Harmonics partials overtones distortions THD - sengpielaudio
Calculate harmonics overtones partials distortion distortions nonlinear amplifiers amplifier calculations calculation calculate convert converter computation compute even integer harmonics odd partials organ pipe valve tube distortion factor distortion attenuation table tables sound studio techniques technology audio percent db to per cent AIM FIM overtone overtones THD dB percentage per cent total harmonic distortion dBSPL dBV dBu amplifier factor linear frequencies amplitude organ pipe valve tube intermodulation natural tones sengpielaudio Sengpiel Berlin
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Calculations of Harmonics from 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 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.
Overtones   Harmonics
Overwaves   Partial tones
  Frequencies in Hz Partials
Input:  
Fundamental frequency in Hz 1st Harmonic
            
Solution:  
  1st Overtone   2nd Harmonic
  2nd Overtone   3rd Harmonic
  3rd Overtone   4th Harmonic
  4th Overtone   5th Harmonic
  5th Overtone   6th Harmonic
  6th Overtone   7th Harmonic
  7th Overtone   8th Harmonic
  8th Overtone   9th Harmonic
  9th Overtone 10th Harmonic
10th Overtone 11th Harmonic
11th Overtone 12th Harmonic
12th Overtone 13th Harmonic
13th Overtone 14th Harmonic
14th Overtone 15th Harmonic
15th Overtone 16th Harmonic
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 f f f f f f f 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

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.
Harmonics Overtones comparison - sengpielaudio

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.

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:
Formula open pipe - sengpielaudio

Length calculation for a gedackt pipe:
Formula closed pipe - sengpielaudio
Calculation without flute mouth correction.

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