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Sagittal notation of mavila temperament

🔗Herman Miller <hmiller@IO.COM>

11/24/2007 9:04:46 PM

Mavila has a chain of fifths outside the usual range of Sagittal notation, smaller than the fifths of 7-ET. The fifths are so small that major and minor thirds are reversed -- a chain of mavila fourths might be notated B!!/ E!!/ A D G C||\ F||\ (135/128 ||\ is tempered out). It would be nice if there were a consistent way to notate this sequence so that all the thirds are the right size, but C||\ E!!/ represents a minor third here. It could be written as C E!!/ or C||\ E in an appropriate context.

So why not just notate B E A D G C F and accept the fact that DF is a major third while CE is a minor third? Then what's the next note after F? Some kind of B? B\! is technically possible, but it's a higher pitch than B. Alternatively, B)||( would work. But then you have a perfect fourth notated as F : B)||(, which just looks weird!

No matter what you do, something's going to come out notated strangely, since 135/128 is a rather large interval to temper out. Something like this might be a good compromise.

A)!!( 36/25 (+4, -8)
D)!!( 48/25 (+4, -7)
G)!!( 32/25 (+3, -6)
C/| 9/5 (+3, -5)
F/| 6/5 (+2, -4)
B!!/ 8/5 (+2, -3)
E!!/ 16/15 (+1, -2)
A 3/2 (+1, -1)
D 1/1 (+0, +0)
G 4/3 (+0, +1)
C||\ 15/8 (+0, +2)
F||\ 5/4 (-1, +3)
B\! 5/3 (-1, +4)
E\! 10/9 (-2, +5)
A)||( 25/16 (-2, +6)
D)||( 25/24 (-3, +7)
G)||( 25/18 (-3, +8)