Measured Spectrum of Stopped Wood Organ Pipe Shows ALL Overtones

[sophiecentaur]

So 3 times the fundamental is a harmonic (a twelfth) but not 1.5 (fifth). You might find musicians who would disagree that a perfect fifth is not a harmonic interval.

AM

The term 'overtone' can only really describe by the layout of natural modes of vibration (of any musical or not very musical instrument) being put in ascending order of frequency. Tuning of an instrument can only be done with frequency standards (tuning forks) and a 'good ear'. It's all an enormous fudge to get a wind instrument to sound in tune by varying spacings and sizes of holes or the taper of the bore and bell. Same goes for a guitar fingerboard by placing frets in the right spots to make most of the overtones to sit on or near enough to the best place.

If you want to understand how a single pipe can generate odd and even harmonics, then you must not concern yourself with the octave that a particular harmonic falls in.

Your use of the term "harmonic" is seriously inappropriate here. A real instrument has modes of vibration; if you listen to a Hammond style (drawbar) organ then the voices never sound the same as an original instrument because they are achieved by actually mixing amounts of pure harmonics. The pipe organ uses the natural modes of oscillation and these are never exactly harmonically related. The more harmonics you want to fall within a wanted octave then the lower the fundamental frequency you need to start with. The only way one can be convinced is to play with a bugle. If you can make it talk then you find that the higher up you go, the more notes exist within octave intervals but the more and more errors there are with the intonation.