It was made in Gnuplot, just typing explicit expressions in.
Ahh, thanks again!
]]>On reflection "Spin" may have not been the best word for me to have chosen for the tuning fork experiment.
I had NOT meant a fast spin, merely a slow rolling of the tang between thumb and forefinger, a revolution or two per second.
Turning the fork at SLOW speed doesn't introduce the Doppler effect, it just illustrates that phase is audible.
You'd still get subtle but audible tremolo effect. And you can still think of it as being due to the superposition of two very subtle equal and opposite Doppler shifts (too subtle to be audible if you could listen to one tine at a time). Or you can think of it as being due to small relative phase shifts. Mathematically the two are equivalent. Phase is not really audible though. If you listened to the tuning fork in two different fixed orientations (slightly different relative phases for the two sources), they would sound identical (except for a very small change in volume). You only hear the 1-2 Hz sinusoidal variation in the phases while the tuning fork is rotating. But anyway it's a two sources + one detector (ear) situation, which if carefully set up could theoretically result in strong enhancements or cancellations (not with a tuning fork but say two loudspeakers). That's not relevant to phases of a superposition of pure tones in a mono signal though, where one can't hear phase except at the lowest frequencies.
Nice illustration, thank you!
Just for interest, was it made with a spreadsheet-calculation? (the audio-editor audacity for example has no FM plugin to generate those waves).
It was made in Gnuplot, just typing explicit expressions in. The frequencies I chose to best illustrate what's happening. In a realistic scenario there would be a lot more difference in tremolo and tuning fork pitch frequencies and the Doppler shift would be a lot more subtle. But then the plot would be way too busy to see what's happening.
]]>the FM completely disappears and becomes pure AM (amplitude modulation) of the intrinsic fixed pitch tone of the tuning fork. The two perfect vibratos add up to a pure tremolo.
Nice illustration, thank you!
Just for interest, was it made with a spreadsheet-calculation? (the audio-editor audacity for example has no FM plugin to generate those waves).
]]>Spinning the tuning fork will produce a chorus type effect. Yes, you can think of it as two phase or (equivalently) frequency modulated (FM) signals combined. Because of the Doppler effect the frequency of the vibration (pitch of the sound) heard will increase for the tine moving towards your ear and decrease for the tine moving away (like it happens for a train whistle or ambulance siren moving past you). If you could listen to the tines on their own you'd hear an oscillating pitch, i.e., a vibrato.
A very interesting thing happens when these two FM signals combine at your eardrum: the FM completely disappears and becomes pure AM (amplitude modulation) of the intrinsic fixed pitch tone of the tuning fork. The two perfect vibratos add up to a pure tremolo.
On reflection "Spin" may have not been the best word for me to have chosen for the tuning fork experiment.
I had NOT meant a fast spin, merely a slow rolling of the tang between thumb and forefinger, a revolution or two per second.
Turning the fork at SLOW speed doesn't introduce the Doppler effect, it just illustrates that phase is audible.
A very interesting thing happens when these two FM signals combine at your eardrum: the FM completely disappears and becomes pure AM (amplitude modulation) of the intrinsic fixed pitch tone of the tuning fork. The two perfect vibratos add up to a pure tremolo.
]]>aandrmusic wrote:Strike a tuning fork, hold it by the tang fairly close to one ear and slowly spin it around.
The same tone comes from each tine, the phase is different and you can CLEARLY hear the phase changes as you slowly spin it.Probably a varying cancellation effect between the two tines.
Surely that IS the difference in phase between two very similar signals reaching the ONE ear ?
It is about the simplest and "purist" experiment that shows it.
Almost every other experience includes reflected sound and (as we all KNOW) sound reflectors change timbre.
Strike a tuning fork, hold it by the tang fairly close to one ear and slowly spin it around.
The same tone comes from each tine, the phase is different and you can CLEARLY hear the phase changes as you slowly spin it.
Probably a varying cancellation effect between the two tines.
]]>Helmholtz wrote that phase is inaudible, but later writers say that this is only true for sine waves or sounds with few partials. When there are multiple inharmonic partials, particularly, phase differences are audible. Sorry not to have access to the modern quotes right now, but I think the general agreement, now, is that for a piano note, which has both many inharmonic partials, and has two to three, slightly out of unison, strings sounding at once, and with the phase of each string rapidly changing as it bounces off each termination point, the phase is not just audible, but a major component of the timbre. (And there are the bridges to consider. I get lost there. They serve as termination points? Not exactly, since the strings vibrate on both sides of the bridges? And it is the vibrations of the soundboard that we hear, for the most part. On various parts of the soundboard, which itself responds with differing amounts of impedance as it thickens and thins. And then there is the phase change where these various thicknesses and thinesses of wood meet the curving rim...)
Still don't understand the difference in the beat rate that is so audible on these mono-string recordings of two partials. What's going on there? I do understand why there is beating. I don't understand why the beat rates differ so much between the piano note and the modelled note. Is the variation in the pitch of the partials that wide? If so, wouldn't the timbre of the notes sound still more different? The beat rate is much, much faster between partials in the model. Sounds at least twice as fast. Cant imagine how that is possible.
(I still want to talk more about the regularity of the beats in the modelled notes, compared to the "acoustic" notes, too. And the sustain time of the lower partials.)
Very valuable discussion going on. (Only by getting lost can one get found?)
I think it was a grade school teacher who demonstrated that phase change is audible as follows;
Strike a tuning fork, hold it by the tang fairly close to one ear and slowly spin it around.
The same tone comes from each tine, the phase is different and you can CLEARLY hear the phase changes as you slowly spin it.
It is a fairly pure tone, i.e. partials shouldn't come into it.
That was a LONG time ago, so maybe it was a demonstration of something else
]]>Greg.
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