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Pitch

Pitch

“Pitch” refers to the perceived frequency of a sound, determining whether it is heard as high or low. It is a fundamental aspect of music, speech, and the auditory experiences of sounds in our environment. In music, pitch is associated with musical notes, and the relationships between these notes create melodies and harmonies that evoke emotion and meaning. The ability of humans and many animals to discern different pitches is crucial for communication, navigation, and enjoying auditory experiences.

 

 

1.1 Pitch

1.1.1 The Sta

People were talking long before they invented writing. People were also making music long before anyone wrote any music down. Some musicians still play “by ear” (without written music), and some music traditions rely more on improvisation and/or “by ear” learning. But written music is very useful, for many of the same reasons that written words are useful. Music is easier to study and share if it is written down. Western music (Section 2.8) specializes in long, complex pieces for large groups of musicians singing or playing parts exactly as a composer intended. Without written music, this would be too di cult. Many di erent types of music notation have been invented, and some, such as tablature[1], are still in use. By far the most widespread way to write music, however, is on a sta . In fact, this type of written music is so ubiquitous that it is called common notation.

[1] “Reading Guitar Tablature” <http://cnx.org/content/m11905/latest/>

Available for free at Connexions <http://cnx.org/content/col10363/1.3>

1.1.1.1 The Sta

The sta (plural staves) is written as ve horizontal parallel lines. Most of the notes (Section 1.2.1) of the music are placed on one of these lines or in a space in between lines. Extra ledger lines may be added to show a note that is too high or too low to be on the sta . Vertical bar lines divide the sta into short sections called measures or bars. A double bar line, either heavy or light, is used to mark the ends of larger sections of music, including the very end of a piece, which is marked by a heavy double bar.

Figure 1.1: The ve horizontal lines are the lines of the sta . In between the lines are the spaces. If a note is above or below the sta , ledger lines are added to show how far above or below. Shorter vertical lines are bar lines. The most important symbols on the sta , the clef symbol, key signature and time signature, appear at the beginning of the sta

 

Many di erent kinds of symbols can appear on, above, and below the sta . The notes (Section 1.2.1) and rests (Section 1.2.2) are the actual written music. A note stands for a sound; a rest stands for a silence. Other symbols on the sta , like the clef (Section 1.1.2) symbol, the key signature (Section 1.1.4), and the time signature (Section 1.2.3), tell you important information about the notes and measures. Symbols that appear above and below the music may tell you how fast it goes (tempo (Section 1.2.8) markings), how loud it should be (dynamic (Section 1.3.1) markings), where to go next (repeats (Section 1.2.9), for example) and even give directions for how to perform particular notes (accents (p. 56), for example).

Figure 1.2: The bar lines divide the sta into short sections called bars or measures. The notes (sounds) and rests (silences) are the written music. Many other symbols may appear on, above, or below the sta , giving directions for how to play the music.

1.1.1.2 Systems of staves

The sta is read from left to right. Sta s (some musicians prefer the plural staves) are read, beginning at the top of the page, one sta at a time unless they are connected. If staves should be played at the same time (by the same person or by di erent people), they will be connected by a long vertical line at the left hand side, to create a system. They may also be connected by their bar lines. Staves played by similar instruments or voices, or staves that should be played by the same person (for example, the right hand and left hand of a piano part) may be grouped together by braces or brackets at the beginning of each line.

Figure 1.3: (b) When many staves are to be played at the same time, as in this orchestral score, the lines for similar instruments – all the violins, for example, or all the strings – may be marked with braces or brackets.

1.1.2 Clef

1.1.2.1 Treble Clef and Bass Clef

The rst symbol that appears at the beginning of every music sta (Section 1.1.1) is a clef symbol. It is very important because it tells you which note (Section 1.2.1) (A, B, C, D, E, F, or G) is found on each line or space. For example, a treble clef symbol tells you that the second line from the bottom (the line that the symbol curls around) is “G”. On any sta , the notes are always arranged so that the next letter is always on the next higher line or space. The last note letter, G, is always followed by another A.

