Comment by jancsika | Hacker News Reader

Comment by jancsika | Hacker News Reader

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Here's a way to figure out how they work:

Listen to Bach's Fantasia from Fantasia and Fugue in G minor, BWV 542:

https://www.youtube.com/watch?v=LWyiiOkhwoc

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.

Reminds me of the accordion (left hand)... it has only one octave of pitches, so can only descend an octave before returning to the highest pitch. Then it's up to first overtones to continue the illusion.

I'm used to hearing the terms time domain and frequency domain. But I've never heard pitch domain as a separate idea. Isn't pitch just the same as frequency?

In this context, the term is just used to tell you to think in terms of pitch classes — where all notes that are separated by an integer multiple of an octave belong to the same class — and not expect actual Shepard tone trickery related to absolute pitch.

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.

> However, the relationship between absolute pitch and frequency isn't always trivial.

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.

Thanks! Very informative.

In general I've found the world of music theory to be difficult to penetrate as an outsider, just gotta take small bites.

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