Small comma: Difference between revisions

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== Definition ==
== Definition ==
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. Except for the 3-limit commas, the [[Color notation|color name]] refers to both the comma and the temperament created when it is tempered out.
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. The [[Color notation|color name]] refers to both the comma and the temperament created when it is tempered out, except for 3-limit commas, which create edos.


For commas over 100 cents in size, see [[Large commas]]; and for commas under 3.5 cents in size, see [[Unnoticeable commas]]
For commas over 100 cents in size, see [[Large commas]]; and for commas under 3.5 cents in size, see [[Unnoticeable commas]]
Line 90: Line 90:
! [[Cents]]
! [[Cents]]
|-
|-
| Double large yoyo negative 2nd
| double large yoyo negative 2nd
| lala-yoyo
| lala-yoyo
| LLyy-2
| LLyy-2
Line 287: Line 287:
|-
|-
| small diesis, [[magic comma]]
| small diesis, [[magic comma]]
| quinyo
| laquinyo
| Ly<sup>5</sup>-2
| Ly<sup>5</sup>-2
| 3125 / 3072
| 3125 / 3072
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|-
|-
| [[Würschmidt comma]]
| [[Würschmidt comma]]
| saquabigu
| saquadbigu
| sg<sup>8</sup>3
| sg<sup>8</sup>3
| 393216 / 390625
| 393216 / 390625
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|-
|-
| 21-15-comma
| 21-15-comma
|
|tribila-septriyo
|
|L<sup>6</sup>y<sup>21</sup>-8
|  
|  
| {{Monzo| -82 21 21 }}
| {{Monzo| -82 21 21 }}
Line 539: Line 539:
|-
|-
| acute thirds comma
| acute thirds comma
|
|quadsa-thirty-wegu
| s<sup>4</sup>g<sup>31</sup>9
| s<sup>4</sup>g<sup>31</sup>9
|  
|  
Line 546: Line 546:
|-
|-
| 32-15-comma
| 32-15-comma
|
|tritrila-quadquadbiyo
|
|L<sup>9</sup>y<sup>32</sup>-12
|  
|  
| {{Monzo| -125 32 32 }}
| {{Monzo| -125 32 32 }}
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|-
|-
| 34-5-comma
| 34-5-comma
|
|quinsa-sebigu
| s<sup>5</sup>g<sup>34</sup>10
| s<sup>5</sup>g<sup>34</sup>10
|  
|  
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| Schismic thirds chromatic semitone
| Schismic thirds chromatic semitone
|
|
| L<sup>8</sup>y<sup>53</sup>-14
|  
|  
|  
| {{Monzo| -123 0 53 }}
| {{Monzo| -123 0 53 }}
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| 59-5-comma
| 59-5-comma
|
|
| s<sup>9</sup>g<sup>59</sup>16
|  
|  
|  
| {{Monzo| 137 0 -59 }}
| {{Monzo| 137 0 -59 }}
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| 84.467
| 84.467
|-
|-
| Laruru negative 2nd
| laruru negative 2nd
| laruru
| laruru
| Lrr-2
| Lrr-2
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|-
|-
| blackjackisma
| blackjackisma
| lasepruaquabiyo
| lasepru'aquadbiyo
| Lr<sup>7</sup>y<sup>8</sup>-6
| Lr<sup>7</sup>y<sup>8</sup>-6
| 854296875 / 843308032
| 854296875 / 843308032
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|-
|-
| squalentine
| squalentine
| laquadzoatrigu
| laquadzo'atrigu
| Lz<sup>4</sup>g<sup>3</sup>3
| Lz<sup>4</sup>g<sup>3</sup>3
| 64827 / 64000
| 64827 / 64000
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|-
