Topic: A 14-note modmos of meantone

1 scales

Thread (3 messages)

From: Gene Ward Smith (2004-07-13)
Subject: A 14-note modmos of meantone

This is interesting as one way to construct these, though it's
cheating in a way because from another point of view it is mos, or at
least ce.

If you take my comma list for 50 and dispense with one of the TM basis
commas, one of the temperaments you get (above the 7-limit) is 12&50,
which is actually pretty good if you want higher limit consonances.
The 50-et generators are 1/2 and 2/25, and if you take the 14-note
(MOS? DE?) you get, when the result is translated into meantone,

-24, -23, -22, -3, -2, -1, 0, 1, 2, 3, 22, 23, 24, 25

This is a 14-note modmos; it has two 50-et diatonic scales hence the name.

! bidiatonic.scl
14 note modmos of meantone, mos of 12&50
14
!
96.000000
192.000000
288.000000
312.000000
408.000000
504.000000
600.000000
696.000000
792.000000
888.000000
912.000000
1008.000000
1104.000000
1200.000000

From: Paul Erlich (2004-07-13)
Subject: Re: A 14-note modmos of meantone

Is this distinct from Injera in some way? The two scales I originally 
proposed for Injera both had 14 notes: the DE one and the 
omnitetrachordal variant. They're both "double diatonic".



--- In [email protected], "Gene Ward Smith" <gwsmith@s...> 
wrote:
> This is interesting as one way to construct these, though it's
> cheating in a way because from another point of view it is mos, or 
at
> least ce.
> 
> If you take my comma list for 50 and dispense with one of the TM 
basis
> commas, one of the temperaments you get (above the 7-limit) is 
12&50,
> which is actually pretty good if you want higher limit consonances.
> The 50-et generators are 1/2 and 2/25, and if you take the 14-note
> (MOS? DE?) you get, when the result is translated into meantone,
> 
> -24, -23, -22, -3, -2, -1, 0, 1, 2, 3, 22, 23, 24, 25
> 
> This is a 14-note modmos; it has two 50-et diatonic scales hence 
the name.
> 
> ! bidiatonic.scl
> 14 note modmos of meantone, mos of 12&50
> 14
> !
> 96.000000
> 192.000000
> 288.000000
> 312.000000
> 408.000000
> 504.000000
> 600.000000
> 696.000000
> 792.000000
> 888.000000
> 912.000000
> 1008.000000
> 1104.000000
> 1200.000000

From: Gene Ward Smith (2004-07-13)
Subject: Re: A 14-note modmos of meantone

--- In [email protected], "Paul Erlich" <perlich@a...> wrote:
> Is this distinct from Injera in some way? 

Conceptually, at any rate. The tuning map I was proposing was 12&50,
which in the 19-limit is

[<2 0 -8 -26 -31 39 5 -1|, <0 1 4 10 12 -10 1 3|]

For a 14-note MOS this suffers from the defect that you don't actually
get to use the 7, 11, and 13 much; for a 26-note MOS it's a lot
better, and the tuning is considerably more accurate than 26-equal,
which is what injera would more or less amount to.

The two scales I originally 
> proposed for Injera both had 14 notes: the DE one and the 
> omnitetrachordal variant. They're both "double diatonic".

The 7/9 copop generator is (35/24)^(1/7), which translates to
2/5-comma meantone. That's a far more hefty dose of tempering than
5-equal. I'd say 12%26 (injera) was a sibling to 12&50, but no more
than that.