Harmonic complexity

Using scala command "show data" I've found:

Euler's gradus suavitatis, Mersenne's string divisions, Vogel's harmonic complexity, Wille's k value, Wilson's harmonic complexity, Sum of van Prooijen's expressibility, Sum of Tenney's harmonic distance, Sum of Mann's harmonic distance.

I know some of these methods to determine harmonic complexity (which I consider a base for every consideration about tuning) but I don't know all of them. Can someone do a comparison between all these parameters (and other which probably I've omissed)?

Lorenzo

>Using scala command "show data" I've found:
>
>Euler's gradus suavitatis, Mersenne's string divisions, Vogel's harmonic
>complexity, Wille's k value, Wilson's harmonic complexity, Sum of van
>Prooijen's expressibility, Sum of Tenney's harmonic distance, Sum of
>Mann's harmonic distance.
>
>I know some of these methods to determine harmonic complexity (which I
>consider a base for every consideration about tuning) but I don't know
>all of them. Can someone do a comparison between all these parameters
>(and other which probably I've omissed)?
>
>Lorenzo

Hi Lorenzo,

I'm not sure how you want me to compare them. But have you read
the Scala documentation? I think it explains all of these methods.

-Carl

On scala help I've found something but not so much.
Just to do an example: what is "Wille's k value"?
And there'is nothing about "harmonic distance".
I've found more on Monzopedia (again much thanks Joe!) but I would like to know for example what kind of harmonic distance works better for you: Tenney or Mann? And why? Do some of these formula consider octave equivalence or not? Can you synthetically explain me the differences, the pros and cons of these methods?

Ciao

Lorenzo

----- Original Message -----
From: Carl Lumma
To: tuning@yahoogroups.com
Sent: Sunday, January 16, 2005 8:10 PM
Subject: Re: [tuning] Harmonic complexity

>Using scala command "show data" I've found:
>
>Euler's gradus suavitatis, Mersenne's string divisions, Vogel's harmonic
>complexity, Wille's k value, Wilson's harmonic complexity, Sum of van
>Prooijen's expressibility, Sum of Tenney's harmonic distance, Sum of
>Mann's harmonic distance.
>
>I know some of these methods to determine harmonic complexity (which I
>consider a base for every consideration about tuning) but I don't know
>all of them. Can someone do a comparison between all these parameters
>(and other which probably I've omissed)?
>
>Lorenzo

Hi Lorenzo,

I'm not sure how you want me to compare them. But have you read
the Scala documentation? I think it explains all of these methods.

-Carl

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>Just to do an example: what is "Wille's k value"?

Not off the top of my head...

>And there'is nothing about "harmonic distance".
>I've found more on Monzopedia (again much thanks Joe!) but I would
>like to know for example what kind of harmonic distance works better
>for you: Tenney or Mann? And why? Do some of these formula consider
>octave equivalence or not? Can you synthetically explain me the
>differences, the pros and cons of these methods?

There has been extensive discussion on this list and on
the tuning-math list about this. For reasons that are fairly
convincing, Paul Erlich prefers Tenney harmonic distance.
You might also check out the harmonic_entropy list.

Yahoo's Groups search engine has a terrible track record, but
you might try it. You might also try Google web searches for
things like 'Tenney harmonic site:groups.yahoo.com'.

-Carl

> >Just to do an example: what is "Wille's k value"?

It's obtained by bringing all the ratios in the scale under
denominator 1 (see this with SET ATTRIBUTE MULTIPLE). Then divide away
factors of 2, and take the maximum value. Subtract 1 from it and then
divide by two.

There are some definitions in tips.par. Open it in an editor, or go
to Help:Tips and click Show all. I forgot adding that one.

Manuel

On Tuesday 18 January 2005 11:03 am, Manuel Op de Coul wrote:
> > >Just to do an example: what is "Wille's k value"?
>
> It's obtained by bringing all the ratios in the scale under
> denominator 1 (see this with SET ATTRIBUTE MULTIPLE). Then divide away
> factors of 2, and take the maximum value. Subtract 1 from it and then
> divide by two.
>

and then add 33/52 to it.

Huh? can you go further and explain the rationale for this measure, and it's
derivation? Or point us to a reference/link?

Best,

Aaron Krister Johnson
http://www.akjmusic.com
http://www.dividebypi.com