[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:
http://www.youtube.com/watch?v=8KgtQHbQnDk
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:
http://khoomei.com/harmonic.htm
some more resources are listed at the end of the article.
There's a handy calculator at
http://www.sengpielaudio.com/calculator-harmonics.htm
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.
Chris
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!
>Krystel.
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