THE NUMBERS, EXPLAINED
How to use this calculator.
left and right are positive integers up to 1000. Positions start at zero and exclude the end of the cycle. Shared points are derived exactly from the integer rhythm counts (multiples of cycle/gcd(left,right)).
Start with your inputs
Enter left rhythm event count (1-1000), right rhythm event count (1-1000), cycle length (seconds). Keep amounts in the units shown on each field. The example is a starting point, not a recommended value.
| Input | Example value |
|---|---|
| Left rhythm event count (1-1000) | 3 |
| Right rhythm event count (1-1000) | 4 |
| Cycle length (seconds) | 2 |
A worked example
With the example inputs above, left rhythm positions (s) is 0, 0.666667, 1.333333. Change the inputs to explore your own scenario.
| Result | Example answer |
|---|---|
| Left rhythm positions (s) | 0, 0.666667, 1.333333 |
| Right rhythm positions (s) | 0, 0.5, 1, 1.5 |
| Shared event positions (s) | 0 |
How this is calculated
Left rhythm positions (s)
left_seconds (seconds array): i * cycle_seconds / left for i = 0..left-1.
Right rhythm positions (s)
right_seconds (seconds array): j * cycle_seconds / right for j = 0..right-1.
Shared event positions (s)
shared_seconds (seconds array): k * cycle_seconds / gcd(left,right) for k = 0..gcd(left,right)-1, the positions where both rhythms coincide.
Symbols and units
- left
- Left rhythm event count (1-1000)
- right
- Right rhythm event count (1-1000)
- cycle_seconds
- Cycle length (seconds)
Use the units shown. A list keeps the order in which you enter its values. The symbol ^ means “raised to the power of”.
Assumptions and limits
left and right are positive integers up to 1000. Positions start at zero and exclude the end of the cycle. Shared points are derived exactly from the integer rhythm counts (multiples of cycle/gcd(left,right)).
Calculations use the values you enter. Blank or invalid inputs show an error instead of silently substituting zero. Results are displayed to useful precision; calculations retain the underlying numeric precision.
Questions about this tool
What does the result tell me?
Left rhythm positions (s); Right rhythm positions (s); Shared event positions (s). The result applies to the method and inputs described above. Check the units and assumptions before using it in a decision.
Why might another calculator differ?
Differences in units, rounding, timing or model definitions can produce different answers. Compare the input definitions and the method, rather than only the final number. For this tool: left and right are positive integers up to 1000. Positions start at zero and exclude the end of the cycle. Shared points are derived exactly from the integer rhythm counts (multiples of cycle/gcd(left,right)).
Are my inputs stored or sent to AI?
Calculations on this page happen in your browser. The separate AI question finder sends its submitted conversation to OpenAI; these calculator fields are not sent. Favourites and recent tool names are stored locally. A shared link contains the inputs you choose to include.
Further reading
Ableton Learning Music: beat and tempo ↗
Background reading; this does not imply endorsement or independent review of SumFizz.
Review status
Software example and browser checks are recorded in our quality report. No external expert review is claimed. Created with coding assistance; calculations run as ordinary browser code.
Read the quality report →