Hi Yahya

> > thanks for suggesting the
> > above spelling for the chord d4-f#-b4-E5. I don't know
> > if it's significant, but the intervals of this chord
> > have a neat feature not shared by any other high-in-the
> > series 4 note chords which I have been able to find yet
> > (though math adept people could probably 'back engineer'
> > one from the number pattern...)
>
> Exactly! ;-)
>
>
> > To wit, the intervals, being 5/4, 4/3, 4/3, 5/3, 16/9,
> > and 20/9, have the interesting feature that the 'bottom'
> > interval, 5/4, is multiplied by 9 to 'be in the series'
> > at 45/36; and the 'top' interval b4-e5 (4/3) is
> > multiplied by 20 to 'be in the series' at 60:80. And...
> > (drum roll...) the outer interval has the ratio 20/9.
> > (So I'm referring to the appearence of 20 and 9 in both
> > locations.)
>
> 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
>
> So any tetrad am : bm : cn : an has the same
> interesting property you referered 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. And 4:6:7:14 has an octave in it,
which may make it 'too easy' to fit a pattern.

> > 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, or dom 7th
chord you site, I don't really hear the inner intervals, presumably
because they fall fairly nicely into one series. But with the c-e-g#-
b, I strongly hear the g# and b...Are there any more rigourous
psychoacoustical studies of this issue?

Thanks, Kelly