Explain filled in note of chord when harmonising in thirds?
November 26, 2024 9:13 AM Subscribe
When playing the flute and harmonising in thirds we hear the last note of the chord filled in - please explain the science behind this or direct me to explanations! I assume it has to do with the vibration in the inner ear, the bone conduction piece of hearing, and the frequencies of the notes, but would love an actual explanation.
Of note, this occurs live in person only (won't hear it on a recording) which is why I assume this is related to bone conduction hearing. Its a more intense buzz and sound with louder and higher notes which is why I assume related to the frequencies (as the explanation for louder and higher notes is related to the frequency of vibration).
Of note, this occurs live in person only (won't hear it on a recording) which is why I assume this is related to bone conduction hearing. Its a more intense buzz and sound with louder and higher notes which is why I assume related to the frequencies (as the explanation for louder and higher notes is related to the frequency of vibration).
It is combination tones! I used to play recorder in a good group and this was one of the bonus experiences.
posted by lokta at 9:36 AM on November 26 [2 favorites]
posted by lokta at 9:36 AM on November 26 [2 favorites]
You're probably hearing overtones, which are being reinforced by the combination/harmonization of the notes being played. I can't really vouch for this article, but it has a simple explanation of overtones and partials in the context of playing 'harmonics' on the flute: flute harmonics
posted by niicholas at 9:36 AM on November 26
posted by niicholas at 9:36 AM on November 26
Agree with the overtones...
Way back when, when I was in High School, the men in our choir performed "Down in the Valley" at a competition. We were good.
And we got all the overtones. Only time I can ever recall it happening, but it was pretty magical. "No one is singing those notes, where are they coming from?".
posted by Windopaene at 11:17 AM on November 26 [1 favorite]
Way back when, when I was in High School, the men in our choir performed "Down in the Valley" at a competition. We were good.
And we got all the overtones. Only time I can ever recall it happening, but it was pretty magical. "No one is singing those notes, where are they coming from?".
posted by Windopaene at 11:17 AM on November 26 [1 favorite]
There is... a lot going on both with the sounds that instruments make, the room that they're made in, and the human ear, so there's not an easy answer to this question (at least I can't answer it without a corkboard and a bunch of red string).
The way I understand it, it's a combination of the harmonic series, the frequency of the sound + the timbre of the instrument, and the connection between the brain and the ears where the ear is biased/encouraged to hear.
You might enjoy this site, where the concepts are outlined in a bit of a mind map. In particular I think the pages on equal loudness curves and dynamic levels of music might be particularly interesting.
posted by pazazygeek at 11:33 AM on November 26
The way I understand it, it's a combination of the harmonic series, the frequency of the sound + the timbre of the instrument, and the connection between the brain and the ears where the ear is biased/encouraged to hear.
You might enjoy this site, where the concepts are outlined in a bit of a mind map. In particular I think the pages on equal loudness curves and dynamic levels of music might be particularly interesting.
posted by pazazygeek at 11:33 AM on November 26
Anecdote: Cass Elliot mentioned that there was sometimes an overtone voice when they harmonized, they even gave it a pet name when it appeared, which I forget.
posted by ovvl at 5:35 PM on November 26
posted by ovvl at 5:35 PM on November 26
Let's say you play C5 and E5.
C5: fundamental = 523.25, overtones = 1046.50 1569.75 2093.00 2616.26 3139.51 3662.76 4186.01 4709.26 5232.51 5755.76
E5: fundamental = 659.26, overtones = 1318.51 1977.77 2637.02 3296.28 3955.53 4614.79 5274.04 5933.30 6592.55 7251.81
Now, to hear G5 we need the appearance of 783.99, or one of its overtones.
Need to talk about linear vs non-linear mixing now. Not gonna go into heavy math mode but the summary is if you combine two sinusoids linearly, you never get a new frequency, but if there is a nonlinear component you get intermodulation which can create sum and difference frequencies.
In the above example we have the third overtone of C5 (2093.00) and the first overtone of E5 (1318.51) which gives a beat frequency of 774.49 which is quite close to the fundamental G5 of 783.99. It's not exact, but that gets into stuff like how the equal tempered scale was designed, etc.
Anyway, point is if you have non-linear mixing you get those new frequencies generated, and few of them line up with what would be notes in the chord. I suppose the bone conduction thing explains the non-linear component, because generally you want microphones and recording devices to be as linear as possible. Making them non-linear, such as turning up the gain to 11 so that everything distorts, is what brings in all those new frequencies. In the case of an electronic guitar it's why it sounds so good and is done on purpose.
posted by Rhomboid at 10:33 PM on November 26
C5: fundamental = 523.25, overtones = 1046.50 1569.75 2093.00 2616.26 3139.51 3662.76 4186.01 4709.26 5232.51 5755.76
E5: fundamental = 659.26, overtones = 1318.51 1977.77 2637.02 3296.28 3955.53 4614.79 5274.04 5933.30 6592.55 7251.81
Now, to hear G5 we need the appearance of 783.99, or one of its overtones.
