by zumbido » Sat Jul 29, 2006 1:37 am
Hitmaker,
The series of frequencies, in your example, starting at 150 Hz. (as you claim is the fundamental) creates a square wave. There would NOT be any 75 Hz. 'undertone' created by any of these frequencies (i.e., differential tone).
Now, if you were to START at 75 Hz., as the fundamental frequency, you have left out several of the overtones.
Following upto overtone number 'eight', the frequencies (in Hertz) would be: 75, 150, 225, 300, 375, 450, 525 and 600.
Of course, overtones go well beyond 'eight' and these values coincide with chord extensions. All the overtones, through the '9th' overtone, naturally produce a Dominant Ninth chord. All the overtones, through the '11th' overtone, naturally produce a Dominant Augmented Eleventh chord. And, all the overtones, through the '13th' overtone, naturally produce a Dominant Thirteenth chord.
Figuring overtone values is easy. Simply multiply the known fundamental frequency by the overtone number. For instance, if the fundamental frequency of an open 'E' string of a bass guitar is 41.203 Hz. (derived from equal temperment tuning, A = 440 Hz.) and you want to calculate the 3rd overtone - multiply 41.203 by 3. The frequency is 123.609 Hz. or a 'B'. This is approximately/near the same 'B', fourth fret on the G-string.
Remember, overtones are a 'pure Intonation' but we commonly use 'Equal Temperment' so this is why there are slight differences in the values of like-notes.
The volume relationship between the fundamental and its overtones are what gives an instrument it's "sound" - in addition to it's attack, decay and release. By the way, some instruments produce a 'louder' 2nd overtone than the fundamental.