Facilitating the Performance of Polytempo Music
An Overview

by John Greschak
john@greschak.com
August 6, 2001 - September 1, 2001

Introduction
Loose Coordination
Notational Solutions
Technology-Assisted Conducting
Electronic Realizations
Coda
Update History
 

Introduction

In monotempo music, part scores are written against or synchronized with a common sequence of pulses (or points in time), and some individual, be it a conductor or lead player, sets the pace of the underlying pulses. A traditional Western art music ensemble such as a (conductorless) string quartet or an orchestra lead by a single conductor, is well suited to the task of producing a coordinated performance of monotempo music.

In polytempo music, two or more tempi occur simultaneously. In its most general form, polytempo music consists of a set of parts where each part is written against a different sequence of pulses, and the pulse sequences bear no simple relationship to one another. It is difficult (and in some cases, impossible) for a traditional ensemble to produce a coordinated performance of such music.

This article gives an overview of the various approaches that have been taken by composers to facilitate the performance of polytempo music. For detailed descriptions of the techniques and works discussed here, see the article Polytempo Music: An Annotated Bibliography.

Loose Coordination

A composer may facilitate the performance of a given piece of polytempo music by specifying that the work be performed in a less than fully coordinated manner. This might be accomplished through an explicit instruction to perform in an uncoordinated manner, or it might be achieved indirectly as a consequence of some other instruction or method of notation.

In an uncoordinated polytempo texture, some tempo is performed independently, without any regard for the other tempi that occur simultaneously. An instruction to perform in an uncoordinated manner might apply to all performers throughout an entire work, or to just one performer during one section of a work. In the case when an ensemble is partitioned into smaller groups, the groups might be uncoordinated with each other, or the players of a given group might be uncoordinated among themselves.

Sometimes, a conductor is expected to freely select (and cue) the start and stop times of uncoordinated phrases. More often, start and stop times are specified relative to (and thus are to be coordinated with) a musical event that occurs in another part. Here, the sound of some event might serve as a start or stop cue for a conductor or performer. Or, a conductor or performer might be asked to determine start and stop times based on the relative horizontal position of phrases as they appear in the full score. The latter approach is used for start times more often than stop times. In some cases, an uncoordinated phrase is to be halted abruptly, on cue. In other cases, a player is instructed to continue playing up to the next breath mark, stop mark or fermata in their part, after having received a stop cue. Sometimes, an uncoordinated phrase is extended, as needed, by repeating the entire phrase or the last few notes. In some cases, the conductor is permitted to vary the tempo of a conducted part to ensure that it ends at a specified time relative to an uncoordinated phrase.

In many cases, the layout of phrases in the full score of an uncoordinated work does not reflect the coincidence of musical events. Often, only the start time is indicated relative to other parts.

For some uncoordinated works, multiple conductors are used where each conductor beats an independent tempo. Sometimes, an ensemble member temporarily serves as an assistant conductor. Usually, a conductor is assigned to a fixed group of performers. However, in some cases, the conductor to which a given performer is assigned changes frequently throughout a piece. In some cases, a line of sight must be maintained between two given conductors as one is to receive visual start or stop cues from the other. After being cued to start, a conductor might begin by beating a silent measure to establish a new tempo and meter, and prepare his group for entry.

There are many examples from the literature where uncoordinated parts are specified using the techniques described thus far. Charles Ives used uncoordinated parts in The Unanswered Question, Central Park in the Dark and Symphony No. 4. Numerous examples may be found throughout the spatial works of Henry Brant (e.g. Divinity: Dialogues in the Form of Secret Portraits for Harpsichord and Brass Quintet and Prevailing Winds for Invisible Woodwind Quintet). Note: In some works, Brant specifies that parts be uncoordinated even in the case when all performers have the same tempo marking (e.g. American Weather). Examples by György Ligeti are Chamber Concerto for 13 Instrumentalists and Magyar Etüdök (Hungarian Studies) for Mixed A Cappella Choir (16 part). Note: Ligeti suggests that the latter work may be performed in a coordinated manner with the assistance of conducting technology which is discussed later in this article. Other examples would be Karlheinz Stockhausen's Gruppen (Groups) for 3 Orchestras, Luciano Berio's Folk Songs for Viola, Voice, Harp and Cello, Emmanuel Ghent's Helices for Violin, Piano and Tape, Brian Ferneyhough's Missa Brevis and Firecycle Beta, Pierre Boulez's Rituel: In Memoriam Maderna and Michael Colgrass' Letter from Mozart for Orchestra.

