Spectral Calculator
Combination tones, reinforced partials, implied fundamentals.
What combination tones are
When two frequencies sound together loudly enough, the nonlinearities of the ear (and of most instruments) produce additional tones at their sum, their difference, and at second-order products. A 660 Hz and 440 Hz dyad generates a difference tone at 220 Hz — an octave below the lower note — which is why a played perfect fifth feels anchored by an invisible bass. Tartini tones are the classical name for these difference-frequency products, first described by the violinist Giuseppe Tartini in the 1700s.
What the calculator does
Enter two or more input frequencies (as Hz or as pitches). For each pair the module computes:
- Sum tone — f1 + f2.
- Difference tone — |f1 − f2|, the classical Tartini.
- Tartini second-order — 2f1 − f2 and 2f2 − f1, quieter but often audible.
- Second-order products — additional intermodulation products.
Each result shows exact Hz, nearest pitch name, MIDI note, cents deviation, and whether it reinforces an existing input partial. Every tone can be played back individually.
Implied fundamentals
Given a set of input frequencies, the module also searches for a fundamental that would make the inputs a clean harmonic-series subset. If your inputs are 660, 880, and 1100 Hz, the implied fundamental is 220 Hz (the inputs are partials 3, 4, and 5). This is how the ear reconstructs a missing fundamental in organ pipes and in sparse chord voicings.
Who this is for
Spectral composers writing dyads that need a specific Tartini tone to complete a chord. Orchestration students studying why certain close-voiced chords feel bottom-heavy. Sound designers layering fundamentals where none are synthesized. Acousticians teaching psychoacoustic demonstrations. For the full overtone series from a single fundamental (as opposed to combination tones between multiple inputs), use Harmonic Series.