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dissonance curve

🔗Peter.Blasser@oberlin.edu

12/15/1997 10:57:55 AM
I'm not up on my reading, so I'd like to ask a question about a dissonanc
rating system. Is there one where you rate according to the absolute
value of the log of each factor. An example best be placed here:

dissonance of 3/2 = log2(3) + |log2(1/2)| = 1.584963 + 1 = 2.5863
dissonance of 11/8 = log2(11) + |(3 * log2(1/2)| = 3.45 + 3 = 6.45
dissonance of 32/31 = 5 * log2(2) + |log2(31)| = 5 + 4.954 = 9.954

This seems to be "fairer" on the higher limits, where, say a change from
71 to 73 would effect a dissonance change of 73/71, rather than 73-71 as
some systems point to. Do you understand this. I just thought about it
really hard this morning, and I don't know if it is correct. I think that
the systems that assign a number (n-1) to a limit n would point to a
dissonance change of 73-71, which is larger than it should be. e.g.
again:

old system:
dissonance of 73/8 = 72+1+1+1 = 75
dissonance of 71/8 = 70+1+1+1 = 73
change of 2

this system:
dissonance of 73/8 = log2(73) + 3log2(2) = 6.189 + 3 = 9.189
dissonance of 71/8 = log2(71) + 3log2(2) = 6.149 + 3 = 9.149
change of .05

If this exists, what is the name of it?
What do you think of its validity?

Thank you.
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
[Peter Blasser
[Oberlin College Mailroom Box #277, 135 W.Lorain St.,
[Oberlin, Ohio, 44074-1081.
[Peter.Blasser@Oberlin.edu . . . .
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++


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