Sometimes, explicit instructions are given to perform simultaneous different tempi in an uncoordinated manner. However, in many cases, uncoordination (or at least, loose coordination) is a byproduct of some other instruction. Here are some examples of ways by which composers have indirectly specified that ensemble playing be loosely coordinated:

Notational Solutions

Various methods have been used to notate polytempo music in such a way that it may be performed in a coordinated manner by a traditional ensemble, with or without a conductor. In general, each of these methods involves notating the music in such a way that some temporal characteristics (e.g. tempo and meter; barline placement; or the duration of a given type of note) are the same in all parts while other temporal characteristics are allowed to be independent.

An unusual approach is taken by Charles Ives in the second of the Three Harvest Home Chorales and in the piccolo part in Section 8 of the second movement of Symphony No. 4. In these sections, parts share a common meter, tempo, and barline placement, but the durational meaning of a given type of note symbol is not the same in all parts. A form of rhythmic cue line is provided that is aligned with the beats of one part. Arrows are drawn from notes on the cue line to notes of another part to indicate the time at which such notes are to be played relative to the part upon which the cue line is based.

Many composers have chosen to notate polytempo music as monotempo music. With this method, at all points in time, all parts are notated against a common tempo and meter, and changes in tempo or meter occur in all parts simultaneously. Tempi that differ from the common underlying tempo are represented by various means. For some cases, augmentation or diminution (i.e. uniform lengthening or shortening of note durations) may be used to notate the desired multi-rate effects. Similarly, tuplets may be used for this purpose. For example, if the common tempo is MM quarter note = 84, the tempi MM quarter note = 147 may be represented by using tuplets with the ratio 7:4. This approach is discussed in Timothy Sullivan's article "Multiple Tempi: A Survey and Method" (1997) which contains a table of note durations that one could use to notate a beat, or various fractions of a beat, of a tempo that stands in a given ratio to the common tempo, assuming that the duration of a beat in the common tempo equals that of a quarter note. Other tempi for which the ratio might be too complicated to be represented in this way, may be approximated by writing the part in the common tempo, for example, to the nearest sixteenth note. Instances where such techniques have been used are quite common in the literature. For example, see Bach's fourteenth canon Canon a 4 per Augmentationem et Diminutionem of the Goldberg Canons (BWV 1087) (augmentation and diminution), Elliott Carter's String Quartet No. 5 (tuplets), the first movement of Henry Cowell's Quartet Romantic (tuplets), and Elliott Carter's String Quartet No. 2 (approximation). These methods may be extended to represent accelerandos and decelerandos approximately as in Elliott Carter's String Quartet No. 2 (e.g. see the first measure of the cello part).

Another common approach is one in which polytempo music is written as polymetric music whereby each part has an independent tempo marking and meter, but common barlines are used whenever possible. Here, coordination is facilitated by having the first beat of most measures occur at the same time in all parts. For example, with this approach one might find two simultaneous measures (of equal width) for which the barlines are aligned horizontally, and the meters and tempi are 4/4 at MM quarter note = 84, and 7/4 at MM quarter note = 147. This approach is used less frequently than that in which polytempo music is written as monotempo music. Still, it is quite common. For example, see the sketches for Charles Ives' unfinished Universe Symphony, Elliott Carter's String Quartet No. 1, Henry Brant's American Debate: An Antiphonal Overture and Verticals Ascending: After the Rodia Towers: For Two Separated Instrumental Groups, Section I of György Ligeti's Magyar Etüdök (Hungarian Studies) for Mixed A Cappella Choir (16 part), and Mark Applebaum's Tlön (where only conductors are coordinated as this piece calls for no players).

