Topic: Dante Rosati's 21 note scale

1 scales

Thread (2 messages)

From: Gene Ward Smith (2004-04-15)
Subject: Dante Rosati's 21 note scale

This is

[1, 16/15, 10/9, 9/8, 8/7, 7/6, 6/5, 5/4, 9/7, 4/3, 7/5, 10/7, 
3/2, 14/9, 8/5, 5/3, 12/7, 7/4, 16/9, 9/5, 15/8]

Plausible ways of tempering it are with magic and (7-limit) marvel in
the 7-limit, and miracle or 11-limit marvel for adding 11-limit.
Tempering by magic gives (in terms of major third generators)

[-12, -11, -10, -9, -7, -6, -5, -4, -2, -1, 0, 1, 2, 4, 5, 
6, 7, 9,10, 11, 12]

Tempering by miracle gives, in secors,

[-19, -14, -13, -12, -8, -7, -6, -5, -2, -1, 0, 1, 2, 5, 6, 
7, 8, 12, 13, 14, 19]

Below I give the tuning for 1/4-kleismic marvel (225/224-planar),
which is quite a logical way to temper the scale if the rather small
error is not too much for you. I'd be interested to know what tuning
accuracy a guitar can achieve.


! rosatimarv.scl
1/4-kleismic marvel tempering of rosati_21.scl
21
!
115.587047
184.331593
200.054240
231.174094
268.798787
315.641288
384.385833
431.228334
499.972880
584.440073
615.559927
700.027121
768.771666
815.614167
884.358713
931.201214
968.825906
999.945760
1015.668407
1084.412954
1200.000000

From: Gene Ward Smith (2004-04-15)
Subject: Re: Dante Rosati's 21 note scale

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> This is
> 
> [1, 16/15, 10/9, 9/8, 8/7, 7/6, 6/5, 5/4, 9/7, 4/3, 7/5, 10/7, 
> 3/2, 14/9, 8/5, 5/3, 12/7, 7/4, 16/9, 9/5, 15/8]

If we replace 16/15 and 15/8 with 15/14 and 28/15 we have six each of
major and minor tetrads, rather than five. This slightly altered scale
is now the union of its tetrads. Of course, tempered by marvel, the
two are identical, with even more tetrads.

Yahoo sucks.