n+d (Keenan)

>I'm convinced that n+d isn't a good enough complexity measure *in chords*,
>but remind me what is wrong with it for intervals?

Nothing's wrong with it, it's the mediant. Actually, n+d/2 is the mediant.

C.

>>I'm convinced that n+d isn't a good enough complexity measure *in
chords*,
>>but remind me what is wrong with it for intervals?

Carl Lumma wrote,

>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).

From: "Paul H. Erlich" <PErlich@Acadian-Asset.com>
Subject: Re: n+d (Keenan)

Carl Lumma wrote:

>>Nothing's wrong with it, it's the mediant. Actually, n+d/2 is the
>>mediant.

Paul Erlich replied:

>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).

Set b and d to 1, so we're dealing with integers. We get Mediant(a/1,c/1) =
(a+c)/2. So it's not the mediant of the single fraction, but it is the
mediant of its numerator and denominator. Still, it might as well be called
the mean or average. Mediant is only different from these if at least one
arg is a fraction.

Anyone got a better name for the function n+d or n+d/2, of a single
fraction n/d?

Regards,
-- Dave Keenan
http://dkeenan.com

Carl Lumma wrote:

>>>Nothing's wrong with it, it's the mediant. Actually, n+d/2 is the
>>>mediant.

Paul Erlich replied:

>>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).

>Set b and d to 1, so we're dealing with integers. We get
Mediant(a/1,c/1) =
>(a+c)/2. So it's not the mediant of the single fraction, but it is the
>mediant of its numerator and denominator. Still, it might as well be
called
>the mean or average. Mediant is only different from these if at least
one
>arg is a fraction.

(n+d)/2 is different from n+d/2.

>Anyone got a better name for the function n+d or n+d/2, of a single
>fraction n/d?

The Mann limit? (Mann uses n+d extensively in his book, which I hope to
look at again soon).

>Message: 23
> Date: Tue, 16 Mar 1999 15:50:58 -0500
> From: "Paul H. Erlich" <PErlich@Acadian-Asset.com>
>Subject: Re: n+d (Keenan)

Paul Erlich wrote:

>(n+d)/2 is different from n+d/2.

Err. Yes. Thanks. I meant (n+d)/2, and I'm sure Carl did too.

>>Anyone got a better name for the function n+d or n+d/2, of a single
>>fraction n/d?
>
>The Mann limit? (Mann uses n+d extensively in his book, which I hope to
>look at again soon).

I'll keep that in mind, but for now I've decided to just call them n+d and
(n+d)/2, since they're short enough. Certainly fewer syllables than
"Euler's Gradus Suavatis". :-)

Regards,
-- Dave Keenan
http://dkeenan.com