This paper is motivated by two questions, which I will address more or less in order:
Question (1):
[T]he mensural [classical] notational system… proved less effective… where the music makes relatively little use of notes of defined pitch or duration, or of traditional temperament systems. It occurred also in prescriptive notation for indeterminate music, when precise specification is at a minimum, and, perhaps paradoxically, also in descriptive notation at the other end of the spectrum of precision, where scientific accuracy of notation is required--as, for example, in ethnomusicological notations.” --The New Grove Dictionary of Music and Musicians, entry “Notation”, section (vi)
a) pitch
The core of the tuning system of Western classical music is twelve distinct pitches in each octave. Sometimes these pitches are irregularly spaced, and sometimes enharmonic notes have different pitches (for example, D# and Eb), but in Pythagorean, mean-tone, equal temperament, and all other classical tuning systems before the 1800s, there were only twelve main notes in each octave, each with a single pitch. Starting in the early Romantic period, composers began to expand beyond these core tuning systems.
I divide advances in the tuning of Western classical music into three categories. The first is quarter-tones, first used by a classical composer in the early 1800s, which simply extend twelve-tone equal temperament to include a few more intervals, mainly the just harmonic seventh. The second is equal-temperament microtonal music, which divided the octave in more than 12 equal steps, often to better approximate additional just intervals. The third breaks from the idea of dividing the octave entirely, allowing access to all frequencies and intervals. These three advances in freedom of pitch expression have brought with them advances in notation.
To a modern Western ear, influenced either by formal musical training or just the musical sounds of day-to-day life, anything other than either justly or equally tempered classical music with twelve pitches in an octave sounds strange and dissonant. However, to everyone, musical notes form a consonant interval any time their frequencies are in a small integer ratio. In studies, people have been able to identify the most consonant (smallest integer ratio) intervals without training, even when those intervals do not fall into the twelve-tone system (for example, 7:3, which is the basis of the Bohlen-Pierce “wide” triad.)
i) quarter-tones
Composers have considered many notation systems for quarter tones, such as changing the shape of the note heads and the position of stems, but have by now decided on a system of notation where quarter-tones are marked with the special and marks. This is because in the twentieth century, enough musicians have used quarter tones so as to allow standard notation. (Skinner) (New Harvard Dictionary)
ii) non-octave-based systems
It is possible to have a tuning system with many consonant intervals without dividing the octave into equal or near-equal intervals; many microtonal musical systems have been devised for this. Most of them are more difficult to notate, especially when the pitch relationships are irrational. There is however one exception.
The Bohlen-Pierce scale, invented in 1972 by Heinz Bohlen, is an example of a tuning system that does not use the octave as the basic unit of pitch. It can be equally or justly tempered, and consists of thirteen steps in a “tritave”, which is equal to an octave plus a perfect fifth. The tritave serves much the same role that the octave does in classical music; it is the largest important interval, it is subdivided into smaller intervals, and it defines pitch classes: an H# transposed one tritave up is also an H#. The Bohlen-Pierce scale is sometimes referred to as macrotonal because the smallest intervals in the scale are greater than 100 cents. (Walker)
Much as the Bohlen-Pierce temperament is not an addition to 12-EDO but a complete overhaul, Bohlen-Pierce notation must be its own system, not an addition to classical systems. However, classical notation can be re-used with new Bohlen-Pierce meaning. Bohlen-Pierce notation is not yet standardized, but there have been many proposals; most are simple variations on classical notation. A chromatic six-line staff seems to be the simplest idea; others include a five-line staff normalized to a Bohlen-Pierce non-chromatic scale (Muller).
b) music open to interpretation
Experimental composers of the twentieth century (for example, La Monte Young in his Compositions 1960) began to write music that had no specified musical action.
c) ethnomusicology
Recording information that is more precise than typical musicians need also requires an addition to classical notation. The New Grove Dictionary pointed me to the “melograph”, a crude way to visualize recordings of music invented in the late 1920s. (add)
Question (2)
The primary way that experimental notation like Crumb’s becomes standard seems to be by gradual adoption: at first, a composer will include the notation in a piece with a description of what it means. This will occur when the notation significantly improves the music, or if the composer has another motivation to invent the notation. Once the notation becomes widely known, it becomes part of mainstream classical notation.
An example of notation becoming widespread in the musical community is the symbol for “snap pizzicato”/Bartok pizzicato.
Notation, because it is a way that composers transfer their ideas to performers, always changes the relationship between the composer and performer. In fact, notation is intimately connected with the way music is perceived. (Messina) For example, the New Harvard Dictionary says that much of the Western classical emphasis on notation has been derived from the “view of the musical work of art as the unique historical creation of the composer, set down on paper for all times, and merely reproduced by performers”. A more robust notation system will allow pieces that differ from this view. There are two ways that experimental, graphic notation causes a greater freedom for the performer. First, while notation is objective, art is inherently subjective, and second, the accepted interpretation of art can change with the time period and cultural context.
- What causes a need for new forms of music notation?
