Yahoo Tuning Groups Ultimate Backup tuning Renaissance JI article online

Wasn't it Vicentino who thought up the system of - essentially -
quarter-comma with the fifth of each triad adjusted upwards? ... i.e.
adaptive JI ? So I'm wondering why Duffin doesn't consider any ways to
sing other than strict JI, or strict adherence to a temperament.

His remarks on vibrato are unclear. At first he seems to be saying
vibrato can help to 'cover up' for the impure intervals of his
proposed JI versions:

"a pitch variance of 22 cents is negligible for vibrato anyway.
Moreover, using vibrato to cover up imperfections in tuning is
something that happens all the time in performances today, even where
the goal is Equal Temperament."

Not a statement that fills me with hope for performances of
Renaissance music.

But then at the end he enthuses over the Hilliards' largely
vibrato-free Tallis. See the footnote:

"Seashore and Barbour maintain that scooping and pitch wandering make
it impossible for singers to come reliably closer to a certain
frequency than about a fifth of a semitone. (...) But the Hilliard
Ensemble recording excerpt given below, in a sampling of major chords
at eleven points throughout, gives an average major 10th (the most
common voicing for the third) with a ratio of 2.507 above the root.
This compares with the pure ratio of 2.500 and the ET ratio of 2.520,
and represents a predilection for thirds that are twice as close to
pure as they are to ET, as well as a tuning accuracy six times closer
to the intended frequency than that predicted above."

A bit of a contradiction... unless Duffin is thinking that one should
use comma-wide vibrato only at points which are 'difficult' in JI,
which would hardly be practical or artistic. (The Tallis does not
include any 'difficult' spots.)

