stuff (Paul Hahn)

>>This doesn't seem to fix anything, because now the 5/4 and 6/5 are
>>weighted the same.
>
>That's as it should be, as this metric ignores factors of 2.

And in this case, factors of 3. I don't think 8/5 and 5/4 should be the
same either, but I'm willing to except it. But I can't swallow 5/4 = 6/5.

>>Nothing's wrong with it, it's the mediant. Actually, n+d/2 is the
>>mediant.
>
>I'm not familiar with this definition of the mediant. Usually, the
>mediant is defined for a pair of fractions, a/b and c/d, as (a+c)/(b+d).

Well, if the ratio is 5/4, that's like the space between 5/1 and 4/1.
Fractions have to be in lowest terms for this comparo to work.

Carl

Carl Lumma wrote,

>>>This doesn't seem to fix anything, because now the 5/4 and 6/5 are
>>>weighted the same.

Paul Hahn wrote,

>>That's as it should be, as this metric ignores factors of 2.

Carl Lumma wrote,

>And in this case, factors of 3. I don't think 8/5 and 5/4 should be
the
>same either, but I'm willing to except it. But I can't swallow 5/4 =
6/5.

If you make 5/4 simpler than 6/5, then you're making 8/5 simpler than
5/3. Can you swallow that? Not me! If you can't swallow
octave-equivalent formulations at all, you're missing out on something
very useful, since it is often assumed that all octave-equivalents of
all scale tones will be used. In that case, a formulation like mine
treats them all at once.

>>>Nothing's wrong with it, it's the mediant. Actually, n+d/2 is the
>>>mediant.
>
>>I'm not familiar with this definition of the mediant. Usually, the
>>mediant is defined for a pair of fractions, a/b and c/d, as
(a+c)/(b+d).

>Well, if the ratio is 5/4, that's like the space between 5/1 and 4/1.

Lost you there.

>Fractions have to be in lowest terms for this comparo to work.

And they have to be in lowest terms for the conventional mediant too.