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Possible notation for 11-limit hedgehog

🔗Herman Miller <hmiller@IO.COM>

12/9/2007 6:10:04 PM

7-limit hedgehog:
[<2, 4, 6, 7], <0, -3, -5, -5]>
TOP-MAX: P = 598.4467109, G = 162.3159606
TOP-RMS: P = 599.619018, G = 164.247626

11-limit hedgehog:
[<2, 4, 6, 7, 8], <0, -3, -5, -5, -4]>
TOP-MAX: P = 599.090477, G = 163.146764
TOP-RMS: P = 600.129682, G = 164.649752

D/|\ E F||\ | A!// B!!!( C!)
G/|\ A B\!/ | D!// E!!!( F!)
C/|\ D E\!/ | G!// G|||( A|\\
F/|\ G A\!/ | B|) C|||( D|\\
B!!/ C D\!/ | E|) F|||( G|\\

For the (+2, -7) accidental:
The possibilites are /| ~|) (|( /|\ )/|\ )||( . Of these, /| is too small, )||( is too big, and the others are less familiar.

For (+1, -3) you have the usual problems with half-octaves; here the choices are .||) -- or )/|| --, and |||( .

Besides |\\ -- or .(|\ -- for (-1, +4), another good choice is /|) .

The notation for (-3, +11) is very sensitive to the exact tuning. With the TOP-MAX 7-limit tuning, (-3, +11) is negative, and (+3, -11) is notated as ~| . With the TOP-RMS 7-limit tuning, (-3, +11) can be notated as |). Since only F!) and B|) are needed in the 14-note hedgehog MOS, they make the most sense as a 7/4 above G or 8/7 above A.

(This illustrates one problem with notating regular temperaments: whether a small interval ends up as positive or negative may depend on the exact tuning.)