#1, #2, #2.1, #2.1.1, #2.2, #2.2.1, #2.3,
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What is microtonality?
What is paucitonality?
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4.1.# 1. Microtonality and paucitonality: a short answer
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If asked "What is microtonality," members of the Tuning List might
offer definitions taking at least three general approaches, all of
them with delicate and often controversial cultural implications:
(1) MICROTONALITY AS THE USE OF "SMALL" INTERVALS. In the most obvious
definition, microtonality (from Greek _mikro_, "small") is the use of
intervals smaller than the usual whole-tones and semitones of the
best-known Western European compositional traditions, although the use
of such intervals is a routine feature of many world musics.
(2) MICROTONALITY AS THE USE OF "UNUSUAL" INTERVALS OR TUNINGS. In a
second and related definition broadening the first, microtonality is
the use of any interval or tuning system deemed "unusual" or
"different" in a given cultural setting -- in many 20th-21st century
settings, for example, just about any tuning for keyboard or guitar
other than a division of the octave into 12 equal semitones (12-tone
equal temperament, or 12-tET). The composer Ivor Darreg's concept of
_xenharmonics_, which it is tempting to describe in a paraphrase of
the Latin poet Terence as the conviction that "nothing intonational is
alien to me," seems synonymous with this sense of "microtonal."
(3) MICROTONALITY AS A MUSICAL CONTINUUM OR DIMENSION. In a third
definition, microtonality is simply the dimension or continuum of
variation among intervals and tuning systems, embracing _all_ musics.
Seen from another perspective, the first two definitions treating
"microtonality" as a special and often suspect category of music imply
an unspoken norm of what we might term _paucitonality_, literally "few
tones" -- or better, "scarce tones." This concept -- not a tuning
system or musical style, but a confining state of mind -- also invites
at least three definitions:
(1) PAUCITONALITY AS CULTURAL MYOPIA. In its root definition,
paucitonality or "scarce-tonedness" is a state of musical and cultural
myopia in which the use of intervals and intonational nuances
routinely occurring in many world musical traditions -- including some
European ones -- must be relegated to a special "microtonal" category.
(2) PAUCITONALITY AS INTONATIONAL MONOMANIA. In its more aggravated
forms, paucitonality could be defined as an ideology (often unspoken)
restricting musicians (at least in theory) to a single tuning system,
and viewing talented musicians even of one's own historical or
cultural tradition who dare to propose something "different" as
"straying far afield from the mainstream."
(3) PAUCITONALITY AS THE ABSENCE OF CHOICE. In its third definition,
corresponding to the definition of "microtonality" as a universal
property of all music, paucitonality means tuning by default, or by a
decision not to decide, rather than by informed and aware choice.
As the first two definitions of "microtonality" or "paucitonality" may
suggest, defining certain intervals as "unusual" can have witting or
unwitting cultural implications, especially when the definition of
"usual" is based on one subset of European composed music. The less
pleasant overtones -- to use a musical figure of speech -- sometimes
get articulated all too plainly.
In his "A Brief History of Microtonality in the Twentieth Century"[1],
microtonal composer and historian Brian McLaren tells how a German
theorist named Willi von Moellendorf experimented with one of the
popular early 20th-century tuning systems: 24-tone equal temperament
(24-tET). Taking as a starting point the 12-tET system which had then
just recently become the norm in Europe for keyboards, 24-tET divides
each of the 12-tET semitones into two "quartertones."
Often very mistakenly equated with "microtonality" in general, the
24-tET system is simply one equal division of the octave among a
myriad of equal and unequal divisions, not to speak of nonoctave
tunings. In fact, many self-declared microtonalists today might regard
it as a rather conservative and overworked choice, although others
find it charming and exciting, especially when applied to certain less
familiar styles.
In 1917, however, von Moellendorf had to confront not only the usual
objections to any musical innovation, but also the charge that
intervals such as quartertones represent a "primitive, even barbaric
condition of a lower cultural level." Given subsequent history in
Germany and elsewhere in Europe during the years 1933-1945, such
possible cultural implications may have an interest more than
musical.[2]
Indeed the word "barbaric," another Greek-derived term, may say much
about the concept of "microtonal" as applied by "antimicrotonalists"
or "paucitonalists." To the ancient Greeks, the speech of outsiders
sounded like a meaningless "bar-bar," thus the term "barbarian," one
outside the "civilized" world.
