On 14 Jan 2009, at 10:18 AM, Carl Lumma wrote:

> --- In tuning@yahoogroups.com, Daniel Forro <dan.for@...> wrote:
>
> > > I think the original question was why minor chords are less
> > > consonant than major chords.
> >
> > Are they really?
>
> Yes, very much so. In fact the effect is so extreme, minor
> chords beyond the 9-limit are essentially unusable.
>
>
But depending on the voicing and absolute frequency location there
are always some harmonics fighting, in major chord as well as in
minor chord. Major: B-C, G-G#, Bb-B-C... Minor: D-Eb-E, Bb-B-C. From
this point of view grade of percepted dissonance looks similar.
> > For me they both are part of one class of consonant
> > sounding chords based on the chain of thirds (or sixths).
>
> Even in the 5-limit, one may speculate why Bach favored
> the minor keys. I would go so far as to say that counterpoint
> works better in minor keys, partly because the consonance
> of the tonic chord is weaker, and therefore the voices
> are more free and not constantly heard as harmonics of it.
>
>
Maybe. I think that minor key generally offers more chromatism in
functional harmony, more extra-key chords, more harmonic
progressions, more rich harmonies in comparison with major... Chord
progressions which sound boringly in major sound quite well when
emulated in minor tonality, they can be even improved not to sound so
commonly. For example:

Major:
Melody tone: G A A B B C....
Chord: C F D7 G E7 Am....
Function: T S (D7) D (D7) VI....

Minor:
Melody tone: G Ab A Bb B C....
Chord: Cm Fm Adim/Eb Bb/D Db7/Ab C7/G...
Function : T S (VII7) VII bII7 (D7)....

(tabs will be probably ignored after sending, please repair the table)
>
> From the point of music theory C-E-G is the same chord as
> > E-G-C and G-C-E,
>
> That's true if we accept the notion of octave-equivalence
> 100%. However, anyone who has ever scored for orchestra
> or played jazz piano knows, it is not true 100%. Beyond
> the 5-limit, it is even less true. The inversions of the
> 7-limit otonality are very different in character (try it!).
>
> -Carl
>
I was referring just about theoretical and abstract 12 tone ET, not
about microintervals :-)

Daniel Forro