[tuning-math] Small diesic scales
- From: Gene W Smith <genewardsmith@xxxxxxxx>
- To: tuning-math@xxxxxxxxxxxxxxx
- Date: Thu, 18 Jul 2002 00:39:27 -0700
These are related to the samll diesic (126/125 and 1728/1715) linear
temperament. The first is a Fokker block, from the commas <10/9, 126/125,
1728/1715>; the Scala file I present here may be copied and pasted.
! smalldi11.scl
!
Small diesic 11-note block, <10/9, 126/125, 1728/1715> commas
!
11
!
36/35
7/6
6/5
216/175
7/5
10/7
175/108
5/3
12/7
35/18
2/1
We have 18 intervals, 8 triads, and no tetrads; more specifically we get
1-6/5-7/5 and 1-7/6-7/5 chords: roots on degrees 0,6,8,9
1-6/5-7/5-5/3 and 1-7/6-7/5-5/3 chords on degrees 0,9
If we temper this by the 120-et (which is does a good job for small
diesic and makes the scale degrees into nice round numbers in terms of
cents) we get the 11-note small diesic MOS, with generator 31/120:
! smalldimos11.scl
!
Small diesic 11-note MOS, 31/120 version
!
11
!
40.0
270.0
310.0
350.0
580.0
620.0
850.0
890.0
930.0
1160.0
2/1
We now have 34 intervals, 33 triads, and 2 tetrads; the tetrads occur on
degree 7, which might serve as a tonic.
! smalldi19a.scl
!
Small diesic 19-note block, <16/15, 126/125, 1728/1715> commas
!
19
!
36/35
25/24
8/7
7/6
6/5
175/144
5/4
48/35
7/5
10/7
35/24
8/5
288/175
5/3
12/7
7/4
48/25
35/18
2/1
52 intervals, 44 triads, 8 tetrads
! smalldi19b.scl
!
Small diesic 19-note block, <16/15, 126/125, 2401/2400> commas
!
19
!
50/49
21/20
8/7
7/6
6/5
49/40
5/4
48/35
7/5
10/7
35/24
8/5
80/49
5/3
12/7
7/4
40/21
49/25
2/1
50 intervals, 40 triads, 6 tetrads. There are four more tetrads if we are
willing to count those off by 2401/2400, which is less than a cent.
Either of these, when tempered by the 12-et. gives us the 19-note small
diesic MOS:
! smalldimos19.scl
!
Small diesic 19-note MOS, 31/120 version
!
19
!
40.0
80.0
230.0
270.0
310.0
350.0
390.0
540.0
580.0
620.0
660.0
810.0
850.0
890.0
930.0
970.0
1120.0
1160.0
2/1
82 intervals, 105 triads and 18 tetrads
Here is variant 19-note scale containing glumma:
! smalldi19c.scl
!
Small diesic 19-note scale containing glumma
!
19
49/48
21/20
15/14
35/32
6/5
49/40
5/4
9/7
21/16
10/7
35/24
3/2
49/32
5/3
12/7
7/4
9/5
35/18
2/1
53 intervals, 45 triads, 8 tetrads
Tempering this gives the following:
! smalldiglum19.scl
!
Small diesic "glumma" variant of 19-note MOS, 31/120 version
!
19
!
40.0
80.0
120.0
160.0
310.0
350.0
390.0
430.0
470.0
620.0
660.0
700.0
740.0
890.0
930.0
970.0
1010.0
1160.0
2/1
78 intervals, 94 triads, 16 tetrads
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