To "antimicrotonalists" (some of whom might define themselves simply
as "lovers of _normal_ music"), similarly, musics based on unfamiliar
intervals or tuning systems sound like "mistunings" or "random
dissonance." Such judgments would relegate not only self-consciously
experimental or avant-garde composed musics, but age-old musics of a
vast range of world traditions, to an "inferior" (or at best "exotic")
status.
It is against this backdrop of "intonational politics" that champions
of intonational pluralism -- "microtonality" in definition (3) --
consider such issues as "Should I call myself a microtonalist, a
xenharmonicist, an alternative tuning advocate, or simply a musician?"
People hesitating to embrace the "microtonal" label, or even actively
resisting it, often take the principled stand: "My music is an
integral whole, with intonation simply one aspect of this whole: I
leave others to make categorizations."
Other musicians, ranging from Nicola Vicentino (1511-1576) to many
members of this Tuning List, eagerly embrace terms such as
"microtonal" (or earlier historical equivalents such as "enharmonic,"
see Section 4.1.#2.1 below) because they see new intervals and tuning
systems as a central theme of their music.
Also, musicians may embrace the term "microtonal" as an act of
affirmation and solidarity in the face of intonational oppression: "If
that's what the 'mainstream' scene wants to call us and our music,
let's make the most of it."
Our third definition of microtonal as a universal but not universally
recognized aspect of all music may be one way of reconciling these
viewpoints. The decision (active, passive, or unknowing) to use _any_
tuning system places a musician somewhere on the microtonal continuum,
or within the microtonal multiverse.
From this perspective, to declare that one is a "microtonalist" is
simply to acknowledge this reality, and to invite others to join in
this musical act of self-awareness and mutual celebration.
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4.1.# 2. A longer answer: perspectives and paradoxes
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Since both microtonality and paucitonality may be concepts of most
relevance to composed European traditions, questions of how best to
define them may be implicitly ethnocentric, distracting us from a more
balanced survey of the use of intervals both large and small in a
plethora of world cultures through the millennia.
Nevertheless, examining a few historical examples and patterns may
suggest the perennial nature of some European and related issues of
microtonality/paucitonality, and also bring out some of the paradoxes
inherent in definitions sometimes more often cited (on this Tuning
List and elsewhere) than carefully examined.
One 20th-21st century factor which may transform the debate for better
or for worse is technology. On the positive side, electronic means
both of recording and of synthesizing musical sounds have created a
basis for free cultural interchange and mutual knowledge, and also for
realizing just about any known or not-yet-conceived tuning system, and
for quickly switching a keyboard or similar instrument from one system
to another.
On the negative side, mass production can mean mass standardization of
the most confining kind, threatening to produce what composer and
historian Douglas Leedy has described as "an unsavory echo of
imperialism" subjecting the "musical cultures of the world" to a
process of "control and appropriation."[3]
Despite these vital technological changes, a journey to the Europe of
five centuries ago may reveal how many microtonal/paucitonal issues
are not so new in substance.
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4.1.# 2.1. Microtonality/paucitonality and "small" intervals
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In 1482, the often iconoclastic Spanish musician and theorist
Bartolome Ramos published a treatise noted then and now both for its
daring innovations, intonational and otherwise, and for its biting
satire against the musical "establishment" of the time. Both aspects
of his work led to heated controversies.
Discussing the art of finding regular intervals on a keyboard likely
tuned in the new meantone fashion then coming into vogue, Ramos
considered an interesting question: might a 12-note tuning more
usefully include G# or Ab, two distinct notes often differing in
Renaissance meantone temperaments by around a fifth of a tone.
After considering the arguments and opting for Ab, Ramos added that
some people prefer to satisfy both sides of the question by designing
a keyboard with both accidentals -- typically by splitting the key for
an accidental so that pressing the front portion would sound G#, for
example, while the back portion would sound Ab. This approach was
followed, for example, in the organ at Lucca in Italy with such split
keys for G#/Ab and Eb/D#, providing 14 notes in each octave, and
enjoyed widespread favor in 16th-17th century Europe.
Ramos, however, raises the objection that having both Ab and G# would
introduce an interval not part of the diatonic order -- the interval
smaller than a semitone between these two notes. Showing the
Renaissance love for Classic allusions and precedents, Ramos cited the
case of a musician banished from Sparta for the "crime" of adding
extra strings to his instrument beyond those accepted by tradition,
thus upsetting the musical and political order.
