Resolution calculator
How many bars until a scale pattern lands back on the downbeat with the accent? Two clocks are phasing against each other — the bar, and the pattern — and this is the least common multiple of them.
It works for any scale size, so it is just as useful on the major scale or a pentatonic. Six-note scales simply happen to win.
| subdivision | 3sTisra | 4sChatusra | 5sKhanda | 6s | 7sMisra | 9sSankeerna |
|---|---|---|---|---|---|---|
| 8ths | 3bars24 notes · 9s | 3bars24 notes · 9s · locked | 15bars120 notes · 43s | 3bars24 notes · 9s | 21bars168 notes · 60s | 9bars72 notes · 26s |
| triplets | 1bar12 notes · 3s · locked | 1bar12 notes · 3s · locked | 5bars60 notes · 14s | 1bar12 notes · 3s · locked | 7bars84 notes · 20s | 3bars36 notes · 9s |
| 16ths | 3bars48 notes · 9s | 3bars48 notes · 9s · locked | 15bars240 notes · 43s | 3bars48 notes · 9s | 21bars336 notes · 60s | 9bars144 notes · 26s |
| sextuplets | 1bar24 notes · 3s · locked | 1bar24 notes · 3s · locked | 5bars120 notes · 14s | 1bar24 notes · 3s · locked | 7bars168 notes · 20s | 3bars72 notes · 9s |
Gold resolves inside four bars and is camera-friendly. Amber is usable but long. Red will lose a room. “Locked” means the accent already returns on the very next downbeat — only 5 and 7 genuinely fight a 4/4 bar.
Shortest combinations for this setting
The practical lesson for teaching: odd groupings want triplet subdivisions. Fives in straight sixteenths takes 15 bars; the same fives in eighth-note triplets takes 5.
The groupings have names
Counting in 3s, 4s, 5s, 7s and 9s is the Carnatic gati system, and “resolving on the one” is landing on samam. The vocabulary is older than the idea of practising scales this way.
Tisra · 3
Ta Ki Ta
from tri, three
Chatusra · 4
Ta Ka Di Mi
caturaśra, four-sided
Khanda · 5
Ta Din Gi Na Tom
piece, section
Misra · 7
Ta Ka Di Mi Ta Ki Ta
mixed — because 7 = 3 + 4
Sankeerna · 9
Ta Ka Di Mi Ta Din Gi Na Tom
complex — because 9 = 4 + 5
And the ladders have names too
Running 3 → 4 → 5 → 6 → 7 is srotovaha yati, the image being a river widening from its source. Its mirror is gopuccha — a cow’s tail, tapering. There are six of these, not five.
Sama
5 – 5 – 5 – 5 – 5
even
Srotovaha
3 – 4 – 5 – 6 – 7
a river widening from its source
Gopuccha
7 – 6 – 5 – 4 – 3
a cow's tail, tapering
Mridanga
3 – 4 – 5 – 4 – 3
the drum — narrow ends, fat middle
Damaru
5 – 4 – 3 – 4 – 5
hourglass drum — pinched waist
Vishama
4 – 7 – 3 – 9 – 5
uneven, free-form