Need to talk about linear vs non-linear mixing now. Not gonna go into heavy math mode but the summary is if you combine two sinusoids linearly, you never get a new frequency, but if there is a nonlinear component you get intermodulation which can create sum and difference frequencies.
In the above example we have the third overtone of C5 (2093.00) and the first overtone of E5 (1318.51) which gives a beat frequency of 774.49 which is quite close to the fundamental G5 of 783.99. It's not exact, but that gets into stuff like how the equal tempered scale was designed, etc.
Anyway, point is if you have non-linear mixing you get those new frequencies generated, and few of them line up with what would be notes in the chord. I suppose the bone conduction thing explains the non-linear component, because generally you want microphones and recording devices to be as linear as possible. Making them non-linear, such as turning up the gain to 11 so that everything distorts, is what brings in all those new frequencies. In the case of an electronic guitar it's why it sounds so good and is done on purpose.
posted by Rhomboid at 10:33 PM on November 26
Adding to Rhomboid's answer. If you get an app to provide Fourier analysis of sound (possibly called an audio spectrum analyser) , you can get more info. This shows the relative strength of the overtones. IIRC, the first overtone is about half as strong as the fundemental.
There is an amazing site on flute acoustics here.
posted by SemiSalt at 5:10 AM on November 27
There is an amazing site on flute acoustics here.
posted by SemiSalt at 5:10 AM on November 27
(On android, Spectroid is an fft/waterfall app that is free and has no ads.)
posted by Rhomboid at 5:57 AM on November 27
posted by Rhomboid at 5:57 AM on November 27
Hearing sum & difference tones is very common for flautists playing in various ensembles. Difference tones, in particular, are very noticeable because they are typically very noticeably lower than any tone that is actually being played by one of the flutes. You hear a flute ensemble playing and you're like, "Where in the world is that BASS coming from?"
If they're playing something harmonious with the notes you're playing, they're a good sign that you're playing in tune!
Here are a couple of good videos discussing these, from a couple of different perspectives:
* Physics This Week
* Adam Neely
Note that the difference tones are quite soft, and for instance in the above examples you'll likely need to crank up the volume on your earphones or speakers quite a bit to hear them clearly. That is one reason they are audible for you when playing live (esp. when close the instruments you are playing - that naturally increases the volume quite dramatically; usually in listening over headphones or speakers we would never crank up the volume so high) and not so much when listening to recordings.
Also note that in the first example, the solid red line is ascending by one octave. But the dashed red line (the difference tone) is ascending more than FOUR octaves in the same time. It starts out as literally audible beats and then moves to 20, 40, 80 etc hz (very low tones) and then all the way up to A440.
Also note that the dashed red line is softer than the main notes but still, reasonably audible. The dashed green lines are quite a lot softer again, and thus more difficult to hear. They are difference tones of various overtones of the primary tones - roughly half or 1/4 as loud.
posted by flug at 7:30 PM on November 27
If they're playing something harmonious with the notes you're playing, they're a good sign that you're playing in tune!
Here are a couple of good videos discussing these, from a couple of different perspectives:
* Physics This Week
* Adam Neely
Note that the difference tones are quite soft, and for instance in the above examples you'll likely need to crank up the volume on your earphones or speakers quite a bit to hear them clearly. That is one reason they are audible for you when playing live (esp. when close the instruments you are playing - that naturally increases the volume quite dramatically; usually in listening over headphones or speakers we would never crank up the volume so high) and not so much when listening to recordings.
Also note that in the first example, the solid red line is ascending by one octave. But the dashed red line (the difference tone) is ascending more than FOUR octaves in the same time. It starts out as literally audible beats and then moves to 20, 40, 80 etc hz (very low tones) and then all the way up to A440.
Also note that the dashed red line is softer than the main notes but still, reasonably audible. The dashed green lines are quite a lot softer again, and thus more difficult to hear. They are difference tones of various overtones of the primary tones - roughly half or 1/4 as loud.
posted by flug at 7:30 PM on November 27
Just for fun I made this audio file that demonstrates the difference tones. It is very similar to the Physics This Week demo I linked above, except that I made quite a few adjustments that make hearing the difference tones a lot easier. (The pitch moves slower, goes up then back down, has a different waveform that accentuates the difference tones & makes them a lot easier to hear.)
You can look at the chart in the Physics This Week video to see examples of some of the difference tones you should be able to hear while listening to this file.
posted by flug at 10:17 PM on November 27
You can look at the chart in the Physics This Week video to see examples of some of the difference tones you should be able to hear while listening to this file.
posted by flug at 10:17 PM on November 27
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posted by madcaptenor at 9:23 AM on November 26 [1 favorite]