smalldiglum19

Small diesic "glumma" variant of 19-note MOS, 31/120 version

Open in Scale Workshop Scala analysis Download scl

Properties

Notes19
Period1200.0 ¢
JustNo
Source Mailing lists
Referencehttps://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_4541.html#4541
Thread7 scales
Tone (¢) Step (¢)
40 40
80 40
120 40
160 40
310 150
350 40
390 40
430 40
470 40
620 150
660 40
700 40
740 40
890 150
930 40
970 40
1010 40
1160 150
1200 40

Similar scales

FileNotesRotationMax diff (¢)
smalldi19c 19 0 8.8

Parent scales

FileNotesMax diff (¢)
31edo-top 31 5.0
edo-31 31 5.5
xen18-erlich-cynder-31 31 5.7
cbrat31 31 7.0
xen18-erlich-meantone-31 31 7.6
circle31 31 7.6
qx1 31 8.0
vala 31 8.3
xen18-erlich-luna-31 31 8.4
xen18-erlich-miracle-31 31 9.8

Child scales

FileNotesMax diff (¢)
starling7 7 2.4
octone 8 3.7
octone_tuning-math_12214_12214 8 3.7
octo 8 3.7
ch9_2 9 6.8
ch9_1 9 7.6
keen4 5 7.9
keen6 5 7.9
keentet 8 9.3
semimaj1 8 11.3
Mailing list post 
From: Gene W Smith (2002-07-18)
Subject: Small diesic scales

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
Full thread (1 messages) 
From: Gene W Smith (2002-07-18)
Subject: Small diesic scales

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

Raw file

! 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
!
! https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_4541.html#4541
!
! [info]
! source = Mailing lists
! file = tuning-math/messages/yahoo_tuning-math_messages_api_raw_2440-7444.json
! topic_id = 4541
! msg_id = 4541