Overtones harmonics overtone partial partials calculation of the harmonic and the fundamental frequency flute clarinet organ - converter distortions k

Calculations of Harmonics from Fundamental Frequency
In acoustics the fundamental frequency is the 'first harmonic'. The term overtone
is used to refer to any resonant frequency above the fundamental frequency.

"Overtones" = Harmonics minus 1, or "Harmonics" = Overtones + 1

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.

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1st harmonic = fundamental tone	2nd harmonic = octave,
3rd harmonic = fifth over octave	4th harmonic = 2nd octave
5th harmonic = third over 2nd octave	6th harmonic = fifth over 2nd octave
7th harmonic = minor seventh over 2nd octave	8th harmonic = 3rd octave
9th harmonic = whole tone over 3rd octave	10th harmonic = third over 3rd octave

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

gray = even harmonics, (1f), 2f, 4f, 6f..., e.g. triode valve (tube), square wave
white = odd harmonics, 1f, 3f, 5f..., e.g. organ pipe closed at top (gedackt), clarinet
all integer harmonics, e.g. saw tooth wave

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.

An "exciter" is an especial equalizer, which creates new overtones. The processed
signal is added to the original input signal.

Harmonics and overtones comparison - sengpielaudio

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 partial tones 2f, 4f, 6f …
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 partial tones 3f, 5f, 7f …
One can also say, gedackt (covered, stopped) organ pipes, and also the clarinet contain 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 much diminished even-numbered harmonics content.
Look at: http://www.phys.unsw.edu.au/jw/clarinetacoustics.html#harmonics

Notice:  All harmonics are overtones is correct, but ...
                Even-numbered overtones are
                odd-numbered harmonics, or
                partial tones and 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.

Length calculation for an open pipe:

Length calculation for a gedackt pipe:

Calculation without flute mouth correction.

Frequency of concert pitch 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 f2, f4, f6 and therefore promote odd order harmonics,
like (f1), f3, f5 when driven into the nonlinear range.

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