[tuning-math] Square scales

There are three scales deriving from the three orientations of a 3x3
square in the cubic lattice with a major tetrad in the center, and three
more with a minor tetrad. These I give below, along with the
corresponding commas, which turn out to be the same for the major and
minor form of each square.

maj12 := [1, 25/24, 21/20, 35/32, 8/7, 6/5, 5/4, 21/16, 10/7, 35/24, 3/2,
49/32, 5/3, 12/7, 7/4, 9/5]

min12 := [1, 36/35, 21/20, 8/7, 6/5, 5/4, 21/16, 48/35, 10/7, 36/25, 3/2,
5/3, 12/7, 7/4, 9/5, 96/49]

commas 126/125, 1029/1024, 1728/1715

126/125^1029/1024^1728/1715 = 31-et
1029/1024^126/125 = [6, 3, -3, -5, 6, -4], a linear temperament with no
name
126/125^1728/1715 = [10, 9, 7, -9, 17, -9], small diesic
1029/1024^1728/1715 = [3, 12, -1, -36, 10, 12], supermajor seconds


maj13 := [1, 49/48, 15/14, 35/32, 7/6, 6/5, 5/4, 9/7, 7/5, 35/24, 3/2,
25/16, 8/5, 12/7, 7/4, 15/8]

min13 := [1, 36/35, 15/14, 7/6, 6/5, 5/4, 9/7, 48/35, 7/5, 72/49, 3/2,
8/5, 12/7, 7/4, 15/8, 48/25]

commas 225/224, 1728/1715
1728/1715^225/224 = orwell

maj23:=[1, 21/20, 15/14, 9/8, 7/6, 49/40, 5/4, 21/16, 4/3, 7/5, 10/7,
3/2, 5/3, 7/4, 25/14, 15/8]

min23 := [1, 21/20, 15/14, 9/8, 8/7, 6/5, 60/49, 9/7, 4/3, 7/5, 10/7,
3/2, 8/5, 42/25, 12/7, 9/5]

commas 126/125, 225/224, 2401/2400
126/125^225/224^2401/2400 = 31-et
126/125^225/224 = meantone
126/125^2401/2400 = small diesic
225/224^2401/2400 = miracle

------------------------ Yahoo! Groups Sponsor ---------------------~-->
Save on REALTOR Fees
http://us.click.yahoo.com/Xw80LD/h1ZEAA/Ey.GAA/wHYolB/TM
---------------------------------------------------------------------~->

To unsubscribe from this group, send an email to:
tuning-math-unsubscribe@xxxxxxxxxxxxxxx

 

Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/ 


____________________________________________________________

To learn how to configure this list via e-mail (subscribe,
unsubscribe, etc.), send a message to listar@xxxxxxxxxxxxx
with the subject line "info tuning-math".  Or visit the
website:  < http://www.freelists.org/list/tuning-math > .

Other related posts: