wilson_class

Class Scale, Erv Wilson, 9 july 1967

Open in Scale Workshop Scala analysis Download scl

Properties

Notes	12
Period	1200.0 ¢
Just	7-limit
Source	Mailing lists
Reference	https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_2720.html#2720
Thread	1 scale

Tone	Tone (¢)	Step	Step (¢)
25/24	71	25/24	71
28/25	196	672/625	126
7/6	267	25/24	71
5/4	386	15/14	119
4/3	498	16/15	112
7/5	583	21/20	84
35/24	653	25/24	71
8/5	814	192/175	161
5/3	884	25/24	71
7/4	969	21/20	84
28/15	1081	16/15	112
2/1	1200	15/14	119

Similar scales

File	Notes	Rotation	Max diff (¢)
12_class	12	7	0.0
wilcmarv7	12	7	3.9
wilcmarv11	12	7	5.0
wreck_a	12	6	7.3
classr	12	7	7.7
starrc	12	7	9.8
thirds	12	3	13.8
xen18-erlich-augene-12	12	2	23.2

Parent scales

File	Notes	Max diff (¢)
keenan5	22	5.0
mircube	31	3.8
quasic22	22	10.1
circle31	31	5.4
cata34	34	4.5
xen18-erlich-orwell-31	31	6.1
xen18-erlich-orson-31	31	6.2
notchedcube	28	7.7
xen07-chalmers-smith	19	13.6
xen07-chalmers-chalmers	19	13.8

Child scales

File	Notes	Max diff (¢)
xen12-wilson-39-4C2-hexany-00	6	0.0
xen09-wilson-marwa-14b-04	7	13.8
xen09-wilson-marwa-14b-07	7	13.8
CD17_13_Tunisia	6	18.1
xen07-harrison-thoughts-6	5	18.1
CD17_20_Tunisia	7	19.8
CD17_03_Tunisia	7	21.4
xen09-wilson-marwa-11b-04	7	21.5
xen09-wilson-marwa-11b-07	7	21.5
CD17_05_Tunisia	7	23.7

Mailing list post

From: Carl Lumma (1999-05-07)
Subject: Wilson's got class

A while back there was a discussion about 12-note scales with high numbers
of 7-limit dyads.  Paul Hahn found the winner, with 32 dyads...

       5:3---------5:4
       /|\         /|\
      / | \       / | \
     /  |  \     /  |  \
    /  7:6---------7:4  \
   /.-'/ \'-.\ /.-'/ \'-.\
4:3--/---\--1:1--/---\--3:2
  |\ /     \ /|\ /     \ /|
  | /       \ | /       \ |
  |/ \     / \|/ \     / \|
28:15--------7:5--------21:20
    '-.\ /.-'   '-.\ /.-'
       8:5---------6:5

...four tetrads (3 otonal), three 8:10:12:15 "ASS" chords, three
10:12:15:18 ASS's, and 2 hexanies.  Unfortunately it is so melodically
un-even that its chords float around scale degrees like small boats.
Recently, I noticed that I had come across this structure (in this same
position) last July, when I was looking for 12-tone scales that contained
bits of the 7-limit diamond.

I had also discovered this scale...

                     35/32-----105/64
                    ,'/ \`.  ,' /
                 5/4-/---\-15/8/
                 /|\/     \/| /
                / |/\     /\|/
               / 7/4------21/16
              /,'/ \`.\ /,'/
            1/1-/---\-3/2 /
            /|\/     \/| /
           / |/\     /\|/
          / 7/5------21/20
         /,'   `.\ /.' 
       8/5-------6/5      

...Paul Hahn was the first to correctly count the number of consonant dyads
in this structure; 31.  He was also able to count all possible versions of
the two-hexany 12-plex, and found that only three lacked an interval
smaller than 25/24 (the smallest interval in my version is 525/512, or 43
cents)...

a)1/1, 21/20, 35/32, 6/5, 5/4, 21/16, 7/5, 3/2, 8/5, 42/25, 7/4, 15/8
b)1/1, 21/20, 35/32, 6/5, 5/4, 21/16, 7/5, 3/2, 25/16, 42/25, 7/4, 15/8
c)1/1, 21/20, 35/32, 6/5, 5/4, 21/16, 7/5, 3/2, 25/16, 105/16, 7/4, 15/8

...of these, he noticed that (a) and (b) are not covered by their tetrads,
but (c) is, although he seemed to prefer (a) because of its lower diameter.
 I played a bit with these scales, and found I like (c) the best.  Today,
whilst going thru the Scala archive, I found this...

! wilson_class.scl
!
Class Scale, Erv Wilson, 9 july 1967
12
!
25/24
28/25
7/6
5/4
4/3
7/5
35/24
8/5
5/3
7/4
28/15
2/1

...which is identical to (c) when transposed by its 5th degree...

                 25/16
                  /|\
                 / | \
                /35/32\
               /,'/ \`.\
             5/4-/---\-15/8
             /|\/     \/|
            / |/\     /\|
           / 7/4------21/16
          /,'/ \`.\ /,'/
        1/1-/---\-3/2 /
         |\/     \/| /
         |/\     /\|/
        7/5------21/20
          \`.\ /,'/
           \ 6/5 /
            \ | /
             \|/
            42/25

...so there you have it.  Nothing new under the sun (at least since 1967).

-C.

Full thread (3 messages)

From: Carl Lumma (1999-05-07)
Subject: Wilson's got class

A while back there was a discussion about 12-note scales with high numbers
of 7-limit dyads.  Paul Hahn found the winner, with 32 dyads...

       5:3---------5:4
       /|\         /|\
      / | \       / | \
     /  |  \     /  |  \
    /  7:6---------7:4  \
   /.-'/ \'-.\ /.-'/ \'-.\
4:3--/---\--1:1--/---\--3:2
  |\ /     \ /|\ /     \ /|
  | /       \ | /       \ |
  |/ \     / \|/ \     / \|
28:15--------7:5--------21:20
    '-.\ /.-'   '-.\ /.-'
       8:5---------6:5

...four tetrads (3 otonal), three 8:10:12:15 "ASS" chords, three
10:12:15:18 ASS's, and 2 hexanies.  Unfortunately it is so melodically
un-even that its chords float around scale degrees like small boats.
Recently, I noticed that I had come across this structure (in this same
position) last July, when I was looking for 12-tone scales that contained
bits of the 7-limit diamond.

I had also discovered this scale...

                     35/32-----105/64
                    ,'/ \`.  ,' /
                 5/4-/---\-15/8/
                 /|\/     \/| /
                / |/\     /\|/
               / 7/4------21/16
              /,'/ \`.\ /,'/
            1/1-/---\-3/2 /
            /|\/     \/| /
           / |/\     /\|/
          / 7/5------21/20
         /,'   `.\ /.' 
       8/5-------6/5      

...Paul Hahn was the first to correctly count the number of consonant dyads
in this structure; 31.  He was also able to count all possible versions of
the two-hexany 12-plex, and found that only three lacked an interval
smaller than 25/24 (the smallest interval in my version is 525/512, or 43
cents)...

a)1/1, 21/20, 35/32, 6/5, 5/4, 21/16, 7/5, 3/2, 8/5, 42/25, 7/4, 15/8
b)1/1, 21/20, 35/32, 6/5, 5/4, 21/16, 7/5, 3/2, 25/16, 42/25, 7/4, 15/8
c)1/1, 21/20, 35/32, 6/5, 5/4, 21/16, 7/5, 3/2, 25/16, 105/16, 7/4, 15/8

...of these, he noticed that (a) and (b) are not covered by their tetrads,
but (c) is, although he seemed to prefer (a) because of its lower diameter.
 I played a bit with these scales, and found I like (c) the best.  Today,
whilst going thru the Scala archive, I found this...

! wilson_class.scl
!
Class Scale, Erv Wilson, 9 july 1967
12
!
25/24
28/25
7/6
5/4
4/3
7/5
35/24
8/5
5/3
7/4
28/15
2/1

...which is identical to (c) when transposed by its 5th degree...

                 25/16
                  /|\
                 / | \
                /35/32\
               /,'/ \`.\
             5/4-/---\-15/8
             /|\/     \/|
            / |/\     /\|
           / 7/4------21/16
          /,'/ \`.\ /,'/
        1/1-/---\-3/2 /
         |\/     \/| /
         |/\     /\|/
        7/5------21/20
          \`.\ /,'/
           \ 6/5 /
            \ | /
             \|/
            42/25

...so there you have it.  Nothing new under the sun (at least since 1967).

-C.

From: Carl Lumma (1999-05-11)
Subject: Re: Wilson's got class

I found a small error in my post to TD166 (May 8th).  I mixed up the scales
in this list...

>a)1/1, 21/20, 35/32, 6/5, 5/4, 21/16, 7/5, 3/2, 8/5, 42/25, 7/4, 15/8
>b)1/1, 21/20, 35/32, 6/5, 5/4, 21/16, 7/5, 3/2, 25/16, 42/25, 7/4, 15/8
>c)1/1, 21/20, 35/32, 6/5, 5/4, 21/16, 7/5, 3/2, 25/16, 105/16, 7/4, 15/8

...which should read...

a)1/1, 21/20, 35/32, 6/5, 5/4, 21/16, 7/5, 3/2, 8/5, 42/25, 7/4, 15/8
b)1/1, 21/20, 35/32, 6/5, 5/4, 21/16, 7/5, 3/2, 25/16, 105/64, 7/4, 15/8
c)1/1, 21/20, 35/32, 6/5, 5/4, 21/16, 7/5, 3/2, 25/16, 42/25, 7/4, 15/8

...(b) and (c) were switched.  The rest of the post was fine.


a)            35/32 
             ,'/ \`.
          5/4-/---\-15/8
          /:\/     \/:
         / :/\     /\:
        / 7/4------21/16
       /,'/ \`.\ /,'/
     1/1-/---\-3/2 /
     /:\/     \/: /
    / :/\     /\:/
   / 7/5------21/20
  /,'  \`.\ /,'/
8/5-----\-6/5 /
         \ : /
          \:/
         42/25

c)             25/16
                /:\
               / : \
              /35/32\
             /,'/ \`.\
           5/4-/---\-15/8
           /:\/     \/:
          / :/\     /\:
         / 7/4------21/16
        /,'/ \`.\ /,'/
      1/1-/---\-3/2 /
       :\/     \/: /
       :/\     /\:/
      7/5------21/20
        \`.\ /,'/
         \ 6/5 /
          \ : /
           \:/
          42/25

None of these scales are proper, and they all have the same largest and
smallest intervals.  They each have six 5-limit ASS's, but (c) is biased
toward the 10:12:15:18.

-C.

From: Kraig Grady (1999-05-11)
Subject: Re: Wilson's got class

Carl!
Where are these from again, I forgot!

Carl Lumma wrote:

> From: Carl Lumma <[email protected]>
>
> I found a small error in my post to TD166 (May 8th).  I mixed up the scales
> in this list...
>
> >a)1/1, 21/20, 35/32, 6/5, 5/4, 21/16, 7/5, 3/2, 8/5, 42/25, 7/4, 15/8
> >b)1/1, 21/20, 35/32, 6/5, 5/4, 21/16, 7/5, 3/2, 25/16, 42/25, 7/4, 15/8
> >c)1/1, 21/20, 35/32, 6/5, 5/4, 21/16, 7/5, 3/2, 25/16, 105/16, 7/4, 15/8
>
> ...which should read...
>
> a)1/1, 21/20, 35/32, 6/5, 5/4, 21/16, 7/5, 3/2, 8/5, 42/25, 7/4, 15/8
> b)1/1, 21/20, 35/32, 6/5, 5/4, 21/16, 7/5, 3/2, 25/16, 105/64, 7/4, 15/8
> c)1/1, 21/20, 35/32, 6/5, 5/4, 21/16, 7/5, 3/2, 25/16, 42/25, 7/4, 15/8
>
> ...(b) and (c) were switched.  The rest of the post was fine.
>
> a)            35/32
>              ,'/ \`.
>           5/4-/---\-15/8
>           /:\/     \/:
>          / :/\     /\:
>         / 7/4------21/16
>        /,'/ \`.\ /,'/
>      1/1-/---\-3/2 /
>      /:\/     \/: /
>     / :/\     /\:/
>    / 7/5------21/20
>   /,'  \`.\ /,'/
> 8/5-----\-6/5 /
>          \ : /
>           \:/
>          42/25
>
> c)             25/16
>                 /:\
>                / : \
>               /35/32\
>              /,'/ \`.\
>            5/4-/---\-15/8
>            /:\/     \/:
>           / :/\     /\:
>          / 7/4------21/16
>         /,'/ \`.\ /,'/
>       1/1-/---\-3/2 /
>        :\/     \/: /
>        :/\     /\:/
>       7/5------21/20
>         \`.\ /,'/
>          \ 6/5 /
>           \ : /
>            \:/
>           42/25
>
> None of these scales are proper, and they all have the same largest and
> smallest intervals.  They each have six 5-limit ASS's, but (c) is biased
> toward the 10:12:15:18.
>
> -C

-- Kraig Grady
North American Embassy of Anaphoria Island
www.anaphoria.com

Raw file

! wilson_class.scl
!
Class Scale, Erv Wilson, 9 july 1967
12
!
25/24
28/25
7/6
5/4
4/3
7/5
35/24
8/5
5/3
7/4
28/15
2/1
!
! https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_2720.html#2720
!
! [info]
! source = Mailing lists
! file = tuning/messages/yahoo_tuning_messages_api_raw_0-19436.json
! topic_id = 2720
! msg_id = 2720