Although Ramos adds that nevertheless there are good arguments for
having both G# and Ab which he reserves for another discussion (this
discussion is not known in his writings which have come down to us),
his allusion to Spartan paucitonalism may reflect a cultural theme
still quite relevant in the year 2001, as artists facing the
professional consequences of "microtonality" can attest.
Moving ahead in time to the year 1555, we find composer and theorist
Nicola Vicentino publishing his great work on _Ancient Music Adapted
to Modern Practice_. By a happy coincidence, in one popular flavor of
meantone tuning with pure or near-pure major thirds, the diesis or
small interval by which accidentals such as G# or Ab differ happened
to be around the same size as the enharmonic diesis of ancient Greek
theory. Vicentino made the most of this by seeking, as his title
suggested, to combine the expressive enharmonic genus of the Greeks
with 16th-century techniques of polyphony and counterpoint.
Masterfully analyzing the "common practice" of the time as well as
documenting his own experimental music, Vicentino described his
_archicembalo_ or "superharpsichord" dividing the octave into 31
dieses, each equal to 1/5-tone. In 1561, he advertised his similar
_arciorgano_ or "superorgan," sounding a notable cross-cultural theme.
With this instrument, he announced, one could perform "all manner of
songs and airs according to the idiom which all the nations of the
world sing" -- including, for example, the Spanish, French, Polish,
English, Turkish, and Hebrew manners.[4]
Given the special interest of the Renaissance in fitting music to a
text elegantly and expressively, this passage could be read to suggest
an interest both in the melodic intervals and nuances favored by other
cultures, and in the most flexible choice of intervals by a composer
in setting poetic or other texts in a range of world languages.
Along with 16th-century enharmonicists -- or xenharmonicists, to use a
more recent term -- there were also the "anti-enharmonicists," among
them the otherwise often outspokenly radical musician Vincenzo
Galilei, father of the astronomer Galileo.
In Galileo's view, Vicentino's enharmonic dieses were "contrary to the
nature of singing and disproportionate to our sense of hearing."[5]
As his comments on Vicentino and his students revealed, such matters
could be issues of economics as well as theoretical psychoacoustics.
According to Galilei, Vicentino's disciples found it necessary to
abandon the enharmonic style in order to succeed in the marketplace.
Many xenharmonicists of today may also hear a familiar if not so
pleasant ring in another view of Galilei, an accomplished lute player
as well as composer and polemicist: his ridicule of lutenists favoring
the use of _tastini_ or "little frets" added to the instrument in
order to obtain purer thirds.
In 1584, while meantone tunings with pure or near-pure thirds were
standard on keyboards, 12-tET was standard on fretted instruments such
as the lute; but then as now, some players favored alternative or
modified frettings. Galilei seems to be describing a kind of just
intonation scheme or the like adding special frets to the usual ones.
Poking fun at such players when they strive for pure thirds but find
that their fingers stumble into impure fifths or fourths, showing that
their ears are not as fastidious as one might have guessed, Galilei
adds that a truly expert performer (such as himself!) needs no such
special gadgets to impress an audience, thus assuming the 16th-century
role of the author as self-promoter.
For Galilei, both Vicentino's enharmonic music and the just intonation
lute frettings represented the use of intervals smaller than a
diatonic or chromatic semitone -- a concept closely coinciding with
the most familiar definition of "microtonalism." His reaction was not
favorable.
Galilei's views as a musician who felt free to question authority on
many points, and to challenge the conventional rules of counterpoint
and dissonance treatment, are of special interest.
To advocate Nicola Vicentino's enharmonicism, or Ivor Darreg's
xenharmonicism -- a difference of only one letter -- is to take a
stand which may carry an appreciable professional price.
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4.1.# 2.1.1. How small is "small"?
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Accepting for the sake the argument the "small interval" definition of
microtonality, a fine issue arises: "How small is 'small'?"
The standard interpretation of "smaller than a semitone" leaves
considerable room for debate and ambiguity, because diatonic or
chromatic semitones of historical European tuning systems can vary in
size from around 1/3-tone (say 63 cents) to around 2/3-tone (say 126
cents). Semitones of these specific sizes occur in the equal 19-note
division of the octave advocated by the French composer Guillaume
Costeley in 1570, or the almost identical meantone temperament with
pure minor thirds described by the Spanish theorist Francisco Salinas
in 1577.