Unfortunately I can't get his examples to play in my browser, so my
critique will have to remain verbal for the time being.

~~~T~~~

--- In tuning@yahoogroups.com, Jon Wild <wild@...> wrote:
>
>
> Dear tuners,
>
> Some of you might be interested in this article by Ross Duffin that has
> just come out in Music Theory Online:
>
>
http://mto.societymusictheory.org/issues/mto.06.12.3/mto.06.12.3.duffin.html
>
> It's called "Just Intonation in Renaissance Theory and Practice" and it
> demonstrates some synthesised sound clips demonstrating the author's
> suggestions for getting around problems of comma drift.
>
> Best - Jon Wild
>

🔗Margo Schulter <mschulter@calweb.com>

On Sun, 29 Oct 2006, Jon Wild wrote:

>
> Dear tuners,
>
> Some of you might be interested in this article by Ross Duffin that has
> just come out in Music Theory Online:
>
> http://mto.societymusictheory.org/issues/mto.06.12.3/mto.06.12.3.duffin.html
>
> It's called "Just Intonation in Renaissance Theory and Practice" and it
> demonstrates some synthesised sound clips demonstrating the author's
> suggestions for getting around problems of comma drift.
>
> Best - Jon Wild
>

Hello, Jon, and thank you for calling this article to my attention.

My own reaction is a bit like that I saw on the Tuning List: what about
adaptive JI a la Vicentino? This is not to say that singers would
necessarily follow any precise mathematical model (something that Vincenzo
Galilei says explicitly, and that Zarlino may be implying when he says
that singers tend toward pure vertical concords, but do not encounter
the kinds of difficulties found on keyboards tuned in the syntonic
diatonic).

A small technical correction, or rather quibble: the schisma by which
a Pythagorean diminished fourth at 8192:6561 differs from a pure 5:4
major third, 32805:32768, is minutely smaller than the amount by which
a fifth is tempered in 12n-EDO, or 1/12 Pythagorean comma. Some years
ago this minute difference between a 700-cent fifth and one at the
just ratio of 16384:10935 was playfully referred to on the Tuning List
as the "Scintilla of Artusi," because of Artusi's criticism of Monteverdi,
as discussed by Mark Lindley, for writing vocal music in a style which,
to Artusi, suggested the influence of equal temperament on the lute.
(Actually Wert, applauded by Artusi, had likewise used the diminished
fourth in vocal music -- but that's another discussion.) Anyway, Artusi's
conclusion was that 12-note equal temperament was fine on fretted
instruments, but not should be adopted for voices until it could be
described in terms of known integer ratios! Kirnberger relied on the
near-identity of the schisma and 1/12-Pythagorean comma for a proposal
of 1766 on how keyboards could be placed in virtual 12-EDO by just
intonation techniques -- if one could actually tune pure intervals so
precisely by ear in long chains, as Owen Jorgensen adds! Thus the
"scintilla of Artusi" was a humorous reference to Artusi's desire
for 12-EDO by known integer ratios, and Kirnberger's approximate
solution.

Getting back to Renaissance just intonation, I would say that fractional
comma shifts could possibly help resolve the puzzle of understanding not
only Zarlino's remark that singers are untroubled by comma problems, but
also Galilei's remarks finding the same (and suggesting that singers
seem to approximate a kind of meantone temperament somewhere between
12-EDO and the 2/7-comma both he and Galilei favor for keyboards
(in Galilei's case, despite his theoretical preference for 12-EDO as
a perfect or "spherical" music).

Maybe empirical studies of what good Renaissance ensembles do is one
approach, albeit to demonstrate what is possible rather than necessarily
what happened in the 16th century.

Vicentino's model offered by his second archicembalo or arciorgano
tuning, in principal with two 19-note keyboards (Gb-B#) in something
like 1/4-comma or 31-EDO at 1/4-comma apart if this appealing
interpretation is correct, seems still a useful one at least to
experiment with. (In practice, he could not fit E# and B# on his
upper keyboard, thus leaving him with a 36-note instrument.)

For people curious to hear what this sounds like in a crude MIDI
rendition, here are some examples:

<http://www.bestII.com/~mschulter/LassoPrologue.mid>
<http://www.bestII.com/~mschulter/GesualdoGagliardaAJI.ogg>
<http://www.bestII.com/~mschulter/GesualdoGagliardaAJI.mp3>
<http://www.bestII.com/~mschulter/GesualdoGagliardaAJI.mid>

A possible caution is that while the article eloquently advocates
a 5-limit (or "6-limit," following Zarlino's senario) aesthetic
for Renaissance music, applying this aesthetic to "late medieval"
music is a more complicated proposition. If we have in mind the
later Dufay, say, such a proposal is not unlikely. However, for
the 14th century -- to me still "late medieval," if we conceive
of medieval in music as roughly 500-1420 or a bit later -- a
Pythagorea or even Marchettan aesthetic might be more applicable
to certain styles. The latter term refers to the vocal intonation
described by Marchettus of Padua (1318) in his Lucidarium, where
major thirds and sixths resolving in directed progressions are
made rather larger than Pythagorean, and cadential semitones or
dieses rather smaller. For a more "extremophile" interpretation,
with major thirds and sixths around 450 and 950 cents, this
brief example may give some idea:

<http://www.bestii.com/~mschulter/PythEnharImprov01.mp3>

The point here is that an appreciation for Renaissance JI can be
one instructive instance of sensitivity to the stylistical
implications of any era.

Another small point on the article: what Zarlino does in 1571
is not to abandon his 2/7-comma meantone of 1558, but to note
that 1/4-comma and also 1/3-comma are also available, with
1/4-comma easy to tune and pleasing to the ear, and 1/3-comma
somewhat "languid" in effect. What this may imply between the
lines (as Mark Lindley has suggested) is that either 1/4-comma
or 2/7-comma may be in the range of optimal meantone euphony
(with Kornerup's Golden Meantone, for example, somewhere
in between), but the former is easier to tune by ear.

One might wonder why adaptive JI has not received more
attention in the literature on Renaissance JI, especially from
advocates. Roger Wibberley did an article in MTO concluding
that JI _was_ practical, taking Willaert's famous puzzle
