Mailing list post
From: Gene Ward Smith (2004-08-31)
Subject: Twelve notes, 31 intervals, 26 triads, six tetrads, two pentads
Tuning message #3 describes a 7-limit scale with 12 notes, 31 7-limit
dyads and 26 triads. It also had a smallest step size of 25/24. It's
listed in the Scala directory as hahn_7.scl.
If we relax the condition on the size of the smallest note, we can up
the ante to six tetrads, instead of four, and two pentads, instead of
one. I give six such scales below; they all have the same
characteristic polynomial and are presumably congruent.
! max1.scl
31 intervals 26 triads 6 tetrads 2 pentads smallest step 49/48
12
!
8/7
7/6
6/5
5/4
4/3
7/5
3/2
8/5
5/3
12/7
7/4
2
! max2.scl
31 intervals 26 triads 6 tetrads 2 pentads smallest step 49/48
12
!
8/7
7/6
6/5
5/4
4/3
10/7
3/2
8/5
5/3
12/7
7/4
2
! max3.scl
31 intervals 26 triads 6 tetrads 2 pentads smallest step 50/49
12
!
8/7
7/6
6/5
5/4
4/3
7/5
10/7
3/2
8/5
5/3
12/7
2
! max4.scl
31 intervals 26 triads 6 tetrads 2 pentads smallest step 50/49
12
!
7/6
6/5
5/4
4/3
7/5
10/7
3/2
8/5
5/3
12/7
7/4
2
! max5.scl
31 intervals 26 triads 6 tetrads two pentads smallest step 50/49
12
!
8/7
7/6
6/5
5/4
4/3
7/5
10/7
3/2
5/3
12/7
7/4
2
! max6.scl
31 intervals 26 triads 6 tetrads 2 pentads smallest step 50/49
12
!
8/7
7/6
6/5
4/3
7/5
10/7
3/2
8/5
5/3
12/7
7/4
2
Full thread (2 messages)
From: Gene Ward Smith (2004-08-31)
Subject: Twelve notes, 31 intervals, 26 triads, six tetrads, two pentads
Tuning message #3 describes a 7-limit scale with 12 notes, 31 7-limit
dyads and 26 triads. It also had a smallest step size of 25/24. It's
listed in the Scala directory as hahn_7.scl.
If we relax the condition on the size of the smallest note, we can up
the ante to six tetrads, instead of four, and two pentads, instead of
one. I give six such scales below; they all have the same
characteristic polynomial and are presumably congruent.
! max1.scl
31 intervals 26 triads 6 tetrads 2 pentads smallest step 49/48
12
!
8/7
7/6
6/5
5/4
4/3
7/5
3/2
8/5
5/3
12/7
7/4
2
! max2.scl
31 intervals 26 triads 6 tetrads 2 pentads smallest step 49/48
12
!
8/7
7/6
6/5
5/4
4/3
10/7
3/2
8/5
5/3
12/7
7/4
2
! max3.scl
31 intervals 26 triads 6 tetrads 2 pentads smallest step 50/49
12
!
8/7
7/6
6/5
5/4
4/3
7/5
10/7
3/2
8/5
5/3
12/7
2
! max4.scl
31 intervals 26 triads 6 tetrads 2 pentads smallest step 50/49
12
!
7/6
6/5
5/4
4/3
7/5
10/7
3/2
8/5
5/3
12/7
7/4
2
! max5.scl
31 intervals 26 triads 6 tetrads two pentads smallest step 50/49
12
!
8/7
7/6
6/5
5/4
4/3
7/5
10/7
3/2
5/3
12/7
7/4
2
! max6.scl
31 intervals 26 triads 6 tetrads 2 pentads smallest step 50/49
12
!
8/7
7/6
6/5
4/3
7/5
10/7
3/2
8/5
5/3
12/7
7/4
2
From: Robert Walker (2004-09-01)
Subject: Re: Twelve notes, 31 intervals, 26 triads, six tetrads, two pentads
Hi Gene,
Yes, I dip in from time to time and see what is happening here.
I've done a longer clip now, also fixed a chord which was a bit
crunchy - it wasn't one of the pure tetrads - had one interval
in it which wasn't pure j.i.
http://www.robertinventor.com/microtonal_piano_romance_with_six_pure_tetrads.mid
It's also now 30 minutes, so you can listen to a longer clip.
The new FTS will be much easier to use I hope when it is released.
This will be one of the new example fractal tunes so you can play
around with it and change it and try other ones like it for
other tunings.
Robert