Description
Use exact integer modular arithmetic for nonnegative step remainder and add its floor-based carry to octave, exporting safe numeric integers.
Cyclic musical positions need a cycle length, origin and tie policy. Negative positions and half-cycle differences require careful modular conventions, especially when returning both a local phase and a whole-cycle carry.
Use exact integer modular arithmetic for nonnegative step remainder and add its floor-based carry to octave, exporting safe numeric integers.
When to use this tool
Use Tuning Reference Octave Carry when you need an explicit rhythmic or tuning-cycle coordinate calculation.
How to use the tool and how it works
- Enter step, octave, stepsPerOctave. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read normalizedStep, normalizedOctave. Use the output convention below.
Require integer step/octave and positive integer stepsPerOctave. Use exact integer modular arithmetic for nonnegative step remainder and add its floor-based carry to octave, exporting safe numeric integers.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| step | Step | Required. Safe integer. |
| octave | Octave | Required. Safe integer. |
| stepsPerOctave | Steps Per Octave | Required. Safe integer; minimum 1. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| normalizedStep | Normalized Step | Required. Safe integer. |
| normalizedOctave | Normalized Octave | Required. Safe integer. |
{
"input": {
"step": 14,
"octave": 4,
"stepsPerOctave": 12
},
"output": {
"normalizedStep": 2,
"normalizedOctave": 5
}
}Limitations and assumptions
- Negative steps carry into the prior octave. The supplied step system is not assumed twelve-tone and no frequency or cultural tuning standard is inferred.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Use the intended musical notation and source annotations to establish the cycle and origin. A numerical wrap cannot determine meter, tuning practice or cultural meaning by itself.
References
Similar or alternative tools
- Public Rhythm Cycle Phase Shift
Add with exact integer arithmetic, return nonnegative phase modulo length and floor-based cycle carry as safe numeric integers.
- Source Tuning Step Ratio
Return periodRatio^(steps/stepsPerPeriod).