Open the Textbook Activity called 1.1. The Keyboard. Click the mouse cursor on the piano key labeled C, and slide it to D. The difference in sound between those two is a whole step. Now play D, E. Another whole step. But what about E, F? Though the keys appear to be the same distance apart, the sound difference between E and F is a half step. Can you find the other white keys that are a half step apart?

Once you've familiarized yourself with the sounds of the half step and whole step, test your ability to tell the difference between them with Textbook Activity 1.2. Whole Step - Half Step.

Figure 1. Halfsteps among the white keys

Solmization (solfège)	2

Octaves and Pitch Class

You can see in figure 1 that the white keys of the piano create a pattern of seven letters, A through G, in alphabetical order. From any starting point, the pattern will begin again at the eighth note, which is an octave away from where you started (octo = eight). The octave of any note sounds like a higher or lower version of the same pitch, so we give it the same letter name. Musicians say notes that are octaves of each other, such as the Fs or the Gs, have the same pitch class. The keyboard's white keys really include only seven pitch classes, and all the others are octaves of those seven. This should make your task of learning music seem much easier: a piano may have fifty-two white keys, but they are just the same seven pitch classes repeated in different octaves. All our scales continue as far as the octave of their starting note and then they repeat. You could say that a scale is a pattern of steps for filling in the space of an octave.

	Select Practica Musica's Textbook Activity 1.1. The Keyboard again. Begin on any C and play the piano's white keys in ascending order. Can you hear the pattern begin again on the eighth note? Now listen to the sound of two notes that are an octave apart (notes with the same letter name). Can you hear the difference between notes that are octaves of each other and two notes with different letter names?
	The Textbook Activity 1.3. Octaves will test you on your ability to recognize the sound of octaves.

Solmization (solfège) The major scale consists of this pattern of whole and half steps: W, W, H, W, W, W, H. A good way to remember the major scale pattern is to practice singing it with the solmization syllables do, re, mi, fa, sol, la, ti, pronounced "dough, ray, mee, fah, soul, lah, tea" (sometimes si is used instead of ti).	Figure 2.
In the C major scale (the major scale that begins on C), do is C, re is D, mi is E, and so on. So the half steps E-F and B-C use the syllables mi-fa and ti-do. Since the word "scale" comes from the Latin word for "ladder " you could visualize the scale steps as unequal rungs on a ladder, as shown at right.

The Staff and its Clefs	3

Moveable Do and Fixed Do In this book the syllable do will always represent the first note of a major scale, a system that is called moveable do. So if we start a major scale on E then E would be called do. In France and Italy fixed do is traditional; in that system the note C is always called do, even if it is not the first note of the current scale. Each system has its advantages, but you'll find that the moveable do system makes it easier for you to sing the major scale starting on any pitch. Writing Pitches With Solmization Syllables Most popular melodies can be played on the white keys of the piano, since they usually consist of no more than the seven notes of a single major scale. That makes it possible to write the pitches of a melody just with letters or solmization syllables, like this:

The melody so far consists of five pitches: ti, do, re, mi, and fa in the major scale that starts on C. Very few well-known tunes include more than seven pitches, and many have less, so you could use letters or syllables as a type of music notation. Solmization syllables would be best, since they are the same for any starting note. However, writing this way is awkward, and it doesn't tell you the octave of the scale notes referred to, and it doesn't show the rhythm of the tune. Staff notation is both more graceful and more informative.

The Staff and its Clefs

Staff notation has evolved over the last thousand years to a form that is very efficient for tonal music. It is based on the idea of writing note symbols on a group of horizontal lines that represent the scale. The vertical position of a note identifies the pitch - a higher position means a higher pitch - and the shape of each note tells the rhythm. For now we'll use only one note shape, the whole note.

The whole note

The staff used today has five lines (originally it was just one and for a while it was four), and notes can be drawn either on a line or on the space between two lines. The lines and spaces refer to the same notes as the white keys of the keyboard, and a clef sign is placed at the beginning of the staff to indicate which lines are which.

Reading Pitches in the Common Clefs	4

The most common clefs are the G clef and the F clef, usually presented in the treble and bass positions. Clef comes from the French word for "key," and you can see that it does act as a key to understanding the staff notation: the G clef circles the line representing the G above "middle C" (the C that is midway between the two clefs) and the two dots of the F clef mark the line taken by the F below middle C. Often the treble and bass staves are used together in a combination known as the grand staff, as in figure 4.

