EXAMPLE 1
Third partial
55 Hz × 3
165.00 Hz · E3 +2¢
The natural perfect fifth sits about two cents above its 12-TET counterpart.
Overtone calculator
Harmonic Series Calculator
Build the first sixteen partials above any fundamental, inspect their frequencies and see where natural harmonics diverge from equal-tempered notes.
FreeNo loginWorks offlineWeb and desktop
Core formula
partial frequency f(n) = fundamental × n
idealized amplitude a(n) = 1 / n
MIDI position = 69 + 12 × log2(f(n) / A4)
cents offset = (MIDI position - nearest note) × 100
The amplitude rule describes the simple playback model in Amanita; real instruments emphasize and suppress partials according to their construction.
The harmonic series in numbers
A harmonic series contains integer multiples of a fundamental frequency. If the fundamental is 55 Hz, its second partial is 110 Hz, the third is 165 Hz, and so on.
Octave harmonics align exactly with equal temperament, but many other partials do not. The fifth partial is close to a major third and the seventh is noticeably flatter than the equal-tempered minor seventh. Amanita shows that difference in cents and lets you hear it.
Worked examples
Concrete values you can verify in the calculator and transfer directly to a production session.
EXAMPLE 2
Fifth partial
55 Hz × 5
275.00 Hz · C#4 -14¢
This natural major third is visibly and audibly flatter than the equal-tempered note.
EXAMPLE 3
Seventh partial
55 Hz × 7
385.00 Hz · G4 -31¢
The harmonic seventh falls far below the 12-TET minor seventh and has a distinctive color.
| Partial | Frequency | Nearest note | Offset |
|---|---|---|---|
| 1× | 55.00 Hz | A1 | 0.0 cents |
| 2× | 110.00 Hz | A2 | 0.0 cents |
| 3× | 165.00 Hz | E3 | +2.0 cents |
| 4× | 220.00 Hz | A3 | 0.0 cents |
| 5× | 275.00 Hz | C#4 | -13.7 cents |
| 6× | 330.00 Hz | E4 | +2.0 cents |
| 7× | 385.00 Hz | G4 | -31.2 cents |
| 8× | 440.00 Hz | A4 | 0.0 cents |
Use it in a session
The calculator is deliberately direct: set the musical context, inspect the result and copy it where you need it.
- Choose a fundamentalSelect a note and octave to establish the first partial.
- Inspect the overtone ladderCompare each multiple with its nearest 12-TET note and cents offset.
- Audition partialsToggle harmonics, play them together or sweep upward through the series.
Where it helps
Additive synthesis
Choose partials and understand the pitch structure behind a complex tone.
EQ decisions
Predict harmonic regions above a bass note or resonant source.
Timbre analysis
Relate brightness and tone color to the strength of upper partials.
Just intonation
Compare natural harmonic intervals with their equal-tempered approximations.
Studio note: The first few partials contribute most strongly to perceived pitch and chord color. Start with 1× through 6× before adding the more dissonant upper harmonics.
Calculate it in Amanita
Open the exact tool with your saved tempo and tuning values intact. Nothing to install, no account and no ads.