notation of 16-tET

Kraig Grady wrote,

>I have a 16 tone scale based on the Chopi in S.E. Africa. It is not an
equal
>scale but is close using higher harmonics. It was formed by just doing
simple
>modulations until it formed a cycle. The closest scale you would have
to this
>tuning would occur if you superimposed 7 units of your tuning. You
would end
>up with an MOS at 5,7,9,&16. On the keyboard I have for this tuning I
have a
>conventional keyboard that alternates 3 blacks and 4 blacks instead of
2 and
>3.

This is the same keyboard design that Goldsmith proposed for 16-tET with
inhamonic overtones. He named the 9 white keys with the first 9 Greek
letters.

"Paul H. Erlich" wrote:

> From: "Paul H. Erlich" <PErlich@Acadian-Asset.com>
>
> Kraig Grady wrote,
>
> >I have a 16 tone scale based on the Chopi in S.E. Africa. It is not an
> equal
> >scale but is close using higher harmonics. It was formed by just doing
> simple
> >modulations until it formed a cycle. The closest scale you would have
> to this
> >tuning would occur if you superimposed 7 units of your tuning. You
> would end
> >up with an MOS at 5,7,9,&16. On the keyboard I have for this tuning I
> have a
> >conventional keyboard that alternates 3 blacks and 4 blacks instead of
> 2 and
> >3.
>
> This is the same keyboard design that Goldsmith proposed for 16-tET with
> inhamonic overtones. He named the 9 white keys with the first 9 Greek
> letters.

As I said it is close to 16- equal but not quite and I can't provide
details at the moment due to powers beyond my control but yes I'm glad
someone else looked into this one. Who is goldsmith and did he actually
make it. Although it is derived from the Chopi is S.E. Africa it bares
strong resemblance to a pelog, more of the sumatra and burma type of scale,
but I sure Wolf can fill us in on this one. For those who don't know, the
indonesians were colonizing Madagascar and S.E. Africa between 100-700AD.
Its hard to say who got the scale from who. I have also seem Slendro like
tunings in west Africa. I could see using the Greek letters but it seems
maybe Chopi letters would be better. Despite Wilsons use of mixing greek
with traditional, I have personally found it not to my liking. All greek
would be better. For notation I don't worry about letter names though. I
just use a klarscripo notation of 4 lines alternating with 3 lines! Those
that have my FROM THE INTERIORS OF ANAPHORIA, the long organ piece Court
music of the mesa (5th transpription)is in this tuning
-- Kraig Grady
North American Embassy of Anaphoria Island
www.anaphoria.com

Kraig Grady wrote,

>Who is goldsmith and did he actually
>make it.

The relevant article is:

Goldsmith, David S. 1971. "An Electronically Generated Complex
Microtonal System of Historical and Vertical Harmony", _Journal of the
Audio Engineering Society_ vol. 19 no. 10 pp. 851-858.
John Chalmers brought this article to my attention -- the Harvard Music
Library had a photocopy.
I don't remember whether he actually built the keyboard he designed, but
I'm pretty sure he listened to the inharmonic complexes he proposed as I
recall him writing about some musical problem connected with chords
resembling traditional diminished chords.