RE: Re: Response to Dave Hill on JI and European composi tion

Margo Schulter wrote,

>In a recent article on "Pythagoras at the forge: tuning in early
>music," in _Companion to Medieval and Renaissance Music_, ed. Tess
>Knighton and David Fallows (New York, Schirmer Books, 1992),
>pp. 316-326, Rogers Covey-Crump suggests that many vocal consorts
>"tend towards Mean Tone tuning, but the best performers, when
>thoroughly rehearsed, are capable of Just or Pythagorean tuning." He
>recommends Pythagorean for most medieval styles through Machaut and
>his late 14th-century successors, and Just (i.e. 5-limit) for
>Renaissance music. For some English or Anglo-Norman medieval styles of
>the 13th and 14th centuries, he notes the possibility of "alternative
>or mixed tunings of thirds" which might lean toward a kind of 5-limit
>JI (as suggested around 1300 by Walter Odington).

>At the same time, he observes (like Paul Erlich here) that "tuning is
>mainly about vertical chording and not about solo melodic lines," and
>that "consistency of interval size ... is a feature of the best
>western European singers."

>This suggests that either Renaissance or 20th-century singers
>approaching the 16th-century repertory may in fact be doing at least
>some adaptive JI with tempering of melodic intervals.

That's what I would suggest as a possible solution for not only 16th but
even 17th and 18th century music on variable-pitch instruments. Though JI
harmonies would be achieved, it runs counter to the standard JI line, which
goes more like this:

>While Ramos set a possible precedent with his monochord of 1482,
>16th-century theorists such as Fogliano and Zarlino championed the
>syntonic diatonic of Ptolemy with its unequal 9:8 and 10:9 whole-tones
>as the natural intonation for unaccompanied voices.

and discards consistency of interval size (and forces comma shifts/drifts)
to uphold an abstract mathematical ideal. Meanwhile, even Zarlino became the
first champion of a mathematically precise meantone in practice, namely
2/7-comma meantone.

>Describing the common practice as "tempered and mixed music," and
>basing the tuning of the first 19 notes of his instrument on usual
>meantone (likely 1/4-comma with pure major thirds), [Vicentino] directed
that
>the 17 notes of his second manual should be tuned in perfect fifths
>with those of the first manual. The result, assuming a basic 1/4-comma
>temperament, would be sonorities with pure fifths and minor thirds, as
>well as major thirds, if the performer can reach the appropriate keys
>on both manuals simultaneously.

This would provide all the pitches necessary for rendering most 16th-19th
century music in the form of "adaptive JI" I've been suggesting to John
deLaubenfels. While acheiving the same harmonic purity as strict JI, this
scheme would reduce the size of the shifts and drifts involved by a factor
of 4, down to an imperceptible level, without substantially increasing the
total number of pitches required. I independently conceived this idea of
combining vertical JI and horizontal meantone in late 1993, after attending
my first AFMM concert and speaking with Johnny Reinhard.

>While Vicentino's advice to singers to rely on his instrument for
>finding their intervals would most obviously apply to his first tuning
>with 31 notes arranged to divide the octave into more or less equal
>dieses or fifthtones (the remaining 5 notes used for adaptive JI for a
>few frequent sonorities), it could also apply to this second tuning.
>In other words, singers might have emulated this tuning to realize a
>kind of JI based on melodic intervals at or very close to those of
>1/4-comma meantone

So Vicentino is on record for recommending his instrument as a model for
singers, but we don't know which instrument?

>From the viewpoint of practical composition, the issue of classic
>vs. adaptive JI for voices (or either model vs. keyboard meantone)
>might not have much observable impact.

I would disagree -- in those cases where the second degree of the major
scale is in the upper melody and is forced to shift up by a comma because of
a change in the harmony from subdominant to dominant, or else the overall
pitch level is forced to shift down by a comma, classic JI is audibly a poor
solution. When the shift occurs in an inner voice, I agree that it is hard
to hear, though I'd still prefer the sensation of melodic "certainty" that
occurs in meantone or Vicentino's adaptive JI.

>On a personal note, I might add that while playing a keyboard in
>classic 5-limit JI is an exacting experience, it is also a unique one,
>and that I do not find unequal 9:8 and 10:9 whole-tones unpleasant. At
>least for some music some of the time, this experience is not only
>possible but most rewarding.

Certainly unequal whole-tones can be an acquired taste. When there is no
harmonic progression or modulation, they can take on a melodic certainty of
their own. Such a situation arises in Indian music, where the "natural"
scale is the same as the "syntonic diatonic" except with the sixth degree
raised by a comma. I think it significant that this "alteration" (it is only
an alteration by Eurocentric standards) creates an upper tetrachord
identical to the lower one.

>Finally, I might suggest a pragmatic study of intonation as practiced,
>for example, by vocal groups famed for their "just" tuning of
>16th-century music. Would we find some approximation of Zarlino's
>syntonic diatonic, or of a Vicentino/Erlich adaptive tuning, or
>something else?

Though I doubt any vocal group would be able to control their melodic
intonation to much better than 10 cents, the comma shifts implied by the
"classic JI" or "syntonic diatonic" tuning would amount to 21.5 cents, and
their presence or absence should be clearly ascertainable by such a study.