fred@inuxc.UUCP (08/26/83)
My Piano Teacher tells me that the pleasing harmony comes from the fact that the overtones, i.e. the multiple frequencies of the base note, match up in notes that sound pleasing together. Fred AT&T CP
debray@sbcs.UUCP (Saumya Debray) (08/30/83)
Does anyone know whether phase relationships between the fundamental tone and the higher harmonics are important in determining how "musical" a sound sounds, and if so, to what extent? It seems to me that since the phase relations also play an important role in shaping the composite waveform, they shouldn't be entirely irrelevant. Saumya Debray SUNY at Stony Brook
philipl@bronze.UUCP (Philip Lantz) (08/31/83)
It would seem that since phase relations play an important role in shaping the composite waveform of a sound, they would have an effect on the way the sound is heard, but it ain't so. I have experimented with a waveform generator, with a number of oscillators, changing the relative amplitudes and phases of the different frequencies. Changing the relative amplitudes is very audible, and changing the relative phases is completely inaudible, though the waveform as seen on an oscilloscope may be completely different. Philip Lantz tekmdp!bronze!philipl
mmt@dciem.UUCP (Martin Taylor) (09/05/83)
================== The human ear determines pitch by having cilia in the colea of the inner ear that resonate. It is a pretty specatular realtime Fourier transformer. Since each cilium(?) only detects pitch and not phase, the ear cannot detect phase differences. The typical vibrations and waves physics experiment is to have two tone generators whose phase difference can be adjusted. The ear cannot tell the difference. ================== This statement is a load of hogwash. It is a physicist's idea of how the auditory system works. Errors: (i) Phase information is available in the different neural frequency channels up to around 4 kHz, and is routinely used in binaural detection of direction up to about 1500Hz. (ii) Pitch and frequency are completely different concepts. The individual nerve fibres have maximally sensitive frequencies, and if the ear is reasonably normal, a sine wave of a given frequency will sound as if it has a unique corresponding pitch. However, it is possible to set up conditions using high harmonics of a low fundamental frequency, so that the pitch heard is that of the non-existent fundamental. Furthermore, if the frequencies of all these "harmonics" are shifted up or down by a certain amount, the perceived pitch will shift by a smaller amount. (iii) Under laboratory conditions, it is possible to demonstrate perceptual effects that DO depend on the relative phases of fundamental and harmonics. (iv) The auditory system is very complex, and by no shred of the imagination could it be considered as a Fourier transformer. To say so is like equating the visual system to a camera! If you are interested, look through a few back issues of the Journal of the Acoustical Society of America. There is a good index in every June and December issue. Martin Taylor PS. Psychoacousticians please don't flame at the oversimplifications above -- I'm trying to make it brief.
DCP@MIT-MC@sri-unix.UUCP (09/08/83)
From: David C. Plummer <DCP @ MIT-MC> The human ear determines pitch by having cilia in the colea of the inner ear that resonate. It is a pretty specatular realtime Fourier transformer. Since each cilium(?) only detects pitch and not phase, the ear cannot detect phase differences. The typical vibrations and waves physics experiment is to have two tone generators whose phase difference can be adjusted. The ear cannot tell the difference. An anology can be made with they eye. The eye has roughly four resonators; red, green, blue and black/white. They have a much broader response curve than the cilia of the ear, but since the eye percieves a more detailed spatial image, such things as intensity, contrast, and shading play a greater role.
crandell@ut-sally.UUCP (09/08/83)
In continuous tones, the instantaneous phase relationships of the
harmonics do NOT affect the quality of the tone. You can demonstrate
this to yourself with a relatively simple experiment. Obtain four or
five sine-wave oscillators and mix their outputs through a resistor
network (or an audio mixer, if you happen to have one) feeding the output
to a speaker or headphones. Then adjust the frequencies of the oscil-
lators to the first four or five (as appropriate) integer multiples of
some convenient frequency (e.g., 300, 600, 900, 1200, 1500). Observe
the composite waveform on a 'scope; you'll have to, in order to get the
frequencies reasonably precise, and that's exactly the point! As long as
even one of the components is even a fraction of a Hz off the exact
multiple, it seems to be a harmonic whose phase is continually shifting,
and the waveform as displayed by the 'scope will "roll" correspondingly.
In the middle range, a reasonably good ear has a pitch sensitivity in
the neighborhood of 0.25%; as long as the harmonic's frequency error
doesn't exceed that bound, the tone sounds uniform and stable.
The explanation of this effect is not very obscure. For about
20 years, hearing researchers have been reasonably confident that the
ear actually analyzes a continuous composite tone into its sinusoidal
components, and transmits some form of spectral plot to the brain. The
information in this plot seems to consist of frequencies (well, pitches,
actually) and loudnesses. The times at which the individual pitch re-
ceptors are stimulated are fairly precisely detected, however, so the
maintenance of phase IS important to accurate reproduction of transient
sounds. For example, you can easily discern the difference between the
simple "click" of a step function and a bird-call-like "chirp", but trans-
mission through a dispersive medium is all it takes to transform one
into the other!
Jim (ihnp4!ut-sally!crandell)
P.S. If you can't get a hold of enough oscillators, see if you can get
your hands on an old, electric Hammond. The experiment is then trivial.