Yahoo Tuning Groups Ultimate Backup makemicromusic Re: automated harmony/counterpoint (MIDI example)

On 8 Feb 2002, Kraig Grady <kraiggrady@...> wrote:

> Micromakers!

> Well thought i would start some movement here with automated
> harmony and or counterpoint. The idea of a priori methods of generated
> such.

> Parallel harmony has to be the simplest, mirror writing or mirror
> chords against melody as a variation is another. i remember that
> Slonimsky had ones that used major chords. Here if the melody goes up
> you used chords that treat this as the root the fifth then the third
> of such chord, opposite if you go down. I have applied this to
> pentatonic chords, wondering if any other have such instant methods
> they find useful at times!

Hello, there, Kraig, and your question ties in with some "algorithms"
for generating harmony or counterpoint at a keyboard that I sometimes
use, or maybe quite often if we can consider passages or chains of a
few notes as a unit of interest.

In the medieval and Renaissance terminologies of Europe, this is
sometimes known as _discantus supra libram_ ("discant" or improvised
polyphony "over the book," while reading a chant melody upon which the
ensemble extemporizes added parts), or _quintoyer_ ("fifthing," a
technique for improvised discant mostly in fifths, with phrases often
beginning and ending on octaves), or around the early 15th century,
_faburden_ (English) or _fauxbourdon_ (French).

This kind of technique is a special favorite for me in a just
intonation system I call _Sesquisexta_, the Latin term for a ratio of
7:6, where two 12-note Pythagorean keyboards are tuned at this
distance apart (~266.87 cents).

Using a curly brace symbol (}) to show a note on the upper keyboard
raised by a 7:6, I can harmonize a melody in "21st-century
fauxbourdon" using a chain of parallel 14:18:21:24 sonorities starting
and ending with a pure 2:3:4.

Taking a simple chantlike melody in the medieval Dorian mode, let's
say D4 E4 G4 A4 G4 F4 E4 D4 C4 D4, putting the melody in the highest
voicee, we get a texture like this:

D4 E4 G4 A4 G4 F4 E4 D4 C4 D4
A3 B}3 D}4 E}4 D}4 C}4 B}3 A}3 G}3 A3
A3 B3 D4 E4 D4 C4 B4 A4 G3 A3
D3 E}3 G}3 A}3 G}3 F}4 E}4 D}4 C}3 D4

Here's a MIDI file of this:

http://value.net/~mschulter/seskg001.mid

There are some interesting melodic aspects here. The highest voices
moves entirely in regular Pythagorean steps: 9:8 whole-tones and
256:243 semitones. However, in moving from the opening 2:3:4 to the
following 14:18:21:24 which starts the chain of parallel sonorities,
the lowest and next to highest voices ascend by a 21:16 (D3-E}3,
A3-B}3), a 9:8 plus a 7:6.

From there, all the voices move by identical steps in the parallel
motion, something that makes it different from the parallel thirds and
sixths of styles like 15th-century fauxbourdon, and maybe a bit like
an organ mixture stop. Then we come to the final cadence, where the
upper voice and the next to lowest ascend by usual 9:8 steps, while
the other voices descend by 28:27 steps. It's a counterpoint of
epimores.

Anyway, thanks for this topic, which gave me a good excuse to produce
a bit of actual music for sharing here, albeit via MIDI rather than
with the kind of acoustical instruments you have crafted over the
years.

Also, thanks to Robert Walker for a beautiful CD I want to review here
soon, including a wonderful chant melody in Sesquisexta.

Most appreciatively, with peace and love,

Margo

Re: automated harmony/counterpoint (MIDI example)

🔗M. Schulter <MSCHULTER@...>

🔗Robert Walker <robertwalker@...>

🔗jpehrson2 <jpehrson@...>