Calculates partials for harmonic & subharmonic (utonal) series using
scaling, exponent and addition constants. Output is tab-delimited for Excel, with MIDI
mapping and cents adjustment.
Auto-filled from note+octave; editable for fine
tuning.
1.0 = normal
1.0 = normal
Add or subtract Hz as per formula
Harmonic / Subharmonic Table
#
Frequency (Hz)
MIDI #
Keyboard Key
Pitch
Adjustment (cents)
Play
No harmonics
generated yet — click Generate.
Partial Frequency MIDI# KeyboardKey Pitch Adjustment
(cents)
Frequencies shown to 2 decimal places; internal calculations use full
precision. MIDI numbers rounded to nearest integer. Adjustment = cents difference between
frequency and rounded MIDI note.
This Harmonic Series Calculator helps you compute the sequence of harmonic overtones and
frequency intervals from a given base pitch. Enter a base frequency in hertz (Hz) to display corresponding
harmonics, ratios, and pitch relationships — ideal for musicians, acousticians, and sound designers.
Formulas used:
Harmonics:
f_n = f0 * ( s*(n-1) + 1 )^e + α
Subharmonics (Utonality):
f_n = f0 * ( s*(n-1) + 1 )^e - α
Where:
f0 = fundamental frequency (Hz)
s = scaling factor
n = partial number (1..N)
e = exponent
α = frequency addition (Hz)
Quantize: microtones quantized by rounding semitone value to selected fraction.
Use cases
Study overtone structure and timbre components.
Create additive synthesis patches with custom partials.
Compare harmonic partials to equal-tempered MIDI notes using cents adjustment.
Export data to Excel/DAW for analysis or tuning work.
FAQ
Utonality (subharmonics) are frequencies below the
fundamental produced by inverting the harmonic series (partials like 1/2, 1/3
... of the fundamental). This tool approximates subharmonics using the provided
formula.
Quantization rounds microtonal pitches to the nearest
fraction of a semitone (1/4-tone, 1/8-tone etc.), useful for mapping to
microtonal systems or simplifying data before export.