Spectral Calculator
Explore combination tones, input-harmonic reinforcement, and 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 strongly played perfect fifth can feel anchored by an invisible bass. These difference-frequency products are often called Tartini tones, after the 18th-century violinist who first described them.
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, cents deviation, and whether it sits near a harmonic of one of the inputs. 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 subset of a single harmonic series. 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 the same mechanism by which the ear reconstructs a missing fundamental in organ pipes and in sparse chord voicings.
Who this is for
The Spectral Calculator is aimed at anyone thinking about the sonorities that emerge between notes rather than the notes themselves. Spectral composers use it to write dyads that need a specific Tartini tone to complete a chord, orchestration students use it to understand why certain close-voiced chords feel bottom-heavy, sound designers use it to layer fundamentals where none are synthesized, and acousticians use it for psychoacoustic demonstrations. For the full overtone series from a single fundamental, rather than combination tones between several inputs, use Harmonic Series.