Trying to explain hetrodyning and other electronic principles to my son, a trumpet playing EE student.
One trumpet blows a 500 Hz note and a second one plays an 800 Hz note, you get a 1300 Hz note and a 300 Hz note, right? (sum and difference)
One trumpet plays a note and second one simultaneously plays the same note, you get a 3 dB louder note, right?
I presume a real trumpet note isn't nearly clean enough to actually do that, or is it?
Don't overlook the fact that the sum and difference tones will be at less amplitude.
Musically speaking, there are also times when the difference note, much more so than the additive, which can be at such higher audio frequencies that we assume irrelevance, will be useful. The Perfect 4th, Perfect 5th and Octave of the Tempered Scale actually reinforce the Root. For example, the pipe organist often utilizes this by playing a P5 with one hand or the feet on the pedals, gaining an apparent root one octave lower than the root played, at half the amplitude. The Classical Organists term this the, "Resultant". Fast Forward to the Rock and Roll age and we find that Rock Guitarists often play what we now term as "5 chords" -- basically two note chords consisting of Root and Fifth, taking advantage of the same "resultant" situation and making for a chord with more apparent fullness or punch.
In teaching music intonation, as in with the given example of the Trumpet (my first instrument after piano as a kid), I find it much easier to teach them to hear the Beats that result from heterodyning of two notes that are very close together in pitch rather than so far apart as your example.
The tuning slide should be used to start with the slide further out than it should be to match the target tuning note, then, with the right hand, have the student slowly move that slide inwards, getting a little sharper incrementally, while listening for those beats.
As the beats get slower and slower, the note is getting closer to nailing the target pitch, until at some sweet point, the beats disappear altogether and the two notes reinforce, which means that the sound in the air will get a little bit louder (actually higher in amplitude as vs Loudness, which is really referring to an EQ situation and the Fletcher-Munson curve thing).
It is also important to have the student keep moving the slide further inward than the sweet spot of being dead in tune with the reference pitch, just so they'll understand that the beats will begin to speed up again the further north of the reference they go.
A very good thing to pick up and give the young student is one of those small quartz tuners. For a Trumpet player, make sure that the Tuner is a Chromatic type and it is easier to use one that automatically changes pitches rather than one that is manually set to only one note at a time. This kind of visual feedback, if used for ten minutes a day for awhile in their regular practice regimen can really speed up the process that a Trumpet player must develop, which is the ability to hear the next tempered note in a scale in their head *before* attempting to play said note. The first drill here is to play the simple Bb Major scale (C scale on the Bb Trumpet) and endeavor to lock that tuning indficator dead center for each note played. The Trumpet actually has a few intonation problems inherent in the instrument design that we must learn to overcome. For example, the low D above Middle C is inherently sharp (fingering 1 and 3 valves) and that's why modern Trumpets all come with a Third Valve Slide on them, shoot that slide out to more easily play the low D in tune. There is also a bit of "lipping" involved with nailing the Tempered Scale on the Trumpet. Classical orchestral players also typically like to have a 1xt valve slide available, for the D above thirdspace C as well. Then there are the uses of so-called "false fingerings" such as playing the top space E with 1 & 2 or just 4 by itself instead of Open.
Get the lad a good electronic chromatic tuner. The entry price is low indeed due to imports and availability.
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