Overtone question

[Blackquill]

A wind ensemble I played with recently played a piece... I forgot the name of it already, but it ends with a concert B-flat chord (C chord for b-flat trumpet). Trumpet 1 is a high C, trumpet 2 plays a G below that, and I was on trumpet 3, who plays an E below that. Almost every time during rehearsal and the performance, when we played that final chord I heard what I believe was an overtone... I would hear a "B" on top of the staff! It sounded really awesome!

That means the ovetone is... a major 7th? That can't be right! I then theorized that some players in the group must be playing that note on the final chord. But then when I heard the recording our of performance, I heard no such note!

So what was it that I was hearing? Was I hearing an overtone of a 5th on top of the G and E that were being played? I'm just not sure...
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[trpt.hick]

I think what you heard was a combination tone, where the stronger overtones of the three trumpets all lined up on the same note, making it strong enough to be heard fairly well as a fourth player. With the notes you listed, the combination tone was likely a note much higher than the three notes being player. . . perhaps a high G.

David Hickman

[Blackquill]

In other words, are you saying it's an overtone of an overtone? (i.e. the first overtone being the 3rd of the chord, which then has an overtone of a 5th stacked on top that?)
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[trpt.hick]

No. When any note is played by an instrument, a whole series of overtones are sounded very faintly. These line up exactly like the "bugle" notes on a trumpet: octave above note played, fifth above that, fourth above that, etc. Some overtones are relatively weak, and some are relatively strong.

When more that one note is sounded at the same time, the overtones of each note are sounding very faintly. If overtones have a common note together that overlap (each being relatively strong), that particular overtone can seem like an extra player is performing.

Example:

If trumpet 1 plays a high C, the following (higher) overtones will sound very faintly within that note: double-high C, G above that, triple-high C, E above that, G above that, B-flat above that, quadruple-high C, D above that, E above that, F above that, G above that, etc. until the overtones are too high for humans to hear.

If trumpet 2 plays a G on top of the staff, the following overtones will sound very faintly: high G, high D, double-high G, B above that, D above that, F above that, triple-high G, A above that, B above that, C above that, D above that, etc.

If trumpets 1 and 2 are sounding their notes at the same time, there may be some overlapping overtones, making those overtones stronger that the other overtones. In the case above, overlapping overtones are G above double-high C and G above triple-high C. So, these two very high Gs will possibly sound strong enough for people to hear them as extra pitches.

Combination tones are not to be confused with "resultant" (or "difference") tones, which we hear as faint, buzzy tones BELOW the two notes being sounded by two players. This is a bit complicated to explain, too, because these notes do not actually exist. We humans merely "hear" them because our brains do not know how to process them

Example:

Two players are producing two different pitches within the same space of air: A=440 (2nd -space A concert) and E above that = 660. The two sets of sound waves overlap 220 times per second, making those particular sound waves stronger that the other sound waves. As all of the sound waves hit the ear drum, some of the waves are louder. The brain will not know how to process this, so it interprets the stronger waves as a separate pitch: low A = 220. Of course, this pitch is not actually being sounded, but we swear we hear it.

I hope I didn't confuse you even more!

DH

[Tpt_Guy]

[trpt.hick]

Yes, Tartini wrote a lengthy theory book about resultant tones. However, the correct usage of the term "Tartini Tone" is resultant tones stemming from the various intervals between the overtones. These create extremely faint lower pitches. However, when all of these Tartini Tones are heard collectively, they create the warmth we like in our sound.

To clarify:

Overtone: One of dozens of faint higher pitches within any pure sound. The notes in the overtone series are exactly the same as the sequence of notes played as "bugle" tones on a brass instrument when ascending from the fundamental. These (together) create the brilliance in a sound.

Resultant Tone (Difference Tone): A perceived pitch lower than any two notes played at the same time. It is calculated by simply subtracting the frequency of the lower note from the frequency of the upper note. (Examples: A = 880 minus A = 440 is 440, reinforcing the lower note of this octave interval; A = 880 minus E = 660 is 220, which sounds as a low A.)

Tartini Tone: Guiseppe Tartini, the great Baroque violinist and composer, was the first to write a theory book about resultant tones. He was also first to theorize about difference tones produced from the overtones in a pure sound. These create the warmth in a sound.

[PH]

Excellent information. Thank you!
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[Jerry Freedman]

I probably should add that in my younger days, before I found the actual spiritual truth of trumpet playing I also played bluegrass guitar. I had ( still have) a Martin Dreadnought guitar which is a big, booming acoustic guitar. I tuned it listening and feeling for the difference tones. If you held the guitar closely and lightly next to your body and played two strings that should be in unison but were slightly off you could hear and feel a very, very low pitched sound. You tuned ( or attempted to tune) that sound or slow vibration away

[Derek Reaban]

Thanks Dave! Great summary!
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Derek Reaban
Tempe, Arizona
Tempe Winds / Symphony of the Southwest

[BPL]

[Tpt_Guy]

I read somewhere about Tartini using this principle in a composition, but on a search just now couldnt find anything.

I did find this, however:

https://earslap.com/article/combination-tones-and-the-nonlinearities-of-the-human-ear.html

Which demonstrates the potentiality of using them.
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-Tom Hall-

"A good teacher protects his pupils from his own influence."
-Bruce Lee

[iiipopes]

Helmholtz expanded on Tartini in his tome, "On the Sensations of Tone." He described additive heterodyning, or what he calls summational tones, as well Tartini's subtractive heterodyning, or what we call the low difference tones. So yes, it is possible to hear upper harmonics as well as lower difference tones, and they are real, not a construct of the brain, and unlike difference tones, may or may not be in the harmonic series of the fundamental - page 153.

https://books.google.com/books?id=wY2fAAAAMAAJ&pg=PR3&source=kp_read_button#v=onepage&q&f=false

https://www.amazon.com/Sensations-Tone-Dover-Books-Music/dp/0486607534
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[Billy B]

Bill Adam was quite adept at using resultant tones in his arranging for brass choir. He told me a well known conductor was visiting IU and stopped by to listen to Adam's brass choir rehearsal. He remarked the quality of the ensemble except on that final chord the third was being played too loudly. There was no third written.
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Bill Bergren