- In the 20th century, how has music notation changed in response to these pressures, and what has changed about the roles of the composer and performer in musical pieces that use these new forms of notation?
Question (1):
[T]he mensural [classical] notational system… proved less effective… where the music makes relatively little use of notes of defined pitch or duration, or of traditional temperament systems. It occurred also in prescriptive notation for indeterminate music, when precise specification is at a minimum, and, perhaps paradoxically, also in descriptive notation at the other end of the spectrum of precision, where scientific accuracy of notation is required--as, for example, in ethnomusicological notations.” --The New Grove Dictionary of Music and Musicians, entry “Notation”, section (vi)
a) pitch
The core of the tuning system of Western classical music is twelve distinct pitches in each octave. Sometimes these pitches are irregularly spaced, and sometimes enharmonic notes have different pitches (for example, D# and Eb), but in Pythagorean, mean-tone, equal temperament, and all other classical tuning systems before the 1800s, there were only twelve main notes in each octave, each with a single pitch. Starting in the early Romantic period, composers began to expand beyond these core tuning systems.
I divide advances in the tuning of Western classical music into three categories. The first is quarter-tones, first used by a classical composer in the early 1800s, which simply extend twelve-tone equal temperament to include a few more intervals, mainly the just harmonic seventh. The second is equal-temperament microtonal music, which divided the octave in more than 12 equal steps, often to better approximate additional just intervals. The third breaks from the idea of dividing the octave entirely, allowing access to all frequencies and intervals. These three advances in freedom of pitch expression have brought with them advances in notation.
To a modern Western ear, influenced either by formal musical training or just the musical sounds of day-to-day life, anything other than either justly or equally tempered classical music with twelve pitches in an octave sounds strange and dissonant. However, to everyone, musical notes form a consonant interval any time their frequencies are in a small integer ratio. In studies, people have been able to identify the most consonant (smallest integer ratio) intervals without training, even when those intervals do not fall into the twelve-tone system (for example, 7:3, which is the basis of the Bohlen-Pierce “wide” triad.)
i) quarter-tones
Composers have considered many notation systems for quarter tones, such as changing the shape of the note heads and the position of stems, but have by now decided on a system of notation where quarter-tones are marked with the special and marks. This is because in the twentieth century, enough musicians have used quarter tones so as to allow standard notation. (Skinner) (New Harvard Dictionary)
ii) non-octave-based systems
It is possible to have a tuning system with many consonant intervals without dividing the octave into equal or near-equal intervals; many microtonal musical systems have been devised for this. Most of them are more difficult to notate, especially when the pitch relationships are irrational. There is however one exception.
The Bohlen-Pierce scale, invented in 1972 by Heinz Bohlen, is an example of a tuning system that does not use the octave as the basic unit of pitch. It can be equally or justly tempered, and consists of thirteen steps in a “tritave”, which is equal to an octave plus a perfect fifth. The tritave serves much the same role that the octave does in classical music; it is the largest important interval, it is subdivided into smaller intervals, and it defines pitch classes: an H# transposed one tritave up is also an H#. The Bohlen-Pierce scale is sometimes referred to as macrotonal because the smallest intervals in the scale are greater than 100 cents. (Walker)
Much as the Bohlen-Pierce temperament is not an addition to 12-EDO but a complete overhaul, Bohlen-Pierce notation must be its own system, not an addition to classical systems. However, classical notation can be re-used with new Bohlen-Pierce meaning. Bohlen-Pierce notation is not yet standardized, but there have been many proposals; most are simple variations on classical notation. A chromatic six-line staff seems to be the simplest idea; others include a five-line staff normalized to a Bohlen-Pierce non-chromatic scale (Muller).
b) music open to interpretation
Experimental composers of the twentieth century (for example, La Monte Young in his Compositions 1960) began to write music that had no specified musical action.
c) ethnomusicology
Recording information that is more precise than typical musicians need also requires an addition to classical notation. The New Grove Dictionary pointed me to the “melograph”, a crude way to visualize recordings of music invented in the late 1920s. (add)
Question (2)
The primary way that experimental notation like Crumb’s becomes standard seems to be by gradual adoption: at first, a composer will include the notation in a piece with a description of what it means. This will occur when the notation significantly improves the music, or if the composer has another motivation to invent the notation. Once the notation becomes widely known, it becomes part of mainstream classical notation.
An example of notation becoming widespread in the musical community is the symbol for “snap pizzicato”/Bartok pizzicato.
Notation, because it is a way that composers transfer their ideas to performers, always changes the relationship between the composer and performer. In fact, notation is intimately connected with the way music is perceived. (Messina) For example, the New Harvard Dictionary says that much of the Western classical emphasis on notation has been derived from the “view of the musical work of art as the unique historical creation of the composer, set down on paper for all times, and merely reproduced by performers”. A more robust notation system will allow pieces that differ from this view. There are two ways that experimental, graphic notation causes a greater freedom for the performer. First, while notation is objective, art is inherently subjective, and second, the accepted interpretation of art can change with the time period and cultural context.