Re: [tuning] Digest Number 3529

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One of the interesting and often the more musically interesting set of scales are both the the Bi level MOS scales and the same with the Constant Structures (CS). These scale often fall through the crack of the other scales.
I still have not seen reproductions of any of the scales found in the keyboard mappings found in the early xenharmonikons , especially those at the end of vol 3. by other methods despite their simplicity
To take a set of predetermined number of scale tones and using the mapping template as to how and where different to fill out a scale of one own is a rewarding experience that involves much less math and with a hands on approach to building an actual scale that one can hear in the process of putting it together.
While unison vector omit distinctions between accumulated ratio, this simple method allow often at a certain key point two alternatives to which note one would like to use. The making of such a decision at a key point become often an artistic desicion that has implications for the scale that one will be using. One can always go back and change a particular scale point also. I think thereris allot to be said about how we get our scales as much as the final result. Short cuts can be deceiving
Obviously different methods produce different results which is there value. In this case it is the process also that is important to actually understanding what tones one has and can choose.

This paper http://anaphoria.com/RAST.PDF
shows him using two different staring points from which to extend a generator. page 10 showing variations of the size of the neutral third according to ones wishes (allows for regional fluctuation) .

In a different way his Helixsongs use the duel generator idea in a different way as the generators are two harmonic series. also one has the diaphonic cycles in his treasure chest

Message: 9
Date: Thu, 26 May 2005 06:36:44 -0000
From: "Dave Keenan" <d.keenan@bigpond.net.au>
Subject: Re: question about just intonation scales

Paul Erlich pointed out that there _are_ proper scales which are not
CS, such as 8 notes in a chain of just minor thirds.

So CS is neither a stronger nor weaker condition than propriety.

This usage of "weaker" does not imply any inferiority, only greater
inclusiveness.

Paul also pointed out that all MOS/DE scales are also CS but not
necessarily the other way 'round, so in that sense CS is a weaker
condition than MOS/DE. But of course no-one expects a JI scale to be
MOS or DE.

By the way, I hate limiting the term "MOS" to tunings with only a
single chain of generators per octave.

George Secor recently asked Erv Wilson in a letter, whether he thought
tunings with N parallel chains of generators 1/N of an octave apart
could also be called "linear" and therefore "MOS" when they have only
two step sizes. Unfortunately he did not address the question at all
in his reply.

-- Dave Keenan

--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/>
The Wandering Medicine Show
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