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.

![[Kite's color notation|Color Name]]

! Ratio

! Monzo

! Cents

| limma, Pythagorean minor second

|sw2, small wa 2nd

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

| {{Monzo| 8 -5 }}

| 90.225

|LLw-2, wa comma

| 531441/524288

| [[17-comma]]

|ssw3, wa-17 comma

|s⁴w4, wa-29 comma

| 70368744177664/68630377364883

| 43.305

|s⁶w5, wa-41 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 -->

|w-200, wa-200 comma

|L⁸w-6, wa-53 comma

| 19383245667680019896796723/

19342813113834066795298816

![[Kite's color notation|Color name]]

! Ratio

! Monzo

! Cents

| Twenty-two thirds limma

|L³y²²-6, triple large 22-fold yo neg. 6th

| sibbolet

|L⁴y²⁵-7, quad-large 25-fold yo neg. 7th

| {{Monzo| -58 0 25 }}

| 57.843

| Hunt 5-cycle comma

|L⁴y²⁸-8, quad-large 28-fold yo neg 8ve

| acute thirds comma

|s⁴g³¹9

| 34-5-comma

|s⁵g³⁴10

| Schismic thirds chromatic semitone

|L⁸y⁵³-14

| 59-5-comma

|s⁹g⁵⁹16

|  

| {{Monzo| 137 0 -59 }}

| 7.4909

| 10-15-comma

|

|  

| {{Monzo| -39 10 10 }}

| 82.687

| 11-15-comma

|

| {{Monzo| 43 -11 -11 }}

| 29.044

| 32-15-comma

|

| Huntian 15-cycle comma

|

| 56-syntonic comma

|

|  

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

| 4.3522

| 53-15-comma

|

| {{Monzo| -207 53 53 }}

| 78.242

| 76-15-comma

|

|  

| {{Monzo| 297 -76 -76 }}

| 91.578

| [[250/243|250 / 243]]

| diesis, augmented comma

| [[128/125|128 / 125]]

| {{Monzo| 7 0 -3 }}

| unicorn

| syntonic / Didymos / meantone comma

|g1, gu unison, gu comma

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

| [[Maquila family|maquila comma]]

|s³g¹⁷6, triple small 17-fold gu comma

| [[diaschisma]]

|sgg2, small gugu 2nd, gugu comma

| ditonma

|LLy¹³-4, double large 13-fold yo neg. 4th

| [[misty comma]]

|ssg³3, double small triple gu 3rd

| [[pental comma]]

|L³g⁵-2, triple large quintgu negative 2nd

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

|LLg⁶1, double large sixfold gu unison

| quartonic

|sy¹¹-2, small 11-fold yo negative 2nd

| medium semicomma, [[sensipent comma]]

|g⁷2, sevenfold gu 2nd

|sg⁸3, small eightfold gu 3rd

| [[semicomma]], Fokker comma

|Ly⁷-3, large sevenfold yo negative 3rd

| [[escapade comma]]

|ssg⁹4, double small ninefold gu 4th

| [[kleisma]], semicomma majeur

|y⁶-2, sixfold yo negative 2nd

| [[qintosec comma]]

|s⁴g¹⁰5, quad-small tenfold gu 5th

| unidecma

|Lg¹²2, large 12-fold gu 2nd

| [[mutt comma]]

|L³y²¹-6, triple large 21-fold yo neg. 6th

| [[amity comma]]

|sy⁵1, small quintyo unison

| [[parakleisma]]

|g¹³3, 13-fold gu 3rd

| gammic comma

|Ly²⁰-5, large 20-fold yo negative 5th

| 95105071448064 / 95367431640625

| [[vulture comma]]

|ssy⁴2, double small quadyo 2nd

| 23-3/5-comma

|g²³5

|  

| {{Monzo| 17 23 -23 }}

| 59.750

| 34-3/5-comma

|y³⁴3

|-

| 53-3/5-comma

|  

| {{Monzo| -39 -53 53 }}

| 71.012

! Ratio

! Monzo

! Cents

| hexadecatone comma, 16-7-comma

|  

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

| 98.785

| 21-7-comma

|  

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

| 54.656

| Hunt 7-cycle comma

| German sixth comma

| 33.603

|-

| large deep red comma

| 6561 / 6272

| {{Monzo| -7, 8, 0 -2 }}

| 77.988

| 65.182

| {{Monzo| 1123 0 0 -400 }}

| Huntian 21-cycle comma

| 33-21-comma

| 8-35-comma

|  

| {{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 }}

|-

| blackjackisma

| squalentine

| keema

| gariboh

| nuwell

| tolerma

| mirwomo