piece often interpreted as a demonstration of 12-EDO or the
like as in fact a lesson in JI through remote Pythagorean
accidentals (with schismatic thirds treated as equivalent
to 5-limit).

He assumed, however, that vertical JI must imply the
problem of the comma -- with the best practical solution
for pitch stability, which he sees at play in some music
of Willaert, requiring the composer carefully to note
and keep track of comma shifts so that they balance out.
However, I am tempted to question the conclusion which he
draws, not so surprisingly, once the premise is granted:
that most music of composers contemporary with Willaert,
but who do not attend to balancing the comma shifts, was
actually performed by vocalists in Pythagorean intonation!
The hypothesis of adaptive JI seems more attractive, unless
the style of a piece seems to fit a Pythagorean ethos --
which might be more applicable to Ockeghem or even Josquin,
in certain situations, than to music by the 1540's or so.
This is not to rule out the possibility of a "common
practice" based on some kind of adaptive JI, and a more
"select" one based on the deliberate use of unequal
whole-tones and commas in pieces where the composer
balances shifts as proposed for Willaert by Wibberley.

If this article by Ross Duffin prompts more discussion --
and it is very readable and engaging -- then our
understanding both of Renaissance music and of the "art
of the possible" for vocalists may be improved as we
continue the exploration urged by the author.

Most appreciatively,

Margo Schulter
mschulter@calweb.com

🔗Gene Ward Smith <genewardsmith@coolgoose.com>

--- In tuning@yahoogroups.com, Margo Schulter <mschulter@...> wrote:

> A small technical correction, or rather quibble: the schisma by which
> a Pythagorean diminished fourth at 8192:6561 differs from a pure 5:4
> major third, 32805:32768, is minutely smaller than the amount by which
> a fifth is tempered in 12n-EDO, or 1/12 Pythagorean comma. Some years
> ago this minute difference between a 700-cent fifth and one at the
> just ratio of 16384:10935 was playfully referred to on the Tuning List
> as the "Scintilla of Artusi," because of Artusi's criticism of
Monteverdi,
> as discussed by Mark Lindley, for writing vocal music in a style which,
> to Artusi, suggested the influence of equal temperament on the lute.

Since this interval involves a twelfth root, it isn't rational and
hence not a rational comma. However, taking the twelfth power gives
the amount by which twelve Kirnberger fifths of 16384/10935 are sharp
of seven octaves; this is the Atom of Kirnberger, |161 -84 -12>. That
means the Scintilla is |161 -84 -12>/12 = |161/12 -7 -1>.

> Kirnberger relied on the
> near-identity of the schisma and 1/12-Pythagorean comma for a proposal
> of 1766 on how keyboards could be placed in virtual 12-EDO by just
> intonation techniques -- if one could actually tune pure intervals so
> precisely by ear in long chains, as Owen Jorgensen adds!

It's not exactly practical, but at least it's a Fokker block.:)

> Another small point on the article: what Zarlino does in 1571
> is not to abandon his 2/7-comma meantone of 1558, but to note
> that 1/4-comma and also 1/3-comma are also available, with
> 1/4-comma easy to tune and pleasing to the ear, and 1/3-comma
> somewhat "languid" in effect.

That's interesting. I wish I knew the range of tunings in actual use
then; 2/7 is an interesting value.

> What this may imply between the
> lines (as Mark Lindley has suggested) is that either 1/4-comma
> or 2/7-comma may be in the range of optimal meantone euphony
> (with Kornerup's Golden Meantone, for example, somewhere
> in between), but the former is easier to tune by ear.

The Woolhouse fifth, 7/26-comma, is also in between. As for tuning by
ear, if you can tune pure 9/7s, you perhaps you can tune the
(224/9)^(1/8) fifth, at 695.614 a little flat of 2/7-comma. This sets
the diminished fourth, which takes the place of the major third in
remote keys, to a pure 9/7.

> However, I am tempted to question the conclusion which he
> draws, not so surprisingly, once the premise is granted:
> that most music of composers contemporary with Willaert,
> but who do not attend to balancing the comma shifts, was
> actually performed by vocalists in Pythagorean intonation!

Do you agree with the premise that Willaert balanced comma shifts?

🔗Jon Wild <wild@music.mcgill.ca>

Gene wrote (quoting Margo):

>> Another small point on the article: what Zarlino does in 1571
>> is not to abandon his 2/7-comma meantone of 1558, but to note
>> that 1/4-comma and also 1/3-comma are also available, with
>> 1/4-comma easy to tune and pleasing to the ear, and 1/3-comma
>> somewhat "languid" in effect.
> > That's interesting. I wish I knew the range of tunings in actual use > then; 2/7 is an interesting value.

Yes, it's the harmonic mean of 1/4 and 1/3 - so it's adjusted to have the best compromise, in a sense, between major thirds and minor thirds. When Zarlino first describes 2/7-comma in 1558 he doesn't say where it comes from, but you would expect it must have been derived as a "cross" between 1/4-comma with its pure M3s and 1/3-comma with its pure m3s - especially given the emphasis Zarlino places on major and minor thirds in the rest of his treatise.

You mention "the range of tunings in use then"--if we're talking about 1558 then 2/7-comma is *all* we know about for sure--Zarlino's is the earliest surviving unambiguous meantone description. We know (from Ramis) that some kind of meantone was in use in the 1480s, but we don't know which one. The New Grove article on "Regular meantone temperaments to 1600" by Mark Lindley has lots of information - it mentions 1/4, 2/7, 1/3, 1/5, 1/6, 2/9. It's a bit long to paste in the whole article, sorry. 3/14 and 5/18 seem to be the only other fractions that crop up in the follow-up article "Regular mean-tone temperaments from 1600" and in the "mean tone" article itself (which is very short). I think those complex fractions are reverse-engineered from the equal divisions they represent.

Renaissance JI article online

🔗Jon Wild <wild@music.mcgill.ca>

🔗Tom Dent <stringph@gmail.com>

🔗Margo Schulter <mschulter@calweb.com>

🔗Gene Ward Smith <genewardsmith@coolgoose.com>

🔗Jon Wild <wild@music.mcgill.ca>

🔗Gene Ward Smith <genewardsmith@coolgoose.com>