Another interpretation might take as "microtonal" an interval too
small to be perceived in a given musical context as a usual semitone.
Under this definition, the enharmonic diesis or fifthtone of Nicola
Vicentino at around 41 cents clearly qualifies, certainly in the
setting of his music: it has a radically different effect than the
diatonic semitone of his system at around 117 cents (or 3/5-tone), or
the smaller chromatic semitone at around 76 cents (or 2/5-tone).
In contrast, a single step of 22-tET at 1/22 octave or about 55 cents
makes a very convincing semitone in connection with a whole-tone of
four steps, 4/22 octave or about 218 cents. This is an example of how
in the right setting a literal "quartertone" can serve as a regular
diatonic semitone, thus arguably falling outside the category of
"microtonal" in the sense of "too small to be heard as a usual scale
step."
This 22-tET interval, by the way, illustrates how a "quartertone" can
take on various sizes or shapes; while a step of 1/24-octave or 50
cents may be the most familiar example because of the popularity of
24-tET in the 20th century, it's only one possible form.
One curious conclusion is that an interval of around 50-55 cents might
be "microtonal" in one musical setting, and a regular "semitone" in
another.
If we regard the drawing of such a blurred line as an engaging but
rather parochial study in the ethnomusicology of one regional
compositional tradition among the many musics of the world, then the
exercise can be at once edifying and harmless.
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4.1.# 2.2. Microtonalism as "unusual" intervals or tuning systems
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When introduced into a European style of composition where diatonic or
chromatic semitones are the smallest recognized intervals, smaller
intervals such as Vicentino's diesis at around 41 cents can have a
strikingly "unusual" effect, in 1555 or 2001. A broadening of the
"microtonal" concept focuses on this perception of the "unusual,"
whether induced by intervals of small size, or simply of
_unaccustomed_ size.
Consider, for example, a division of the octave into five equal parts,
each an interval of 240 cents, which a listener accustomed to
historical European tuning systems might hear as either a very large
major second or whole-tone, or a very small minor third. This creative
ambiguity, by the way, lends a special charm to tunings such as 20-tET
when used for "Western European-like" styles.
This interval of 1/5-octave or 4/20-octave is much larger than a
semitone, and therefore not "microtonal" in the narrow sense, but it
arguably has a strikingly "different" quality for the uninitiated
listener analogous to that of Vicentino's diesis.
One should hasten to add that for members of many world musical
cultures, an interval of around 240 cents dividing the octave into
five roughly equal parts is not "unusual" at all, but the routine
norm, known simply as "everyday musical practice."
Again, we find that "unusualness" is in the ear of the listener, and
that paradoxically defining something like 240 cents as "microtonal"
in order to celebrate its "unusual" qualities may be tacitly accepting
a definition of "usualness" with definite ethnocentric implications.
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4.1.# 2.2.1. How unusual is "unusual"?
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Some intonational activists will argue that "everything is microtonal
except for 12-tET," including historical European tuning systems such
as medieval Pythagorean intonation, Renaissance meantone, and
17th-19th century unequal well-temperaments.
One curious paradox of this interpretation is that it leads to the
conclusion that "Renaissance and Manneristic music of the 16th century
in Europe may generally be considered microtonal -- ranging from the
most conventional settings to the most radical enharmonic styles of
Vicentino and his colleagues -- except for anything which happened to
be written for or performed on a 12-tET lute or similar instrument."
Applying our narrow definition of "small intervals" would lead to a
distinction more like that which might be drawn and evidently was
drawn, both by Vicentino and his critics such as Vincenzo Galilei,
between "usual" music and "enharmonic" styles using the diesis or
fifthtone.
If we do apply the broader "microtonal-as-unusual" concept in this
16th-century setting, we may well reach the conclusion that while
meantone on a harpsichord is everyday reality, 12-tET on such an
instrument is "xenharmonic" or even "microtonal."
Galilei, much enamored of this "perfect" temperament on the lute,
tried it on a harpsichord -- and found the thirds unsatisfactory, a
not unsurprising result given the nature of 16th-century style with
its restful thirds, and of the harpsichord with its prominent fifth
partial. As a "strange" keyboard tuning, this "spherical" temperament
with its perfect symmetry and easy circumnavigability nevertheless had
an attraction for Galilei and for an abbot named Girolamo Roselli who
also celebrated these qualities.
