Unlike the overtone series of the previous post, there is nothing physical or natural about the undertone series, despite its very similar construction. The overtone series consists of notes at frequencies f, 2f, 3f, 4f, and so on; the undertone series, on the other hand, consists of notes at frequencies f, f/2, f/3, f/4, and so on. The undertone series is the mirror image of the overtone series. If you start at one particular note and go up for the overtone series, you’d go down by the same amount for the undertone series. It’s available in the Offtonic Microtonal Synthesizer as Undertone (C8).

Some music theorists have theorized about this undertone series, claiming, among other things, that the minor triad is derived from it and is therefore just as natural as the major triad. While undertones 4, 5, and 6 do form the minor triad, there’s nothing natural about the undertone series. The tones in the overtone series sound good together due to the small whole number ratios between them, and for any pair of notes, that’s still true here. However, this is not so for chords! For example, consider the overtone seventh chord, 4:5:7. Invert that, and you have (1/7):(1/5):(1/4) = 20:28:35. The numbers are much larger and the small whole number resonances are no longer obvious.

Of course, do not interpret the above paragraph to mean that notes *must* have small whole number ratios to sound good together. As far as I know, this is still unsettled science — I could be wrong — but approximations to small whole number ratios still sound good, and they sound *less* good the further they are from such a ratio. For example, C to a half-sharp G sounds pretty terrible because the interval is so close to yet so far from a perfect fifth, while C to G# is a dissonant but fairly neutral augmented fifth. A lot goes into determining the level of dissonance of chords, including cultural factors.

Anyway, enjoy the undertone series. Its top note is a very high C8 in order to give room for the low notes, but I might change it to C7 at some point since C8 really is rather high.