Small comma: Difference between revisions

A '''comma''' is a small interval that occurs in [[just intonation]], between two intervals which are close in pitch. Commas are always greater than 1 (0 [[cent]]s) and not a power such as a square or cube of any other interval, and generally in a [[Harmonic Limit|low prime limit]]. The word is often used in reference to [[Regular Temperaments|regular tempering]] when the comma is ''[[tempering_out|tempered out]]'', which is to say reduced to a unison, by the temperament, thereby equating the intervals separated by that comma. For example the Syntonic or Didymus comma of 81/80, which occurs between [[10/9]] and [[9/8]], as well as [[81/64]] and [[5/4]], is tempered out by [[Meantone|meantone temperament]]. Commas are usually written as ratios, but they can also be written as monzos. The following lists mostly give both forms, as well as the size in [[cent]]s.

For commas over 100 cents in size, see [[Large commas]]; and for commas under 3.5 cents in size, see [[Unnoticeable commas]]

Due to the wide range of sizes, cents values here and on the other commas pages are listed to 5 significant digits, instead of to a fixed number of decimal places as is the [[conventions|convention]] elsewhere on the wiki.

! colspan="2" |[[Kite's color notation|Color Name]]

| limma, Pythagorean minor second

| small wa 2nd

| sw2

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

| {{Monzo| 8 -5 }}

| 90.225

| wa comma

| [[17-comma]]

| [[29-comma]]

| s⁴w4

|-

| [[41-comma]]

| wa-41 comma

| s⁶w5

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

| wa-53 comma

| L⁸w-6

| 19383245667680019896796723 /<br>19342813113834066795298816

| {{Monzo| -84 53 }}

| 3.6150

| 70-comma

| wa-70 comma

| s¹⁰w8

| 77-comma

| wa-77 comma

| L¹¹w-8

| 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

! colspan="2" |[[Kite's color notation|Color Name]]

| Twenty-two thirds limma

| Hunt 5-cycle comma

|

| L⁴y²⁸-8

| 37252902984619140625 / 36893488147419103232

| {{Monzo| -65 0 28 }}

| 34-5-comma

| {{Monzo| -123 0 53 }}

| 74.627

| 10-15-comma

|

|-

| 11-15-comma

| 32-15-comma

|

|

| Huntian 15-cycle comma

|

|

|  

| {{Monzo| 168 -43 -43 }}

| 4.4453

| 56-syntonic comma

|

|

| {{Monzo| -225 224 -56 }}

| 4.3522

| 54-15-comma

|

|

| 76-15-comma

|

|

| ripple

| quintgu 2nd

| g⁵2

| 6561 / 6250

| {{Monzo| -1 8 -5 }}

| 84.071

| doublewide

| {{Monzo| -9 -6 8 }}

| 78.780

| [[25/24|25 / 24]]

| 60.611

| minimal diesis, [[tetracot comma]]

| quadyo comma

| sy⁴1

| 20000 / 19683

| {{Monzo| 5 -9 4 }}

| 27.660

| roda

|

| ssy³2

| sy¹⁷-3

| syntonic / Didymos / meantone

| gu comma

| [[81/80|81 / 80]]

| [[Maquila family|maquila comma]]

|

| s³g¹⁷6

| [[diaschisma]]

| gugu comma

| ditonma

|

| LLy¹³-4

| [[misty comma]]

|

| ssg³3

| [[pental comma]]

|

| L³g⁵-2

| [[graviton]], [[Gravity family|gravity]] comma

|

| LLg⁶1

| quartonic

|

| sy¹¹-2

| medium semicomma, [[sensipent comma]]

|

| g⁷2

|

| sg⁸3

| [[semicomma]], Fokker comma

|

| Ly⁷-3

| [[escapade comma]]

|

| ssg⁹4

| [[kleisma]], semicomma majeur

| sixfold yo comma

| y⁶-2

| [[qintosec comma]]

|

| s⁴g¹⁰5

| unidecma

|

| Lg¹²2

| [[mutt comma]]

|

| L³y²¹-6

| [[amity comma]]

|

| sy⁵1

| [[parakleisma]]

|

| g¹³3

| gammic comma

|

| Ly²⁰-5

| [[vulture comma]]

|

| ssy⁴2

| 23-3/5-comma

| {{Monzo| 17 23 -23 }}

| 59.750

| 34-3/5-comma

| {{Monzo| -25 -34 34 }}

| 68.196

| y⁵³7

! colspan="2" | [[Kite's color notation|Color Name]]

| Archytas' 1/3-tone

| zo 2nd

| z2

| 28 / 27

| {{Monzo| 2 -3 0 1 }}

| 62.961

| minor semitone

| zogu 2nd

| zg2

| 21 / 20

| {{Monzo| -2 1 -1 1 }}

| 84.467

| hexadecatone comma, 16-7-comma

| {{Monzo| 45 0 0 -16 }}

|-

| 21-7-comma

| 576460752303423488 / 558545864083284007

| {{Monzo| 59 0 0 -21 }}

| 54.656

| German sixth comma

| 37-7/5-comma

|

|  

| {{Monzo| 18 0 37 -37 }}

|-

| 39-7/5-comma

| {{Monzo| 19 0 39 -39 }}

| sr⁵-2

| {{Monzo| 22 -5 0 -5 }}

| 46.095

|  

|

|

| Huntian 21-cycle comma

|

|

| 33-21-comma

|

|

| 8-35-comma

|

| LLz⁸y⁸2

| 2251875390625 / 2199023255552

| {{Monzo| -41 0 8 8 }}

| 41.117

| 15-35-comma

| {{Monzo| -159 0 31 31 }}

| 9.3282

| 39-35-comma

|

|

| {{Monzo| -200 0 39 39 }}

| 50.445

|

|

| [[50/49|50 / 49]]

| {{Monzo| 1 0 2 -2 }}

| {{Monzo| 7 8 0 -7 }}

|-

| {{Monzo| 6 -2 0 -1 }}

| squalentine

|

|

| keema

| zo-triple-yo comma

| zy³1