In the 1630's, the great composer Girolamo Frescobaldi reportedly
advocated that a new organ be tuned in 12-tET -- and was roundly
ridiculed by one theorist of the time for allegedly being ignorant of
the difference between a large and small semitone. Others remarked
that 12-tET might be more palatable if it were less unfamiliar -- a
comment sometimes offered concerning "microtonal" music in more recent
times.
Although a definition of "microtonal" including all tunings except one
may lead to such paradoxes, the "anything but 12-tET" approach does
have a certain political logic. This would seem to be the logic of
"uniting against a common adversary."
A group of xenharmonicists who cannot agree among themselves as to
whether a major third should ideally be tuned at 386 cents, 418 cents,
or 435 cents can nevertheless say "We're all non-400-cents!"
The next step, however, might be to realize, "Hey, 400 cents is
interestingly different, somewhere `between the cracks' of the smaller
or larger interval sizes (maybe both) we typically use -- and that
makes it `microtonal!'"
The adversary, then, is not 12-tET or any other tuning, but
intonational monopoly, in other words, paucitonality. The problem is
not how to distinguish between 12-tET and the "microtonal" universe,
but rather how to put 12-tET squarely within that universe, somewhere
on one arm of a certain spiral galaxy of equal tunings.
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4.1.# 2.3. Microtonality as an open continuum
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Defining "microtonality" not as a property of a specific interval or
tuning, but as a dimension of variation encompassing all intervals and
tuning systems, may avoid some of the pitfalls and paradoxes of the
"small interval" and "unusual interval/tuning" concepts, while
affirming the ideal of intonational pluralism often embodied by the
"small" or "unusual" in a European-related setting.
More specifically, the "microtonality as universal continuum" concept
may suggest a kinder and gentler strategy for convincing innocent
bystanders or even decided opponents that 12-tET is only _one_ of the
myriad of possibilities.
Rather than arguing why 12-tET is "bad" or "dissonant" or
"out-of-tune," all judgments based on stylistically specific
assumptions which when generalized become just as questionable as the
categorical assertion that "12-tET is ideal," we can argue that
"12-tET is a fine tuning -- but only one."
From that starting point, as musician and mathematician Dan Stearns
has said, there are fertile fields in all directions. An enthusiast of
12-tET, or someone who has simply used it by default, might try a
regular tuning making the fifths pure, or tempering them somewhat more
heavily in the narrow direction, or tempering them a bit unevenly. A
different strategy involving at once a small step and quantum leap is
to tune _two_ 12-tET chains in 24-tET or 24-out-of-36-tET, discovering
whole new families of intervals.
These approaches, and others, can help curious and inquiring minds and
ears recognize the xenharmonic universe they already inhabit, with
12-tET simply as one place (more attractive to some than to others) in
a very rich musical cosmos.
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Notes
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1. Brian McLaren, "A Brief History of Microtonality in the Twentieth
Century," _Xenharmonikon_ 17:57-110 (Spring 1998), at pp. 61.
2. Ibid. On the prejudice against 1/24 octave as representing a "lower
cultural level," McLaren remarks, "Shades of Himmler and Heydrich."
While students of this period must address the question of any direct
political lineage between Moellendorf's critics in 1917 and the Third
Reich, the affinity between the concept of a "primitive ... condition
of a lower cultural level" and the Nazi category of "subhuman" are all
too unpleasantly evident. It is sobering to reflect that such cultural
prejudices are not neatly confined to one narrow range of the
political spectrum, and that today the 500-year struggle for the
survival of Indigenous peoples, cultures, musics, and intonational
systems continues.
3. Douglas Leedy, "Review of Martin Vogel's _On the Relations of
Tone_," ibid., pp. 120-123 at 123.
4. Henry W. Kaufmann, "Vicentino's Arciorgano: An Annotated
Translation," _Journal of Music Theory_ 5:32-53 (1961) at 36-37.
5. Karol Berger, _Theories of Chromatic and Enharmonic Music in Late
Sixteenth Century Italy_ (Ann Arbor, MI: UMI Research Press, 1980),
ISBN 0835710653, p. 73.