Acoustic 'beats' from mismatched musical frequencies - Comments

[andrewkirk]

andrewkirk submitted a new PF Insights post

Acoustic 'beats' from mismatched musical frequencies

Continue reading the Original PF Insights Post.

 

[Stephen Tashi]

Physics students might be more motivated to delve into the phenomena of beats if, in addition to the phenomenon of physical beats, they were also told about the physical/psychological phenomenon of binaural beats. https://en.wikipedia.org/wiki/Binaural_beats.

It isn't clear to me whether the mathematics of predicting binaural beats is exactly in correspondence with the math of predicting physical beats.

 

[Stephen Tashi]

The correct link is https://en.wikipedia.org/wiki/Binaural_beats, but my correction in the "Discuss in the Community" pages didn't get made to the Insights comment.

 

[jim mcnamara]

Great article!

My wife and myself geocache a lot, and I constructed a cache last week, based on part of what you discussed. Fun. As you tune closer to a 440 A (for example) the beats between a tuning fork and an instrument come further apart until they are no longer perceived.

55 Hz is indeed a next-to-lowest A, A0 being 27.50 Hz, but your wording confused me. FWIW the 440 value for A4 is not cast in stone as the primary tuning point for Western music. Different values have been and are still in use, especially for older music.

 

[Svein]

I have played recorders in a group, and the beat is very much alive there. Since the recorder tone has almost no overtones, the beat between two recorders playing the "same tone" (even using recorders of the same make, tuned at the beginning of the piece) can be very prominent (we call it the "phantom bass").

 

[Dr. Courtney]

Great article. Thanks for writing it.

 

[sophiecentaur]

I have played recorders in a group, and the beat is very much alive there. Since the recorder tone has almost no overtones, the beat between two recorders playing the "same tone" (even using recorders of the same make, tuned at the beginning of the piece) can be very prominent (we call it the "phantom bass").

Piano strings (in mid register) are in threes and deliberately offset around the nominal note frequency in order to make it 'sound right'. If they were matched to within only 0.1Hz, there could be some very unfortunate (5s) delay for some of the notes to emerge at full amplitude.

 

[EricL]

Piano strings (in mid register) are in threes and deliberately offset around the nominal note frequency in order to make it 'sound right'. If they were matched to within only 0.1Hz, there could be some very unfortunate (5s) delay for some of the notes to emerge at full amplitude.

That's really cool. I knew about beats and the fact that establishing just the right amount of "error" among the three strings was critical, but it hadn't occurred to me that there could be a delay in production of the proper sound if the difference in frequency were too small.

On that note, I'm vaguely aware of something called "tempering", a method of tuning keyboard instruments so that the whole mood of the music changes ever so slightly according to the key in which it is played, as the relationships between the notes ends up not being the same in every key. Fascinating stuff.

 

[sophiecentaur]

That's really cool. I knew about beats and the fact that establishing just the right amount of "error" among the three strings was critical, but it hadn't occurred to me that there could be a delay in production of the proper sound if the difference in frequency were too small.

On that note, I'm vaguely aware of something called "tempering", a method of tuning keyboard instruments so that the whole mood of the music changes ever so slightly according to the key in which it is played, as the relationships between the notes ends up not being the same in every key. Fascinating stuff.

It would definitely affect the 'attack' of each note. (My extreme example would not be realistic because it would require only two strings and for them to be struck in different directions; not what happens in a real piano.)

"Tempering" of the scale is something that can be achieved with an instrument in which all notes are tuned individually. A piano can be tuned with 'equal tempering', which means that the ratio of the frequencies of all semitones is ¹²√2. This means that 12 semitones will always take you an octave up, wherever you start. Modern music is mostly based on this. A brass instrument, otoh, has its notes based on overtones that the length of the open, flared tube will produce (overtones depart a long way from Harmonics in some cases). If you listen to the sound from ancient instruments, even the octaves sound dodgy and the higher overtones depart further and further from what we are used to as they are based on 'simple' ratios. Listen to 'Roman" music, for instance. It sounds terrible. Bugles have a similar problem and they only have one tube length (no valves). You have to pull notes to make them sound right and bugles can also sound 'strange'. When an instrument is not equal tempered, music played in different keys will sound different (key colour). Some people claim that there is colour for an equal tempered piano but I am not so sure - it may be because of the physical arrangement of black and white notes and the consequential different way that the fingers strike the keys.

 

[enorbet]

Musical instruments by nature, or perhaps "evolution' strive to be harmonically rich and this richness is heavily influenced by so many variables they are too complex for casual, fundamental study. An example of this is that during the 1980s both Fender and Gibson (who at that time had over 50 years of experience in designing and building instruments) found to their horror that many of their long scale electric basses exhibited "dead spots", frets that would greatly diminish or even functionally eliminate certain notes, usually more than just a few. The controversy rages on to this day in both instrument design and even amplifier design, layout and component choice.

A much simpler study can be had with harmonically simple devices, such as Helmholz Resonators, that tend to produce only fundamentals and in some cases a true octave harmonic. I first experienced such resonance and beating at age 17 while traveling in a group of motorcycles whose "exhaust notes" change some with rpm but are heavily influenced by the exhaust system. When traveling at somewhat constant cruising speed the interaction between motorcycles in close proximity cause beating and speeding up, slowing down (altering RPM), or changing the relative separation distance affects the frequency of the beat. It is quite lovely to hear and utterly fascinating to contemplate. I'm pleased to witness a serious discussion on the phenomena.

 

[olivermsun]

Piano strings (in mid register) are in threes and deliberately offset around the nominal note frequency in order to make it 'sound right'. If they were matched to within only 0.1Hz, there could be some very unfortunate (5s) delay for some of the notes to emerge at full amplitude.

Very interesting. Do you have a good reference you could point me to about this?

 

[sophiecentaur]

Very interesting. Do you have a good reference you could point me to about this?

Sorry, I haven't and I am only quoting what a couple of competent musician friends have told me. They are also pretty competent chartered Engineers so I accepted what they were saying.
I know it sounds pretty dire when they are too far apart - a la Pub Piano- but that's a different matter.