Notes are named using scientific pitch notation. For example, C2 corresponds to the lowest string on a cello, C4 is middle C, and a viola's highest string is tuned to A4.
This harmonics calculator uses 12-tone equal temperament to calculate the frequencies of notes. Note input may be converted to its enharmonic equivalent. For example, if you enter Gb6, this will be interpreted as equivalent to F#6.
- The fundamental for which a match was found.
- The number of note in the harmonic series of the fundamental. For example, 1 is the fundamental itself; 2 is the note one octave above it; 3 is the fifth above that etc.
- Error in cents
- The pitch difference between the harmonic and the checked note in 12-tone equal temperament. This may be important in ensembles that include equally tempered instruments such as a piano. If the error is high, the note you are producing by playing the harmonic will sound out of tune with the equally tempered instrument.
- Largest prime
- The largest prime factor of the harmonic number. If you are using a variety of just intonation, this may help you decide whether a match is acceptable: Tunings which build scales using the harmonic series usually impose a prime limit. For example, 5-limit tuning will only use harmonics that are powers of 2, 3, or 5, or a combination of them; while the stricter Pythagorean tuning is 3-limit, which means only 2 and 3 are allowed. Please note that this tool converts notes to frequencies using equal temperament. If you want to create scales based on pure intonation, you'll have to use other tools or do your own calculations.
The following are currently fixed settings:
- Concert pitch is set to A4 = 440Hz. This only matters for the reported frequency of the note input. You can use this tool even if you tune to a different standard.
- The lowest note the tool will consider is C0; the highest is G9. There needs to be some limit for performance reasons, and I believe this should cover most use cases in music.
- Similarly, harmonics are only considered up to number 16 (4 octaves above the fundamental). Some limit is necessary for performance reasons and while it could be set a good deal higher, I think any higher harmonics would be impractical to use in music anyway.
- Harmonics are only reported as matches if the error is within 50 cents.