A bass clef symbol tells you that the second line from the top (the one bracketed by the symbol’s dots) is F. The notes are still arranged in ascending order, but they are all in di erent places than they were in treble clef.

1.1.2.2 Memorizing the Notes in Bass and Treble Clef

One of the             rst steps in learning to read music in a particular clef is memorizing where the notes are. Many students prefer to memorize the notes and spaces separately. Here are some of the most popular mnemonics used.

Figure 1.6: You can use a word or silly sentence to help you memorize which notes belong on the lines or spaces of a clef. If you don’t like these ones, you can make up your own.

 

1.1.2.3 Moveable Clefs

Most music these days is written in either bass clef or treble clef, but some music is written in a C clef. The C clef is moveable: whatever line it centers on is a middle C (p. 114).

Figure 1.7: All of the notes on this sta are middle C.

The bass and treble clefs were also once moveable, but it is now very rare to see them anywhere but in their standard positions. If you do see a treble or bass clef symbol in an unusual place, remember: treble clef is a G clef; its spiral curls around a G. Bass clef is an F clef; its two dots center around an F.

Figure 1.8: It is rare these days to see the G and F clefs in these nonstandard positions.

Much more common is the use of a treble clef that is meant to be read one octave below the written pitch. Since many people are uncomfortable reading bass clef, someone writing music that is meant to sound in the region of the bass clef may decide to write it in the treble clef so that it is easy to read. A very small “8” at the bottom of the treble clef symbol means that the notes should sound one octave lower than they are written.

Figure 1.9: A small “8” at the bottom of a treble clef means that the notes should sound one octave lower than written.

1.1.2.4 Why use di erent clefs?

Music is easier to read and write if most of the notes fall on the sta         and few ledger lines (p. 3) have to be used.

Figure 1.10: These scores show the same notes written in treble and in bass clef. The sta    with fewer ledger lines is easier to read and write.

The G indicated by the treble clef is the G above middle C (p. 114), while the F indicated by the bass clef is the F below middle C. (C clef indicates middle C.) So treble clef and bass clef together cover many of the notes that are in the range (Section 2.7) of human voices and of most instruments. Voices and instruments with higher ranges usually learn to read treble clef, while voices and instruments with lower ranges usually learn to read bass clef. Instruments with ranges that do not fall comfortably into either bass or treble clef may use a C clef or may be transposing instruments[1].

[1] “Transposing Instruments” <http://cnx.org/content/m10672/latest/>

1.11: Figure Middle C is above the bass clef and below the treble clef; so together these two clefs cover much of the range of most voices and instruments.

Exercise 1.1.2.1                                                                                                                           (Solution on p. 62.)

Write the name of each note below the note on each sta         in Figure 1.12.

Figure 1.12

Exercise 1.1.2.2                                                                                                                                       (Solution on p. 62.)

Choose a clef in which you need to practice recognizing notes above and below the sta in Figure 1.13. Write the clef sign at the beginning of the sta , and then write the correct note names below each note.

Exercise 1.1.2.3                                                                                                                                       (Solution on p. 63.)

Figure 1.14 gives more exercises to help you memorize whichever clef you are learning. You may print these exercises as a PDF worksheet[1] if you like.

[1] 5See the          le at <http://cnx.org/content/m10941/latest/ClefWorksheet.pdf>

1.1.3 Pitch: Sharp, Flat, and Natural Notes

The pitch of a note is how high or low it sounds. Pitch depends on the frequency (Section 3.1.4: Wavelength, Frequency, and Pitch) of the fundamental7 sound wave of the note. The higher the frequency of a sound wave, and the shorter its wavelength (Section 3.1.4: Wavelength, Frequency, and Pitch), the higher its pitch sounds. But

musicians usually don’t want to talk about wavelengths and frequencies. Instead, they just give the di erent pitches di erent letter names: A, B, C, D, E, F, and G. These seven letters name all the natural notes (on a keyboard, that’s all the white keys) within one octave. (When you get to the eighth natural note, you start the next octave (Section 4.1) on another A.)