|-
| gariboh
| gariboh
| triruaquinyo
| triru'aquinyo
| r<sup>3</sup>y<sup>5</sup>-3
| r<sup>3</sup>y<sup>5</sup>-3
| 3125 / 3087
| 3125 / 3087
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|-
|-
| nuwell
| nuwell
| quadruayo
| quadru'ayo
| r<sup>4</sup>y-3
| r<sup>4</sup>y-3
| 2430 / 2401
| 2430 / 2401
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|-
|-
| quince
| quince
| lasepzoagugu
| lasepzo'agugu
| Lz<sup>7</sup>gg4
| Lz<sup>7</sup>gg4
| 823543 / 819200
| 823543 / 819200
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|-
|-
| mirkwai
| mirkwai
| quinruaquadyo
| quinru'aquadyo
| r<sup>5</sup>y<sup>4</sup>-4
| r<sup>5</sup>y<sup>4</sup>-4
| 16875 / 16807
| 16875 / 16807
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|-
|-
| hemimage
| hemimage
| satrizoagu
| satrizo'agu
| sz<sup>3</sup>g3
| sz<sup>3</sup>g3
| 10976 / 10935
| 10976 / 10935
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|-
|-
| 8-35-comma
| 8-35-comma
| lala-quabizoyo
| lala-quadbizoyo
| LLz<sup>8</sup>y<sup>8</sup>2
| LLz<sup>8</sup>y<sup>8</sup>2
| 2251875390625 / 2199023255552
| 2251875390625 / 2199023255552
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|-
|-
| hexadecatone comma, 16-7-comma
| hexadecatone comma, 16-7-comma
| sasa-quaquadru
| sasa-quadquadru
| ssr<sup>16</sup>-6
| ssr<sup>16</sup>-6
| 35184372088832 / 33232930569601
| 35184372088832 / 33232930569601
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|-
|-
| quarter tone comma
| quarter tone comma
| quinquinrugu
|  
|
|
|  
|  
Line 1,153: Line 1,153:
| 80.537
| 80.537
|-
|-
| Lalu unison
| lalu unison
| lalu
| lalu
| L1u1
| L1u1
Line 1,203: Line 1,203:
|-
|-
| thuja comma
| thuja comma
| saquinluayo
| saquinlu'ayo
| s1u<sup>5</sup>y2
| s1u<sup>5</sup>y2
| 163840 / 161051
| 163840 / 161051
Line 1,280: Line 1,280:
|-
|-
| orgonisma
| orgonisma
| satriluaruru
| satrilu'aruru
| s1u<sup>3</sup>rr1
| s1u<sup>3</sup>rr1
| 65536 / 65219
| 65536 / 65219
Line 1,572: Line 1,572:
| 50.184
| 50.184
|-
|-
|
|solu 2nd
| solu
| solu
| 17o1u2
| 17o1u2
Line 1,586: Line 1,586:
| 34.283
| 34.283
|-
|-
|
|sutho unison
| sutho
| sutho
| 17u3o1
| 17u3o1
Line 1,593: Line 1,593:
| 33.617
| 33.617
|-
|-
|
|soruyo unison
| soruyo
| soruyo
| 17ory1
| 17ory1
Line 1,607: Line 1,607:
| 14.730
| 14.730
|-
|-
|
|suruyo comma
| suruyo
| suruyo
| 17ury-2
| 17ury-2
Line 1,701: Line 1,701:
| 88.801
| 88.801
|-
|-
|
|nutho unison
| nutho
| nutho
| 19u3o1
| 19u3o1
Line 1,708: Line 1,708:
| 44.970
| 44.970
|-
|-
|
|noru unison
| noru
| noru
| 19or1
| 19or1
Line 1,715: Line 1,715:
| 30.642
| 30.642
|-
|-
|
|nuruyo comma
| nuruyo
| nuruyo
| 19ury-2
| 19ury-2
Line 1,722: Line 1,722:
| 25.840
| 25.840
|-
|-
|
|nogugu 2nd
| nogugu
| nogugu
| 19ogg2
| 19ogg2
Line 1,743: Line 1,743:
| 18.128
| 18.128
|-
|-
|
|noluzo 2nd
| noluzo
| noluzo
| 19o1uz2
| 19o1uz2
Line 1,757: Line 1,757:
| 11.352
| 11.352
|-
|-
|
|nosugu unison
| nosugu
| nosugu
| 19o17ug1
| 19o17ug1
Line 1,778: Line 1,778:
| 8.2637
| 8.2637
|-
|-
|
|nusu comma
| nusu
| nusu
| 19u17u-2
| 19u17u-2