tetra
{225/224, 385/384} tempering of two-tetrachord 12-note scale
Properties
| Notes | 12 |
|---|
| Period | 1200.0 ¢ |
|---|
| Just | No |
|---|
| Source |
Mailing lists
|
|---|
| Reference | https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_4567.html#4567 |
|---|
| Thread | 1 scale |
|---|
| Tone (¢) |
Step (¢) |
| 85 |
85 |
| 201 |
116 |
| 317 |
116 |
| 383 |
66 |
| 469 |
85 |
| 585 |
116 |
| 701 |
116 |
| 817 |
116 |
| 883 |
66 |
| 968 |
85 |
| 1084 |
116 |
| 1200 |
116 |
Similar scales
Parent scales
Child scales
Mailing list post
From: Gene W Smith (2002-08-01)
Subject: Another 12-note scale
Here's a 12-note scale which is comparable to the ones I just did by
tempering Carl's. I took all the JI scales built from (15/14)^3 (16/15)^4
(21/20)^3 (25/24)^2 which consisted of two indentical tetrachords
separated by a 9/8=15/14 21/20. I got two scales and their inversions,
isomorphic by the 21/20 <==> 25/24 transformation. These scales turned
out to be adapted to the {225/224, 385/384} temperament, and on tempering
I ended up with just one scale (modulo modes) and its inversion. I took
this down a fourth to get some dominant harmony, and ended up with this:
1-21/20-9/8-6/5-5/4-21/16-7/5-3/2-8/5-5/3-7/4-28/15
27 (7-limit) intervals, 20 triads
Tempering it, I got the following:
! tetra.scl
! [61, 83, 83, 47, 61, 83, 83, 83, 47, 61, 83, 83]
{225/224, 385/384} tempering of two-tetrachord 12-note scale
! 858-et version of 1-21/20-9/8-6/5-5/4-21/16-7/5-3/2-8/5-5/3-7/4-28/15
12
!
85.31468531
201.3986014
317.4825175
383.2167832
468.5314685
584.6153846
700.6993007
816.7832168
882.5174825
967.8321678
1083.916084
2/1
46 (11 limit) intervals 74 triads
Something for Carl to think about.
Full thread (1 messages)
From: Gene W Smith (2002-08-01)
Subject: Another 12-note scale
Here's a 12-note scale which is comparable to the ones I just did by
tempering Carl's. I took all the JI scales built from (15/14)^3 (16/15)^4
(21/20)^3 (25/24)^2 which consisted of two indentical tetrachords
separated by a 9/8=15/14 21/20. I got two scales and their inversions,
isomorphic by the 21/20 <==> 25/24 transformation. These scales turned
out to be adapted to the {225/224, 385/384} temperament, and on tempering
I ended up with just one scale (modulo modes) and its inversion. I took
this down a fourth to get some dominant harmony, and ended up with this:
1-21/20-9/8-6/5-5/4-21/16-7/5-3/2-8/5-5/3-7/4-28/15
27 (7-limit) intervals, 20 triads
Tempering it, I got the following:
! tetra.scl
! [61, 83, 83, 47, 61, 83, 83, 83, 47, 61, 83, 83]
{225/224, 385/384} tempering of two-tetrachord 12-note scale
! 858-et version of 1-21/20-9/8-6/5-5/4-21/16-7/5-3/2-8/5-5/3-7/4-28/15
12
!
85.31468531
201.3986014
317.4825175
383.2167832
468.5314685
584.6153846
700.6993007
816.7832168
882.5174825
967.8321678
1083.916084
2/1
46 (11 limit) intervals 74 triads
Something for Carl to think about.
Raw file
! tetra.scl
! [61, 83, 83, 47, 61, 83, 83, 83, 47, 61, 83, 83]
{225/224, 385/384} tempering of two-tetrachord 12-note scale
! 858-et version of 1-21/20-9/8-6/5-5/4-21/16-7/5-3/2-8/5-5/3-7/4-28/15
12
!
85.31468531
201.3986014
317.4825175
383.2167832
468.5314685
584.6153846
700.6993007
816.7832168
882.5174825
967.8321678
1083.916084
2/1
!
! https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_4567.html#4567
!
! [info]
! source = Mailing lists
! file = tuning-math/messages/yahoo_tuning-math_messages_api_raw_2440-7444.json
! topic_id = 4567
! msg_id = 4567