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rasputin1963

Understanding Odd and Even harmonics...

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Basic engineering wisdom tells us that the Even harmonics are the "musical" or "pretty" harmonics...   while the Odd are the "rough" or "noisy" harmonics.

Is there any more lore,  wisdom,  factoids or experience you care to share regarding the difference between the two,   and how they might be creatively used and understood?    e.g.,   In micing,   recording,  EQ,   creative filtration,   reverb or convolution situations?

 

Thanks,  ras

 

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Even harmonics are some number of octaves above the original note. 

Examples (for A at 440 Hz)

2nd harmonic:  880 Hz -- up one octave 

4th harmonic:  1760 Hz -- up two octaves

and so forth.

 

The 3rd odd harmonic is an octave plus a fifth above the fundamental.

3rd harmonic:  1320 Hz -- E above the A at 880 Hz

 

Even harmonics sound more 'musical' because the original note is reproduced, although 1 or more octaves higher (like playing a note on a 12 string guitar).

The 3rd harmonic create a dissonance because, in any given chord, having the 5th of every note is not always appropriate to the chord.  A simple example, again using an 'A' chord:

A -->  3rd harmonic = E  (ok)

C#--> 3rd harmonic = G# (not ok, for a simple A chord; it's a major 7th)

E -->  3rd harmonic = B (not ok for a simple A chord, it's a 9th)

 

When you start adding in 5th, 7th or higher harmonics, it gets much worse.  For example, the 5th harmonic of A (440Hz) is 2200 Hz, which is not a 'note'.   If falls between C and C# above A at 1320 Hz.  If you do that for all the notes in a chord, you get sonic mush. 

That's why heavy metal & other music using lots of distortion rely on power chords so much (tonic + 5th) - - the odd harmonics of chords with additional notes all turn it into mush.  Not that this is a bad thing; it's just something not everyone enjoys....

 

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Philbo's explanation of the musicality of harmonics is correct. So if you're looking to create a new sound, keep the harmonics above the third in mind, and play with them. As far as harmonic distortion that occurs in electronics is concerned, unless something is broken (intentionally or not) only the 2nd and 3rd harmonics are of great enough amplitude to have a noticeable effect on what you're hearing. Generally the signal-to-noise ratio of the fundamental or one of those first two harmonics is low enough to be insignificant.

As far as being creative with harmonics, this is most easily explored with a synthesizer, where you can pile up frequencies in any ratio that you want. And of course in real musicial instruments, the harmonic content is what determines the timbre of that instrument. It's why a tom tom sounds different from a bongo. Or why an oboe sounds diffrenet from an alto sax.

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Odd and even refers to the numbering of the harmonic partials

1th fundamental

2nd, 4th, 6th, 8th... are even partials

3rd, 5th 7th, 9th... are odd partials

Depending on the sound analysed with a Fourier analysis the harmonic partials are at particular frequencies, in other words the harmonic partials of a Bell are different constituent frequencies then a violin, just to name one example.. 

 

And then there is the theoretic overtone table, as for example included in older additive synthesizers which are usually based on following frequencies, and a Fourier analysis measuring grid permits comparison when the harmonic partial are extremly different for example in a Bell or gong.

 

The theoretic table of harmonic partials found in olde synths:

 

1st octave:

1 fundamental

2nd octave:

2 octave 1200 cent above fundamental

3rd octave:

3 pure fifth 701,955 cent, 1901,955 cent above fundamental

4 pure fourth 498,045 cent ,  cent above fundamental

5 major third 386,314 cent,  2786,314 cent above fundamental

6 minor third 315,641 cent, 3101,955 cent above fundamental

266,871 cent, 3368,826 Cent above fundamental

4th octave:

231,174 Cent, 3600,000 Cent above fundamental

9

10

11

12

13

14

15

5th octave:

16 4800,000 Cent

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31 56,767 Cent, 5945,036 above fundamental

6th octave:

32 5945,036 Cent above fundamental

33 54,964 Cent

... and so on 

 

Todays additive synthesizer however, the frequencies distances of the harmonic partials can be stretched or companded, which generate all kind of sounds, and with a little practice you can program a bellspiel with 64 bells artificially.

 

Creativity: With a vovel formant filter you can make the sound talk.

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I find it's the other way around: odd harmonics sound musical, even ones sound harsh (once past the first few).  But evidently we're just counting them differently, but as I count, the first harmonic is one octave higher than the fundamental.

A square wave is all odd harmonics, and to me sounds more musical than a sawtooth, which contains all harmonics.  I don't know of a basic waveshape that's all even harmonics, but my guess is it would be harsh.

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The process of counting the harmonics can be confusing until you distinguish harmonics from overtones. Example: 2000 Hz is the first OVERTONE of 1000 Hz, but 1000 Hz is the first HARMONIC of 1000 Hz. Since explanations and demonstrations of the Harmonic Series are often identical to explanations of the Overtone Series, this only adds to the confusion. An easy way to remember the difference is to simply keep in mind that the fundamental cannot mathematically be an overtone, but that it IS ENHARMONIC with itself. Thus, this confirms that it's the even-numbered harmonics that are the more musical sounding ones.

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Wow, deja vu moment. I was reading the post, and thought, hey that's a pretty good explanation. Then I noticed I wrote it, back when my username was philbo... I must be getting senile....

Edited by philboking

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The process of counting the harmonics can be confusing until you distinguish harmonics from overtones. Example: 2000 Hz is the first OVERTONE of 1000 Hz' date=' but 1000 Hz is the first HARMONIC of 1000 Hz. [/quote']

 

"Overtone" is a musical term, "harmonic" is a physics term. When talking about harmonics, we say "fundamental" rather than "first harmonic."

 

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