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"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 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. The term harmonic has a precise meaning - that of an integer (whole number) multiple of the fundamental frequency of a vibrating object. A harmonic frequency is a multiple of a fundamental frequency, also called "harmonic". When it comes to counting, do not say: "overtones are harmonics". |
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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 |
| Example 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-numbered harmonics, (1f), 2f, 4f, 6f..., e.g. triode valve (tube) white = odd-numbered harmonics, 1f, 3f, 5f..., e.g. organ pipe closed at top (gedackt), clarinet all integer harmonics, e.g. saw tooth wave The frequency spectrum of a symmetric square wave signal (pulse-pause ratio of 1:1) has exclusively odd-numbered harmonics of 3, 5, 7… or even-numbered overtones 2, 4, 6… Tympanic membranes (eardrums) 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 often 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. An "exciter" is an especial equalizer, which creates new overtones. The processed signal is added to the original input signal. |
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| Even-numbered harmonics Odd-numbered harmonics |
| Typical "warm" tube sound, particularly triodes, contains predominantly in the spectrum even-numbered multiples of the fundamental frequency, and thus outstanding even-numbered harmonics, or even-numbered partial tones 2, 4, 6… One can also say, tube amplifiers at high levels (distortion) contain strong odd-numbered overtones - that are even-numbered partials or harmonics. 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-numbered multiples of the fundamental frequency and thus outstanding odd-numbered harmonics, or odd-numbered partial tones 3, 5, 7… One can also say, gedackt (covered, stopped) organ pipes, and also the clarinet contains mostly even-numbered overtones - that are odd-numbered partials or harmonics. Because a clarinet acts like a closed tube resonator, it theoretically produces only odd-numbered harmonics. But there is also some even-numbered harmonics content. Look at: http://www.phys.unsw.edu.au/jw/clarinetacoustics.html#harmonics |
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Notice: All harmonics are overtones is correct, but ... Even-numbered overtones are odd-numbered harmonics, or partial tones. Odd-numbered overtones are even-numbered harmonics, or partial tones. Harmonics do not have the same counting like the overtones. Do not mix overtones with harmonics. It is recommended to mention odd and even multiples of the fundamental frequency, because that coincides with the counting of the harmonics and the partial tones, and if possible avoid the mention of even and odd overtones, which have a different counting, what contibutes to typical errors. Avoid the word combination "harmonic overtones". |
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Length calculation for an open pipe:
 Length calculation for a gedackt pipe:  |
Frequency of concert pitch A4 and the counting of harmonics and overtones
| Frequency | Order | Harmonics | Overtones |
| 1 × f = 440 Hz | n = 1 | 1st (odd) harmonic | fundamental |
| 2 × f = 880 Hz | n = 2 | 2nd (even) harmonic | 1st (odd) overtone |
| 3 × f = 1320 Hz | n = 3 | 3rd (odd) harmonic | 2nd (even) overtone |
| 4 × f = 1760 Hz | n = 4 | 4th (even) harmonic | 3rd (odd) overtone |
| 4 × f = 2200 Hz | n = 5 | 5th (odd) harmonic | 4th (even) overtone |
| Symmetrical amplifier push/pull circuits must cancel even order harmonics, like 2, 4, 6… and therefore promote odd order harmonics, like 1, 3, 5… when driven into the nonlinear range. |
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