Figure 1.15: The natural notes name the white keys on a keyboard.

But in Western (Section 2.8) music there are twelve notes in each octave that are in common use. How do you name the other ve notes (on a keyboard, the black keys)?

Figure 1.16: Sharp, at, and natural signs can appear either in the key signature (Section 1.1.4), or right in front of the note that they change.

A sharp sign means “the note that is one half step (Section 4.2) higher than the natural note”. A at sign means “the note that is one half step lower than the natural note”. Some of the natural notes are only one half step apart, but most of them are a whole step (Section 4.2) apart. When they are a whole step apart, the note in between them can only be named using a at or a sharp.

Notice that, using ats and sharps, any pitch can be given more than one note name. For example, the G sharp and the A at are played on the same key on the keyboard; they sound the same. You can also name and write the F natural as “E sharp”; F natural is the note that is a half step higher than E natural, which is the de nition of E sharp. Notes that have di erent names but sound the same are called enharmonic

(Section 1.1.5) notes.

Sharp and at signs can be used in two ways: they can be part of a key signature (Section 1.1.4), or they can mark accidentals. For example, if most of the C’s in a piece of music are going to be sharp, then a sharp sign is put in the “C” space at the beginning of the sta (Section 1.1.1), in the key signature. If only a few of the C’s are going to be sharp, then those C’s are marked individually with a sharp sign right in front of them. Pitches that are not in the key signature are called accidentals.

A note can also be double sharp or double at. A double sharp is two half steps (one whole step) higher than the natural note; a double at is two half steps (a whole step) lower. Triple, quadruple, etc. sharps and ats are rare, but follow the same pattern: every sharp or at raises or lowers the pitch one more half step.

Using double or triple sharps or ats may seem to be making things more di cult than they need to be. Why not call the note “A natural” instead of “G double sharp”? The answer is that, although A natural and G double sharp are the same pitch, they don’t have the same function within a particular chord or a particular key. For musicians who understand some music theory (and that includes most performers, not just composers and music teachers), calling a note “G double sharp” gives important and useful information about how that note functions in the chord (Chords, p. 80) and in the progression of the harmony (Section 5.5).

Figure 1.20: Double sharps raise the pitch by two half steps (one whole step). Double ats lower the pitch by two half steps (one whole step).

 

1.1.4 Key Signature

The key signature appears right after the clef (Section 1.1.2) symbol on the sta (Section 1.1.1). In common notation, clef and key signature are the only symbols that normally appear on every sta . They appear so often because they are such important symbols; they tell you what note is found on each line and space of the sta . This can change from one piece of music to another, so the musician must know the clef and key signature in order to read the music correctly; in a way, the written music is a coded message, with each note standing for a sound with a particular pitch (Section 1.1.3), and the clef and key signature are the key that tell you how to decode this particular message. (For an explanation of why things are done this way, please see how to read music.)

The clef tells you the letter name of the note – for example, the top line on a bass clef sta is always some kind of A; but you need the key signature to tell you what kind of A. It may have either some sharp (Section 1.1.3) symbols on particular lines or spaces, or some at (Section 1.1.3) symbols, again on particular lines or spaces. If there are no ats or sharps listed after the clef symbol, then the key signature is “all notes are natural”.

The key signature is a list of all the sharps and ats in the key (Section 4.3) that the music is in. When a sharp (or at) appears on a line or space in the key signature, all the notes on that line or space are sharp (or at), and all other notes with the same letter names in other octaves are also sharp (or at).

Figure 1.22: This key signature has a     at on the “B” line, so all of these B’s are              at.

