MUSICAL SPACE That music is a temporal art is an easy notion to grasp. It is, also, spatial, and in more than one way. It is most clearly spatial in that sound has location in space. Where a sound comes from can affect the listener. Thus the loca- tion of a sound can be an integral aspect of the compositional conceptioning... This fact has often been ignored by composers, but its use in antiphonal church music during the Renaissance, and its "rediscovery" and de- velopment by some composers (like Henry Brandt) in the 20th century, illustrate its viability. At this time, however, we are not going to consider this kind of spatiality, but rather the metaphorical sense in which the pitch of sounds is thought of as corresponding to relative height, the "up and down" axis. Pitch, as the frequency (rate of vibration) of a sound, has, of course, no direct spatial higher or lower coordinate. Why we re- present frequency in this way, and have throughout history, as well as cross-culturally, is a matter of speculation. Be that as it may, pitch is conceived of and represented in spatial terms. And it is most destinctly a character- istic of music, to be shaped and controlled. It is often thought of as the chief incrediant of melody, although the other parameters of sound also contribute their share. Pitch is decidely the stuff of which intervals and scales are made, and since these in turn are primary organizing factors in most musics, knowledge of how pitch is notated is of help in understanding music. Pitch, being a vibratory rate and perceived on an up versus down axis, affects the human physiology in both clear and subtle ways. Extremes of pitch, high or low, produce tensions, both muscular and mental. Frequencies in the middle range of the audible spectrum, expecially within the speech range, are more soothing. These are generalities, of course, for other factors such as loudness and timbre also affect the mind and body. Subtle shadings of pitch, especially melodies employing microtones (East Indian music, for instance, or the Blues), produce very distinct reactions in us which can be felt bodily in changing breath rate and heart contractions, among other things. Every physical body resonates in response to sonic vibrations, hence pitch has very direct effect on material objects. The destructive uses to which sound has been put, described in the chapter on sound pollution, illustrate this. There is also, in occult literature, speculation that particular frequencies can be and have been used to produce levitation, and are capable of healing properties. However we approach the issue, pitch is an essential ingredient of music and knowledge of its notation crucial for our better comprehending how music works. The Staff Pitch is most commonly represented on some form of vertical axis. Generalized pitch level could be notated around a single line specified as a particular pitch. Or, as has occasionally been done as a reminder of pitch relationships learned by rote, with up or down gestures of the hand. The extension of this idea into the use of more lines to stand for other specific pitches, called a staff, is attributed to Guido d'Arezzo (c. 990-1050 AD), who suggested the use of a 3- or 4-line staff to denote specific pitches (the pitches we now call F2, A2, and C3). The four-line staff is still employed for the notation of Gregorian Chant, but as early as the 13th century, a 5-line staff was used to notate polyphonic ("many-voiced") music, and it is this staff which is in general use today. The convention in referring to pitch placement on the modern 5-line staff is to count from the bottom line or space upwards. Thus we say "note such and such" is on the 3rd line up, or the 2nds space up, etc. Pitch Names In our investigation of acoustics, we discovered that each doubling of frequency produces an octave. The term octave was used because the most common number of pitches employed in melodies in Western music within this doubling of frequencies has been 7,the 8th pitch being twice the frequency above or below some starting point--hence, octave. PRELIMINARY EXERCISE Hit "H" (to HEAR) to play "Doe A Deer" from The Sound of Music. Try to determine how many distinctly different pitches there are within the octave this tune encompasses. (You should be helped by association with the "do-re-mi" format)! Proceed to next page to see the tune written out. You will see notes on different lines and spaces adding up to the number you heard from lowest to highest. Careful observation of this tune should have lead you to hear and see 8 different notes, from an extra line below the staff to the third space up. These 8 notes, when arranged in sequential ascending order, produce what is called a scale (from the Latin scala, meaning "ladder"). The bottom note and the top note constitute the frequency ratio of 2:1, the octave. Each of the seven different pitches within the octave is designated by a letter name, from A to G. If a line or space on the staff is reserved for one of these pitches, the location of the other pitches can easily be de- termined by counting, in order, up or down (forward or back- ward) the letter names of the pitches. For instance, on the 4-line staff of the Gregorian Chant tune you heard a while ago, the stylized "C" at the top left of each staff desig- nates that line as what we know via the piano as "middle" C (261.6 hz). Counting, in order, down the lines and spaces, one arrives at the pitch F as the