MusicReasonPitch, Tuning, Intonation, and Fret Geometry
What are the overtones of this fundamental?
Choose a fundamental frequency and how many harmonics to list. This tool computes each harmonic's exact frequency as a whole-number multiple of the fundamental, plus its approximate nearest equal-tempered note. It does not model any specific instrument's actual overtone spectrum, only the idealized integer-multiple series.
Answer
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Understand
The harmonic series is the set of whole-number multiples of a fundamental frequency: 1×, 2×, 3×, and so on. Low harmonics land close to familiar equal-tempered notes (the 2nd is exactly an octave, the 3rd close to a fifth above that), but higher harmonics drift further from any equal-tempered pitch, which is why "harmonic" and "overtone" are related but not identical terms: an overtone is any partial above the fundamental, while a harmonic specifically means a whole-number multiple of it.
Worked examples
The first harmonic is always the fundamental itself, exactly 1× its own frequency. The second harmonic is always exactly one octave above the fundamental, 2× its frequency, regardless of what that fundamental actually is. Every successive harmonic's frequency is strictly higher than the one before it, since each is simply the fundamental times a larger whole number.
Method and limitations
Each harmonic's frequency is the fundamental multiplied by its harmonic number; the nearest equal-tempered note and its cents deviation come from the same frequency-to-note formula used throughout the site. Amplitude is shown only as an illustration, not a prediction of any real instrument's actual overtone strength, since real instrument spectra vary enormously by construction, playing technique, and register. This tool describes the idealized mathematical series only.
The 7th harmonic is a well-known case where the equal-tempered approximation is noticeably rough: it sits closer to a flattened minor seventh than to any note a 12-TET instrument can produce exactly, with a cents deviation large enough to be clearly audible if compared directly. This is exactly why brass and wind players sometimes describe certain overtone-series notes as "naturally out of tune" relative to equal temperament, even though nothing is actually wrong with the instrument.