Description
Interpolate their natural logarithms, exponentiate for ratio and convert interpolated log ratio to cents.
Frequency ratios express pitch relationships, while cents express their logarithm relative to an octave. Playback speed and pitch-preserving time changes obey different models; the relevant reference and physical assumptions must be supplied.
Interpolate their natural logarithms, exponentiate for ratio and convert interpolated log ratio to cents.
When to use this tool
Use Recording Pitch Drift Two Anchors when you need a stated pitch-ratio, reference or playback-speed term.
How to use the tool and how it works
- Enter firstTime, secondTime, firstRatio, secondRatio, time. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read interpolationFraction, ratio, cents. Use the output convention below.
Require ordered anchor times, query within them and positive anchor ratios. Interpolate their natural logarithms, exponentiate for ratio and convert interpolated log ratio to cents.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| firstTime | First Time | Required. Finite number. |
| secondTime | Second Time | Required. Finite number. |
| firstRatio | First Ratio | Required. Finite number; strictly above 0. |
| secondRatio | Second Ratio | Required. Finite number; strictly above 0. |
| time | Time | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| interpolationFraction | Interpolation Fraction | Required. Finite number. |
| ratio | Dimensionless ratio under the numerator/denominator convention above. | Required. Finite number. |
| cents | Cents | Required. Finite number. |
{
"input": {
"firstTime": 0,
"secondTime": 10,
"firstRatio": 1,
"secondRatio": 4,
"time": 5
},
"output": {
"interpolationFraction": 0.5,
"ratio": 2,
"cents": 1200
}
}Limitations and assumptions
- This is geometric interpolation, not linear-frequency interpolation. It models supplied drift between two anchors without estimating audio speed or calibration uncertainty.
- 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 calibrated audio measurements and the appropriate processing method for actual recordings. Retain cultural tuning context and verify reference frequency, speed history and instrument assumptions separately.
References
Similar or alternative tools
- Recording Pitch Reference Factor
Multiply measured frequency by 2^suppliedOctaveOffset and divide by reference.
- Archival Disc Speed Pitch Correction
Multiply frequency by target/source speed ratio, divide duration by it and express ratio as cents.