I wonder if someone could answer regarding the terminology used when we tune a violin. One common way to tune is using stackable perfect fifths. My question is, when listening to the fifths, what are we listening to in order to decide whether they are in or out of tune? Do we term it a beat? A Tartini Tone? Overtones? Harmonics? Consonance (as opposed to dissonance) and if so what actually causes the consonance or dissonance? Or is it something else?
The pleasant, smooth sound of well tuned open strings comes from the coincidence of a maximum of their overtones.
What Adrian wrote is certainly correct.
Usually we listen for (lack of) beats when tuning 5ths. It takes some practice to get it right - when the tuning is close, the beats can be very slow.
Tuning is tricky. If you tune pure fifths (3:2 ratio), then your third between C and E in a string quartet context will be too wide. If you are playing with piano tuned to Equal Temperament, your pure fifths will also be too wide compared to the tempered fifths in ET.
I apologize in advance if I'm messing up something - but in my world (or should I say instruments/ear/physics combination) the beats get faster = more narrow the closer two strings are tuned to perfect fifths. When the beats cannot be distinguished anymore from each other, then I know I'm almost there.
So I will start a sentence with a "so" in the hope that Paul will jump in with his knowledge about nature laws and clear this up.
"but in my world (or should I say instruments/ear/physics combination) the beats get faster = more narrow the closer two strings are tuned to perfect fifths."
Paul, thanks for your efforts. I think what we here is an interference pattern of the two frequencies we're playing. And about the direction it goes - I'll check this in the evening. (Memory often 0lays tricks to us...)
When we tune perfect fifths , frequency ratio 3/2, slightly out of tune, the beats that we hear are the interference pattern , the difference between the second overtone of the lower string with the first overtone of the upper string. When that beat pattern gets fast enough, more than 16 Hz, we start to hear it as a difference tone, or Tartini tone. I usually hear it as an annoying buzz. This is easily demonstrated by playing a high double-stop third on the A and E strings. The difference between a perfect fifth and a piano fifth is only 2 cents, (2/100 of a half-step), not enough to worry about in practice. Sometimes Cellos and Violists will want to tune the C- string up 6 cents to match the piano C.
People might be conflating different psychoacoustics phenomena that are all caused by the same process: two tones sounding at the same time.
A concrete example - if you had a string at 200Hz and another at 300HZ, you'd listen for the beating of the 600Hz overtones of each.
Thanks, Carmen, for that elaboration. jq
Thank you for all your enlightening replies.
Two pitches a perfect fifth apart share at least two coincident partials. The first, in order from low to high, is the
The effect that gives rise to the two Tartini tones also gives rise to the "beating" one hears when two tones are close to the same frequency.
While we are in a scientific mood, I should like to point out a very common error: Tartini tones are >not accelerated beats!
Adrian, are you sure? There are so many phenomenon like additive tones, subtractive tones, and various other combinations which can result in many volume pulses in between (which can be perceived as tones), that I am questioning that.
David, of course in double stops, beats and difference-tones will occur simultaneously,but the beats will disappear when the difference-tones are in tune!
Tuning is easy.... right... at least that is what I thought! And how is the base resonnance frequency of the instrument body (which is somewhat different for every instrument) affecting the perception of being in tune? We keep talking about two different strings resonnance and how they interact, but the body has resonnance of its own (not to mention the other 2 strings). Are some instruments easier to tune than others? Is an easier to tune instrument better or worse?
Okay so here's a question for y'all wave-mechanics physicists. If I want to bring up my viola intervals by 1 Hz, how many beats per second should I hear considering I'm not tuning a unison?
Piano tuners have to learn what different numbers of beats sound like when they are learning to tune. When I was in band instrument repair school I was right next to a piano tuning/rebuilding class and all of us students became friends and I was fascinated to learn that they use a special metronome to help them learn the sound of the different numbers of beats for different intervals.
Oops, I wasn't clear. I was talking about tuning
Paul, beats at 880 Hz are probably too fast to be perceived as "beats", but more as tones.
No no no David. Okay ... let's go back to unisons. Let's say we have two tuning forks, one at 440 Hz and one at 441 Hz. We will hear "beats" at 1 Hz. But suppose we could magically listen to just the first overtone instead of the principals? Then we'd be hearing 880 Hz and 882 Hz. That would be a 2 Hz beat. When we listen to fifths, the principals are too far apart to hear actual beating, but as Joel says, we can hear the first overtone of one beating against the second overtone of the second. So I'm envisioning that if one wants the interval to be 1 Hz wide, one needs to hear a 2 Hz beat.
Yup, lots of different ways to choose intonation, whether from an Excel program, or via listening.
I am Not an expert, but, I do remember an electronics experiment in school. Two sine wave signals, at slightly different frequencies, sent into an oscilloscope showed a combined sine wave that varied much slower in amplitutde, there was an overall "envelope" and time between the amplitude peaks would be the difference, heard as "beats"
Joel, yeah that's how it works and it's easily simulated in Excel.
"When we listen to fifths, the principals are too far apart to hear actual beating, but as Joel says, we can hear the first overtone of one beating against the second overtone of the second. So I'm envisioning that if one wants the interval to be 1 Hz wide, one needs to hear a 2 Hz beat."
880Hz with 882Hz give a tone of 881hz: (880 plus 882) divided by 2
Roger, the natural modes of vibration of the violin will vibrate at the frequencies of the notes being played.
When two pure tones are sounded together, call them f1 and f2, it *always* creates an acoustic effect that is the same as one tone sounding with a frequency of (f1+f2)/2, and another tone sounding with a frequency of (f1-f2)/2.
... wow ...
There I agree with David: reality is always richer than pure maths!
This takes me back to my youth, when I studied both music and radio. The music part was the cornet. Perhaps the beating phenomenon is easier to detect with wind instruments, but I had no trouble hearing the beat frequency when tuning to another instrument. I could easily hear a warbling that would slow down to a fraction of a cycle per second; when it stopped completely I was perfectly tuned.
"There I agree with David: reality is always richer than pure maths!"
Paul, I think you'd need to ask someone in the particular ensemble whose tuning you wish to match.
Squeezing the fifths is what happens in Equal Temperament!
We might be moving from the challenge of tuning tones in Just Intonation to perceptions of polyphonic sound and confusing different psychoacoustic effects.