first note of the piece. The other notes can be determined accordingly. The Clefs Given a set of parallel horizontal lines on which to designate specific pitches, all that is necessary is to indicate a starting point: one line or space of the staff being a particular frequency. Music notation, evolving at the same time as different styles and genres of music, developed primarily to accomodate vocal music. It was reasonable then that the pitches the staff evolved to denote should essentially represent the human voice range. We will accept this tradition, even though instruments can sound frequencies well outside the range of the voice. The TREBLE CLEF was invented to represent the frequency range of female voices. Originally called the "G" clef, it marks where the pitch "G" within the SOPRANO and ALTO ranges is to be notated. This is on the second line up, using the stylized "G" symbol. This is, specifically, 392.2 hz. The BASS CLEF was designed to accomodate the lower voice ranges (tenor and bass). It originated as the "F" clef, which designates where F (174.6 Hz), is written. Originally, the Bass and Treble clefs were movable, so that their placement on the staff indicated slightly higher or lower ranges. Today, however, these clefs remain fixed. But there is a clef which is movable. It originated to designate a range between treble and bass, and is known as the "movable C' clef. It is used to locate "middle C." LEDGER LINES Notes outside the range of the five lines of the staff may be written with the use of ledger lines. The same order of notes is continued above or below the staff and the lines themselves are drawn with the same distance between them as on the staff itself. G A B C D E F G B C D E F G A B D C B A G F E D F E D C B A G F Notes several ledger lines above or below a staff exceed normal vocal ranges, but are useful for instruments whose ranges are greater. THE OTTAVA SIGN Sometimes, to avoid excessive and confusing addition of ledger lines, the ottava sign is employed, which shifts the entire range of the notes under the bracketed sign by an octave. If the sign is above the notes, the shift is obviously upward; if below the notes, and often accompanied by the word basso, the shift is down one octave. Previous convention called for the abbreviation of ottava as 8va. Mod- ern usage, however, accepts the numeral 8. In either case, the length of time the octave displacement is to occur must be indicated by the dotted lines. Occasionally, some instruments (the piano, for one) play in extreme high or low registers, which may call for so many ledger lines as not to be accomodated by even one octave's shift. A double octave shift may then be called for, the sign for which is the numeral 16. Use of ledger lines, the ottava sign, and the double ottava sign, is determined by common sense and custom. Flutists, for instance, are trained to read notes which extend by five ledger lines above the treble staff, while violinists, by training, are generally more comfortable reading these same notes under an ottava sign. In writing music for several instruments, use of these different procedures is often a matter of what is appropriate for the particular score format being used. If staves are too crowded together, with parts extending above and below, the ottava sign would be called for. THE GRAND STAFF Much music, including that for piano, is notated in a format known as the grand staff, which conjoins the treble and bass staves with middle C being the common link between them, one ledger line below the treble staff, and on ledger line above the bass staff. Specific Pitch Designation Often, it is necessary to distinguish a specific pitch in a speci- fic octave range. If you were asked, for instance, to notate "A" on a grand staff, you would have to know which of the several oc- tave displacements of "A" was meant. There are several systems for designating specific pitches. With the advent of digital synthe- sizers and especially the development of MIDI (Musical Instrument Digital Interface), one method seems to be emerging as a standard. It simply labels "Middle C" as C3 and every pitch within the octave up to the next "C" with this number. Thus the octaves from middle C to the highest note on the piano are labelled as follows: Beyond Basic Notes All of the pitches under discussion so far are known as "basic" notes. In the chapter on acoustics, we discussed the fact that in Western music the octave is normally divided into twelve equal parts. Our pitch notation system enables us to denote 7 of these, so far - the "basic" notes "A" to "G". Accidentals are used to indicate the additional 5 pitches on the 5-line staff. Each of the smallest increments between the twelve notes within an octave is known as a half-step. A sharp sign (#) increases the frequency of a basic note by a half-step: A flat sign (b) decreases the frequency of a basic note by a half- step: Accidentals apply to an entire measure in which they are found. The bar line "erases" the effect of an accidental unless the acci- dentalized note is tied over the bar-line, or, for clarity's sake, there has been an accidental just prior to the bar-line, whose effect is to be cancelled out in the new measure. To cancel the effect of a sharp or flat, a natural sign is used, which returns the note to its "basic" frequency ( ). Sometimes it is necessary to raise or lower a basic note by two half-steps, in which case a double sharp or double flat is used: