Twelve Working Temperaments.

Here is a list of twelve working temperaments in 41tet which can be
used for musicological comparisons with historical temperaments. They
are all unequal transpositions of each other. If your favorite
temperament is near any of these twelve tables then it might mean
that there is some sort of basin of attraction in
operation.
Table One: 0-59-205-263-380-498-585-702-761-878-966-1083-
1200.
Table Two: 0-146-205-322-439-527-644-702-820-907-1024-1141-
1200.
Table Three: 0-59-176-293-380-498-556-673-761-878-995-1054-
1200.
Table Four: 0-117-234-322-439-498-615-702-820-937-995-1141-
1200.
Table Five: 0-117-205-322-380-498-585-702-820-878-1024-1083-
1200.
Table Six: 0-88-205-263-380-468-585-702-761-907-966-1083-
1200.
Table Seven: 0-117-176-293-380-498-615-673-820-878-995-1112-
1200.
Table Eight: 0-59-176-263-380-498-556-702-761-878-995-1083-
1200.
Table Nine: 0-117-205-322-439-498-644-702-820-937-1024-1141-
1200.
Table Ten: 0-88-205-322-380-527-585-702-820-907-1024-1083-
1200.
Table Eleven: 0-117-234-293-439-498-615-732-820-937-995-1112-
1200.
Table Twelve: 0-117-176-322-380-498-615-702-820-878-995-1083-
1200.
The methodology used to determine these tables need not
necessarily be confined to 41tet. The same procedure can be scaled to
fit 31tet and 53tet and whatever. They are only meant to be a
guideline in classifying historical temperaments.

robert thomas martin wrote:
> Here is a list of twelve working temperaments in 41tet which can be > used for musicological comparisons with historical temperaments. They > are all unequal transpositions of each other. If your favorite > temperament is near any of these twelve tables then it might mean > that there is some sort of basin of attraction in > operation. <snip>

For folks reading along at home, here are the scales (what definition of "temperament" is this?) as steps from 41tet.

Table One 2 5 2 4 4 3 4 2 4 3 4 4
Table Two 5 2 4 4 3 4 2 4 3 4 4 2
Table Three 2 4 4 3 4 2 4 3 4 4 2 5
Table Four 4 4 3 4 2 4 3 4 4 2 5 2
Table Five 4 3 4 2 4 3 4 4 2 5 2 4
Table Six 3 4 2 4 3 4 4 2 5 2 4 4
Table Seven 4 2 4 3 4 4 2 5 2 4 4 3
Table Eight 2 4 3 4 4 2 5 2 4 4 3 4
Table Nine 4 3 4 4 2 5 2 4 4 3 4 2
Table Ten 3 4 4 2 5 2 4 4 3 4 2 4
Table Eleven 4 4 2 5 2 4 4 3 4 2 4 3
Table Twelve 4 2 5 2 4 4 3 4 2 4 3 4

Graham

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>
> robert thomas martin wrote:
> > Here is a list of twelve working temperaments in 41tet which can
be
> > used for musicological comparisons with historical temperaments.
They
> > are all unequal transpositions of each other. If your favorite
> > temperament is near any of these twelve tables then it might mean
> > that there is some sort of basin of attraction in
> > operation.
> <snip>
>
> For folks reading along at home, here are the scales (what
> definition of "temperament" is this?) as steps from 41tet.
>
> Table One 2 5 2 4 4 3 4 2 4 3 4 4
> Table Two 5 2 4 4 3 4 2 4 3 4 4 2
> Table Three 2 4 4 3 4 2 4 3 4 4 2 5
> Table Four 4 4 3 4 2 4 3 4 4 2 5 2
> Table Five 4 3 4 2 4 3 4 4 2 5 2 4
> Table Six 3 4 2 4 3 4 4 2 5 2 4 4
> Table Seven 4 2 4 3 4 4 2 5 2 4 4 3
> Table Eight 2 4 3 4 4 2 5 2 4 4 3 4
> Table Nine 4 3 4 4 2 5 2 4 4 3 4 2
> Table Ten 3 4 4 2 5 2 4 4 3 4 2 4
> Table Eleven 4 4 2 5 2 4 4 3 4 2 4 3
> Table Twelve 4 2 5 2 4 4 3 4 2 4 3 4
>
>
> Graham
>
From Robert. Thankyou for simplifying my posting even more.
What "definition" of temperament is this? I'm not sure. It is simply
a mathematical tool which might be used to classify historical
temperaments and put them into a form which can be translated into
other equal temperaments.