--- In harmonic_entropy@yahoogroups.com, "yahya_melb" <yahya@...> wrote:
>
Hi Yayha,
> Hi again Kelly,
>
> --- In harmonic_entropy@yahoogroups.com, "traktus5" wrote:
> [snip]
> > > The tetrad am : bm : cn : dn has the property
> > > that dn/am = n/m if and only if a = d. (Here
> > > juxtaposition means multiplication: am = a x m
> > > etc.) m and n play the roles of your 9 and 20.
> > > That means a and b correspond to 4 and 5, and
> > > that c and d correspond to 3 and 4:
> > > 36 : 45 : 60 : 80
> > > = 4 x 9 : 5 x 9 : 3 x 20 : 4 x 20
> > >
> > > 45/36 = 5 x 9 / 4 x 9 = 5/4
> > >
> > > 80/60 = 4 x 20 / 3 x 20 = 4/3
> > >
> > > 80/36 = 4 x 20 / 4 x 9 = 20/9
>
> Errata: in the above, I should have written:
> 45/36 = (5 x 9) / (4 x 9) = 5/4
> 80/60 = (4 x 20) / (3 x 20) = 4/3
> 80/36 = (4 x 20) / (4 x 9) = 20/9
>
> according to the usual expression-writing rules.
>
>
> > > So any tetrad am : bm : cn : an has the same
> > > interesting property you [referred] to
> > > Eg 2x2 : 2x3 : 1x7 : 2x7
> > > = 4 : 6 : 7 : 14 is an example with a low limit.
> > > Another example, engineered from yours, is
> > > 4 x 7 : 5 x 7 : 3 x 17 : 4 x 17
> > > = 28 : 35 : 51 : 68.
> > > Or again,
> > > 3 x 7 : 5 x 7 : 2 x 18 : 3 x 18
> > > = 21 : 35 : 36 : 54.
> > > This latter example has a highly dissonant 35:36,
> > > so ...
> >
> > Hmmm...I'm not sure if I would include the latter two
> > chords in the same category as the one I cited...
>
> This was *exactly* my point in the comment marked ***
> below!
>
>
> > ... And 4:6:7:14 has an octave in it, which may make
> > it 'too easy' to fit a pattern.
>
> You make it a bit hard to follow your thinking when you
> keep changing the rules! ;-)

Sorry. You guys really keep me on my toes.

I just chose very small
> values for c and a, namely 1 and 2. If you don't want
> octaves, you can of course bar any of a:b, b:c and c:a
> from having that ratio.
>
>
> > > > Do you think this could have any acoustical significance?
> > > > It's a very nice sounding chord!
> >
>
> ***
> > > ... no, I don't think it guarantees an overall
> > > "nice" sound.
> ***
>
> >
> > > > Also, speaking of 'bottom' and 'top' intervals: in a four
> > > > note chord, do intervals formed by adjacent notes (eg,
> > > > 5/4 and 4/3, from our chord) have any more prominance to
> > > > our hearing system than do intervals formed by non-
> > > > adjacent notes (eg, the 5/3 and 16/9 in the above chord)?
> > >
> *****
> > > It's my impression that middle voices and
> > > intervals are usually the hardest to hear.
> > > After the melody, most people pick up the
> > > bass.
> *****
> >
> > > Try this experiment: play a Cma7 chord:
> > > C E G B
> > > then alter it to Cmima7:
> > > C Eb G B
> > > and C #5 ma7:
> > > C E G# B.
> > > They all have a family resemblance, don't
> > > they?
> > >
> > > Now play Cdom7:
> > > C E G Bb
> > > and Cm7:
> > > C Eb G Bb.
> > > It's a different family, right?
> > >
> > > Wait! I can already hear the objection! ;-)
> > > "The two minor chords make one family,
> > > and the rest make another." Well, yes.
> > > The third above the root is usually very
> > > salient in determining mood and mode. But
> > > apart from the third (of whatever size, but
> > > clearly more than a second and less than a
> > > fourth) above the root, if present, the most
> > > salient interval seems to me to be usually
> > > the outside one.
> >
> > For me, with 'consonant' chords like the maj 7th chord,
>
> I find the major 7th chord very pleasantly dissonant.
> YMMV ...

Personally, I find the interval of a major seventh more consonant than
an octave, sort of a 'near octave'. Perhaps tuning disprepancies are
more of an issue with octaves.

>
> > or dom 7th chord you site, I don't really hear the
> > inner intervals, ...
>
> This was the point I made at the note marked *****
> above.
>
>
> > ... presumably because they fall fairly nicely into
> > one series.
>
> Seems like a fair analysis.
>
>
> > ... But with the c-e-g#-b, I strongly hear the g#
> > and b...
>
> ... presumably because they *don't* fall fairly nicely
> into one series?
>
>
> > ...Are there any more rigourous psychoacoustical
> > studies of this issue?

Oh, I find your comments very rigorous! I just thought there might be
peer-reviewed research, backed up by laboratory studies, etc (like by
acousticians such as Helmholtz, Parncut, etc), which bear on this
question.

> More rigorous than what? My impressions? Your
> impressions? Your analysis?
>
> Regards,
> Yahya
>