[Menvi-discuss] Ergent, can someone explain the harmonic series in words in the next few hours.

Chris Smart csmart8 at cogeco.ca
Wed May 1 12:37:43 EDT 2013

Hi Kristel.
By "need to know the order of the partials," do 
you mean you need the ratios? or an example using 
frequencies measured in Hertz?

Have you had this demonstrated in audio form yet?
If not, take a listen to:

In that clip, an electronic filter dissects a 
waveform (82 Hz, pitch E) into the first 
twenty-four partials of the harmonic series. 
You'll first hear 2nd octave E, then slowly hear 
harmonics of the fundmental being added, then taken away again.

The name of the note played is the 
fundamental  frequency or the first harmonic, the 
second harmonic is twice the fundamental 
frequency, the third harmonic is three times the 
fundamental frequency, and so on. This series is 
called the harmonic series. For instance, when 
one plays an A440Hz, "A" refers to the 
fundamental or first harmonic, but this sound 
also contains the second harmonic, 880Hz, the 
third, 1320Hz, and so on, at varying amplitudes. Taken from:
some more resources are listed at the end of the article.

There's a handy calculator at

Enter a fundamental frequency in the box and it 
generates a list of partials. For example, enter 
10 into the box, and you get: 2nd harmonic 20, 
third harmonic 30, 4th harmonic 40, 5th harmonic 50 etc.

To put this in intervallic terms:
1st harmonic = fundamental tone
2nd harmonic = octave, above fundamental
3rd harmonic = octave plus fifth above fundamental
4th harmonic = 2nd octave above fundamental
5th harmonic = 2 octaves plus a third above fundamental
   6th harmonic = two octaves plus a fifth above fundamental
  7th harmonic = two octaves plus minor seventh above fundamental
8th harmonic = three octaves above fundamental
9th harmonic = three octaves plus second
  10th harmonic = three octaves plus third
etc. etc.

This goes on a long long time if the sound is 
particularly bright in character, like a low note 
on an acoustic guitar with steel strings or 
harpsichord, or a low note on an organ with many stops pulled.

Here's a table that gives intervals, note names, 
frequencies and ratios:

Comparison: Fundamental  Interval: Previous 
Frequency: Ratio: Example  Frequency:
fundamental frequency fundamental   1:1 C     65
double frequency octave   2:1 c   130
trifold frequency fifth   3:2 g   195
fourfold frequency fourth   4:3 c'   260
fivefold frequency major third   5:4 e'   325
sixfold frequency minor third   6:5 g'   390
sevenfold frequency     7:6 natural seventh   455
eightfold frequency     8:7 c''   520
ninefold frequency large whole tone   9:8 d''   585
tenfold frequency small whole tone 10:9 e''   650
elevenfold frequency   11:10 alphorn F5   715
twelvefold frequency   12:11 g''   780
thirteenfold frequency   13:12     845
fourteenfold frequency   14:13     910
fifteenfold frequency   15:14 b''   975
sixteenfold frequency minor second 16:15 c''' 1040

The frequency ratios result in a natural tone 
series, natural or pure intervals found in 
nature. These intervals will not sound like the 
intervals you are used to hearing, from the equal 
tempered twelve tone scale that has been in use for a few centuries.

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
(numbers are octaves)

As far as I know, an instrument like the clarinet 
has lots of odd number harmonics, whereas brass 
such as trumpet has many even harmonics.

After all that math, click on the video link 
again and hear it in action.


At 10:14 AM 5/1/2013, you wrote:
>Hi everyone.
>I am having trouble finding somewhere on line 
>that explains the harmonic series with out 
>diagrams and images and am having no luck.
>I need to recap for a test at uni tomorrow 
>morning, and the explaination in my text book, 
>as well as those offered in class all include lovely pictures!
>In particular I need to know the order of the parcials.
>Thanks for any help. I really appreciate it!
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