Definitions of tuning terms
© 1998 by Joseph L. Monzo
All definitions by Joe Monzo unless otherwise cited
Adaptive JI
A form of
temperament in which some algorithm
is used which keeps the ratios of simultaneous sounds exactly
in just-intonation,
but uses non-JI
melodic intervals to reduce the retuning motion and/or
drift relative to a
strict JI realization.
While retuning motions and/or drifts in strict JI renditions are one
or more commas in magnitude,
adaptive JI reduces these to fractions of a
comma by spreading the motion among all the
chord changes in a progression.
The desideratum, at least
in more modern times (making use of the computer) is usually
to allow dynamic alterations of the pitches during the
performance of the music.
Various approaches have been tried, one of the earliest examples
being by Nicola Vicentino
in the 1500s. In 1999, John deLaubenfels and
Paul Erlich were very active in developing a good Adaptive JI
algorithm. deLaubenfels explains his method in detail in
these Tuning List posts:
Wed Jan 19, 2000 3:24 am and
Tue Sep 12, 2000 3:09 pm.
Below are two musical illustrations of the first 5 measures of
Orlando di Lasso's motet Ave regina coelorum, tuned
in Vicentino's adaptive-JI tuning. This example was chosen
because it is used as an illustration by Easley Blackwood
of the unsuitability of strict-JI for "common-practice" repertoire
(see Blackwood 1985, p 133-135).
The first illustration uses
Pythagorean tuning
as the basis for the letter-names and
accidentals, and
shows the deviation of Vicentino's tuning from Pythagorean.
[click on the illustration to hear a MIDI-file of it]
The second illustration uses
1/4-comma meantone
as the notational basis and shows the deviation of Vicentino's
tuning from that.
[click on the illustration to hear a MIDI-file of it]
See also pain,
COFT,
adaptive tuning.
[from Joe Monzo, JustMusic: A New Harmony,
with help from Paul Erlich]
Paul Erlich made the following comment:
In adaptive JI the
pain of having vertical
sonorities deviate from JI is infinite, while in adaptive tuning, all the
different components of pain get traded off against one another.
Paul Erlich posted the following in a
Tuning
List posting, Wed Oct 18, 2000 9:03pm
The idea of adaptive tuning goes back to
Vicentino in 1555,
who proposed the two chains
of 1/4-comma meantone tuning a pure fifth (or equivalently, a pure
minor third, or 1/4
comma) apart.
This proposal would never compromise the melodic
integrity of the chain
of identical (in this case, meantone) fifths by more than a
melodically inaudible interval,
1/4-comma, while attaining perfect vertical JI in all triads.
To me,
this amounts to audibly
"perfect" tuning within the Renaissance theoretical ideal (as
expressed by, say, Zarlino),
and much of the subsequent repertoire well into the 18th century --
until enharmonic
equivalents began to be used.
Though Vicentino's two-keyboard
implementation was not
practical at the time, with computers (or, perhaps, AFMM performers),
we can acheive
his goals, and even surpass him in cases where his proposal runs into
difficulties.
From Paul Erlich,
Yahoo Tuning Group, message 32139
Date: Sat Dec 29, 2001 9:57 pm
Subject: Re: Freestyle misunderstood
Lou Harrison's freestyle strikes me as one of the two types
of "Strict JI", so I wouldn't call it "Adaptive JI". The two types of
Strict JI would be
(a) one with a finite set, though not necessarily
closed, set of fixed pitches, so that drift doesn't occur; and
(b)
one with a potentially infinite use of pitches from the JI lattice,
with a preference for observing common tones, so that drift may
occur.
I've called the former "Fixed-pitch JI" and the
latter "Freestyle JI" -- the term "strict" qualifies both these
subcategories.
217edo provides, among other things, an excellent set of
pitches to achieve fixed-pitch adaptive-JI.
Below is an illustration of how 217edo may be considered
as 7 bike-chains
of 31edo, each approximately
1/4-comma apart.
Below is an example by Dave Keenan of a I-VI-II-V-I
"comma-pump"
chord progression, written in the "sagittal" notation
developed by he and George Secor in 2002, and tuned
by me in 217edo (click on the graphic to hear the MIDI-file).
152edo is a more concise fixed-pitch tuning which works as adaptive-JI,
in the form of 8 bike-chains of 19edo, each separated by
approximately 1/3-comma.
REFERENCEs
Vicentino, Nicola. 1555.
L'antica musica ridotta alla moderna prattica
["ancient music restored to modern practice"]
Antonio Barre, Rome. republished 1557.
English translation:
Ancient music adapted to modern practice
Maria Rika Maniates (ed.), Claude V. Palisca (ed.),
Yale University Press, New Haven CT, 1996, p. xlix.
Blackwood, Easley. 1985.
The Structure of Recognizable Diatonic Tunings
Princeton University Press, Princeton, NJ.
ISBN 0-691-09129-3
Updated:
2002.11.30 -- graphic and audio of Lasso motet added
2001.12.29
