Re Triadic HE-- Compared to Cook and Fujisawa's work

Has anyone compared Steve Martin's charts to Cook and Fujisawa's work on triadic harmony?

--John

--- In tuning@yahoogroups.com, "John H. Chalmers" <JHCHALMERS@...> wrote:
>
> Has anyone compared Steve Martin's charts to Cook and Fujisawa's
> work on triadic harmony?

Are you volunteering? :)

-Carl

--- In tuning@yahoogroups.com, "John H. Chalmers" <JHCHALMERS@...> wrote:
> Has anyone compared Steve Martin's charts to Cook and Fujisawa's work on triadic harmony?

I can provide an additional column to Table 1 in "Harmony is a Three-Tone Phenomenon" (2006). As I understand it, experimental results of L.Roberts give an empirical rank order for the sonority of 10 common chords; Table 1 compares this to the rank order given by five previous models, then Cook and Fujisawa's own (using 12-tET). I have added the rank order given by T.H.E. (also using 12-tET) but I leave any interpretation to others: please see:
/tuning/files/SteveMartin/C&F.csv

Steve M.

--- In tuning@yahoogroups.com, "martinsj013" <martinsj@...> wrote:

> [comparing] Steve Martin's charts to Cook and Fujisawa's work on triadic harmony ...
> I can provide an additional column to Table 1 in "Harmony is a Three-Tone Phenomenon" (2006). As I understand it, experimental results of L.Roberts give an empirical rank order for the sonority of 10 common chords; Table 1 compares this to the rank order given by five previous models, then Cook and Fujisawa's own (using 12-tET). I have added the rank order given by T.H.E. (also using 12-tET) but I leave any interpretation to others: please see:
> /tuning/files/SteveMartin/C&F.csv

I should have said: that is assuming that low T.H.E. is equivalent to high sonority ...

Note that in the paper, Cook and Fujisawa talk about:
<<dissonance models>>
and
<<relative "stability" (~ "consonance")>>
and they say that
<<the perceptual "stability" ("sonority", "tonality", "consonance", "pleasantness", "beauty") of the triads of diatonic harmony has been measured in diverse human populations, and rather consistent results obtained>>

Steve M.

Hi Steve,

> I should have said: that is assuming that low T.H.E. is
> equivalent to high sonority ...

I note that none of the models reproduce the Roberts ranking.
T.H.E. seems to be doing about as well as the any of them.

Below I'll copy my reactions to this C&F paper, which I
originally sent to John Chalmers offlist.

-Carl

>On to specifics, the last column of Table 1 is doing nothing for
>morale on page 3 of 21! They conveniently don't underline their
>own erroneous predictions.
>
>The subsequent invocation of gestalt psychology as the basis of
>their model isn't soothing me either. The hypothesis that triads
>whose interior intervals are the same size are more tense is of
>course going to work out, since the harmonic series contains
>consecutive intervals of shrinking size, and the relative
>shrinkage is most pronounced low in the series.
>
>At this point I bailed and tried the American Scientist piece
>instead
>http://www.res.kutc.kansai-u.ac.jp/~cook/AmSci.pdf
>Again, we're off to a good start...
>
>"We believe ... that the different emotional responses to minor
>and major have a biological basis."
>
>I agree. But then...
>
>"If interval dissonance and triad tension were the only factors
>determining the sonority of triads, we should expect that all of
>the major and minor chords would sound rather similar."
>
>To solve this problem, they simply declare that if the bottom
>interior interval is the smaller one, you get minor 'sadness',
>and if it's the larger, major 'happiness'. That's not any kind
>of explanation of the asymmetry they (correctly) take pains to
>point out.
>
>In extended JI, we know this asymmetry between major and minor
>continues, and indeed gets rapidly more severe. But even in
>the 5-limit, minor chords are more tense and not as consonant
>as major chords. By drawing conclusions from two models that
>are symmetrical -- the usual P&L sensory dissonance, and their
>"tension" based on "intervallic equidistance" -- they can
>hardly expect to explain this.