Minors chords

Paul H. Erlich wrote:
This is because the otonal interpretation of the minor
> triad can
> slide pretty smoothly between 10:12:15, 16:19:24, and 6:7:9 without
> huge
> changes in the harmonic entropy -- but similar changes in the thirds
> of a
> major triad will take you up the pretty steep walls around the 4:5:6
> and be
> more disturbing.

Perhaps the following topic is far from the one which gives the answer
of Paul...

For my mind and my ears, there is only one real "minor chord" :
16-19-24.
10-12-15 is a Major Chord with a major 7th and without bass.
6-7-9 is a 9th dominant chord without bass and 3rd.

Xavier

--- In tuning@egroups.com, "Xavier J.-P. CHARLES" <xcharles@c...>
wrote:
> Paul H. Erlich wrote:
> This is because the otonal interpretation of the minor
> > triad can
> > slide pretty smoothly between 10:12:15, 16:19:24, and 6:7:9
without
> > huge
> > changes in the harmonic entropy -- but similar changes in the
thirds
> > of a
> > major triad will take you up the pretty steep walls around the
4:5:6
> > and be
> > more disturbing.
>
> Perhaps the following topic is far from the one which gives the
answer
> of Paul...
>
> For my mind and my ears, there is only one real "minor chord" :
> 16-19-24.
> 10-12-15 is a Major Chord with a major 7th and without bass.
> 6-7-9 is a 9th dominant chord without bass and 3rd.

Hi Xavier, I remember you from a while back.

At one point since your last visit, we put up a bunch of minor triads
and asked people to listen to them, blindly. Those acculturated to
12-tET seemed to prefer those in the vicinity of 16:19:24, with its
strong root implication. However, once familiarity is acquired with
10:12:15, its smoothness is appreciated. 10:12:15 is the appropriate
tuning for minor triads in Renaissance music, for example.

When voiced with the minor third in the bass, i.e., 6:10:15, one
easily appreciates its greater smoothness as compared with 19:32:48.
But when voiced with the minor third in the soprano, i.e. 10:15:24
or especially 10:15:48, the 8:12:19 or 4:6:19 tunings are more
convincing due to their lower harmonic entropy. Meanwhile, if the
fifth is in the bass, 3:7:9 may sometimes be a stronger "attractor"
than either 15:40:48 _or_ 12:32:38.

This is all to point out the fluidity of the tuning of the minor
triad
as opposed to that of the major triad, and I'd be happy to initiate
another series of listening experiments to explore this issue.

-Paul

Xavier wrote
> > For my mind and my ears, there is only one real "minor chord" :
> > 16-19-24.
> > 10-12-15 is a Major Chord with a major 7th and without bass.
> > 6-7-9 is a 9th dominant chord without bass and 3rd.

Paul answer:
> Hi Xavier, I remember you from a while back.
>
> At one point since your last visit, we put up a bunch of minor triads
> and asked people to listen to them, blindly. Those acculturated to
> 12-tET seemed to prefer those in the vicinity of 16:19:24, with its
> strong root implication. However, once familiarity is acquired with
> 10:12:15, its smoothness is appreciated. 10:12:15 is the appropriate
> tuning for minor triads in Renaissance music, for example.

I'm really not a specialist of Renaissance music, but for me it's
possible that you are right, that in this music there are minor chords
which are not really minor chord but III� in a major scale. A short
example would be interesting for a discussion. Have you one?

Paul Wrote
> When voiced with the minor third in the bass, i.e., 6:10:15, one
> easily appreciates its greater smoothness as compared with 19:32:48.
> But when voiced with the minor third in the soprano, i.e. 10:15:24
> or especially 10:15:48, the 8:12:19 or 4:6:19 tunings are more
> convincing due to their lower harmonic entropy. Meanwhile, if the
> fifth is in the bass, 3:7:9 may sometimes be a stronger "attractor"
> than either 15:40:48 _or_ 12:32:38.
> This is all to point out the fluidity of the tuning of the minor
> triad
> as opposed to that of the major triad, and I'd be happy to initiate
> another series of listening experiments to explore this issue.

I think that all chords whith whole numbers are good, differents but
usable. The problem is "just" to know what seems the best for a precise
serie of chords in a score. I'm going to sent an example of an exercise
for violin I play usually with my analyse. Probably this evening (this
afternoon in US...).
Wait few minutes...

--- In tuning@egroups.com, "Xavier J.-P. CHARLES" <xcharles@c...>
> I'm really not a specialist of Renaissance music, but for me it's
> possible that you are right, that in this music there are minor
chords
> which are not really minor chord but III° in a major scale. A
short
> example would be interesting for a discussion. Have you one?

Xavier, there was no "major scale", nor "tonal music", until well
after the Renaissance was over. Listen to some music by Lassus,
Palestrina, or Victor