All Pitches of Kepler's Music, Graphics

Graphs as we know them were introduced by Nicole Oresme around 1350 CE, but the staff notation for musical pitch was already 400 years old. We may then regard staff notation as the source of our graph tradition.

Pitch graphics: the staff and the keyboard

We wish to represent all pitches of Kepler's Music of the Spheres graphically. As eleven octaves are required and the traditional staff notation is awkward for more than four octaves, we will replace the staff (as a scale of pitch) with a piano keyboard image, suitably extended on each end. Thus a time series of pitches (let us say of constant volume) may be represented as a graph, with the time line horizontal, and the extended keyboard vertical. We are going to make use of the keyboard as a vertical axis.

Pitch graphics: the keyboard vs pitch frequency

Suppose the pitch frequency of Middle C on the piano were 256 Hz. We may denote this as C-256. Then an octave above would be C-512, an octave below would be C-128, and so on. As these frequencies are powers of 2, we may also write C-28 = C-256, and so on. Perhaps it will not be too peculiar, in fact, to just write C8 for C-256.
Here is a graph relating pitch frequency to our keyboard scale. This is, of course, the exponential function, and may have been involved in the discovery of logarithms. The gray rectangle indicates the range of the standard piano keyboard.
And here, on the same scale, are the pitch ranges for the planets, assuming a mean pitch of 20 Hz for Saturn.

Note that the vertical scale from C4 (16 Hz) to C15 (ca 32,000 Hz) is appproximately the normal range of human hearing.
Rev'd 07 jan 2002 by ralph abraham