Re: A Scale of two notes. P,S,

you might want to look at Yassers book who goes down what appears to be the same lane as your self.
talso the recurrent sequence and cscales of Mt Meru are all continured fractions.
the continued fraction up the scenter of the range it appears you are touching up here was possibly done by Konerup
which i have an excerpt from here
http://anaphoria.com/korn.PDF

> Date: Fri, 23 Sep 2005 08:15:00 -0000
> From: "microtonalist" <mark@equiton.waitrose.com>
>Subject: Re: A Scale of two notes
>
>
>
>Interpretation 1 is analogous to the meantone interpretation of the >Diatonic scale, EDOs being 19 or 31 etc
>
>Interpretation 2 is analogous to the twelve-tone interpretation of >the diatonic scale.
>
>Interpretation 3 is analogous to the pythagorean interpretation of >the diatonic scale, one EDO being 17.
>
>
>The various settings of L and s I gave in my original post were to >show how this scale could be interpreted as the ancient Greek 'scale' >used for poetic recitation, consisting of just two notes, placed a >fifth apart. But, importantly, with increasing numbers of notes >(settings of L and s), other scales that approximate these relations >and are used ethnically, such as 5EDO and 7EDO (or 5 and 7 ADO - >approximate divisions of the Octave) embed this most basic scale.
>
>This was supposed to show that this most basic scale is embedded in >all scales. (But you knew that anyway) >
>This was as a consequence of reading an article on factual and >conuterfactual recomposition, which explores different >interpretations of basic scale theory. >
>I leave as an exercise for the reader to perform the same experiment >on other Ls patterns.
>
>I hope this helps.
>
>Mark
>
>Has anyone else heard of semiconvergents and continued fractions?
>Without indulging in too much mathematics it is of the form
>
>y = log2(ratio) = series of continued fractions
>
>
>
>--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@y...> wrote:
> >
>>--- In tuning@yahoogroups.com, "microtonalist" <mark@e...> wrote:
>> >>
>>>Let us look at the simplest possible scale
>>>
>>>Ls
>>>
>>>Let us label the two primary pitches as 0 and 1
>>>
>>>0------1---(0...
>>>
>>>Transposing the scale to begin on 1, we arrive at
>>>
>>>0-----1---0------1
>>> 1------0#--1
>>> >>>
>>I must say, you lost me with the # notation, and much of the
>>subsequent discussion. Is there another way you could explain
>>this? (And what's the idea behind it?)
>>
>>-Carl
>> >>
>
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--
Kraig Grady
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