Reply to John

> A relation simpler than either Sauveurs or Henflings is the one
> Blackwood uses, the relation of the whole tone to the diatonic
> semitone. The octave has 5T+2D steps. When d is 0, one gets
> 5-tet, when T and D are both 1, 7 steps, when 2:1, 12; 3:2, 19;
> 5:3, 31; 3:1, 17; 4:1, 22 4:3, 26; etc.

To which might be added that Sauveur's table of 1711 consists of
divisions which have the chromatic 12-tone scale embedded in them and
hence the diatonic scale too. The connection between Sauveur's and
Blackwood's relation is rather simple. The comma plus the chromatic
semitone is the diatonic semitone and the chromatic semitone plus the
diatonic semitone is the whole tone.
So for instance if the ratio comma:chromatic semitone is 2:3
(for 50-tET), then the next is 3:5 and thus D:T is 5:8.

> Hypocaffeinemia this AM, alas.

With American coffee, that means lots of drinking :-)

Manuel Op de Coul coul@ezh.nl

Received: from eartha.mills.edu [144.91.3.20] by vbv40.ezh.nl
with SMTP-OpenVMS via TCP/IP; Tue, 30 Jul 1996 07:57 +0100
Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI)
for id WAA13755; Mon, 29 Jul 1996 22:57:51 -0700
Date: Mon, 29 Jul 1996 22:57:51 -0700
Message-Id: <199607300555.WAA04902@dnai.com>
Errors-To: madole@ella.mills.edu
Reply-To: tuning@eartha.mills.edu
Originator: tuning@eartha.mills.edu
Sender: tuning@eartha.mills.edu