Tuning Artefacts

In matters of temperament one must carefully distinguish between equal
divisions of the octave that are temperaments, and those which are
merely tuning artefacts. A temperament constitutes a system wherein
every note can be obtained by a cycle of any one of the consonant
intervals; in such systems every pitch can be introduced into music by a
consonant disjunct interval, if desired, and not only by singing a
conjunct dissonance, the exact pitch of which is difficult either to
sing or to integrate into instrumental music. The prinicipal
temperaments are 12- 19- 31- 43- 50- & 55-tone equal.

A tuning artefact on the other hand has good representations of the
consonances, but as in just intonation, these consonances are not
reduced to a system wherein all consonances stand in a fixed proportion
or equipartient ratio to one another, as for example in 19-tone equal
the major third is always 6/11 as wide as the perfect fifth.

In tuning artefacts on the contrary we find that these ratios are
variable, which results in diminished or augmented fifths at divers
places in the tonal fabric, or else similarly impure thirds. Moreover in
such tuning artefacts, at least 1/2 of the tones form no part of the
cycle of fifths - I mean those fifths that have consonant thirds - but
lie forever outside it. Just intonation itself is far more tolerable
than these inconsistent systems; examples are the 22-, 29- 41- & 53-tone
equal systems. Very strangely, the last of these was lauded by Bosanquet
(among others) as the ne plus ultra of intonational perfection! And so
it is - in the same way that just intonation is mathematically perfect
but perfectly unusable in practical music (of this or any other
century), becuse of its undistributed, commatic errors.


SMTPOriginator: tuning@eartha.mills.edu
From: Gregg Gibson
Subject: Just Intonation
PostedDate: 14-12-97 01:47:51
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