Figure 4. The grand staff

Remember that the lines and spaces of the staff correspond to the white keys of the piano! If you move to the next line or space you move to the next white key and the next letter name, the sound of which can be either a whole step or a half step higher. For example, from the second line of a treble clef to its second space is the whole step G-A. But the distance from the third line to the third space is the half step B-C:

Figure 5. Whole step and half step

Reading Pitches in the Common Clefs
Students of music often use mnemonic devices to remember which staff notes are which in the bass and treble clefs. For example, "FACE" and "All Cows Eat Grass" remind you of the notes for the spaces in the treble and bass clefs. "Every Good Boat Does Float" can be used for the lines of the treble clef, and a similar device is illustrated at right for the lines of the bass clef. If you forget these mnemonics just remember that the treble clef circles G and the bass clef points to F, and that every line and space represents a letter in ascending alphabetical order from A through G. But the time will soon come when you recognize each pitch without thinking about it.
	Figure 6. Remembering the staff pitches

Ledger Lines	5

Launch the Textbook Activities 1.4. Reading Treble Clef and 1.5 Reading Bass Clef for practice in reading the notation of the pitches represented by the white keys of the piano. All you have to do in these exercises is to play the piano key that corresponds to each note in the staff. Rhythm and speed don't matter in this case; just find the notes. If you'd like more practice later, try the first level of Pitch Reading in the standard Practica Musica activities - that exercise rewards you for speed as well as for accuracy.

Ledger Lines What if you want to write a pitch that is higher or lower than the staff's five lines allow? You could change to a different clef (see below), but in most cases it is simpler to add a ledger line (sometimes spelled leger), which is an extension of the staff system. To write a note that is higher or lower than the limits of the staff you add more lines, but you make them short just a little wider than the note, like this:

Figure 7. Ledger lines

The first C below the treble clef staff is called "middle C" because it is between the treble and bass clefs, but middle C is also approximately in the center of a full-size piano. Middle C has one ledger line, whether it is written descending from the treble clef staff or ascending from the bass clef staff. Ledger lines provide a good way to extend the reach of the staff without making it much harder to read (the alternative would be to add more lines to the staff, which might confuse the eye). You'll find that notes written with several ledger lines quickly become familiar.

Writing Music by Hand	6

Notating a Melody in the Treble Clef Staff If we ignore rhythm, we can now put the melody of "My Country, 'tis of Thee" into staff notation. Listen to Practica Musica play the music in figure 8 (Textbook Activities, Examples, Chapter 1) and follow along as the corresponding piano keys highlight.

Figure 8. Notating pitches.

Writing Music by Hand Even though computers can do an excellent job of printing music there will be many times when you will need to be able to write it by hand. This skill is particularly useful if you happen to think of a nice musical idea at a time when all you have to work with is a paper and pencil. There's also a certain pleasure to be found in writing music by hand, which you can discover as you gain skill. Finally, writing musical exercises by hand is a good way to help you learn the material. Remember that everyone has an individual style of handwriting, and yet the symbols need to be easily recognizable by others. Your first efforts at writing should be made with great care to follow a model; later you can go more quickly and you'll find that your own style will develop naturally. You can practice on the staff paper at the end of this book (or if you're looking at this online you can print staff paper with Practica Musica), beginning with the treble and bass clefs.

	Figure 10. Handwriting by Bach, Mozart, and Beethoven.
Figure 9. Drawing the treble and bass clefs.

Origins of the Black Keys	7

The C Clef The C clef points to middle C, and can be placed on any of the five lines of the staff, reducing the need for ledger lines. In its alto position it is the traditional clef used in music for the viola. The tenor C clef is sometimes found in music for the cello, bassoon, or trombone. The soprano, mezzo, and baritone positions of the C clef are mostly of historical interest today. Here in figure 11 are all the C clefs, each followed by a whole note on middle C:

Figure 11. Various positions of the C clef.

The Octava G Clef The G clef can be drawn with an 8 below it to indicate that it is an octave lower than its normal treble position. This variation makes a convenient substitute for the alto or tenor C clefs, and is often used in their place in modern music. It covers almost the same range as the alto and tenor clefs, but can be easily read by anyone who knows the treble clef. In the illustration at right it is followed by a whole note on middle C:

Figure 12. Middle C in the octava G clef.

Origins of the Black Keys Early keyboards those made about the same time that solmization was invented had only white keys, since they were designed to play a limited pattern of scale steps that corresponds to the notes we use today for the C major scale. But if your keyboard has only white keys, what happens if you want to play the major scale starting on some note other than C? This would be called transposing the major scale pattern. If you have only the white keys to work with you'll run into trouble on the step between your third and fourth notes (A and B) it will make a whole step instead of the required half step. But you can fix your keyboard by adding another key whose pitch is midway between A and B. Then the major scale on F can be played as below:

Since the fourth note of the scale was going to be named B we will say that this lowered version is still a kind of B: it is "B flat," a B played a half step lower than its unaltered form. In fact, this was the first black key to be added to the keyboard, and that's how the flat symbol came to resemble a small "b": early composers wrote the
	Figure 13. Playing the F major scale.

