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Octaves and the Major-Minor Tonal System

Module by: Catherine Schmidt-Jones. E-mail the author

Summary: Introduces the relationship between frequency, octaves, major, minor, and chromatic scales, and tonal music.

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Where Octaves Come From

Musical notes, like all other sounds, are made of sound waves. A note can be high or low or very low, or anywhere in the range of what people can hear. When scientists and engineers talk about how high or low a sound is, they talk about its frequency. The higher the frequency of a note, the higher it sounds. They can measure the frequency of notes, and like most measurements, these will be numbers, like "440 vibrations per second."

Figure 1: A sound that has a shorter wavelength has a higher frequency and a higher pitch.
High and Low Frequencies
High and Low Frequencies (octaves1a.gif)

But people have been making music and talking about music since long before we knew that sounds were waves with frequencies. So when a musician talks about how high or low a note sounds, they usually don't talk about frequency; they talk about the note's pitch. And instead of numbers, they give the notes names, like "C".

But to see where octaves come from, let's talk about frequencies a little more. Imagine a few men are singing a song together. Nobody is singing harmony; they are all singing the same pitch - the same frequency - for each note.

Now some women join in the song. They can't sing where the men are singing; that's too low for their voices. Instead they sing notes that are exactly double the frequency that the men are singing. That means their note has exactly two waves for each one wave that the men's note has. These two frequencies fit so well together that it sounds like the women are singing the same notes as the men, in the same key. They are just singing them one octave higher. Any note that is twice the frequency of another note is one octave higher.

Notes that are one octave apart are so closely related to each other that musicians give them the same name.(For more discussion of how notes are related because of their frequencies, see Sound, Physics, and Music and The Harmonic Series.) A note that is an octave higher or lower than a note named "C" will also be named "C".

Figure 2: When two notes are one octave apart, one has a frequency exactly two times higher than the other - it has twice as many waves. These waves fit together so well, in the instrument, and in the air, and in your ears, that they sound almost like different versions of the same note.
Octave Frequencies
Octave Frequencies (octaves1b.gif)

Naming Octaves

The notes in different octaves are so closely related that when musicians talk about a note, a "G" for example, it often doesn't matter which G they are talking about. We can talk about the "F sharp" in a G major scale without mentioning which octave the scale or the F sharp are in, because the scale is the same in every octave. Because of this, many discussions of music theory don't bother naming octaves.

But sometimes it does matter, so the different octaves do have names. Figure 3 shows the names of the octaves most commonly used in music. (Lower octaves are named "CCC" or "C2" and so on; higher are named "four-line c" and so on.) Octaves are named from one C to the next higher C. For example, all the notes between "great C" and "small C" are "great". One-line c is also often called "middle C". No other notes are called "middle", only the C.

Figure 3: The octaves are named from one C to the next. For example, all the notes in between "one line c" and "two line c" are "one line" notes.
Naming Octaves
Naming Octaves (octaves2a.gif)

Example 1

Figure 4
Figure 4 (octavesexample1.gif)

Exercise 1

Give the correct octave name for each note.

Figure 5
Figure 5 (probfig2a.gif)

Solution

Figure 6
Figure 6 (solufig2a.gif)

Dividing the Octave into Scales

The word "octave" comes from the Latin root meaning "eight". It seems an odd name for a frequency that is two times, not eight times, higher. But that is because it is musicians, not scientists, who named it. Octaves aren't the only notes that sound good together. The people in different musical traditions have different ideas about what notes they think sound best together. In the Western musical tradition - that is, most familiar music from Europe and the Americas - the octave is divided up into twelve equally spaced notes. If you play all twelve of these notes in one octave, say from one C to the next C, you are playing a chromatic scale. