The Circle of Fifths

Today, I'll introduce the first in a number of background topics you may wish to familiarize yourself with as you explore Ulysses. Sources for these topics range from the impressionistic to the frighteningly technical, so I'll try to include some links that land somewhere in the middle (mainly as a futile gesture of resistance against Wikipedia). In addition, the list of topics could easily be infinitely long, so I'll be hoping to offer only a rather selective version, in rather a sporadic and haphazard manner. Or less. Take these as far as you like - which may legitimately be exactly nowhere.

Topic One: The Circle of Fifths as the basis of key signatures in diatonic music.

I'm guessing that C and m, having been properly taught as musicians, are solid on this, but I have no reason to suspect (or doubt) the same of Calvin, MCP, and kph2. The basic idea is that starting with the natural key of C Major/a minor (no sharps or flats in the scale/key signature), you can use the interval called a musical fifth to derive two "key" structures in Western music:

• the sequence by which first one, then two, then three (etc.) sharps or flats are added to the key signature (upward fifths - F, C, G, D, A, ... for sharps; downward - B, E, A, D, G, ... for flats) in generating the entire set of musical key signatures, up to six flats or six sharps;
• the sequence of tonic notes that define the "key" (and start the musical scale) corresponding to each successive key signature, starting with the key corresponding to zero sharps or flats, and building up to the keys corresponding to six sharps or six flats.

For example,

• the key of C Major, named for the tonic or "starting" note of its scale, has no sharps or flats;
• add the first sharp, which goes on the note F, and now you are in the key of G Major, whose tonic note (G) is a fifth up from the tonic note (C) of C Major;
• add the second sharp, which goes on the note C, a fifth up from the first sharp on F, and now you are in the key of D Major, whose tonic (D) is a fifth up from the tonic (G) of G Major;
• and so on.

Note that the, um, note that lands on the fifth (i.e., the fifth note in the scale, starting from the tonic) in a given key is referred to as the "dominant"*, and is also the note that defines the key (and is the tonic) for the next key signature in the sequence. In C Major, the dominant is G; add a sharp and G becomes the G Major tonic, with D as its dominant; another sharp, and D is the tonic, with A as its dominant.**

*Okay - but, like, what does music theory have to do with Ulysses, anyway?

**Readers eager for evidence of the deity's existence will be struck by the convenience with which a stringed instrument, when tuned to an interval so musically significant as the fifth, may be played by a creature with four articulated (dactylic) digits opposing its thumb. Players of the stringed bass, which is typically tuned in fourths, secretly imagine that they are among the elect, as theirs is the instrument that offers exactly one chromatic step for each of the four available fingers in the interval between adjacent strings. They fail, however, to offer a coherent theoretical framework for diatonic music based on fourths. Cellists, by contrast, treat with skepticism any messianic claims coming from persons whose left hands bear fewer than seven fingers, not including the thumb.