phillips19_1
Pauline Phillips 5 cent margin optimized
Properties
| Notes | 19 |
|---|---|
| Period | 1200.0 ¢ |
| Just | No |
| Source | Mailing lists |
| Reference | https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_40185.html#40185 |
| Thread | 2 scales |
| Tone (¢) | Step (¢) |
|---|---|
| 84 | 84 |
| 152 | 68 |
| 199 | 48 |
| 269 | 69 |
| 384 | 115 |
| 401 | 17 |
| 468 | 67 |
| 500 | 33 |
| 584 | 84 |
| 668 | 84 |
| 700 | 32 |
| 768 | 69 |
| 852 | 84 |
| 900 | 47 |
| 968 | 68 |
| 1084 | 116 |
| 1103 | 19 |
| 1168 | 65 |
| 1200 | 32 |
Similar scales
| File | Notes | Rotation | Max diff (¢) |
|---|---|---|---|
| phillips19_3 | 19 | 0 | 1.6 |
| phillips19 | 19 | 0 | 3.1 |
| quasi-phillips | 19 | 0 | 15.9 |
| xen07-chalmers-rvf-3 | 19 | 2 | 16.7 |
| xen07-chalmers-fifth-comma | 19 | 2 | 24.0 |
| xen13-grady-19-1 | 19 | 11 | 24.8 |
| xen07-chalmers-rvf-2 | 19 | 2 | 24.9 |
Parent scales
| File | Notes | Max diff (¢) |
|---|---|---|
| phillips | 22 | 7.7 |
| compton48 | 48 | 2.9 |
| 41cosine | 41 | 7.6 |
| Tolerant-Secor-29 | 29 | 14.1 |
| edo-41 | 41 | 9.3 |
| valamute | 31 | 13.5 |
| secor29tolerant | 29 | 14.6 |
| septenarian29 | 29 | 14.7 |
| breezb | 27 | 16.1 |
| xen18-erlich-garibaldi-41 | 41 | 10.1 |
Child scales
| File | Notes | Max diff (¢) |
|---|---|---|
| phillips_tuning_39746_39990 | 12 | 0.7 |
| Ghana_Tomora_Ba | 7 | 1.2 |
| keen6 | 5 | 1.7 |
| xen03-wilson-acute-05 | 5 | 2.2 |
| xen07-harrison-thoughts-5 | 5 | 2.2 |
| lumma_wauchope-major | 8 | 4.2 |
| xen12-wilson-09-4C2-hexany-02 | 6 | 4.2 |
| xen09-chalmers-tritriadic-10-14-15 | 7 | 4.5 |
| xen09-chalmers-tritriadic-3-7-9 | 7 | 4.5 |
| xen09-chalmers-tritriadic-6-7-9 | 7 | 4.5 |
Mailing list post
From: Gene Ward Smith (2002-10-26) Subject: Least squares optimized Phillips scales I did a least-squares fit to 7-limit intervals within 5 cents and 2.5 cents, and the results were revelatory. ! phillips19_1.scl ! Pauline Phillips 5 cent margin optimized 19 ! 84.3139369 151.8583699 199.4177206 268.7134087 383.8258631 400.9748406 467.6441078 500.2450361 584.1379555 668.1811654 699.7491415 768.3582599 852.4717660 899.7040367 967.8513128 1084.072482 1102.929842 1167.567841 2/1 6 major and 5 minor tetrads, 9 major and 7 minor triads, all within an error of 3 cents. ! phillips19_3.scl ! Pauline Phillips 2.5 cent margin optimized 19 ! 84.3723294 153.1326370 199.4516985 268.4554748 384.0592956 400.9792756 467.9551626 500.1311909 583.9525259 668.1674854 699.8776326 768.0935174 854.1073992 899.6726293 968.0465972 1084.139777 1102.934277 1167.481701 2/1 One less minor tetrad, and the error is not much smaller; I think the first version may be what Pauline was shooting for.
Full thread (4 messages)
From: Gene Ward Smith (2002-10-26) Subject: Least squares optimized Phillips scales I did a least-squares fit to 7-limit intervals within 5 cents and 2.5 cents, and the results were revelatory. ! phillips19_1.scl ! Pauline Phillips 5 cent margin optimized 19 ! 84.3139369 151.8583699 199.4177206 268.7134087 383.8258631 400.9748406 467.6441078 500.2450361 584.1379555 668.1811654 699.7491415 768.3582599 852.4717660 899.7040367 967.8513128 1084.072482 1102.929842 1167.567841 2/1 6 major and 5 minor tetrads, 9 major and 7 minor triads, all within an error of 3 cents. ! phillips19_3.scl ! Pauline Phillips 2.5 cent margin optimized 19 ! 84.3723294 153.1326370 199.4516985 268.4554748 384.0592956 400.9792756 467.9551626 500.1311909 583.9525259 668.1674854 699.8776326 768.0935174 854.1073992 899.6726293 968.0465972 1084.139777 1102.934277 1167.481701 2/1 One less minor tetrad, and the error is not much smaller; I think the first version may be what Pauline was shooting for.
From: prophecyspirit@aol.com (2002-10-26) Subject: Re: [tuning] Least squares optimized Phillips scales In a message dated 10/26/02 8:05:33 AM Central Daylight Time, genewardsmith@juno.com writes: > I think the first version may be what Pauline was shooting for. > When I invented my scales, I was seeking to play in JI music already composed for tempered scales with 12 keyboard notes per octave. And do so with the least extra notes anad keys above 12. I found 19 noes to the octave would do this when slightly tempered. Some of the results were free extras. Such as being to play in C major, 7c minor and tertian e minor with the same tuning. And having several secondary scales related to these with the same tuning. Pauline
From: Carl Lumma (2002-10-27) Subject: Re: Least squares optimized Phillips scales [Gene wrote...] >I did a least-squares fit to 7-limit intervals within 5 cents >and 2.5 cents, and the results were revelatory. Least-squares fit from what starting scale? How were they relevatory? -Carl
From: Gene Ward Smith (2002-10-27) Subject: Re: Least squares optimized Phillips scales --- In tuning@y..., "Carl Lumma" <clumma@y...> wrote: > [Gene wrote...] > >I did a least-squares fit to 7-limit intervals within 5 cents > >and 2.5 cents, and the results were revelatory. > > Least-squares fit from what starting scale? How were they > relevatory? I adjusted the Phillips scale to the 7-limit consonant intervals in included with a margin of 5 cents, and then of 2.5 cents, and it showed the errors needn't be as great, and suggested how the 5-limit substructure looked.
Raw file
! phillips19_1.scl ! Pauline Phillips 5 cent margin optimized 19 ! 84.3139369 151.8583699 199.4177206 268.7134087 383.8258631 400.9748406 467.6441078 500.2450361 584.1379555 668.1811654 699.7491415 768.3582599 852.4717660 899.7040367 967.8513128 1084.072482 1102.929842 1167.567841 2/1 ! ! https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_40185.html#40185 ! ! [info] ! source = Mailing lists ! file = tuning/messages/yahoo_tuning_messages_api_raw_40000-49986.json ! topic_id = 40185 ! msg_id = 40185