[sdiy] decaves?

[Dave Krooshof]

>>I was just curious as to whether or not anybody had ever heard (or heard of)
>>dividing octaves into 10 semitones (evenly spaced).
>>I'm guessing it wouldn't sound very musical most of the time, but I'm still
>>curious.
>>
>>Stephen
>
>The slendro scale used in gamelan music divides an octave (roughly) into
>5 equal intervals, so it's sort of a subset of your idea. Once I've got used
>to it (which didn't take long) I find this scale very musical. The good thing
>with slendro in improvising is, there are just no wrong notes ;-)
>
>Ingo
All notes are equal!!!!!
(let's hope the anti-communist dept of the CIA is not reading this list,
We'll be banned! I saw this paralel with communism and so called
atonal music before, although Schoenberg was an anti-comm as well.)

In www.koncon.nl, I worked with a 42 equal tone pine organ, which had
midi-in (coooool) an and a massive 2D keyboard with lot's of keys,
in different shapes and different feel due to the use of different kinds
of wood for each note of the octave.
According to the teacher Clarence Barlow, 52 equal tones per octave
is closer to pure harmonical intervals then the 12 tone scale, which can
be off by 22% of a semitone.

It seems there are three ways a tonality can be perceived:
comparing frequencies, evenly devided octaves and timbre.

* 1. comparing frequencies (string length and tube length)
like the greek pythagoras said: The more simple two tone relate,
the more harmonic they sound. So an octave relates as 1:2. Very harmonic.
a fifth is 2:3, also very harmonic. A fifth like that is 702 cents distance
from the root. The tempered scale has a fifth that's 2% of a semitone to low!

Pythagoras designed a scale that is built on these 2 building blocks:
1:2 and 2:3. A forth would be up an octave, then down a fifth.
A scale designed like this results in a maximum "off-scale-ness" of 22 cents,
which is called the pythagorian comma.
Blues appeared to be using the next prime number, 5, as an extra building
block. This is the reason blues musicians bend their notes to what they
feel they need to be, that happens especially to the third.
Adding a 7 was not to usefull, but going up to 11 for a building block,
led to the well know turkish "half minor", being something like
150 cents.

The pythagorian theory has a malfunction:
It doen't describe how it can be that a not that's a little off
is perceived as nearly correct, as it is way off according to the
theory: you need high primes to describe the relation
(example: 217:347 is nearly 2:3).
Does the ear round up to the next harmonic note?
Then why do we perceive just intonated music different
from equal temepered?
If pythagoras was completely right, it's a mystery how the
next scales work:

* 2. designer scales (on numbers)
The most famous one is the equally tempered scale. That's a designer
scale based on twelve equal semitones (100 cents each). Mathematically
it's something like 2 root 12 or something. (can't remember). The scale
is in my ears as rediculus as a 10 based equal scale might be.

I've heard an 8 base scale. It worked. The thing with designer scales
is that you can learn to like them, when musical meaning is expressed
by a composer or musician.

You do not need any extra hardware when you have midi, as you
can add a pitchbend commando to each of the notes.
The cents values are 120 cents per tone for an 10 based scale.
This is your scale:
000, 120, 240, 360, 480, 600, 720, 840, 960, 1080, 1200.
First thing you will notice, is that the fifth is off so much.
Secondly, the devil in th music, ogmented forth is right on: 600!
The third is realy bluesy. Nice. The others are pleasantly off. Nice.
I can put an mp3 online by tuesday, if you want to hear this
scale from my programmable max-msp pitchshifter.


3. designer scales (on timbre (or tradition)).
This is my way of hearing harmony. I hear it as a timbre.
Here is one of my favorite scales, Yaman:
000, 205, 386, 590, 702, 906, 1088, 1200

An african equivalent to the gamalan scale is this balofone scale:
000, 152, 338, 498, 715, 908, 1040, 1200.


Note: misspellings (c) Dave

B.A.I.


Ps: Nature is not harmonic. The rings around saturnus have gaps, due
to the fact that anything that was orbitting harmonically to any of
the moons, has been pulled away due to regular pullings.
The rings left are the inharmonic orbitting object. This must give
you an interesting insight the next time you are asked for your
astrological sign by a person at a party. Avoid being in harmony,
as you'll be pulled out and thrown onto a near by moon!

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