Discrimination of Intervals in Melody

> Perhaps that's too elementary of a distinguishing task though. But even
> among some more subtle tasks, like noticing 19TET's flat M3 and P5, and
> comparing that to 31's right-on M3 and slightly flat P5, or to 12TET's
> way-sharp M3 and almost exact P5, I have found that there are many musical
> settings where those factors are audible.
>
> I certainly do agree that there are many musical settings where the
> notes are just simply wizzing by too fast to hear those aspects of a tuning
> as such. If that's the sort of distinction exercise you're talking about,
> then I'd agree with your conclusion up to a point anyway.
>
I did not of course intend to question the ear's ability to distinguish
quite minute intervallic differences in harmony or in tones considered
not in respect to their melodic category, but rather in respect to their
absolute height or hauteur. In melody however, which is the primary
means by which harmony is produced (at least ideally) the critical limen
of intervallic perception is on the order of 55-60 cents. If a given
melody has one of its members altered by less than this limen, the
melody may well be heard as vaguely different, but there will be _no_
fundamental change in melody. Were differences of 30 or 40 cents
melodically significant, assuredly there would be no such thing as a
reproducible melody at all, for singers very commonly diverge from one
anothers' performances by at least these intervals, when rendering the
'same' melody!

Granted that the limen is on the order of 55-60 cents, it follows that
that temperament is melodically richest whose tuning degree is just
wider than 60 cents. Indeed, such a temperament is melodically far, far
richer and more varied than all other musical tuning systems combined,
be they just or tempered. Simple probability theory suggests that
19-tone equal has about 70 times more distinct melodies than 12-tone
equal, for example. Hence my interest in the 19-tone equal.

This temperament also has permitted me to study all the various modes
which are melodically distinct to the ear.

Of the heptatonic modes, the familiar seven of the diatonic genus
have consonant chords on six of the seven degrees, as is universally
known. More subtly, every one of these degrees is part of at least one
consonant chord (actually, of at least two) within the untransposed
diatonic order. No other heptatonic modal genus has above four of its
seven degrees which are the roots of consonant chords within the genus,
all of whose degrees are included within at least one consonant chord.
These genera are four in number, including 28 modes. On C these are:

C D E F G Ab B C
C D E F G Ab Bb C
C Db E F Gb A Bb C
C D E F G# A B C

The so-called 'minor' mode of the Baroque is to be found on A within the
last of these four, so it is evident that here we have quite a new field
for melodic and harmonic experiment.

I hope to publish some articles on this, when I can find the time.

In harmony I agree that quite small intervallic variations can of course
have a remarkable effect.

I agree also that the fifths major thirds of 31-tone equal are slightly
but noticeably smoother and more pleasing than those of the 19-tone
equal. However, if the 19-tone octave is stretched by 2-3 cents, its
fifths become quite as good as those of the 31-tone. Further, because
the fourth is less sensitive to mistuning than the fifth, merely to make
these intervals equally deteriorated one should stretch the octave. On
my DX-7IIs and my Proteus/Mac setup I use a tuning degree of 63.3 cents
with an octave of 1202.7 cents, and I find this noticeably more
brilliant than the 19-tone equal without an octave stretch; I even
prefer its harmonies to those of the 31-tone equal.

I remember when I first became interested in more than 12 tones in the
octave, I liked the _idea_ of as many tones within the octave as
possible, and tended to consider 31 as the absolute minimum. But
experience has taught me that the only viable alternative to the 12-tone
equal is the 19 system.

The 22-tone equal system is rather a tuning artefact than a temperament.
Like that other much-over-rated system the 53-tone equal, it merely
reproduces one of the primary flaws of just intonation, viz. the
presence of two varieties of tone, with the consequent failure to close
the cycle of fifths. These systems are therefore certainly no more
musically viable than just intonation itself.


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