Another way by which common barlines may be used to simplify coordination is found in Section III of György Ligeti's Magyar Etüdök (Hungarian Studies) for Mixed A Cappella Choir (16 part). Here, the tempi are independent but the meter (4/4) is common to all parts. The tempi used in this work (MM quarter note = 90, 110, 140, 160 and 190) are such that the duration (or width) of some whole number of bars in one part equals the duration (or width) of some other whole number of bars in another part. As a result, some barlines of different parts coincide periodically. More generally, this will occur in cases for which the tempo numbers have a common divisor (other than one). A further simplification occurs in Ligeti's case, because one of the tempo numbers (i.e. 160) is evenly divisible by the product (40) of the greater common divisor (10) and the number of beats in a measure (4). Thus, in this case, four measures of the part which is written in the tempo MM quarter = 160 serves as a unit of organization to which the tempi of the other parts may be coordinated.

In other cases, polytempo music has been notated as polymetric music with independent meters, barlines and tempi for each part, but where the tempi are such that the duration of a given type of note (e.g. a quarter note) is the same in all parts, at all points in time. In this case, since each part has its own meter, the duration of beats, and consequently the tempo, is not the same in all parts. For example, one might find three measures of meter 4/4 at MM quarter note = 84, occurring simultaneously with (and having the same total width as) four measures of meter 6/8 at MM dotted-eighth note = 56. This approach is used in the final section of George Crumb's Black Angels which is titled Threnody III: Night of the Electric Insects.

For some polymetric works such those discussed here, it has been suggested that one conductor be used to beat two different patterns simultaneously as in Charles Ives' Three Places in New England (Orchestral Set No. 1) (Note: According to the version of the score edited by by James B. Sinclair, this appears to have been more the idea of the conductor Nicholas Slonimsky than of Ives, and for this work, Ives preferred to have all the material notated against a common meter and tempo). This approach has limited applicability as it is not well suited to cases involving more than two simultaneous different tempi, and it is difficult for a conductor to beat two sequences of pulses when the pulse sequences do not bear a simple relationship to one another. For other polymetric works, it has been suggested that two or more conductors might be used to facilitate coordination. For example, this is done in Elliott Carter's Double Concerto for Harpsichord and Piano with Two Chamber Orchestras.

Finally, for some works, ossia lines have been used to notate a given part with an alternative tempo and meter. In most cases, one of the two representations of the part is written in the meter and tempo of the other parts, and sometimes this is only an approximation of how the part is to be played. For example, ossia lines of this type are given in Charles Ives' Three Places in New England (Orchestral Set No. 1) and Elliott Carter's String Quartet No. 2.

Technology-Assisted Conducting

Various technology-based conducting systems have been used to help ensembles perform polytempo music in a coordinated way. With these devices, some number of automated conductors are employed to lead the performance.

For most of the devices that have been used thus far, cue signals are transmitted to players by sound or light. For sound-based systems, players are equipped with headphones through which they may hear various cue signals. If light is used, players are provided with a light that blinks. Sound has been used more often than light for transmitting cues.

In most cases, the cue signals for a given work are defined before a performance. Signals might be recorded on audio tape or as MIDI data in a sequencer.

Most often, cue signals have been used to indicate the time at which downbeats are to occur. However, in some cases, they have been used for other purposes as well such as: to indicate the time of sub-beats (or upbeats); to establish a new tempo before notes are to be played; to signal the entire rhythmic pattern of a complicated phrase before it is to be played; and to provide a reassuring checkpoint cue or an alerting cue just before the end of a long rest.

For a given performance, the number of automated conductors used and the way in which they are configured depends upon the particular demands of the work being performed. In some cases, each player of an ensemble might be provided with a dedicated automated conductor. In arrangements that involve multiple groups, each member of a given group of players might be lead by a single automated conductor, identical signals of which might be distributed to each player of the group (e.g. through headphones). Or, if each group has its own human conductor, each human conductor might follow the lead of a different automated conductor.

For some electro-acoustic works, the mechanism that is used to generate cue signals has also been used to automatically play additional electronic parts (which might have their own tempo). Depending upon the type of mechanism that is used, such parts might be sounded from tape or played by a synthesizer that is controlled by a sequencer. In some cases, the parts that are played automatically might be of a type that could not possibly be played by human performers in real time.

