Re: (OT) non-octave scales (was Re: various infotaining natlang tidbits)

>From: Jonathan Chang <Zhang2323@...>
>In a message dated 2000/06/14 12:17:34 PM, thorinn wrote:
>
> >Are there actually intonation systems out there where you don't have
> >any pitches in a 2:1 ratio at all?
>
>     Yep, & for lack of a classification they are generally called
>"non-octave
>scale tuning systems.
I have heard of a 3:1 scale, but it's a modern invention.  The term for the
inteval would be 'dodecade'.  I forgot how many tones the scale was divided
in, but 19 tones (not the same thing as the 19-tone octave scale below)
would produce a scale just off the 12-tone octave scale.

>     Quite a number of scale tuning systems in South East Asia, Oceania &
>parts of Africa have scales in which 2:1 ratios are not used - preferences
>tending to near-octave pitches or pitches beyond the octave by as much as a
>quartertone are fairly common. In recent years, fractal-based scale tunings
>have also added to the "non-octave" class of tunings - besides other
>mathematicallly-based scale tuning systems.
The non-octave scales, from my impression, seem to be focused not on the
ability to melodize and harmonize many tones, but on the aesthetic qualities
of each invididual tone within a small set number, and the instruments
(gamelan set, kalimba, pan flute or bagpipes) are tuned accordingly.  It's
pure melody with much less concern for harmony except inherent harmony
resulting from intervals, and rhythm without a bass line.  So it takes a lot
of listening to appreciate gamelan music as much as a Bach concerto.
Likewise for a raga or a hornpipe (both of which perform a carefully-tuned
melodic system set against a fixed drone pitch, so harmony of a different
form results).

>     I simply loaded up my JI-Calc (Just Intonation Calculator) program on
>my
>computer & demonstrated a random series of different scale systems - in
>example, 13-tone Equal Tempered scale (very alien sounding), 19-tone Equal
>Tempered scale (very aggressive sounding... imagine a weird mix of Wagner &
>Klingon), the Indian _sruti_ system of 22-pitches, Harry Partch's
>Monophonic
>Fabric with it's 43-tones, Mercator II's 53-pitch scale, etc..
What is the Klingon scale based on anyway?

Nineteen-tone is supposed to be of Arabic origin (traditionally not equal
temperament), and I use it myself.  I'd like to construct a keyboard based
on a 19-tone scale.  In this scale, notes like C-sharp and D-flat are no
longer enharmonic; instead a diatonic step is not cut in half, but thirds.

Comparing the two scales, with C as the basis tone:

12-tone   19-tone
C         C
C#-Db     C#
D         Db
D#-Eb     D
E         D#
F         Eb
F#-Gb     E
G         E#-Fb
G#-Ab     F
A         F#
A#-Bb     Gb
B         G
          G#
          Ab
          A
          A#
          Bb
          B
          B#-Cb

Note 19-tone has two enharmonic pairs: E-sharp and F-flat, and B-sharp and
C-flat, which cross each other and differ by a chromatic step in 12-tone.

The 22-tone scale is a feature of South Indian (Karnatic) music, not North
Indian (Hindustani).  The latter case is basically Arabic-Persian-based
music theory, which often involves a 'quarter-tone' offset somewhere in the
scale.  My personal diatonic scale, for example, is based upon those lines,
and the result for C-minor, to cite an example:

C D- Eb F G A- Bb C

D- and A- are D and A a quarter tone flat.  Actually Arabo-Persian scales
only have one 3/4-step, not the two I have.  I'll work on some MIDI
examples, including a rather jarring chord I came up with -- a major seventh
with half-flatted third and seventh (three consecutive intervals of 3 1/2
chromatic steps, to be crude).

But Karnatic music is different in that the instrument (sitar, vina etc.) is
tuned to one of 72 [!] possible modes.  The unison and the fifth are always
fixed to a 3:2 ratio.

>     (There is also a few scale tuning systems that have as many as several
>hundred pitches to an octave range, but these IMHO tend to be just "special
>effects" oddities.)
The scale is nothing more than a gliss in that case.  A virtual
infinite-tone scale, since the human ear doesn't hear steps, but the same
note detuned.

>     At the other extreme, there are interesting scale tunings with less
>than
>5-tones per octave range as well. These I find to be deceptively "simple"
>and
Magnavox had a video game system called Odyssey II (there was an Odysey I
which came out in 1971; you had to put overlays on the screen).  Odyssey II
only played notes that were the root and fifth, approximately Eb and Bb.  A
two-tone scale in other words.

The Atari 2600 used scales based on the formula F = C / N, where F is
frequency, C is a fixed tone, and N is the scale number.  It was a
descending reciprocal step, which formed a rough minor sixth chord at first,
then in the lowest pitches became a glissando.

Real musical ability for home video games didn't come along until the
Nintendo (the classic 8-bit console system), which just plays square,
sawtooth and triangle waves at most any pitch.  It also plays noise which
simulates percussion.

a "mutated"/prepared toy
>piano, *musical mad scientist gigglabytefit*).
Huh, I never even heard a toy piano that was in tune.  I guess the only way
to tune one is to file the metal bars, but what if you want to *lower* the
pitch?

DaW.
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