Correction Reply 2 to Graham Breed

In haste, I wrote:

> Then, go to the subdom:
>
> i -> v -> i -> IV -> III+ -> IV+ -> v (of i)
>
> [IX+] -> [X+] -> i (of v)

This should be:

i -> v -> i -> IV -> III* -> IV* -> v (of i)

[IX*] -> [X*] -> i (of v)


Sorry for any confusion.


Steve


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From: Peter.Blasser@oberlin.edu
Subject: dissonance curve
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> If this exists, what is the name of it?

Looks like a harmonic distance to me.

> What do you think of its validity?

I think of the logarithm of the LCM (which is what Peter used)
as the LCM on a pitch, rather than frequency, scale. As such,
it appears to be closer to perception, but is harder to calculate.
Taking logarithms to base 2 means dissonance in octaves.

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

73/8 has an LCM of 73*8=584. 71*8=568. The correct comparison
is 73/71=1.028, so a 2.8% increase in dissonance. No need for
logarithms.

I think Euler came up with the LCM first.

Some people leave out multiples of 2 when calculating dissonances.
Then 15/8 and 6/5 come out the same. The LCM can be evaluated for
a whole chord, where C-E-G-B comes out unduly consonant. A way
round this problem is to calculate Euclidian distances on a
parallelogram lattice.


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From: gbreed@cix.compulink.co.uk (Graham Breed)
Subject: Re: Septimal Intervals
PostedDate: 19-12-97 18:46:46
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