The sharps or ats always appear in the same order in all key signatures. This is the same order in which they are added as keys get sharper or atter. For example, if a key (G major or E minor) has only one sharp, it will be F sharp, so F sharp is always the rst sharp listed in a sharp key signature. The keys that have two sharps (D major and B minor) have F sharp and C sharp, so C sharp is always the second sharp in a key signature, and so on. The order of sharps is: F sharp, C sharp, G sharp, D sharp, A sharp, E sharp, B sharp. The order of ats is the reverse of the order of sharps: B at, E at, A at, D at, G at, C at, F at. So the keys with only one at (F major and D minor) have a B at; the keys with two ats (B at major and G minor) have B at and E at; and so on. The order of ats and sharps, like the order of the keys themselves, follows a circle of fths (Section 4.7).

If you do not know the name of the key of a piece of music, the key signature can help you nd out. Assume for a moment that you are in a major key (Section 4.3). If the key contains sharps, the name of the key is one half step (Section 4.2) higher than the last sharp in the key signature. If the key contains ats, the name of the key signature is the name of the second-to-last at in the key signature.

Example 1.1

Figure 1.24 demonstrates quick ways to name the (major) key simply by looking at the key signature. In at keys, the second-to-last at names the key. In sharp keys, the note that names the key is one half step above the nal sharp.

The only major keys that these rules do not work for are C major (no ats or sharps) and F major (one at). It is easiest just to memorize the key signatures for these two very common keys. If you want a rule that also works for the key of F major, remember that the second-to-last       at is always a perfect fourth (p. 133) higher than (or a perfect  fth lower than) the              nal           at. So you can also say that the name of the key

If the music is in a minor key, it will be in the relative minor (Section 4.4.3: Relative Minor and Major Keys) of the major key for that key signature. You may be able to tell just from listening (see Major Keys and Scales (Section 4.3)) whether the music is in a major or minor key. If not, the best clue is to look at the nal chord (Chords, p. 80). That chord (and often the nal note of the melody, also) will usually name the key.

Exercise 1.1.4.1                                                                                                                           (Solution on p. 65.)

Write the key signatures asked for in Figure 1.26 and name the major keys that they represent.

 

1.1.5 Enharmonic Spelling

1.1.5.1 Enharmonic Notes

In common notation (Section 1.1.1), any note can be sharp, at, or natural (Section 1.1.3). A sharp symbol raises the pitch (Section 1.1.3) (of a natural note) by one half step (Section 4.2); a at symbol lowers it by one half step.

This content is available online at <http://cnx.org/content/m11641/1.14/>.

 

Why do we bother with these symbols? There are twelve pitches available within any octave (Section 4.1). We could give each of those twelve pitches its own name (A, B, C, D, E, F, G, H, I, J, K, and L) and its own line or space on a sta . But that would actually be fairly ine cient, because most music is in a particular key (Section 4.3). And music that is in a major (Section 4.3) or minor (Section 4.4) key will tend to use only seven of those twelve notes. So music is easier to read if it has only lines, spaces, and notes for the seven pitches it is (mostly) going to use, plus a way to write the occasional notes that are not in the key.

This is basically what common notation does. There are only seven note names (A, B, C, D, E, F, G), and each line or space on a sta (Section 1.1.1) will correspond with one of those note names. To get all twelve pitches using only the seven note names, we allow any of these notes to be sharp, at, or natural. Look (Figure 1.28) at the notes on a keyboard.

Figure 1.28: Seven of the twelve possible notes in each octave (Section 4.1) are “natural” notes.

Because most of the natural notes are two half steps apart, there are plenty of pitches that you can only get by naming them with either a at or a sharp (on the keyboard, the “black key” notes). For example, the note in between D natural and E natural can be named either D sharp or E at. These two names look very di erent on the sta , but they are going to sound exactly the same, since you play both of them by pressing the same black key on the piano.

Figure 1.29: D sharp and E at look very di erent when written in common notation, but they sound exactly the same when played on a piano.

This is an example of enharmonic spelling. Two notes are enharmonic if they sound the same on a piano but are named and written di erently.

Exercise 1.1.5.1                                                                                                                           (Solution on p. 66.)

