Table of 3-limit commas: Difference between revisions

A [[3-limit]] comma is the amount which separates m [[3/2|fifth]]<nowiki/>s from n [[octave]]<nowiki/>s. It is the simplest kind of comma a tuning may [[Tempering out|temper out]]. All commas not equal to the perfect fourth listed here generate interlaced pentatonic scales when tempered out.

!Name(s)

! colspan="2" |[[Color notation|Color Name]]

!Ratio

!Monzo

|{{monzo| -37 24}}

|1246.92

|{{monzo| 77 -48 }}

|1106.16

|{{monzo| -64 41 }}

|1080.155

|{{monzo| -45 29 }}

|1156.695

|{{monzo| -26 17 }}

|1133.235

|{{monzo| -80 51 }}

|999.705

|{{monzo| 69 -44 }}

|886.02

|{{monzo| -53 34 }}

|835.485

|{{monzo|29 -19}}

|1062.855

|{{monzo| 50 -31 }}

|1039.395

|{{monzo| 67 -43 }}

|1015.395

|{{monzo| -61 39 }}

|976.25

|{{Monzo|23 -14}}

|972.63

|{{monzo| -44 27}}

|952.785

|{{Monzo|-23 15}}

|929.325

|{{monzo| -61 38 }}

|925.71

|{{Monzo| 34 -21}}

|858.945

|{{Monzo| -31 20}}

|839.1

|{{monzo| 53 -33 }}

|835.485

|{{monzo| -58 37 }}

|772.335

|{{Monzo| -39 25}}

|748.875

|{{monzo| 45 -28}}

|745.26

|{{Monzo| -20 13}}

|725.415

|{{monzo| -85 54 }}

|705.57

|{{monzo| 83 -52 }}

|698.33

|Pythagorean wolf fifth, 11b-comma

|small wa 5th

|sw5

|{{monzo| 18 -11}}

|678.495

|47b-comma

|wa-47b comma

|w-47b

|

|{{monzo| 75 -47 }}

|610.115

|47-comma

|wa-47 comma

|w-47

|{{monzo| -74 47 }}

|591.885

|{{monzo| 67 -42 }}

|517.89

|{{monzo| 37 -23}}

|655.055

|{{monzo| -47 30 }}

|658.65

|{{monzo|29 -18}}

|564.81

|{{monzo| -36 23}}

|544.965

|Pythagorean wolf fourth, 11-comma

|Large wa 4th

|177147 / 131072

|{{monzo| -17 11}}

|521.505

|{{monzo| 63 -40 }}

|478.2

|{{Monzo| 21 -13}}

|474.585

|perfect fourth

|wa 4th

|w4

|[[4/3|4 / 3]]

|{{monzo| 2 -1}}

|498.045

|{{Monzo|-25 16}}

|431.28

|{{monzo| 78 -49 }}

|404.205

|{{monzo| 59 -37 }}

|427.665

|{{monzo| -71 45 }}

|387.975

|Pythagorean diminished fourth, 8-comma

|small wa 4th

|sw4

|{{Monzo| 13 -8 }}

|384.360

|{{monzo| -52 33 }}

|364.515

|{{monzo| 51 -32 }}

|337.44

|Pythagorean augmented second, 9-comma

|large wa 2nd

|Lw2

|{{Monzo| -14 9 }}

|317.595

|{{monzo| -79 50 }}

|404.205

|Pythagorean minor third, 3-comma

|wa 3rd

|w3

|{{Monzo| 5 -3 }}

|294.135

|{{monzo| -41 26 }}

|250.83

|{{monzo| 43 -27 }}

|247.215

|{{monzo| 62 -39 }}

|223.75

|{{monzo| -87 55 }}

|207.525

|whole tone

|wa 2nd

|w2

|[[9/8|9 / 8]]

|{{monzo| -3 2 }}

|203.91

|{{monzo| -68 43 }}

|184.065

|{{monzo| 100 -63 }}

|176.835

|[[31-comma_temperaments|31-comma]]

|wa-31 comma

|w-31

|{{monzo| -49 31 }}

|160.605

|{{monzo| 73 -46 }}

|110.07

|limma, Pythagorean minor second

|small wa 2nd

|sw2

|[[256/243|256 / 243]]

|{{monzo| 8 -5 }}

|90.225

|[[17-comma]]

|wa-17 comma

|ssw3

|134217728 / 129140163

|{{monzo| 27 -17 }}

|66.765

|70-comma

|wa-70 comma

|77-comma

|wa-77 comma

|w-77

|{{monzo| -122 77 }}

|50.535

|[[29-comma]]

|wa-29 comma

|w-29

|{{monzo| 46 -29 }}

|43.305

|{{monzo| -103 65}}

|-

|[[Pythagorean comma]]

|lalawa comma

or wa comma

|LLw-2

|{{monzo| -19 12 }}

|23.460

|[[41-comma]]

|wa-41 comma

|w-41

|{{monzo| 65 -41 }}

|19.845

|{{monzo| 149 -94 }}

|16.230

|200-comma, Pythagorean integer cents comma<!--the meaning of "integer cents" is ambiguous, because this comma is both near an integer in cents and involves integer cent fifths (702 cents), causing that term to be inconsistently used for one or the other-->

|wa-200 comma

|w-200

|{{monzo| 317 -200 }}

|8.9998

|[[Mercator's comma]], 53-comma

|wa-53 comma

|w-53

|{{monzo| -84 53 }}

|3.6150

|359-comma

|wa-359 comma

|w-359

|{{monzo| -569 359 }}

|1.8453

|[[Sasktel comma]]

|wa-306 comma

|w-306

|{{monzo| 485 -306 }}

|1.7697

|{{monzo| -1054 665 }}

|0.075575

|{{monzo| 24727 -15601 }}

|0.031499

|31867-comma

|wa-31867 comma

|w-31867

|{{monzo| -50508 31867 }}

|0.012577