THE NUMBERS, EXPLAINED
How to use this calculator.
Signed interval: positive when to_hz is above from_hz, negative when below. Nearest semitone uses round-half-toward-positive-infinity.
Start with your inputs
Enter from frequency (hz), to frequency (hz). Keep amounts in the units shown on each field. The example is a starting point, not a recommended value.
| Input | Example value |
|---|---|
| From frequency (Hz) | 440 |
| To frequency (Hz) | 660 |
A worked example
With the example inputs above, frequency ratio is 1.5. Change the inputs to explore your own scenario.
| Result | Example answer |
|---|---|
| Frequency ratio | 1.5 |
| Interval (cents) | 701.955001 |
| Nearest interval (semitones) | 7 |
How this is calculated
Frequency ratio
ratio (dimensionless): to_hz divided by from_hz.
Interval (cents)
cents (cents): 1200 * log2(ratio); one octave is 1200 cents, so the value is signed by the direction of the interval.
Nearest interval (semitones)
nearest_semitones (semitones): cents/100 rounded to the nearest integer, with halves rounded toward positive infinity.
Symbols and units
- from_hz
- From frequency (Hz)
- to_hz
- To frequency (Hz)
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
Signed interval: positive when to_hz is above from_hz, negative when below. Nearest semitone uses round-half-toward-positive-infinity.
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?
Frequency ratio; Interval (cents); Nearest interval (semitones). 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: Signed interval: positive when to_hz is above from_hz, negative when below. Nearest semitone uses round-half-toward-positive-infinity.
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
UNSW Music Acoustics: note names, MIDI numbers and frequencies ↗
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.
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