Topic: Nonoctave ennealimmal

4 scales

Thread (1 messages)

From: Gene Ward Smith (2004-03-15)
Subject: Nonoctave ennealimmal

The 1 in the wedgie for ennealimmal (<18 27 18 1 -22 -34|) caught my
eye, and it occurred to me that a generator of 5/3 and a period of 3
(or 5, but 3 seems more plausible) works for a non-octave ennealimmal.
We can take the generators as the TOP tunings of 3 and 5/3, or as
3 and 3^(451/970), etc etc. The mapping is [<9 1 1 12|, <-18 0 1 -22|].
I accidentally shut down my Maple session, so I'm giving DE scales of
size 13, 15, 28 and 43 within the "tritave" in terms of the Scala
files I created. These are justly tuned versions; if you temper this
by your favorite ennealimmal tuning you get tempered versions, but you
can simply take them as is, and make use of the inherent approximations.

! ennon13.scl
Nonoctave Ennealimmal, [3, 5/3] just tuning
13
!
27/25
7/6
63/50
10/7
54/35
5/3
9/5
35/18
21/10
50/21
18/7
25/9
3

! ennon15.scl
Nonoctave Ennealimmal, [3, 5/3] just tuning
15
!
27/25
7/6
63/50
250/189
10/7
54/35
5/3
9/5
35/18
21/10
245/108
50/21
18/7
25/9
3

! ennon28.scl
Nonoctave Ennealimmal, [3, 5/3] just tuning
28
!
21/20
27/25
245/216
7/6
49/40
63/50
250/189
49/36
10/7
72/49
54/35
100/63
5/3
7/4
9/5
189/100
35/18
49/24
21/10
108/49
245/108
50/21
49/20
18/7
500/189
25/9
20/7
3

! ennon43.scl
Nonoctave Ennealimmal, [3, 5/3] just tuning
43
!
36/35
21/20
27/25
10/9
245/216
7/6
6/5
49/40
63/50
35/27
250/189
49/36
25/18
10/7
72/49
3/2
54/35
100/63
81/50
5/3
12/7
7/4
9/5
50/27
189/100
35/18
2
49/24
21/10
54/25
108/49
245/108
81/35
50/21
49/20
5/2
18/7
500/189
27/10
25/9
20/7
35/12
3