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The Equivalent Representations of Pitch

Music consists of two main elements, pitch and time. When we hear two different sounds played on the guitar, we hear one of them as being "higher" or "lower" than the other. This property of sound, its apparent highness or lowness is called pitch. Both pitch and time (or rhythm) are equally important in the proper playing of music, but generally speaking, on the guitar, pitch is actually more difficult to master. This is due to the repeated notes and harmonics, timbre, non constant intervals between strings, etc., as discussed in the Introduction. We're not saying that rhythm isn't difficult on the guitar, simply, we believe that pitch needs extra dedication to fully master. We therefore begin our studies focused on pitch and study rhythm later.

In music theory, pitch is generally represented in four interchangeable ways: name, (such as "C Sharp"), notation, instrument location (for guitar, the fret), and most importantly, its SOUND. Generally, all four quantities are called "notes", and we will use the word note to signify any of the four quantities within this manual. (The next chapter will describe the music notation that we are about to present.)

The following figure illustrates the interchangeable equivalent representations of pitch:

(click in this figure to play the note)

Virtualoso Guitar readily displays these equivalent representations. After initializing, Virtualoso Guitar comes up in Explore Music mode. This mode consists of the Sheet Music, the Explore Music and the Virtualoso Guitar windows. When the mouse is moved into the Sheet Music window or the Virtualoso Guitar window, the equivalent pitch representation appears in all three windows (or you hear it!)

Notice that in these images:

Combined, the displayed name, notation, frets and the resulting sound are the equivalent representations of this pitch. This is an important concept to thoroughly understand. People that are able to rapidly interchange between these representations are looked upon as geniuses, when in fact, they have simply learned something that most other people are never taught.

Your ability to interchange between these equivalent representations of pitch, is a major step in mastering music theory.

This ability greatly simplifies the performance of music, since all you have to worry about is when and how long to play each note. There's no magic involved. Virtualoso Guitar drills you on these equivalence representations in many ways, so that the locations of the sounds on the guitar become second nature, and you can concentrate on other aspects of playing.

ACTIVITY: Observe the equivalent representations of pitch.

Start Virtualoso Guitar (even if you haven't registered yet), and move the mouse into the Sheet Music window.

By moving the mouse up and down on the Sheet Music window, you change the Pitch of the note. Now, move the mouse to the middle of the five lines of the staff. Looking at the Virtualoso Guitar window shows you all of the different places where this notes lies on the guitar.

By CAREFULLY moving the mouse left and right on the Sheet Music window (on the same line or space), you change the location of the note on the guitar (FOR THE SAME PITCH!). The other equivalent pitched notes are still shown lightly outlined.

Now Click and Hold the Mouse down. You will hear the note play, release the mouse when you want to stop hearing the note. Try DRAGGING the mouse (hold the mouse down and move), in the Sheet Music window, up and down changes the pitch and left and right change the location (and more subtly - the timbre or pitch quality). See if you can hear the difference!

You may also Shift-Click the Mouse, this "frets" the note. If you fret a note on the same string as one that is already fretted, the original note is deleted (on a guitar you can only ever play one note on a given string at a time). Fret some notes on different strings and click and hold down the mouse on the "Play All" button in the Explore Music window. All of the notes that are fretted will play at once as long as you hold the "Play All" button down.

Conversely, by moving the mouse around in the Virtualoso Guitar window, you can observe the equivalent representations of pitch in the Sheet Music and Explore Music mode windows as well.

Virtualoso Guitar also allows you to study natural harmonics. Natural harmonics are diamond shaped notes in the music notation, and we display them with diamond shapes in the Virtualoso Guitar window as well. You can only play natural harmonics at special places along the string. You play harmonics by lightly touching the string with your fretting hand, but not pressing it all the way down to the fretboard. Your plucking hand, picks or finger picks the notes as usual. Once the harmonic is played, you move your fretting hand away from the string so as not to dampen the sound.

ACTIVITY: Experiment with natural harmonics.

Click on the diamond shaped button in the Sheet Music window. Now you are displaying all equivalent natural harmonic notes! Keep in mind that the harmonics don't always lie directly over a fret!

Move the mouse around in either the Sheet Music or Virtualoso Guitar window.

Click and hold the mouse down, drag the mouse,
you're playing natural harmonics! You may have noticed that the Snap Chromatic button in the Sheet Music is now set. (This is due to the fact that if you are snapping to a Key Signature, you can "miss" some of the harmonics depending on what Key Signature you are playing in.)

The equivalent representations of this pitch are shown in all three windows.

Virtualoso Guitar allows you to move the mouse in the Sheet Music window as if you were constrained to a scale or constrained to a particular accidental. From the viewpoint of the guitar, a note at a certain fret can have multiple names in the sheet music window, but always has the same pitch. Notes of the same pitch with different names are known as enharmonic equivalents. For example, the pitch originally discussed in this chapter (C sharp) is also known as D flat.

ACTIVITY: Experiment with "Snap"

When you change the input mode back to "Fundamentals", (the round note button in the Sheet Music window), you're still in "Snap Chromatic", now move the mouse up and down in the sheet music and you'll see accidentals. You are actually snapping (or constraining) the mouse to the 12 note chromatic scale. You'll learn about accidentals and scales in later chapters.

Watch the fretboard of the guitar as you move the mouse up and down in the Sheet Music window, you'll notice that you move one fret at a time! (Although you may jump strings).

Now click on "Snap Key Signature" and notice that when you move up and down in the Sheet Music, sometimes you move 2 frets at a time on the fretboard. You're actually observing that the scale associated with a key signature contains steps of different sizes!

You are Exploring Music and the equivalent representations of pitch!

The only way to master these concepts is through continued practice, so that you can understand the general concept and apply it to create any pitch desired on the guitar. You will learn the pitches on the guitar with the "Learn Notes", "Learn Harmonics" and "Perfect Pitch" modes that are described later in this manual.

A brief note on acoustics

Before we begin studying the notation of music, we must take a step back and discuss acoustics briefly. Sound itself is a sensory perception caused when vibrating air hits your eardrum. Musical instruments create vibrations in the air, causing us to perceive sound. The frequency (in Hertz) of the sound is simply the number of vibrations per second of the sound wave. A high pitched sound has a larger frequency than a low pitched sound. Instruments produce sound with a fundamental frequency, however, for a given pitched note, the sound usually contains higher pitched "overtones" that give each instrument its individual personality. In short, it is why a guitar does not sound like a trumpet.

For stringed instruments such as the guitar, the shorter the length of the vibrating string, the higher the pitch. Also, the light strings vibrate faster than the heavy strings for a given length, giving them a higher pitch.

Western civilization developed the main musical system that is in use today. It is based upon these "overtones". It turns out that by doubling, tripling, etc., the frequency of the note produced, you eventually wind up with a group of 12 notes that are useful in creating harmony. This system took hundreds of years to produce and consists of various tradeoffs which temper the actual note frequencies to be fairly close to the overtones. Keeping the relative frequency ratio between the notes a constant, allows us to modulate between different keys, or in other words, use each of the 12 notes as the main note, or tonic note. (Each note is about 6 percent higher in frequency than the next lower note). This tuning system is known as Equal Temperament.

A note that has twice the frequency of another note is said to be an octave higher. The 12 notes can be played in steps that lead to a note that is an octave higher. These steps are called semitones or half steps. Notes that differ by an octave sound remarkably similar. This allows us to name each of the 12 notes uniquely, regardless of octave, meaning that notes that differ by an octave or multiple octaves share the same name.

Now that you have a basic idea behind the theory of sound and the equivalent representations of pitch, you are ready to study the elements of music notation.

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