Description
Predict frequency as referenceFrequency×referenceLength/targetLength and return the supplied equalTensionDensity flag.
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.
Predict frequency as referenceFrequency×referenceLength/targetLength and return the supplied equalTensionDensity flag.
When to use this tool
Use Instrument String Speaking Length Ratio when you need a stated pitch-ratio, reference or playback-speed term.
How to use the tool and how it works
- Enter referenceLength, targetLength, referenceFrequency, equalTensionDensity. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read lengthRatio, predictedFrequency, assumptionSatisfied. Inspect assumptionSatisfied before interpreting the associated values.
Require positive reference/target lengths and reference frequency. Predict frequency as referenceFrequency×referenceLength/targetLength and return the supplied equalTensionDensity flag.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| referenceLength | Reference Length | Required. Finite number; strictly above 0. |
| targetLength | Target Length | Required. Finite number; strictly above 0. |
| referenceFrequency | Reference Frequency | Required. Finite number; strictly above 0. |
| equalTensionDensity | Equal Tension Density | Required. Boolean. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| lengthRatio | Length Ratio | Required. Finite number. |
| predictedFrequency | Predicted Frequency | Required. Finite number. |
| assumptionSatisfied | Echo of equalTensionDensity, not verification; prediction is computed even when false. | Required. Boolean. |
{
"input": {
"referenceLength": 0.6,
"targetLength": 0.4,
"referenceFrequency": 220,
"equalTensionDensity": true
},
"output": {
"lengthRatio": 1.4999999999999998,
"predictedFrequency": 330,
"assumptionSatisfied": true
}
}Limitations and assumptions
- The prediction is still calculated when the assumption flag is false. The ideal string law needs equal tension and linear density; stiffness, end effects and actual instrument setup are not verified.
- 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.
- Public Tuning Reference Pitch Shift
Scale by target/original and return factor, shifted frequency and 1200×log2 factor cents.