More of Septimals

Gregg Gibson said:
> > There do exist a few septimal triads that seem to escape this argument,
> > e.g. 5:6:7, 4:5:7, 4:6:7. But a few triads do not begin to compare with
> > the richness and variety of the harmonies of the senario.

Graham Breed said:
> Exactly what are you trying to say, Gregg? You come up with an
> "undeniable" argument, and then deny it! Or, am I
> misunderstanding? To my ears, these chords are certainly more
> concordant than their constituent dyads. Three examples are quite
> enough to disprove that little theory.

I mean, for example, if you add a fourth note to the triad 4:6:7, e.g.
4:6:7:8 or 4:6:7:12 you very often get an undoubtedly dissonant chord.
4:6:7:8 is dissonant because of 8:7, 4:6:7:12 is dissonant because of
12:7. This is what I mean when I say the senario (i.e. the consonant
chords of the senario, the least consonant of which are more consonant
than the least disssonant septimal chords) are consistent with
themselves, while the septimal chords give rise to dissonance when a
fourth tone is added.

For what it is worth, I find the septimal triads 4:6:7 and 4:5:7 more
'major' in effect than 'minor', but definitely dissonant. I have heard
them in many different temperaments, but of course the just versions are
the standard.

There are excellent acoustical reasons for supposing the septimals
dissonant. Musical dissonance and consonance are not absolutely
relative, but must remain to the physical constraints of nature if they
are to have any artistic meaning.

A translation of Mersenne has been done, although maybe not the relevant
part.
You are very well-informed about the modern habits of thought, but the
older writers also repay study.

The '5-limit' and '7-limit' habit of thought can be very dangerous if it
is not carefully borne in mind that each include very different
intervals and chords, with different effects. I have heard people wrap
themselves in knots trying to 'hear' 9:7 as consonant because they got
it into their muddled heads (I was one of them, boy have I had some
strange notions) that it somehow had something to do with the 'consonant
7-limit'.


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