The song "Fold4, Wrap5" by Autechre is a cool example. It's not hard to see how it works, but it's a delightful effect regardless. Each bar has a point at which the beat shifts to a double-time version of itself, while the tempo of the track constantly decreases so that the double-time rhythm transitions back to the original rhythm.
Here's a youtube link if anyone else is interested: https://www.youtube.com/watch?v=SLvFsP1izS4
Listen to Bach's Fantasia from Fantasia and Fugue in G minor, BWV 542:
At about 3:54 you'll hear a famous section where Bach starts "circling" around fifths. The general pattern is that the notes of the chords in the hands "rise" while the feet descend.
Listen to the bass line. It seems to descend by step for thirty notes in a row. But try singing any note and singing down a scale for thirty notes in a row. You probably can't do it. And if Bach did that in the bassline the final note would be really low and flabby.
So how does the bassline seem to continue descending by step while remaining in the same general range?
The answer is a two-word phrase that is usually met by profound boredom in first-year music theory classes. But that concept is what Bach uses in the pitch domain here to achieve his aim. And its analogous to what happens in the frequency domain to produce a Shepard tone.
However, the relationship between absolute pitch and frequency isn't always trivial. The latter is a physical phenomenon, but the former is psycho-acoustic. When you have sounds with a normal set of overtones that align with a harmonic series, the perceived pitch matches the fundamental frequency. But that frequency doesn't actually need to be audible. By weighting the amplitudes of the partials in a certain way, you can also construct a sound that will be perceived as different pitches by different listeners, or by the same listener under different circumstances.
With sounds whose frequencies aren't all harmonic, assigning a pitch can get more complicated.
Not only is it not trivial, it is undefined. For example, "middle C" can map to different frequencies depending on your tuning system, for just one example.
Pitch is the higher level abstraction. Especially on the organ, "middle C" may get interpreted as "middle C plus a C an octave below, plus another octave below for good measure" depending on context. I assume that's what Carpenter is changing when he's putting his hand on those pads where the stops should be.
In general I've found the world of music theory to be difficult to penetrate as an outsider, just gotta take small bites.
It would probably be boring to listen to all the time, but interesting to hear it playing a piece which usually makes use of lots of dissonance.
(Coltrane's) Giant Steps in C. https://www.youtube.com/watch?v=qTYzYpb1MY0
For jazz musicians it's very funny, in a horrifying kind of way, maybe listen to the 1959 original first if you don't know it. https://www.youtube.com/watch?v=Lu0Lhysn_X8
And thank you! While getting the links I found this wonderful animation of a shortened version of the original: https://www.youtube.com/watch?v=rh6WTAHKYTc
p.s. Woohoo! Coltrane on HN! :-)
Pentatonic scales have that property, mostly how even beginner guitarists can achieve picking solos (as long as you know what the root note is and keep rhythm)
Same for some harmonicas.
Sounds like you're describing a vocoder or auto-harmonizer but I can't be sure.
Suppose I play an F-sharp above middle C on your "averager" keyboard. What is heard? Is it only various C pitches? C pitches and a single F-sharp? Something else?
Do the C pitches have harmonics or is it only the fundamental?
I imagine the best you can get will sound like playing the horn. By that I mean a simple horn, without pistons nor slide. Because horns have a fixed length, they can only play one note, but skilled players can control harmonics to create a melody.
Good insight, but these variations are correlated with variations in pitch. It's a single note in the sense that it's always a C; not necessarily always the same octave.
> horns [...] can only play one note
A piece in bugle scale doesn't sound like one note to an average listener, nor does playing such an instrument feel like staying on one note. I'd rather compare this to a didgeridoo than a horn.
But if I concede that we don't need to adhere to lower grade music theory and that the performer will not use advanced techniques that can alter pitch without the use of a slide or valve, what argument could be made to support the "one note" claim?
To clarify what I'm looking for, here's an example of such an argument (but I don't know how much, if at all, it applies to actual fixed-length horn instruments): If the exact frequencies of a note's overtones deviate from a pure harmonic series, one could make a distinction between pitch-shifting a note and varying the timbre. I.e. playing the next note above the instrument's fundamental pitch doesn't multiply the individual frequencies by a constant factor, but repeats the exact frequencies of the fundamental's overtones, thus reordering the frequency ratios between adjacent overtones.