The following composers have written compositions and articles related to the use of automatic conducting technology (Note: A more detailed discussion of the works mentioned here is given in the article Polytempo Music: An Annotated Bibliography.):

Electronic Realizations

By using recording technology in a studio, some composers have realized their polytempo works as an audio recording that may be performed at a later time. With this process, it is possible to record each tempo, one at a time. Depending upon the structure of the piece, this might involve recording each instrument, one at a time. Or, it might mean recording each phrase one at a time, where any given phrase might be performed by one instrument or a group of instruments. During the recording process, sequencer-controlled electronic instruments may be used in combination with traditional instruments, or either may be used exclusively. After each component part has been recorded, the total work may be assembled from the parts by digital means. Using a digital signal processing technique know as time-scale modification (TSM), individual elements may be scaled in time to increase or decrease their tempo as needed (without pitch change). These techniques may be used to realize works for traditional acoustic instruments with human players that might be difficult or impossible to perform in real time.

In some cases, a special score called a "recording score" might be devised that is tailored more to the needs of performance in the recording studio than real-time performance. For example, in the case when a piece consists of a sequence of overlapping phrases where each phrase may have a different instrumentation and tempo, the recording score might consist of a sequence of pages on which there is one phrase per page. Additional instructions would be provided to indicate how the individual phrases are to be assembled to form the composite work. For example, phrases might be numbered and coincidence points (in time) could be labeled in each phrase.

For a composition that is intended to be realized by using recording technology, one might impose limitations during the process of composition that would ensure that the work will be (at least theoretically) possible to perform in real time by human players. For example, one might use the constraint that an instrument that usually plays only one note at a time, never sounds more than one note at the same time after independent phrases have been overlapped to form the composite recording.

As an alternative to using recording technology, polytempo music may be performed in real-time before an audience by using automated instruments only, such as an ensemble of synthesizers that are centrally controlled by a sequencer, or a player piano. In this case, musical information is encoded prior to a performance, for example, as a MIDI file or a paper piano roll.

There are many composers who have realized polytempo music as electronic music. Some examples would be: Conlon Nancarrow's recordings and live performances of his Studies for Player Piano; Larry Austin's recordings of acoustic instruments for an early version of his Life Pulse Prelude (1975) and later synthetic realizations of the same work (1981); Frank Zappa's use of the technique that he called xenochrony (strange synchronizations), for example, in his recordings Friendly Little Finger from Zoot Allures (1976), Rubber Shirt from Sheik Yerbouti (1979), and Packard Goose and Keep it Greasy from Joe's Garage (1979), whereby various recorded tracks of unrelated material were assembled into new composite recordings; Emmanuel Ghent's synthetic realization of his Dithyrambos for Brass Quintet (1977); and Paul Dolden's recording L'Ivresse de la Vitesse (Intoxication by Speed) (1992-3) in which various separate human performances are processed digitally (e.g. speeded up) and then combined.

Coda

Any of the approaches discussed in this article may be used to facilitate the performance of polytempo music. In some cases, one might use more than one approach for a given work. For example, one might notate a given piece in more than one way: as a recording score that would be well suited to the task of recording the work in a studio, and as a set of part scores that would be tailored to the task of real-time performance before an audience. Or, one might notate a given polytempo piece as a polymetric piece with common barlines throughout, and coordinate the performance with technology-assisted conductors.

As an alternative, one might choose not to facilitate performance in any way. At this time, there is no standard way to realize polytempo music in a coordinated manner, and one cannot possibly envision the requirements of systems that might be used in the future to perform such works. Under these conditions, one might choose to notate a polytempo piece in an abstract way that most naturally represents the musical material with no concern for the degree to which it serves the needs of a particular mode of performance. Or, perhaps any abstract representation of the music would be sufficient.

Update History

August 6, 2001: Completed the first version of this page.

August 23, 2001: Added mention of Emmanuel Ghent's click track for Henry Cowell's Quartet Romantic.

September 1, 2001: Added mention of Timothy Sullivan's article "Multiple Tempi: A Survey and Method".