semi-comprehensive list of performable tuplets

version 1.0, written and maintained by CAK


About This List

What is a tuplet? By common definition it is a note that, when represented as a fraction, doesn't feature a power of 2 (1, 2, 4, 8, 16, etc.) as the denominator. The most common tuplet in existence is the triplet, which is three notes in the time of either two or four (3:2 or 3:4).

The following is a listing of all tuplets under the given conditions:

• Tuplet length is less than 15/16 of a measure and greater than 1/16 of a measure.

• One level of nested tuplets is included. A nested tuplet is basically a further subdivision of a regular tuplet. (example: three notes in the time of a 1/3 note, or three "1/9" notes) For the purpose of this list, nested tuplets with a denominator no greater than 15 are simply categorized as regular tuplets.

• Also included are tuplets generated from unconventional 16th-note groupings. (example: five notes in the time of seven 16th notes, or five "7/80" notes)

Have fun, and be sure to read the info below the list if you have trouble deciphering the fractions.



basic tuplets
1/ 3,5,6,7,9,10,11,12,13,14,15
2/ 3,5,7,9,11,13,15
3/ 5,7,10,11,13,14
4/ 5,7,9,11,13,15
5/ 6,7,9,11,12,13,14
6/ 7,11,13
7/ 9,10,11,12,13,15
8/ 9,11,13,15
9/ 10,11,13,14
10/ 11,13
11/ 12,13,14,15
12/ 13
13/ 14,15
14/ 15

total:64

based on groups of 16th notes
3/ 20,28,32,40,44
5/ 24,32,48,56,64,72
7/ 24,32,40,48,64,72,80,88,96,104
9/ 32,64,80,112,128
11/ 32,48,64,80,96,112,128,144,160
13/ 32,48,64,80,96,112,128,144,160,176,192
15/ 32,64,112,128,176,208,224

total:53

nested (one level)
2/ 21,25,27
3/ 22,25,26,35
4/ 21,25,27,33,35,39,45,49,55,63
5/ 18,21,22,26,27,28,33,36,39,42,44,49,52,54,63,66,77,78
6/ 35,49,55,65,77,91
7/ 18,20,22,26,27,30,33,36,39,44,45,50,52,54,55,60,65,66,75,
78,81,90,99,100,108,110

8/ 27,33,39,45,55,63,65,75,77,81,91,99,105,117,121
9/ 20,22,26,28,40,44,50,52,55,56,65,70,77,88,91,98,100,104,
110,121,130,140,143

10/ 33,39,77,91,99,117,121,143
11/24,26,28,30,36,39,42,45,52,56,60,65,70,72,75,78,84,90,91,
98,104,105,108,117,120,126,130,135,140,150,156,168,169

12/ 65,91,143,169
13/ 28,30,42,45,56,60,70,75,84,90,98,105,120,126,135,140,
150,154,165,168,180,194

14/ 45,75,135,165,195

total:177



Converting The Fractions To Ratios

tuplets based on 16th-note groups

Multiply top AND bottom of the fraction until the denominator is divisible by 16. Replace the new denominator with 16; the resultant fraction represents the 16th-note group upon which the tuplet is based. Now go back one step and divide the newer denominator by 16; the result represents the number of notes to be played in the time of the 16th-note group. An example...

tuplet: 3/28, 3/28 becomes 12/112
16th-note group: 12/16
112 / 16 = 7

tuplet interpreted as: seven notes in the time of 12/16

nested tuplets

Divide the denominator by a number between 1 and 16 (the result must always be a whole number and greater than the numerator). The resultant fraction represents the "root" tuplet, and the divisor represents the number of notes performed in the time of the root tuplet. An example...

nested tuplet: 2/25
25 / 5 = 5
root tuplet: 2/5

nested tuplet interpreted as: five notes in the time of 2/5

Additionally, some non-nested tuplets may be reinterpreted as nested tuplets in order to make performance easier...

tuplet: 2/9
9 / 3 = 3

tuplet interpreted as: three notes in the time of 2/3