Using Accidentals	8

higher form of B (the one on the white key) with square edges () and the lower form with rounded edges (). They called the higher form "hard" (B durum) while the lower one played on the black key was "soft" (B molle). You may recognize the "hard B" symbol as the precursor of the modern natural sign () which is now used to indicate a note played in its unaltered form, on the white keys. Another descendant of the former "hard B" sign is the sharp () which is used for notes that are raised a half step. Soon black keys were added to fill in every whole step on the keyboard; they allow you to play major or minor scales or melodies beginning on any note you choose. The black keys ended up grouped in threes and twos because the original white keyboard had half steps between E and F and between B and C a black key was unnecessary in those places. Using Accidentals The signs for the sharp and flat are placed before the note they affect, on the same line or space as the note head, and when placed this way are called accidentals, though of course they are actually put there on purpose. A sharp () before a note raises it a half step; a flat ( ) means to lower it by a half step. In most cases a sharp or flat will put you on a black key, but not always. Notice, for example, that a "C" will be played on the same key as B (since B is a half step lower than C). The natural sign () reminds you that a note is to be played in its natural form, on the white key that bears its name. There are times when you need to sharp a note that is already sharped, while keeping the same letter name, or to flat a note that is already flat. For those unusual cases we have the double sharp () and the double flat (), which raise and lower a note by two half steps.

Figure 14. Flatted or sharped notes are not always played on black keys.

Diatonic vs. Chromatic	9

Enharmonic Equivalents The names of the black keys vary according to how you're using them: the one between F and G, for example, might be called "F sharp"(F), an F raised one half step, or it might be called "G flat" (G), a G lowered one half step. In fact, any of the piano's keys can have different names.

Figure 15. Some enharmonic equivalents: F sharp and G flat, A sharp and B flat, E and F flat

How do you know which name to use for a note that can have several? It depends on the context of the melody and harmony. If you are playing a melody based on the major scale starting on D, the third note of the scale must be some kind of F. (Remember that scale steps follow the alphabet.) Since the third note needs to be played a half step higher than the natural F, we name it F. G would sound the same on a piano, but G doesn't belong in the D major scale, and using it would imply things that you probably don't intend. F and G are examples of enharmonic equivalents -- pitches that have different names but which are played on the same piano key. In theory, enharmonic equivalents are not exactly the same pitch, but for convenience we tune the piano so that the same key can play both. Diatonic vs. Chromatic You will sometimes need to know the difference between the diatonic half step and the chromatic half step. The diatonic half step is the one found in the major scale; it is always spelled with a change in letter name, such as E to F, or A to B. The chromatic half step is one in which the letter name stays the same, such as C to C, or B to B natural. Although C to C and C to D look like the same half step on the piano, the difference in spelling has different musical implications. See Chapter V, page 36 for more on the subject of enharmonic equivalents.

Reading the pitches gets harder now that a note can be altered by accidentals. This is the time to open the Textbook Activities folder again and choose 1.6. Reading Accidentals. When you hear a round of applause it means you understand the material so far and have graduated from the activity.

Summary, Chapter I	10

Summary, Chapter I 1. The two basic elements of music are pitch and rhythm. 2. The basic units of pitch are the half step and the whole step, patterns of which form our common scales, such as the major scale. 3. The major scale can be seen as a repeating pattern of whole (W) and half (H) steps: W W H W W W H. The piano's white keys C, D, E, F, G, A, B, C follow this pattern. 4. Notes with the same letter name are octaves of each other and have a similar sound. Such notes are said to have the same pitch class: all the Cs on the piano have the same pitch class, though they are different in octave. 5. The solmization syllables Do, Re, Mi, Fa, Sol, La, Ti are a traditional way of memorizing the sound of the major scale pattern. 6. Most well-known melodies are limited to the notes of a single scale, such as the major scale. 7. Pitches are notated on a five-line staff whose lines and spaces correspond to the major scale pattern, which also matches the white keys of the piano. 8. The clefs drawn on a staff tell which lines or spaces are which. The treble G clef circles the note G above middle C, the bass F clef marks the note F below middle C. 9. Ledger (or leger) lines are short extensions of the staff that are used to write notes that go above or below the range of the current clef. 10. The C clefs mark middle C; the most common C clefs are the alto C clef and the tenor C clef. 11. The octava G clef is a treble clef with an "8" below; it marks a G one octave lower than that of the treble clef, and makes a good substitute for the alto and tenor C clefs. 12. Sharps () and flats () are used to raise or lower the pitch of a note by one half step. A natural sign () means to play the note in its unaltered form, corresponding to a white key on the piano. Sharps and flats make it possible to play a given scale beginning on any note. 13. Sharps and flats are not necessarily black keys: for example, the piano key used to play B natural can also be called "C flat." 14. Enharmonic equivalents are pitches that have different names but are played on the same piano key. 15. A diatonic half step is one whose letter name changes, such as A to B. A chromatic half step repeats the same letter, as in A to A.

Table of Contents	End of Chapter I	Go to Chapter 2