Topic: novel circulating temperaments?

1 scales

Thread (1 messages)

From: Carl Lumma (2003-06-05)
Subject: novel circulating temperaments?

All;

I've created some tools in Scheme that make playing with
circulating temperaments easy.  Inspired by Gene's notions
that...

() The ideal octave for 7-limit meantone is flat
() 14:11 may sound better than other wide major thirds

...I've come up with the following...

! 5151.scl
!
 5151 temperament III (1197/709.5/696).
 12
!
 97.5
 195.
 292.5
 390.
 487.5
 598.5
 696.
 793.5
 891.
 988.5
 1086.
 1197.
!
! Carl Lumma, June 2003.

The octave is three cents flat, and there are two sizes of
fifth -- ten meantone fifths and two 709.5-cent fifths.

My basic idea is to look at the major thirds, while keeping
the fifths between 695 and 710 cents and the octave within
3 cents of just.  The range for the minor third is so wide,
with anything from 6:5 to 19:16 to 13:11 to 7:6 being okay,
that I ignore it.  Sure, sticking to these exact ratios maybe
better than not, but the range of the major third is just so
much more important -- anything much flat of a 5:4 sounds off
to my ear and the sweetness of the interval says goodbye
somewhere around 400 cents -- that I focused on that.

Anyway, the above scale has the two large fifths separated
by 5 small fifths and gives the following major 3rds...

(390.0 390.0 403.5 403.5 403.5 403.5 390.0 390.0 403.5 403.5
403.5 403.5)

...four are way better than equal, and eight are not much
worse.

If we separate the large fifths by 2 small fifths, we get...

(390.0 403.5 390.0 403.5 390.0 403.5 403.5 390.0 417.0 390.0
403.5 403.5)

...five of the better thirds, 7 near-equal ones, and one
14:11!

Separate the large fifths by one small fifth, get 6 good,
4 near-equal, and 2 14:11 thirds.  Make the large fifths
adjacent on the chain and make that 7, 3, and 3.

All of these variants will enjoy some minor 7ths much closer
to 7:4.

I've been listening to them, and they sound killer.

Anybody know if there are any historical "improved meantones"
of which these could be considered 1197-cent-octave versions?

-Carl