Notation discrepency for the Well-Tuned Piano

Hi folks
We here at the SEJIS were retuning our OmniII with the digital mod to
LaMonte Youngs' frequencies used in the Well-tuned Piano. We were using
the book,Sound and light. What we discovered after a little frustration
that the tuning is listed rather strangely....on the staff section in
the portion written by Kyle Gann the 21/16 is notated in the 5th scale
position when it should be in the 6th and the 7/4 and the 441/256 are
switched as well. Does anyone have a clue to why this is notated that
way?
Darren and I figured it out but it caused about an hour of
miscommunication while we were tweaking divide by n dipswitches.....
Pat

the listing for the cents is correct though

Patrick Pagano wrote:

> From: Patrick Pagano <ppagano@bellsouth.net>
>
> Hi folks
> We here at the SEJIS were retuning our OmniII with the digital mod to
> LaMonte Youngs' frequencies used in the Well-tuned Piano. We were using
> the book,Sound and light. What we discovered after a little frustration
> that the tuning is listed rather strangely....on the staff section in
> the portion written by Kyle Gann the 21/16 is notated in the 5th scale
> position when it should be in the 6th and the 7/4 and the 441/256 are
> switched as well. Does anyone have a clue to why this is notated that
> way?
> Darren and I figured it out but it caused about an hour of
> miscommunication while we were tweaking divide by n dipswitches.....

I think that is intentionally done to maintain the interval relationship
across the keyboard. This is mentioned somewhere...the Sound &
Light book, the WTP liner notes or the Ganns Perspectives in New Music
article on the WTP.

--
* D a v i d B e a r d s l e y
* xouoxno@virtulink.com
*
* J u x t a p o s i t i o n E z i n e
* M E L A v i r t u a l d r e a m house monitor
*
* http://www.virtulink.com/immp/lookhere.htm

Darren called me today and had experimented with it and it is according to
him more intuitive so we shall go ahead and re-tune those intervals and let
you know how we make out
Pat

David Beardsley wrote:

> From: David Beardsley <xouoxno@home.com>
>
> Patrick Pagano wrote:
>
> > From: Patrick Pagano <ppagano@bellsouth.net>
> >
> > Hi folks
> > We here at the SEJIS were retuning our OmniII with the digital mod to
> > LaMonte Youngs' frequencies used in the Well-tuned Piano. We were using
> > the book,Sound and light. What we discovered after a little frustration
> > that the tuning is listed rather strangely....on the staff section in
> > the portion written by Kyle Gann the 21/16 is notated in the 5th scale
> > position when it should be in the 6th and the 7/4 and the 441/256 are
> > switched as well. Does anyone have a clue to why this is notated that
> > way?
> > Darren and I figured it out but it caused about an hour of
> > miscommunication while we were tweaking divide by n dipswitches.....
>
> I think that is intentionally done to maintain the interval relationship
> across the keyboard. This is mentioned somewhere...the Sound &
> Light book, the WTP liner notes or the Ganns Perspectives in New Music
> article on the WTP.
>
> --
> * D a v i d B e a r d s l e y
> * xouoxno@virtulink.com
> *
> * J u x t a p o s i t i o n E z i n e
> * M E L A v i r t u a l d r e a m house monitor
> *
> * http://www.virtulink.com/immp/lookhere.htm
>
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[Patrick Pagano:]
>in the portion written by Kyle Gann the 21/16 is notated in the 5th scale
position when it should be in the 6th and the 7/4 and the 441/256 are
switched as well. Does anyone have a clue to why this is notated that way?

Because the 63/32 is a 3/2 above the 21/16, and the 441/256 is a 3/2 above
the 147/128.

[David Beardsley:]
>I think that is intentionally done to maintain the interval relationship
across the keyboard. This is mentioned somewhere...the Sound & Light book,
the WTP liner notes or the Ganns Perspectives in New Music article on the
WTP.

This is a slightly edited excerpt from:
<http://home.earthlink.net/~kgann/wtp.html>

"The tuning, in all octaves, is as follows, given first in frequency ratios
to the tonic E-flat, then in cents (1/1200ths of an octave) above E-flat:

Notes: Eb, E, F, F#, G, G#, A, Bb , B, C, C#, D

Ratios: 1/1, 567/512, 9/8, 147/128, 21/16, 1323/1024, 189/128, 3/2, 49/32,
7/4, 441/256, 63/32

Cents: 0, 177, 204, 240, 471, 444, 675, 702, 738, 969, 942, 1173

Note that the scale does not uniformly ascend: G# is lower than G, and C#
is lower than C. This is so that all perfect fifths (3/2 ratios) will be
spelled as perfect fifths on the keyboard."

Thanks Dan
We were up late when we were doing the tuning and did not realise the reasoning
until the posts. Right now we have th Omni tuned regularly
We'll let you know how we make out
Thanks for your reply
Pat

> Because the 63/32 is a 3/2 above the 21/16, and the 441/256 is a 3/2 above
> the 147/128.
>
>