Name the other enharmonic notes that are listed above the black keys on the keyboard in Figure 1.28. Write them on a treble clef sta . If you need sta paper, you can print out this PDF le[1]

But these are not the only possible enharmonic notes. Any note can be at or sharp, so you can have, for example, an E sharp. Looking at the keyboard (Figure 1.28) and remembering that the de nition of sharp is “one half step higher than natural”, you can see that an E sharp must sound the same as an F natural. Why would you choose to call the

note E sharp instead of F natural? Even though they sound the same, E sharp and F natural, as they are actually used in music, are di erent notes. (They may, in some circumstances, also sound di erent; see below (Section 1.1.5.4: Enharmonic Spellings and Equal Temperament).) Not only will they look di erent when written on a sta , but they will have di erent functions within a key and di erent relationships with the other notes of a piece of music. So a composer may very well prefer to write an E sharp, because that makes the note’s place in the harmonies of a piece more clear to the performer. (Please see Triads (Section 5.1), Beyond Triads (Section 5.4), and Harmonic Analysis (Section 5.5) for more on how individual notes t into chords and harmonic progressions.)

In fact, this need (to make each note’s place in the harmony very clear) is so important that double sharps and double ats have been invented to help do it. A double sharp is two half steps (one whole step (Section 4.2)) higher than the natural note. A double at is two half steps lower than the natural note.

Exercise 1.1.5.2                                                                                                                                       (Solution on p. 66.)

Give at least one enharmonic spelling for the following notes. Try to give more than one. (Look at the keyboard (Figure 1.28) again if you need to.)

  1. E natural
  2. B natural
  3. C natural
  4. G natural
  5. A natural

1.1.5.2 Enharmonic Keys and Scales

Keys and scales can also be enharmonic. Major keys, for example, always follow the same pattern of half steps and whole steps. (See Major Keys and Scales (Section 4.3). Minor keys also all follow the same pattern, di erent from the major scale pattern; see Minor Keys (Section 4.4).) So whether you start a major scale on an E at, or start it on a D sharp, you will be following the same pattern, playing the same piano keys as you go up the scale. But the notes of the two scales will have di erent names, the scales will look very di erent when written, and musicians may think of them as being di erent. For example, most instrumentalists would nd it easier to play in E at than in D sharp. In some cases, an E at major scale may even sound slightly di erent from a D sharp major scale. (See below (Section 1.1.5.4: Enharmonic Spellings and Equal Temperament).)

Figure 1.31: The E at major and D sharp major scales sound the same on the piano, although they look very di erent. If this surprises you, look again at the piano keyboard (Figure 1.28) and nd the notes that you would play for each scale.

Since the scales are the same, D sharp major and E at major are also enharmonic keys. Again, their key signatures will look very di erent, but music in D sharp will not be any higher or lower than music in E at.

Figure 1.32: The key signatures for E          at and D sharp look very di erent, but would sound the same on a keyboard.

Exercise 1.1.5.3                                                                                                                                       (Solution on p. 66.)

Give an enharmonic name and key signature for the keys given in Figure 1.33. (If you are not well-versed in key signatures (Section 1.1.4) yet, pick the easiest enharmonic spelling for the key name, and the easiest enharmonic spelling for every note in the key signature. Writing out the scales may help, too.)

1.1.5.3 Enharmonic Intervals and Chords

Chords (Chords, p. 80) and intervals (Section 4.5) also can have enharmonic spellings. Again, it is important to name a chord or interval as it has been spelled, in order to understand how it ts into the rest of the music. A C sharp major chord means something di erent in the key of D than a D at major chord does. And an interval of a diminished fourth means something di erent than an interval of a major third, even though they would be played using the same keys on a piano. (For practice naming intervals, see Interval (Section 4.5). For practice naming chords, see Naming Triads (Section 5.2) and Beyond Triads (Section 5.4).

For an introduction to how chords function in a harmony, see Beginning Harmonic Analysis (Section 5.5).)

 

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