Yahoo Tuning Groups Ultimate Backup tuning Fwd: What is porcupine?

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
--- In tuning@yahoogroups.com, "Stephen Szpak" <stephen_szpak@h...>
wrote:
>--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
>--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
>
> >"Porcupine" refers to a class of "experimental" scales and tuning
systems.
> >A lot could be said about it, but roughly speaking, the
>idea
> >is to use an interval of about 163 cents to generate the notes,
repeating
> >the interval as many times as one wishes (scales of 7, 8, 15,
22 . . .
> >notes are the most logical stopping places though) and wrapping
around the
> >octave.
>
>An example which stops at 13 is this:
>
>http://66.98.148.43/~xenharmo/ogg/exotic/porcupinized/bald.ogg
>
>The music may sound strangely familiar.
>
>--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
>
>
>
>"Porcupine" refers to a class of "experimental" scales and tuning
>systems. A lot could be said about it, but roughly speaking, the
idea
>is to use an interval of about 163 cents to generate the notes,
>repeating the interval as many times as one wishes (scales of 7, 8,
>15, 22 . . . notes are the most logical stopping places though) and
>wrapping around the octave. There are some nice harmonies to be
found
>in such scales, with decently-tuned renditions of both conventional
>triads (though fitting together into progressions not possible in
>conventional tunings) and "extended" harmonies deriving from higher
>up in the harmonic series.
>
>I've explored the 7-note porcupine scale in 22-tone equal
temperament
>in some of my performances. The scale can evoke a unique blend of
>Thai, Arabic, and Western Renaissance flavors, or something
>altogether otherworldly, depending on how you use it.
>
>-Paul
>--- End forwarded message ---
>
>
> STEPHEN SZPAK WRITES::::::::::::::::::::::::::::::::
>
> As usual I need a explanation of a explanation. (Please don't
chop off
>parts of this
> message, for the time being.)
> First, how can a 7 note scale exist in 22 tone equal temperament?

It's a subset (and unequal of course). If you play something on the
white keys of the piano, you're using the diatonic scale, a 7-note
scale, within the 12-tone equal temperament tuning system.

>Is the performer
> playing in 7 or 22?

Playing in a 7-note scale, within the larger tuning system (some or
all of which may also avaliable to the performer, say for modulating
the 7-note scale to other pitch levels) of 22-note equal temperament.
--- End forwarded message ---
STEPHEN SZPAK WRITES:::::::::::::::::::

So the objective of taking the 15 EDO scale (which interests me) and applying
a porcupine generator to it is to change the notes of the scale. Some notes
exist in 15 EDO and some don't afterwards?
Also porcupine [15] in 7-limit minimax tuning (whatever all that means) has
10 or so fifths that are <10 cents sharp I think, comparted to 15 EDO's >18 cents sharp.
So these are 2 reasons why porcupine scales would be used?

S. Szpak

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
--- In tuning@yahoogroups.com, "Stephen Szpak" <stephen_szpak@h...>
wrote:
> STEPHEN SZPAK WRITES:::::::::::::::::::
>
> So the objective of taking the 15 EDO scale (which
interests me)
>and applying
> a porcupine generator to it is to change the notes of the scale.

To someone else, the objective might be to find useful and
melodically and harmonically coherent subsets of 15-equal.

>Some notes
> exist in 15 EDO and some don't afterwards?

If you're changing the generator from the exact 160-cent value it has
in 15-equal, then at most one note will be in common between your new
tuning system and your 15-equal.

> Also porcupine [15] in 7-limit minimax tuning (whatever all that >means)

Think of it as a particular porcupine generator, designed to best
approximate ratios of 7 and below, extended out to 15 notes. Since
you've changed the generator relative to 15-equal, you'll have
a "garbage" interval connecting the two ends of your chain.

>has
> 10 or so fifths that are <10 cents sharp I think, comparted to
15 EDO's
> >18 cents sharp.

Right, and the other fifths are "wolves" because they are not formed
purely from instances of the desired porcupine generator, but instead
contain the "garbage" interval replacing one instance of the
generator in its makeup.

> So these are 2 reasons why porcupine scales would be used?

Getting subsets of 15-equal, and getting 15-note scales with many
intervals and chords in better tune, are 2 reasons -- don't know if
that's exactly what you're referring to.

Are you familiar with the history of 12-note tunings in Western
music? All of this has analogues in more familiar, conventional
territory.
--- End forwarded message ---

STEPHEN SZPAK WRITES:::::::::::::

I know about 12 EDO (sort of).
What do you mean by "melodically and harmonically coherents subsets of 15 equal"?

S Szpak
stephen_szpak@hotmail.com

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🔗wallyesterpaulrus <paul@stretch-music.com>

I'm clipping excess quoted material because many have asked that this
be done.

--- In tuning@yahoogroups.com, "Stephen Szpak" <stephen_szpak@h...>
> STEPHEN SZPAK WRITES:::::::::::::
>
> I know about 12 EDO (sort of).

And meantone, well-temperament, etc.?

> What do you mean by "melodically and harmonically coherents
>subsets of 15
> equal"?

Subsets which have a rich supply of "near-just" harmonies, and can be
understood as a "scale" in their own right, with each generic
interval coming in at most two specific sizes.

For example, if you start with a note and build a 7-note scale
downwards from it by porcupine generators in 15-equal, you have 1200
1040 880 720 560 400 240, then assume octave-repetition to get 0, etc.
"Near-just" harmonies here include 0-400-720, 1040-240-560, 880-0-
400, 720-1040-240, and even 0-240-400-560-720 which resembles an
8:9:10:11:12 chord.

Meanwhile, if you look at the 1-step intervals in the scale, you see
only 240 and 160; 2-step intervals, 320 and 400; 3-step intervals,
480 and 560; 4-step intervals, 640 and 720; 5-step intervals, 800 and
880; 6-step intervals, 960 and 1040; and 7-step intervas, all 1200.
This means the listener is going to have an easy time understanding
motives as they are moved to different starting points in the scale;
they will still sound recognizable and familiar, but with interesting
changes in character.

Gotta run!

🔗Stephen Szpak <stephen_szpak@hotmail.com>