rat19
171-et Hahn reduced 7-limit 19-almost-equal
Properties
| Notes | 19 |
|---|
| Period | 1200.0 ¢ |
|---|
| Just | 7-limit |
|---|
| Source |
Mailing lists
|
|---|
| Reference | https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_55054.html#55054 |
|---|
| Thread | 2 scales |
|---|
| Tone |
Tone (¢) |
Step |
Step (¢) |
| 28/27 |
63 |
28/27 |
63 |
| 672/625 |
126 |
648/625 |
63 |
| 125/112 |
190 |
78125/75264 |
65 |
| 125/108 |
253 |
28/27 |
63 |
| 6/5 |
316 |
648/625 |
63 |
| 56/45 |
379 |
28/27 |
63 |
| 1323/1024 |
444 |
8505/8192 |
65 |
| 75/56 |
506 |
3200/3087 |
62 |
| 25/18 |
569 |
28/27 |
63 |
| 36/25 |
631 |
648/625 |
63 |
| 112/75 |
694 |
28/27 |
63 |
| 2048/1323 |
756 |
3200/3087 |
62 |
| 45/28 |
821 |
8505/8192 |
65 |
| 5/3 |
884 |
28/27 |
63 |
| 216/125 |
947 |
648/625 |
63 |
| 224/125 |
1010 |
28/27 |
63 |
| 625/336 |
1074 |
78125/75264 |
65 |
| 27/14 |
1137 |
648/625 |
63 |
| 2 |
1200 |
28/27 |
63 |
Similar scales
Parent scales
Child scales
Mailing list post
From: Gene Ward Smith (2004-07-28)
Subject: Rational 12 and 19 nearly equal
Below I give a 12-note 7-limit well-temperament obtained by Hahn
reducing a chain of fifths according to 7-limit 72-et, meaning via the
commas 225/224, 1029/1024 and 4375/4374. The result has three 112/75
meantone fifths, a 125000/83349 quasi-pure fifth (it's flat by an
interval of 250047/250000, which is less than a third of a cent) and
eight pure fifths. As a well-temperament the main problem with it is
that it doesn't seem to help the thirds much; rearranging the fifths
so that the meantone fifths were in the same part of the chain would
seem to be a good plan if we wanted a well-temperament with sweeter
home keys.
I also give a 19-note 7-limit pseudo 19-equal which is the Hahn
reduction via the commas of 171-et of a chain of minor thirds. It is
interesting for being rational and having a lot of pure minor thirds.
! rat12.scl
72-et Hahn reduced 12-fairly-equal well-temperament
12
!
200/189
9/8
25/21
63/50
4/3
625/441
3/2
100/63
42/25
16/9
189/100
2
! rat19.scl
171-et Hahn reduced 7-limit 19-almost-equal
19
!
28/27
672/625
125/112
125/108
6/5
56/45
1323/1024
75/56
25/18
36/25
112/75
2048/1323
45/28
5/3
216/125
224/125
625/336
27/14
2
Full thread (1 messages)
From: Gene Ward Smith (2004-07-28)
Subject: Rational 12 and 19 nearly equal
Below I give a 12-note 7-limit well-temperament obtained by Hahn
reducing a chain of fifths according to 7-limit 72-et, meaning via the
commas 225/224, 1029/1024 and 4375/4374. The result has three 112/75
meantone fifths, a 125000/83349 quasi-pure fifth (it's flat by an
interval of 250047/250000, which is less than a third of a cent) and
eight pure fifths. As a well-temperament the main problem with it is
that it doesn't seem to help the thirds much; rearranging the fifths
so that the meantone fifths were in the same part of the chain would
seem to be a good plan if we wanted a well-temperament with sweeter
home keys.
I also give a 19-note 7-limit pseudo 19-equal which is the Hahn
reduction via the commas of 171-et of a chain of minor thirds. It is
interesting for being rational and having a lot of pure minor thirds.
! rat12.scl
72-et Hahn reduced 12-fairly-equal well-temperament
12
!
200/189
9/8
25/21
63/50
4/3
625/441
3/2
100/63
42/25
16/9
189/100
2
! rat19.scl
171-et Hahn reduced 7-limit 19-almost-equal
19
!
28/27
672/625
125/112
125/108
6/5
56/45
1323/1024
75/56
25/18
36/25
112/75
2048/1323
45/28
5/3
216/125
224/125
625/336
27/14
2
Raw file
! rat19.scl
171-et Hahn reduced 7-limit 19-almost-equal
19
!
28/27
672/625
125/112
125/108
6/5
56/45
1323/1024
75/56
25/18
36/25
112/75
2048/1323
45/28
5/3
216/125
224/125
625/336
27/14
2
!
! https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_55054.html#55054
!
! [info]
! source = Mailing lists
! file = tuning/messages/yahoo_tuning_messages_api_raw_52482-55189.json
! topic_id = 55054
! msg_id = 55054