It should be noted here that it is common in musicology to denote the pulse where a rhythm starts as pulse 0, however, instead of viewing it as the initial pulse it can also be viewed as the final pulse as at the point where a rhythmic pattern is repeated the pulse is the start of the next rhythmic pattern and at the same time it is the end of the last rhythmic pattern. I.e. whether we count a 4-pulse structure as 0, 1, 2, 3, 0, 1, 2, 3,… or 4, 1, 2, 3 4, 1, 2, 3, … is irrelevant. To make this theory more accessible for dancers we will count the final pulse instead of the initial pulse in this blog as when we count the steps in salsa classes we will usually count 1, 2 ,3, (4), 5, 6, 7, (8) instead of counting (0), 1, 2, 3, (4), 5, 6, 7.
An onset rotation of a rhythm is defined as a rotation where one of the onsets falls on to pulse 0 (or pulse 8 in the below examples). As the tresillo rhythm has exactly three onsets, there are exactly 3 onset rotations if we count the tresillo rhythm itself. To make this rhythm robust according to Toussaint, all three rotations need to be used in practice which is indeed the case as illustrated below.
If we graphically represent the tresillo pattern as a necklace based on the 3 onsets across 8 pulses represented as coloured pearls we obtain something like the following illustration:
If we rotate the tresillo pattern to the right until we obtain the next onset rotation we obtain the Nandon Bawaa bell pattern of the Dagarti people of Ghana which can also be found in Bulgaria and Namibia.
The last onset rotation is the rhythm known in Korea as Samhyon Toduri which is almost a mix between the tresillo and the nandon bawaa necklace having the onsets on beats 3, 5 and 8. This rhythm is also used in Eastern Angola, Bulgaria and Turkey and is a thirteenth century Indian tala called Mathya-Tisra.
All of the examples quoted so far are popular onset rotations of the tresillo pattern proving that the tresillo necklace is robust. However, other rotations exist as well (albeit less common) which do not have an onset on pulse 8. I.e. Judith Becker describes a bass-drum used in Burmese music which is effectively a rotation of tresillo although it is not an onset rotation:
