modmos13a

13 note modmos of hemiwuerschmidt in 229-et poptimal

Open in Scale Workshop Scala analysis Download scl

Properties

Notes13
Period1200.0 ¢
JustNo
Source Mailing lists
Referencehttps://yahootuninggroupsultimatebackup.github.io/tuning/topicId_54579.html#54579
Thread1 scale
Tone (¢) Step (¢)
47 47
84 37
157 73
314 157
388 73
472 84
545 73
702 157
739 37
933 194
969 37
1017 47
1200 183

Parent scales

FileNotesMax diff (¢)
xen18-erlich-cynder-26 26 8.3
valamute 31 5.8
xen18-erlich-cynder-31 31 8.3
xen18-erlich-meantone-31 31 8.5
cbrat31 31 8.8
31edo-top 31 8.9
circle31 31 9.8
xen18-erlich-luna-31 31 9.8
edo-31 31 10.1
xen18-erlich-wurschmidt-31 31 10.4

Child scales

FileNotesMax diff (¢)
ch9_1 9 1.5
keen1 5 4.3
keen3 5 4.3
keen5 5 4.3
keen4 5 5.1
keen6 5 5.1
Ethiopia_AI_540_83_1939 5 14.0
Ethiopia_AI_513_121_1939 5 14.6
CD11_12_bayati_Iraq 6 17.5
pentatonic-proper_5-prime 5 17.8
Mailing list post 
From: Gene Ward Smith (2004-07-13)
Subject: A 13-note hemiwuershmidt modmos

Hemiwuerschmidt (99&130) has a 7-limit Graham complexity of 16, so we
need to get up at least to the 19-not MOS before having complete tetrads
in a MOS. Here I give a 13-note modmos, found via more pen & paper
fiddling, which has three major tetrads and two minor tetrads, which
is not bad for 13 notes tempered in something more accurate than
miracle. It JI lattice terms, it has [-2,0,0], [0,0,0] and [1,1,0] for
major tetrads and [-1,0,0] and [0,1,0] for minor tetrads, so the
harmony links together nicely. In terms of hemiwuerschmidt generators
it is
0,2,5,7,9,10,11,14,16,19,21,25,30 which reduces mod 13 to a complete
set of residues. Here it is in the 229-et poptimal tuning:

! modmos13a.scl
13 note modmos of hemiwuerschmidt in 229-et poptimal
13 
!
47.161572
83.842795
157.205240
314.410480
387.772926
471.615721
544.978166
702.183406
738.864629
932.751092
969.432314
1016.593886
1200.000000
Full thread (2 messages) 
From: Gene Ward Smith (2004-07-13)
Subject: A 13-note hemiwuershmidt modmos

Hemiwuerschmidt (99&130) has a 7-limit Graham complexity of 16, so we
need to get up at least to the 19-not MOS before having complete tetrads
in a MOS. Here I give a 13-note modmos, found via more pen & paper
fiddling, which has three major tetrads and two minor tetrads, which
is not bad for 13 notes tempered in something more accurate than
miracle. It JI lattice terms, it has [-2,0,0], [0,0,0] and [1,1,0] for
major tetrads and [-1,0,0] and [0,1,0] for minor tetrads, so the
harmony links together nicely. In terms of hemiwuerschmidt generators
it is
0,2,5,7,9,10,11,14,16,19,21,25,30 which reduces mod 13 to a complete
set of residues. Here it is in the 229-et poptimal tuning:

! modmos13a.scl
13 note modmos of hemiwuerschmidt in 229-et poptimal
13 
!
47.161572
83.842795
157.205240
314.410480
387.772926
471.615721
544.978166
702.183406
738.864629
932.751092
969.432314
1016.593886
1200.000000
From: Gene Ward Smith (2004-07-13)
Subject: Re: A 13-note hemiwuershmidt modmos

--- In [email protected], "Gene Ward Smith" <gwsmith@s...> wrote:

In case someone is planning to throw a conniption about discussing
tuning on the tuning list, be it noted that this got posted here by
accident. I had intended to post it to tuning-math, where such
behavior is at least tolerated.

Raw file

! modmos13a.scl
13 note modmos of hemiwuerschmidt in 229-et poptimal
13 
!
47.161572
83.842795
157.205240
314.410480
387.772926
471.615721
544.978166
702.183406
738.864629
932.751092
969.432314
1016.593886
1200.000000
!
! https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_54579.html#54579
!
! [info]
! source = Mailing lists
! file = tuning/messages/yahoo_tuning_messages_api_raw_52482-55189.json
! topic_id = 54579
! msg_id = 54579