[tuning] re : Re: good approximation of the tuning

Dear Monzo

I think about relation between good approximation and JND of nearly 5 cent.is it correct?

I want to know it exactly for my intervalic spectrum of melodic musics like persian with a wide variety of changes in interval?

thanks

*****************************************

hi Mohajeri,

--- In tuning@yahoogroups.com, "Mohajeri Shahin" <shahinm@k...> wrote:

> Dear monzo
>
>
>
> What is the range of a good approximation of the tuning as u told:
>
>
> i looked at 72-edo, but concluded that it wasn't a very good
> approximation, because right off the bat, the very first two
> degrees after the 1:1 (nîm qabâ hisâr and qabâ hisâr) are
> basically midway between two 72-edo degrees.
>
> when i saw that, i took a look at 144-edo, but again, there
> were a lot of notes that fell between the 144-edo degrees.
>
> of course, the amount of absolute error keeps diminishing
> as the cardinality of the EDO increases, but the point is
> that if there are many notes lying between two EDO degrees,
> then that EDO is not a good approximation of the tuning.

unfortunately, i can't really answer your question
"what is the range of a good approximation" ... rather,
i was looking at those pitches which fell almost exactly
between two EDO degrees, and thus indicated that that
tuning was a *bad* approximation to Bey's tuning.

it happened that for 36-edo, none of Bey's pitches
fell midway between two 36-edo degrees. they all
lie closer to one particular 36-edo degree.

(of course, keep in mind that this was when i examined
only the pitches of Bey's scale which are contained in
the bottom perfect-4th, because that was all that Danny
posted in his first post. perhaps if i examined the whole
scale in comparision with 36-edo, it wouldn't fare as well.)

-monz

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Shaahin Mohaajeri

Tombak Player & Researcher , Composer

www.geocities.com/acousticsoftombak

My tombak musics : www.rhythmweb.com/gdg

My articles in ''Harmonytalk'':

www.harmonytalk.com/archives/000296.html

www.harmonytalk.com/archives/000288.html

My article in DrumDojo:

www.drumdojo.com/world/persia/tonbak_acoustics.htm