Be Love was written and arranged on the lattice. I consciously used the lattice as a tool to make the music do what I wanted it to do. Working with this song has taught me a lot about leading the ear. Different parts of the lattice have different sounds. The upper right, the northeast, is…
The simplest untempered tuning of the major scale is: 1 — 0 cents 2 — 204 3 — 386 4 — 498 5 — 702 6 — 884 7 — 1088 Here’s how that tuning compares with the equal tempered scale: The black numbers show the pitches of 12-tone equal temperament. They are equally…
In harmonic space, the clearest name for each note is its ratio — 5/3, 3/2, 4/3, etc. Precise and unambiguous. But the ratios don’t give a very good idea of how to go about playing or singing those notes. There are a few instruments, such as the left hand keyboard on the accordion, that are…
The notes 1, 2, 3, 4, 5, 6 and 7, clustered at the center of the lattice, constitute a major scale. This tuning uses the smallest ratios (the ones with the lowest numbers) available for each position in the scale. It goes back at least to Ptolemy in the 100’s AD. I find it visually…
Musical nomenclature has been cobbled together over the centuries like a medieval city. Different systems leave their imprint in convention, later developments try to be compatible with accepted names, and the whole thing ends up confusing and contradictory. Take enharmonic equivalents, for example. G# and Ab are the same note on the piano, the black…