Huh? Microtonal music? A guide for the perplexed, from Margo Schulter

#1, #2, #2.1, #2.1.1, #2.2, #2.2.1, #2.3

What is microtonality?

What is paucitonality?

contributed by Margo Schulter

# 1. Microtonality and paucitonality: a short answer

If asked "What is microtonality," we 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 micro, "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 current musicians and composers, eagerly embrace terms such as "microtonal" (or earlier historical equivalents such as "enharmonic," see section#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.

# 2. A longer answer: perspectives and paradoxes

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 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.

# 2.1. Microtonality/paucitonality and "small" intervals

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.

# 2.1.1. How small is "small"?

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.

# 2.2. Microtonalism as "unusual" intervals or tuning systems

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.

# 2.2.1. How unusual is "unusual"?

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.

#2.3. Microtonality as an open continuum

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.


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.