Keith Briggs

 home · papers · thesis · talks · meetings · records · maths notes · software · languages · music « · travel · cv · students · maps · place-names · people · photos · links · ex libris · site map

Letter from Keith Briggs to the editor, Early Music Review. Published May 2003

```Martlesham 2003 Mar 31

Dear Clifford,

Paul Simmonds refers in a letter in EMR 88 (March 2003) to Michael Zapf's
interpretations of the squiggles at the top of the 1722 manuscript of WTC I.
I have received details of this directly from Michael Zapf himself.  He claims
the sequence of 1,1,1,0,0,0,2,2,2,2,2 loops refers to an equal-beating tuning
starting from c, where 2 means a beat takes 2 seconds.

I have checked the maths and everything does indeed work out as claimed.  In
fact, it is possible to go further and deduce an absolute pitch for the
starting note.   Assuming that the final fifth f-c beats once per second, the
pitch must be about 127 Hz.   If this is a c, it must be c below middle c.

Sincerely,
Keith Briggs

PS: mathematical details:
g =(3/2)c-1/2
d =(3/4)g-1/4
a =(3/2)d-1/2
e =(3/4)a
b =(3/2)e
f#=(3/4)b
c#=(3/4)f#-1/8
g#=(3/2)c#-1/4
d#=(3/4)g#-1/8
a#=(3/2)d#-1/4
f =(3/4)a#-1/8
c'=(3/2)f-1/2

this gives 2c-c'=-7153/262144c+907109/262144, so that c=126.8.

```