Wide pitch range
Specifying pitch in global notation normally involves drawing a horizontal line for each pitch in the scale that the music (or a part of it) uses. If the music ranges widely in pitch, there is a danger that the number of these lines may become excessive.
This danger is not as grave as may at first appear, for two main reasons. First, the pitch lines in a given system need only cover the pitch range that is actually used in that part of the music. (See the example from George Gershwin’s Rhapsody in Blue in Nonmetrical onset timing with specified pitch.) Second, wherever possible all sounds of specified pitch are notated in a single layer (see Unspecified pitch). This is in contrast to scores in staff notation for ensemble, orchestral, and choral music, in which each vocal or instrumental part is written on at least one separate staff. Although each staff has only five lines, the total number of lines and vertical space required in such a score may be more than for the same music written in global notation.
Still, it is true that some music uses a wide pitch range in a way that can consume a lot of lines and space in global notation. Music for keyboard instruments is often an example, since the keyboard covers a wide range and the player’s two hands are sometimes far apart with nothing in the middle.The following passage from Beethoven’s Piano Sonata “Appassionata” in F Minor, Opus 57, while not particularly extreme, illustrates the difficulty.
The solution is to notate certain sounds an octave lower or higher than they actually are, and to indicate that fact in the score. To do this, an ellipse is drawn around those pitch lines which temporarily represent a pitch an octave higher or lower than would otherwise appear, and a vertical arrow is attached above or below the ellipse to indicate whether the octave transposition is upward or downward.
The horizontal center of the ellipse identifies the moment from which the transposition applies. The ellipse marking operates on a “henceforth” basis: that is, it applies until canceled by another marking of the same kind (although it is also helpful to repeat any ellipse markings that continue to apply at the beginning of a new system).
All of the sounds in the above example are transposed an octave either up or down in the score. At the beginning, the top six pitch lines represent pitches an octave higher than indicated at the beginning of the score; the lowest six pitch lines an octave lower. From the second beat of bar 2, pitch lines 4, 5, and 6 (from the top) join the pitch lines below them in representing pitches an octave lower than the initial standard. The ellipse marking here does not affect the top three pitch lines, which continue to represent pitches an octave higher than the standard. Both transpositions remain in force to the end of the excerpt.
Obviously, we will also have occasion to notate music in which only some of the sounds are very high or low in pitch, calling for a score in which pitch lines sometimes represent their “normal” assigned pitch rather than a transposed one. On the other hand, if high and low registers are used successively rather than simultaneously, we may need to apply octave transpositions to an entire system rather than selected pitch lines.
Both situations are illustrated at the beginning of Chunseol (Spring Snow), a composition by the Korean musician Hwang Byungki (1936–2017) for a modified, 17-string version of the traditional 12-string zither gayageum. Taking advantage of the wider pitch range offered by the additional strings, Hwang begins with three motifs presented in different registers. (Because of the pentatonic scale used, there are five pitch lines per octave. The additional hurdles indicate changes of meter; see Variable beat division.)
In this score, the entire system at first represents the pitch range indicated at the beginning, then an octave lower, then an octave higher. The return to “normal” pitch after a transposed section is indicated by an ellipse without an arrow.
By default, an arrow attached to an ellipse indicates transposition by one octave. Transposition by more than one octave can be indicated with multiple arrowheads.
In music that uses multiple pitch registers simultaneously, octave transposition may not be feasible because the pitch lines we want to use for transposed sounds are needed for sounds at the “normal” pitch level. Sometimes we may have to accept that dense-textured music requires dense notation, and resign ourselves to using a large number of pitch lines. Even here, though, the number of lines can often be reduced if a melody or phrase is sounded in more than one octave simultaneously.
For example, when a group of men, women, and children sing a song together, the women and children usually sing an octave higher than the men. Writing out the melody at both pitch levels may require a large number of pitch lines.
The same information can be given in less space by writing out the melody in the lower octave only and using a sign to indicate that all the pitches are doubled an octave higher. The sign for this is an ellipse around the relevant pitch lines with a + (plus) sign attached to the top of it.
(Any resemblance between these ellipse markings and biological gender symbols is of course entirely coincidental!)
The end of a doubled passage, like that of a transposed one, is signified by a plain ellipse, or by one indicating a different doubling and/or transposition. Similarly to the markings for octave transposition, pitches doubled an octave lower can be indicated with a plus sign below the ellipse, while pitches doubled at more than one octave can be indicated with multiple plus signs.
Sometimes it may be convenient to apply both doubling and transposition, for instance if a melody is doubled in octaves—say by flute and piccolo—while even the flute part is considerably higher than any other sounds in the texture. In this case a combination of arrow(s) and plus sign(s) can be used. If more than one doubling and/or transposition operation is to be applied, the arrows and plus signs are read in order starting from the one closest to the ellipse.
Thus, a double plus sign above an ellipse in effect means “first double this pitch and then double that,” i.e. the pitch is doubled at both one and two octaves higher. If the doubling is at an interval of two octaves only, it is indicated by a plus sign surmounted by an arrow, interpreted as “first double this pitch at the octave and then transpose the resulting pitch an octave higher.” Conversely, the case of the flute and piccolo soaring in octaves above much lower sounds would be handled with one or more arrows surmounted by a plus sign.
By default, an arrow or plus sign indicates transposition or doubling (respectively) at the interval of an octave. However, some music uses doubling at an interval other than an octave or octaves. For instance, in Bolivian panpipe ensemble music, the melody is often doubled in fourths or fifths as well as octaves. Doubling at any interval can be specified by writing the size of the interval(s) in cents above the plus sign (or below it if the doubling is lower than the written pitch).
By applying a combination of these techniques, pitch lines can usually be provided for the scale degrees throughout the music’s pitch range without taking up an excessive amount of space. Our symbols for sounds of specified pitch will normally be placed on one or other of these pitch lines. However, music sometimes uses pitches outside of its prevailing scale, either by “bending” the pitch or by temporarily using a pitch from a different scale, so we may need to represent pitches that don’t fall on our pitch lines as well.
Next: Extra-scalar pitch
Bolivian panpipe ensemble score based on staff notation in:
Schechter, John M. 1996. “Latin America/Ecuador.” In Jeff Todd Titon, ed., Worlds of Music: An Introduction to the Music of the World’s Peoples, 3rd ed., New York: Schirmer Books, pp. 428–494. At p. 438.
Sources of audio:
Ludwig van Beethoven, Piano Sonata in F Minor, Opus 57, first movement, performed by Wilhelm Kempff, Deutsche Grammophon CD 453 724-2, disc 6 track 8.
Hwang Byungki, Chunseol (Spring Snow), from Hwang Pyeonggi gayageum jakpumjip, vol. 4: Chunseol (Spring Snow: Byungki Hwang Kayagûm Masterpieces Vol. 4), C&L Music CD, CNLR 0106-2, track 14.
“Kutirimuapaq” Bolivian panpipe ensemble performance from Ruphay, Jach’a Marca (Folklore Andino De Bolivia), Heriba CD, ASIN: B01J64MPU8, track 5.