diamond9plus
9-limit tonality diamond extended with two secors
Properties
| Notes | 21 |
|---|
| Period | 1200.0 ¢ |
|---|
| Just | No |
|---|
| Source |
Mailing lists
|
|---|
| Reference | https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_92097.html#92097 |
|---|
| Thread | 2 scales |
|---|
| Tone (¢) |
Step (¢) |
| 116 |
116 |
| 182 |
67 |
| 204 |
22 |
| 231 |
27 |
| 267 |
36 |
| 316 |
49 |
| 386 |
71 |
| 435 |
49 |
| 498 |
63 |
| 583 |
84 |
| 617 |
35 |
| 702 |
84 |
| 765 |
63 |
| 814 |
49 |
| 884 |
71 |
| 933 |
49 |
| 969 |
36 |
| 996 |
27 |
| 1018 |
22 |
| 1084 |
67 |
| 1200 |
116 |
Similar scales
Parent scales
Child scales
Mailing list post
From: genewardsmith (2010-08-28)
Subject: Plugging the holes in the 9-limit tonality diamond
Before we attempt to plug them we should first find them. The 9-limit diamond has a 5-limit diamond sitting inside it: {1/1, 6/5, 5/4, 4/3, 3/2, 8/5, 5/3}. In a symmetrical 5-limit pitch-class lattice, this is the hexagon surrounding the central 1/1. Off to one side we find {9/8, 7/6, 5/4, 7/5, 3/2, 14/9}. This is approximately a hollowed-out 5-limit diamond, meaning minus the central 1/1, transposed down a secor, in the sense that half the notes are transposed 15/14 down and half 16/15 down. Similarly, {9/7, 4/3, 10/7. 8/5, 12/7, 16/9} is an approximate hollow 5-limit diamond, or hollow hexagon, transposed up a secor.
Hence, we can fill in the holes by adding a secor (for which we can use sqrt(8/7)) up and down to the diamond, obtaining the following:
! diamond9plus.scl
9-limit tonality diamond extended with two secors
21
!
115.587
10/9
9/8
8/7
7/6
6/5
5/4
9/7
4/3
7/5
10/7
3/2
14/9
8/5
5/3
12/7
7/4
16/9
9/5
1084.413
2/1
Alternatively, we can use marvel temperament, tempering out 225/224 (and not so incidentally, 385/384):
! diamond9plus-marvel.scl
Marvel tempering of diamond9 plus secors up and down
! Tuning is 1/6 septimal kleisma flat fifth
! 1/3 septimal kleisma flat major third
! Minimax over the 9-limit diamond
21
!
115.58705
182.40371
201.33949
231.17409
268.15616
316.92654
383.74321
432.51359
499.33025
585.08270
614.91730
700.66975
767.48641
816.25679
883.07346
931.84384
968.82591
998.66051
1017.59629
1084.41295
1200.00000
Aside from all the 9-limit harmony, there are distinct 11-limit implications in these scales.
Full thread (1 messages)
From: genewardsmith (2010-08-28)
Subject: Plugging the holes in the 9-limit tonality diamond
Before we attempt to plug them we should first find them. The 9-limit diamond has a 5-limit diamond sitting inside it: {1/1, 6/5, 5/4, 4/3, 3/2, 8/5, 5/3}. In a symmetrical 5-limit pitch-class lattice, this is the hexagon surrounding the central 1/1. Off to one side we find {9/8, 7/6, 5/4, 7/5, 3/2, 14/9}. This is approximately a hollowed-out 5-limit diamond, meaning minus the central 1/1, transposed down a secor, in the sense that half the notes are transposed 15/14 down and half 16/15 down. Similarly, {9/7, 4/3, 10/7. 8/5, 12/7, 16/9} is an approximate hollow 5-limit diamond, or hollow hexagon, transposed up a secor.
Hence, we can fill in the holes by adding a secor (for which we can use sqrt(8/7)) up and down to the diamond, obtaining the following:
! diamond9plus.scl
9-limit tonality diamond extended with two secors
21
!
115.587
10/9
9/8
8/7
7/6
6/5
5/4
9/7
4/3
7/5
10/7
3/2
14/9
8/5
5/3
12/7
7/4
16/9
9/5
1084.413
2/1
Alternatively, we can use marvel temperament, tempering out 225/224 (and not so incidentally, 385/384):
! diamond9plus-marvel.scl
Marvel tempering of diamond9 plus secors up and down
! Tuning is 1/6 septimal kleisma flat fifth
! 1/3 septimal kleisma flat major third
! Minimax over the 9-limit diamond
21
!
115.58705
182.40371
201.33949
231.17409
268.15616
316.92654
383.74321
432.51359
499.33025
585.08270
614.91730
700.66975
767.48641
816.25679
883.07346
931.84384
968.82591
998.66051
1017.59629
1084.41295
1200.00000
Aside from all the 9-limit harmony, there are distinct 11-limit implications in these scales.
Raw file
! diamond9plus.scl
9-limit tonality diamond extended with two secors
21
!
115.587
10/9
9/8
8/7
7/6
6/5
5/4
9/7
4/3
7/5
10/7
3/2
14/9
8/5
5/3
12/7
7/4
16/9
9/5
1084.413
2/1
!
! https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_92097.html#92097
!
! [info]
! source = Mailing lists
! file = tuning/messages/yahoo_tuning_messages_api_raw_90000-106393.json
! topic_id = 92097
! msg_id = 92097