octone_tuning-math_12214_12214
octone around 60/49-7/4 interval
Properties
| Notes | 8 |
|---|
| Period | 1200.0 ¢ |
|---|
| Just | 7-limit |
|---|
| Source |
Mailing lists
|
|---|
| Reference | https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_12214.html#12214 |
|---|
| Thread | 1 scale |
|---|
| Tone |
Tone (¢) |
Step |
Step (¢) |
| 15/14 |
119 |
15/14 |
119 |
| 60/49 |
351 |
8/7 |
231 |
| 5/4 |
386 |
49/48 |
36 |
| 10/7 |
617 |
8/7 |
231 |
| 3/2 |
702 |
21/20 |
84 |
| 12/7 |
933 |
8/7 |
231 |
| 7/4 |
969 |
49/48 |
36 |
| 2 |
1200 |
8/7 |
231 |
Similar scales
| File | Notes | Rotation | Max diff (¢) |
|---|
| octo |
8 |
0 |
0.4 |
| octone |
8 |
0 |
0.7 |
Parent scales
Mailing list post
From: Gene Ward Smith (2005-05-26)
Subject: Octone again
If you take the octone to be
1-15/14-60/49-5/4-10/7-3/2-12/7-7/4
then while it isn't Tenney reduced, it has other desireable properties.
It is the union of a justly-tuned otonal tetrad with a utonal tetrad,
and the 2401/2400 approximations have been reduced to an approximate
10/7 relationship from 60/49 to 7/4. Moreover, it is epimorphic and
(by a margin of 2401/2400) a constant structure. If we have 49/40 in
place of 60/49, it falls right on the boundry of being epimorphic and
CS. This strikes me as a rather curious musical example and one worth
keeping in mind.
Here's the replacement octone:
! octone.scl
octone around 60/49-7/4 interval
8
!
15/14
60/49
5/4
10/7
3/2
12/7
7/4
2
Here is the octone in 612, which is very close to the minimax tuning.
In this case, we get that the scale is proper. For 60/49, it was
strictly proper, epimorphic and CS. For 49/40, it was improper and
permutation epimorphic.
! octo.scl
octone in 612 equal
8
!
119.60784
350.98039
386.27451
617.64706
701.96078
933.33333
968.62745
1200.0000
Full thread (1 messages)
From: Gene Ward Smith (2005-05-26)
Subject: Octone again
If you take the octone to be
1-15/14-60/49-5/4-10/7-3/2-12/7-7/4
then while it isn't Tenney reduced, it has other desireable properties.
It is the union of a justly-tuned otonal tetrad with a utonal tetrad,
and the 2401/2400 approximations have been reduced to an approximate
10/7 relationship from 60/49 to 7/4. Moreover, it is epimorphic and
(by a margin of 2401/2400) a constant structure. If we have 49/40 in
place of 60/49, it falls right on the boundry of being epimorphic and
CS. This strikes me as a rather curious musical example and one worth
keeping in mind.
Here's the replacement octone:
! octone.scl
octone around 60/49-7/4 interval
8
!
15/14
60/49
5/4
10/7
3/2
12/7
7/4
2
Here is the octone in 612, which is very close to the minimax tuning.
In this case, we get that the scale is proper. For 60/49, it was
strictly proper, epimorphic and CS. For 49/40, it was improper and
permutation epimorphic.
! octo.scl
octone in 612 equal
8
!
119.60784
350.98039
386.27451
617.64706
701.96078
933.33333
968.62745
1200.0000
Raw file
! octone.scl
octone around 60/49-7/4 interval
8
!
15/14
60/49
5/4
10/7
3/2
12/7
7/4
2
!
! https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_12214.html#12214
!
! [info]
! source = Mailing lists
! file = tuning-math/messages/yahoo_tuning-math_messages_api_raw_9945-12429.json
! topic_id = 12214
! msg_id = 12214