smalldi19c

Small diesic 19-note scale containing glumma

Open in Scale Workshop Scala analysis Download scl

Properties

Notes19
Period1200.0 ¢
Just7-limit
Source Mailing lists
Referencehttps://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_4541.html#4541
Thread7 scales
Tone Tone (¢) Step Step (¢)
49/48 36 49/48 36
21/20 84 36/35 49
15/14 119 50/49 35
35/32 155 49/48 36
6/5 316 192/175 161
49/40 351 49/48 36
5/4 386 50/49 35
9/7 435 36/35 49
21/16 471 49/48 36
10/7 617 160/147 147
35/24 653 49/48 36
3/2 702 36/35 49
49/32 738 49/48 36
5/3 884 160/147 147
12/7 933 36/35 49
7/4 969 49/48 36
9/5 1018 36/35 49
35/18 1151 175/162 134
2/1 1200 36/35 49

Similar scales

FileNotesRotationMax diff (¢)
smalldiglum19 19 0 8.8

Parent scales

FileNotesMax diff (¢)
mircube 31 5.0
xen18-erlich-meantone-31 31 9.4
cbrat31 31 9.8
caleb46_4 46 4.6
caleb44 44 5.4
circle31 31 10.8
xen18-erlich-luna-31 31 10.9
edo-31 31 11.1
xen18-erlich-cynder-31 31 11.4
31edo-top 31 11.5

Child scales

FileNotesMax diff (¢)
ch9_1 9 0.0
ch9_2 9 0.0
octone 8 0.0
octo 8 0.4
octone_tuning-math_12214_12214 8 0.7
keentet 8 3.0
keen4 5 3.0
keen6 5 3.0
starling7 7 5.5
CD07_19_Egypt 5 13.4
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

! 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
!
! 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