 / 274658203125 [38 -2 -15⟩ 1.3843
Ennealimma satritribiyo comma s18y-3 7629394531250 / 7625597484987 [1 -27 18⟩ 0.8618
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