re: Complexity and inaudible primeness

>It may also be due to Denny Genovese. In my spreadsheet I have "Genovese
>DF" calculated as GOF(a)*GOF(b), GOF = Greatest Odd Factor = Remove factors
>of 2. But then I have plotted it (or rather it's square root) on a chart of
>octave-specific measures. I seem to remember Carl Lumma told me that
>"Genovese DF" was simply a*b. Can anyone clarify this?

Denny's "dissonance factor", or "DF", is indeed (a*b); don't know where
you got the formula in the spreadsheet. The (a*b) measure is also mentioned
in _Genesis of a Music_, where it is attributed to Galileo.

I made a series of posts on this complexity measure when I joined the
list in 1997, when Paul Erlich generally denounced its usefulness. The
justification for the measure given by Partch is still the most sensible
one I know.

-Carl

--- In tuning@egroups.com, Carl Lumma <CLUMMA@N...> wrote:

> Denny's "dissonance factor", or "DF", is indeed (a*b); don't know where
> you got the formula in the spreadsheet. The (a*b) measure is also mentioned
> in _Genesis of a Music_, where it is attributed to Galileo.
>
> I made a series of posts on this complexity measure when I joined the
> list in 1997, when Paul Erlich generally denounced its usefulness.

Well, if I was making that denunciation outside of a context in which octave-
invariance is assumed, then I have to retract that denunciation now! I
thought it was Graham Breed who was defending a*b, but if it was you, I thank
you.

> The
> justification for the measure given by Partch is still the most sensible
> one I know.

Could you remind us of the justification for a*b given by Partch? I thought I
remembered reading Partch saying that 32/15 was more consonant than 16/
15 . . . but of course these ratios are beyond the a*b<105 limit within which the
rule can be expected to work at all . . .

Carl Lumma wrote:

> Denny's "dissonance factor", or "DF", is indeed (a*b); don't know where
> you got the formula in the spreadsheet.

Me neither. Maybe I wanted to see what GOF(a)*GOF(b) looked like and
modified Genovese DF temporarily for the purpose and forgot to change it
back. I've fixed it now and added in parenthesis "Gallilean complexity".

>The (a*b) measure is also mentioned
> in _Genesis of a Music_, where it is attributed to Galileo.
>
> I made a series of posts on this complexity measure when I joined the
> list in 1997, when Paul Erlich generally denounced its usefulness.

Aren't practitioners of the scientific method wonderful. They are quite
willing to follow the weight of evidence rather than be locked into dogma.

Notice that sqrt(a*b) and (a+b)/2 only differ for wide intervals. The
functions /2 and sqrt() are monotonic, so they don't affect the way a+b and
a*b rank intervals.

> The
> justification for the measure given by Partch is still the most sensible
> one I know.

Can you tell us what that justification is?

Earlier I missed another factor (register) which modifies the crude
dissonance measure given by a*b complexity. Here's a list

tolerance
span
register
rootedness
timbre

What else have we forgotten?

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

>>I made a series of posts on this complexity measure when I joined the
>>list in 1997, when Paul Erlich generally denounced its usefulness.
>
>Well, if I was making that denunciation outside of a context in which
>octave-invariance is assumed, then I have to retract that denunciation
>now! I thought it was Graham Breed who was defending a*b, but if it was
>you, I thank you.

Graham also defended it, around the time of the '99 complexity thread,
for which Dave Keenan made his spreadsheet. You made the denunciation
in '97, generally because the measure failed to account for tolerance,
like harmonic entropy does. That was one of the first threads I ever
participated in, and you were trying to explain h.e. to me. In fact, the
original, much-quoted, Monz-annotated, h.e. post was part of that thread.

>Could you remind us of the justification for a*b given by Partch?

Sorry guys, looks like Partch doesn't mention the formula (a*b). He
does discuss the justification Denny used for (a*b), and does attribute
that justification (but not the actual formula, a*b) to Galileo. The
justification is: when a & b are relatively prime, their product gives
the period of the composite wave. Presumably, longer composite waves are
harder for the periodicity mechanism to reconcile.

When did Tenney do his work on a*b? Denny may well be the first person
to suggest this metric (1979).

-Carl

Carl Lumma wrote,

<< When did Tenney do his work on a*b? Denny may well be the first
person to suggest this metric (1979). >>

On page 187 of Helmholtz' "On the Sensation of Tone" you'll see a
chart, and in last column under the "intensity of influence" header
are some numbers taken through to one decimal place. These are the
results of a 100/(a*b) metric... be sure to see page 193 as well for
familiar looking 'cols' and valleys!

--Dan Stearns

>>I've fixed it now and added in parenthesis "Gallilean complexity".

>The (a*b) measure is also mentioned
> in _Genesis of a Music_, where it is attributed to Galileo.

I looked in Genesis and didn't find any mention of this measure, attributed
to Galileo or otherwise . . .