Barlow's harmonicity function

Can somebody please confirm what follows:

Barlow(10178/6793) = 15043.29
Barlow(7893/7450) = 2063.15

Thanks in advance,
VC

>Can somebody please confirm what follows:

>Barlow(10178/6793) = 15043.29
>Barlow(7893/7450) = 2063.15

Almost, you need to divide one by those numbers to get
the harmonicity values.

Manuel

--- In tuning@yahoogroups.com, "Manuel Op de Coul"
<manuel.op.de.coul@e...> wrote:
>
> >Can somebody please confirm what follows:
>
> >Barlow(10178/6793) = 15043.29
> >Barlow(7893/7450) = 2063.15
>
> Almost, you need to divide one by those numbers to get
> the harmonicity values.

What is Barlow's function?

See
http://sonic-arts.org/dict/harmcity.htm
http://sonic-arts.org/dict/specificharm.htm

Manuel

--- In tuning@yahoogroups.com, "Manuel Op de Coul"
<manuel.op.de.coul@e...> wrote:
>
> See
> http://sonic-arts.org/dict/harmcity.htm
> http://sonic-arts.org/dict/specificharm.htm

The definition of "indigestible" does not seem to make much sense;
why is 9 treated exactly like 3?

There's an erratum on that page I think, I don't remember
that Barlow meant indigestibility as a measure of dissonance
at all.

>why is 9 treated exactly like 3?

It's not treated alike, 9 is a composite number and 3 is a prime.

Manuel

> Date: Tue, 9 Sep 2003 17:34:50 +0200
> From: "Manuel Op de Coul" <manuel.op.de.coul@eon-benelux.com>
> Subject: Re: Re: Barlow's harmonicity function
>
>There's an erratum on that page I think, I don't remember
>that Barlow meant indigestibility as a measure of dissonance
>at all.
>
>>why is 9 treated exactly like 3?
>
>It's not treated alike, 9 is a composite number and 3 is a prime.

::attempts to play "If 6 were 9" on jaw harp:: :)

--- º°`°º ø,¸¸,ø º°`°º ø,¸¸,ø º°`°º ø,¸¸,ø º°`°º º°`°º ø,¸~->

Hanuman Zhang, musical mad scientist
(no, I don't wanna take over the world, just the sound spectrum...)
http://www.boheme-magazine.net

"What strange risk of hearing can bring sound to music - a hearing whose
obligation awakens a sensibility so new that it is forever a unique, new-born,
anti-death surprise, created now and now and now. .. a hearing whose moment
in time is always daybreak." - Lucia Dlugoszewski

"... simple, chaotic, anarchic and menacing.... This is what people of today
have lost and need most-- the ability to experience permanent bodily and
mental ecstasy, to be a receiving station for messages howling by on the ether from
other worlds and nonhuman entities, those peculiar short-wave messages which
come in static-free in the secret pleasure center in the brain." - Slava Ranko
(Donald L. Philippi)

"There's a rabbinical tradition that the music in heaven will be microtonal"
-annotative interpretation of Schottenstein Tehillim, 92:4, the verse being:
"Upon a ten-stringed * instrument and upon lyre, with singing accompanied by
harp." [* utilizing new tones]

NADA BRAHMA - Sanskrit, "sound [is the] Godhead"

"God utters me like a word containing a partial thought of himself." -Thomas
Merton

LILA - Sanskrit, "divine play/sport/whimsy" - "the universe is what happens
when God wants to play" - "joyous exercise of spontaneity involved in the art
of creation"

Thanks Manuel, I guess you mean I should refer to their
reciprocal in order to get the harmonicity values. Anyway, are
these two values the proper "indigestibilities" associated with
those two intervals? I was wondering if Barlow's (and also
Euler's, why not...) definition of "harmonicity" is useful only when
the intervals are somewhat simpler than this. In this case, the
"harmonic distance" between these two intervals and the unison
interval is not exactly what I expected it to be - I mean:
10178/6793 is a 4-digits best fraction approximation of a 12-tET
fifth...

Cheers,
VC

> >Can somebody please confirm what follows:
>
> >Barlow(10178/6793) = 15043.29
> >Barlow(7893/7450) = 2063.15
>
> Almost, you need to divide one by those numbers to get
> the harmonicity values.
>
> Manuel

--- In tuning@yahoogroups.com, "victorcerullo" <moog@l...> wrote:
> Thanks Manuel, I guess you mean I should refer to their
> reciprocal in order to get the harmonicity values. Anyway, are
> these two values the proper "indigestibilities" associated with
> those two intervals? I was wondering if Barlow's (and also
> Euler's, why not...) definition of "harmonicity" is useful only
when
> the intervals are somewhat simpler than this. In this case, the
> "harmonic distance" between these two intervals and the unison
> interval is not exactly what I expected it to be - I mean:
> 10178/6793 is a 4-digits best fraction approximation of a 12-tET
> fifth...
>
> Cheers,
> VC

hi victor -- "harmonic distance" usually refers to tenney's harmonic
distance function, which is log(n*d) for any two pitches separated by
the ratio n/d. in my "harmonic entropy" model of dissonance (see the
harmonic entropy list, or monz's dictionary again, for more), i found
that tenney's harmonic distance captures the predicted level of
dissonance exceptionally well for the simplest ratios, up to n*d=35
or n*d=105, but beyond that it fails, and one has instead a smooth
curve as a function of interval size, and that includes all
intervals, rational or irrational. this continuity seems to me to be
an essential requirement of any such model. whatever barlow was
trying to measure, if it can't be applied to irrational intervals or
to complex rationals masquerading as simple ones, then it's failing
miserably to capture much about real-world musical hearing.

Victor wrote:

>Anyway, are these two values the proper "indigestibilities" associated
>with those two intervals?

Yes, I got the same numbers.

>I was wondering if Barlow's (and also
>Euler's, why not...) definition of "harmonicity" is useful only when
>the intervals are somewhat simpler than this. In this case, the
>"harmonic distance" between these two intervals and the unison
>interval is not exactly what I expected it to be

That's right. Instead of "harmonic distance", "harmonic complexity"
would be a better description. And indeed with all those kind
of complexity measures based on prime numbers like this and Euler's
etc. one needs to judge whether the result makes sense acoustically.

Manuel

Good. Thanks a lot for your helpful input (as usual), Manuel.

Cheers,
Victor

> Victor wrote:
>
> >Anyway, are these two values the proper "indigestibilities"
associated
> >with those two intervals?
>
> Yes, I got the same numbers.
>
> >I was wondering if Barlow's (and also
> >Euler's, why not...) definition of "harmonicity" is useful only
when
> >the intervals are somewhat simpler than this. In this case, the
> >"harmonic distance" between these two intervals and the
unison
> >interval is not exactly what I expected it to be
>
> That's right. Instead of "harmonic distance", "harmonic
complexity"
> would be a better description. And indeed with all those kind
> of complexity measures based on prime numbers like this and
Euler's
> etc. one needs to judge whether the result makes sense
acoustically.
>
> Manuel