good approximation of the tuning

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.

thanks

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

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