Porcupine[8]

Igliashon Jones pointed out to me that a fixed template of generic
intervals (1-3-6 or 1-4-6 or 1-4-7) rotated through Porcupine[8]
gives three major triads, three minor triads, and two "sus" chords. I
then started playing around more with it, which led to this post on
MakeMicroMusic:

--- In MakeMicroMusic@yahoogroups.com, "Paul Erlich" <paul@s...>
wrote:

--- In MakeMicroMusic@yahoogroups.com, "Igliashon Jones"
<igliashon@s...> wrote:

> 8-note Porcupine

By the way, I've been playing around with this scale a lot, trying to
wrap my ears around it and come up with some confident-sounding
music. Thanks for drawing attention to it, Igs -- it seems that only
the 7-note and 15-note varieties have gotten people's attention
before, while the 8-note version is really the most illustrative of
the Porcupine "Forms of Tonality" as in my paper of that name.

Take the triadic chord progression

F# minor (F#-A-C#)
A major (A-C#-E)
(E sus4) ((A-B-E))
E minor (G-B-E)
G major (G-B-D)
(D sus4) (G-A-D)
D minor (F-A-D)
F major (F-A-C)
F minor (F-Ab-C)

and render it in your favorite tuning system, holding common tones
constant from one chord to the next. Only one note changes from one
chord to the next if you include the optional sus chords in
parentheses. What happens? Well, in 12-equal, clearly you end one
semitone lower than you began. In JI, you end 250:243, or 49.2 cents
lower. But in 15-equal, 22-equal, 29-equal, TOP Porcupine, and other
porcupine tunings, you end right back where you began. The "F# minor"
and "F minor" end up being exactly the same chord! Thus a nice smooth
8-chord cycle is possible in these tunings that isn't possible in JI,
12-equal, meantone, or most other tunings.

What pitches do you need for this chord progression? In porcupine
tunings, you need only 8 pitches, and these form a scale with 7
identical "large" steps and 1 "small" steps. In 22-equal, the pitches
from the chord progression above fall as follows:

Initial A = Final Ab
+Small Step (1 degree of 22)
= Final A
+Large Step (3 degrees of 22)
= B
+Large Step (3 degrees of 22)
= C = C#
+Large Step (3 degrees of 22)
= D
+Large Step (3 degrees of 22)
= E
+Large Step (3 degrees of 22)
= F = F#
+Large Step (3 degrees of 22)
= G
+Large Step (3 degrees of 22)
= Initial A = Final Ab

This is the 8-note Porcupine scale Igliashon was referring to. It
works great for melody, and it works great for chord progressions.
But it's not so great for a homophonic style that plays all the notes
of the scale against chords. There aren't really any tonally stable
modes (to my ears so far). So perhaps it would be best for a kind of
modal counterpoint, where the melodic utility of the scale would be
brought out clearly, but the notes heard sounding together would
largely be restricted to belong to one of the consonant chords in the
progression above.

More on this when there's actual music to present -- and I hope
others will attempt to create some examples too!

-Paul
--- End forwarded message ---