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Calculations of Harmonics from Fundamental Frequency
"Overtones" = Harmonics minus 1 or "Harmonics" = Overtones + 1
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There are integer multiples of a certain frequency (fundamental), that are called harmonics, partial tones (partials) or overtones. It is important to note that the term 'overtones' does not include the the fundamental frequency. The first overtone is therefore already the second harmonic or the second partial. The term overtone should never be mixed with the other terms, as the counting is unequal. |
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| Harmonics | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 |
| Partials | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 |
| Overtones | Fundamental | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
| Frequency | f | 2·f | 3·f | 4·f | 5·f | 6·f | 7·f | 8·f | 9·f | 10·f | 11·f | 12·f | 13·f | 14·f | 15·f | 16·f |
| Hz | 65 | 130 | 195 | 260 | 325 | 390 | 455 | 520 | 585 | 650 | 715 | 780 | 845 | 910 | 975 | 1040 |
| Tone name | C2 | C3 | G3 | C4 | E4 | G4 | Bb4 | C5 | D5 | E5 | F#5 | G5 | Ab5 | Bb5 | B5 | C6 |
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gray = even integer harmonics, e.g. triode valve (tube)
white = odd integer harmonics, e.g. organ pipe closed at the top (gedackt). Tympanic membranes or bells have a large number of individual vibrations, which are not simply the exact multiples of single fundamental frequency. These not harmonic overtones are then called partial tones or partials. Overtones whose frequency is not an integer multiple of the fundamental are called inharmonic and are often perceived as unpleasant. Inharmonics that are not close to harmonics are known as partials. Bells have more clearly perceptible partials than most instruments. A "exciter" is a especial equalizer, that creates new overtones. The processed signal is added to the original input signal. |
| Organ pipes closed at the top (gedackt), which are half as long as open organ pipes of the same pitch, have a slightly dull and hollow sound. The spectrum shows predominantly odd multiples of the fundamental frequency and outstanding odd harmonics, or odd partial tones 3f, 5f, 7f… One can also say, gedackt organ pipes contain mostly even overtones. The typical "warm" tube sound, particularly triodes, contains predominantly in the spectrum even multiples of the fundamental frequency, and thus even outstanding harmonics, or even partial tones 2f, 4f, 6f… One can also say, tube amplifiers at high levels (distortion) contain strong odd overtones. |
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Notice: Even overtones are odd harmonics, or partial tones and odd overtones are even harmonics, or partial tones. Harmonics are not overtones, when it comes to counting. |
Length calculation for an open pipe:
 Length calculation for a gedackt pipe:  |
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