tripenta

6/31 generator supermajor seconds tripentatonic scale

Open in Scale Workshop Scala analysis Download scl

Properties

Notes15
Period1200.0 ¢
JustNo
Source Mailing lists
Referencehttps://yahootuninggroupsultimatebackup.github.io/tuning/topicId_47216.html#47216
Thread1 scale
Tone (¢) Step (¢)
39 39
194 155
232 39
271 39
426 155
465 39
503 39
697 194
735 39
774 39
929 155
968 39
1006 39
1161 155
1200 39

Parent scales

FileNotesMax diff (¢)
xen18-erlich-cynder-16 16 1.8
xen18-erlich-cynder-21 21 1.8
xen18-erlich-cynder-26 26 1.8
edo-31 31 0.0
31edo-top 31 1.5
xen18-erlich-cynder-31 31 1.8
circle31 31 2.2
cbrat31 31 3.0
xen18-erlich-meantone-31 31 3.1
vala 31 5.0

Child scales

FileNotesMax diff (¢)
mothra11sub 11 1.1
xen18-erlich-cynder-11 11 1.7
xen18-erlich-cynder-06 6 1.7
xen18-erlich-cynder-05 5 1.7
xen18-erlich-meantone-05 5 1.8
xen15-gilson-generalized-pythagorean-7-4-5 5 4.3
xen10-wilson-purvi-03a-06 7 5.2
xen10-wilson-purvi-03b-04 7 5.2
xen15-chalmers-triadic-diamond-32-25 7 5.2
xen15-chalmers-triadic-reversed-diamond-17-13 7 5.2
Mailing list post 
From: Gene Ward Smith (2003-09-25)
Subject: The Tripentatonic scale

I was considering how to put three copies of the meantone pentatonic
scale together in a reasonable way, and concluded that the supermajor
seconds temperament was the way to go. This divides a meantone fifth
into three parts to get a supermajor second of around 8/7, which is
the  generator. Hence it has 81/80 and (3/2)/(8/7)^3 = 1029/1024 as
commas.

Tripentatonic has three copies of pentatonic in it, and is
pseudo-Myhill; adding another note gives us a 16-note supermajor
seconds MOS. If we use 6/31 for the generator, tripentatonic is

[0, 1, 5, 6, 7, 11, 12, 13, 18, 19, 20, 24, 25, 26, 30]

Adding a 14 gives us the MOS.

Here is Tripentatonic in Scala format:

! tripenta.scl
6/31 generator supermajor seconds tripentatonic scale
15
!
38.709677
193.548387
232.258065
270.967742
425.806452
464.516129
503.225806
696.774194
735.483871
774.193548
929.032258
967.741935
1006.451613
1161.290323
1200.000000
Full thread (1 messages) 
From: Gene Ward Smith (2003-09-25)
Subject: The Tripentatonic scale

I was considering how to put three copies of the meantone pentatonic
scale together in a reasonable way, and concluded that the supermajor
seconds temperament was the way to go. This divides a meantone fifth
into three parts to get a supermajor second of around 8/7, which is
the  generator. Hence it has 81/80 and (3/2)/(8/7)^3 = 1029/1024 as
commas.

Tripentatonic has three copies of pentatonic in it, and is
pseudo-Myhill; adding another note gives us a 16-note supermajor
seconds MOS. If we use 6/31 for the generator, tripentatonic is

[0, 1, 5, 6, 7, 11, 12, 13, 18, 19, 20, 24, 25, 26, 30]

Adding a 14 gives us the MOS.

Here is Tripentatonic in Scala format:

! tripenta.scl
6/31 generator supermajor seconds tripentatonic scale
15
!
38.709677
193.548387
232.258065
270.967742
425.806452
464.516129
503.225806
696.774194
735.483871
774.193548
929.032258
967.741935
1006.451613
1161.290323
1200.000000

Raw file

! tripenta.scl
6/31 generator supermajor seconds tripentatonic scale
15
!
38.709677
193.548387
232.258065
270.967742
425.806452
464.516129
503.225806
696.774194
735.483871
774.193548
929.032258
967.741935
1006.451613
1161.290323
1200.000000
!
! https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_47216.html#47216
!
! [info]
! source = Mailing lists
! file = tuning/messages/yahoo_tuning_messages_api_raw_40000-49986.json
! topic_id = 47216
! msg_id = 47216