smalldi19b

Small diesic 19-note block, <16/15, 126/125, 2401/2400> commas

Open in Scale Workshop Scala analysis Download scl

Properties

Notes	19
Period	1200.0 ¢
Just	7-limit
Source	Mailing lists
Reference	https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_4541.html#4541
Thread	7 scales

Tone	Tone (¢)	Step	Step (¢)
50/49	35	50/49	35
21/20	84	1029/1000	49
8/7	231	160/147	147
7/6	267	49/48	36
6/5	316	36/35	49
49/40	351	49/48	36
5/4	386	50/49	35
48/35	547	192/175	161
7/5	583	49/48	36
10/7	617	50/49	35
35/24	653	49/48	36
8/5	814	192/175	161
80/49	849	50/49	35
5/3	884	49/48	36
12/7	933	36/35	49
7/4	969	49/48	36
40/21	1116	160/147	147
49/25	1165	1029/1000	49
2/1	1200	50/49	35

Similar scales

File	Notes	Max diff (¢)
smalldimos19	19	6.8
xen18-erlich-myna-19	19	8.5
smalldi19a	19	13.8

Parent scales

File	Notes	Max diff (¢)
woz31	31	0.7
xen18-erlich-miracle-31	31	3.4
keenan5_269	31	3.7
rational_canasta	31	3.9
rational_canasta_tuning_22793_23190	31	3.9
myna23_tuning_66272_66321	23	8.5
xen18-erlich-myna-23	23	8.5
keenan5_tuning_7341_7341	31	4.6
hemw	41	2.1
xen18-erlich-myna-27	27	8.5

Child scales

File	Notes	Max diff (¢)
xen12-wilson-39-4C2-hexany-00	6	0.0
brect35	15	0.7
brect33	9	0.7
keen2	5	2.5
myna7opt	7	4.7
xen18-erlich-orson-05	5	4.8
starling11	11	4.8
xen18-erlich-orwell-05	5	5.1
igs	7	5.5
smalldimos11	11	5.6

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

! 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
!
! 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