Blackwood's Etudes; more on pitch spacin

>Odd
>structural artifacts like this in low-consistency tunings are features
>of, for example, several of Easley Blackwood's 12 Microtonal Etudes, and
>massively cool pieces I think they are. It's just a different path than
>that which I am attempting to follow.

Of the tunings Blackwood uses, 13, 14, 17, 20, and 21 are inconsistent
within the 5-limit. I find the 14, 17, and 20-note pieces to be successful
due to their melodic structures and good 3-limit harmonies. I find the
21-note piece intolerably sour (these days I just skip it), since neither
the scale nor the harmony are in tune. The 13-note piece may be effective as
a piece of atonality, though I've never been a fan of atonal music.

The 17-tone piece is perhaps my favorite, and Blackwood aptly avoids
tonicizing the major triad, as it would necessitate good 5-limit
approximations. The minor triad only necessitates a good perfect fifth for
its tonalness; although the out-of-tune thirds contribute just as much
roughness to both chords, the effect on tonalness is far more pronounced in
the major triad. In the major triad there is pronounced beating between the
difference tones, the root, and the virtual pitch. So much for "dualistic"
theories.

I believe the minor triad in Pythagorean or 12-tET to be subtlely more tonal
than the just minor triad. This is because the fundamental of 16:19:24
(cents: 0, 298, 702) is octave-equivalent to the root, while that of
10:12:15 (or, for that matter, 6:7:9 or the 17-tET m3) is not. My first
impression on retuning a guitar major chord to just was "Ah, that sounds
better," but retuning a guitar minor chord to just, I thought "Hmm, that
really doesn't sit right." However, I learned to like the sound of the
near-just minor triads in meantone tuning -- they are smoother. Perhaps the
use of the Picardy third to tonicize minor keys in the days of meantone
tuning died away because of the adoption of the more tonal near-16:19:24
minor triads.

To summarize: retuning the third of a minor triad can alter its
ratio-interpretation but will not have a large effect on consonance, while
retuning the third of a major triad by the same amount may preserve its
ratio-interpretation but will have a larger effect on consonance.


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