Re: Ben Johnston notation -- a centered universe

Hello, there, Kyle Gann, and thank you for a clarifying message which
suggests that we are indeed in agreement on some basic issues
regarding the Ben Johnston JI notation.

Certainly, as you say, the nature of the Ben Johnston notation is
itself incontrovertible, and I would warmly agree that there is a very
long European history -- maybe a millennium or more -- of taking a
note above a semitone, often C, as a reference point for a hexachord,
or here for the description of a tuning system or the orientation of
its notation.

Guido d'Arezzo (c. 1030), for example, gives some examples of
polyphony cadencing on C, and the famous _Ut queant laxis_ in the
Dorian mode (Mode I) providing a model for the solmization syllables
uses a natural hexachord of C-A.

The C clef is the most common in medieval and Renaissance times, with
the F clef (another note above a semitone) next most common, and these
two predominating until the G clef comes into vogue with the higher
notated ranges of the 16th-17th centuries.

You are, of course, correct that Pietro Aron, for example, starts his
description of how to temper a keyboard by saying that the octave C-C
and the major third C-E should be tuned as "sonorous and just" as
possible, then equally narrowing the fifths in the chain C-G-D-A-E.

Zarlino also presents his reasons for making C-C or Ionian the premier
mode, an outlook fitting his model for the syntonic diatonic of
Ptolemy.

Here one might add that 16th-century keyboards such as the kind
assumed by Tomas de Santa Maria (1565) often have a range defined by
octaves of C-C; his examples use C2 (C two octaves below middle C) as
the lowest note.

At this point, we come to an unfortunate opportunity for semantic
misunderstanding. Please note that in my own usage, I have referred to
C, an octave or octave-species of C-C, or the mode of "C Ionian."

For many people, I realize, "C major" is simply synonymous with this
octave, or the pattern T-T-S-T-T-T-S.

Here the complication is that for some of a medievalist viewpoint,
speaking of "C major" seems to imply not only a reference note,
octave, or modal octave-species, but also conventions of key tonality
of a kind which one diplomatic formulation would propose were
established "sometime during or around the 17th century," tactfully
leaving open the question of just when, where, by whom, and how.

Please let me express my regrets for any part I may have played in
such a misunderstanding, especially since I might now suspect that the
very interesting issues of verticality and modality/tonality in the
Manneristic era may be tangential to the main points of this
notational discussion.

In short, we seem in an agreeable consensus on these points:

(1) Ben Johnston's notational system is centered on C, taking as its
default the syntonic diatonic as modelled by Zarlino, with D as the
diatonic step requiring two versions a syntonic comma apart (81:80) in
order to achieve pure fifths at both G-D and D-A;

(2) Choosing C as a reference point for a tuning system has a very
long and respectable history in Western European theory, with Zarlino
as a fine example of a JI theorist taking this approach both by
precept and example; and

(3) One can recognize these points while leaving lots of room for
different views on the roles of modality and/or tonality in music of
the era 1540-1640, and similar questions.

Turning to the main question of JI notations, I might express my own
point of view that there is no need for everyone to agree on a single
system: it may be a matter both of taste and of the conceptual
approach of a specific composer or school of composition.

For example, if the Ben Johnston notation assumes familiarity with a
lattice basic to a piece, then such an assumption might well be a very
convenient one for likely performers who either have this familiarity
or would wish to gain it in the process of understanding both the
music and the composer's approach to intonation.

A strange if not necessarily logical metaphor occurs to me for the
notational dilemma we are discussing.

In an HEWM notation, the default is Pythagorean, one might say: fifths
pure, and major thirds equal to four such fifths -- the same kind of
situation, notationally, as musicians faced intonationally around 1450
when tuning keyboards for emerging styles where pure or near-pure
thirds were desired in as many positions of the gamut as possible.

In the Ben Johnston notation, the default is the syntonic diatonic
with regularly spelled major thirds pure but a Wolf fifth among the
diatonic notes -- a situation analogous to that in the JI tuning of
Ramos (1482, Wolf at G-D), or Fogliano/Zarlino (1529/1558, Wolf at
D-A).

Is there any kind of notational compromise here analogous to meantone
temperament, maybe some kind of implicit "adaptive tuning," which
could let both fifths and thirds be pure by default? Might a composer,
for example, give an indication like, "There's a comma to be
negotiated somewhere over the next x number of notes or sonorities --
please adjust accordingly"?

By the way, in this dialogue, I might suggest a clear distinction between
the claim that the general scheme of the Ben Johnston follows the outlook
of Fogliano and Zarlino, and the issue of how the fifth D-A was sung in
16th-century practice, or should be sung now.

Zarlino's language suggests very strongly to me that whatever the default
arrangement of large and small whole-tones (9:8 and 10:9), singers or
other performers would make whatever adjustments might be required to
produce pure concords, including fifths.

Vincenzo Galilei pokes fun of certain lutenists who use _tastini_ or
"little frets_ to seek more just thirds, but who stumble into impure
fifths while attempting to negotiate the extra frets.

While these theorists are famous for their disagreements, on some
intonational issues as well as others, they agree that singers avoid the
kind of difficulties which the syntonic comma introduces on fixed-pitch
instruments.

May I emphasize that a notation treating a default "D-A" as 40:27 does not
necessarily imply that such an interval should actually be sung: either
the notation might explicitly indicate each time that an adjustment is
needed so as to achieve a pure fifth, or this adjustment might be left to
the performers. The common medieval and Renaissance convention of writing
a direct leap F-B (German F-H), with F-Bb (German F-B) "understood" as
normally intended to avoid a melodic tritone, might serve as a kind of
precedent.

In other words, if presenting the case for classic 5-limit JI in
Renaissance music, I would argue that singers would choose whatever
versions of the notes D-A might most aptly produce a pure fifth.

Similarly, someone who prefers a JI notation for music in this kind of
style where a default C-E would be 81:64 is not necessarily advocating
Pythagorean intonation as a 16th-century norm, but is likely advocating an
approach where either each inflection to achieve 5:4 is noted, or where
preformers are expected to make unwritten adjustments.

Since we are here discussing especially notations which _do_ seek to make
the inflections explicit, the debate might be one mainly of which default
is easier frequently to override, as must be done in order to combine pure
ratios of 3 and 5.

Most appreciatively,

Margo Schulter
mschulter@value.net

--- In tuning@y..., mschulter <MSCHULTER@V...> wrote:

/tuning/topicId_22447.html#22447

Many thanks to Margo Schulter for this important clarifying post
regarding the Ben Johnston notation. I look forward to the resulting
discussion, as I catch up to it...

Thanks for the help in understanding this...

__________ _____ _____
Joseph Pehrson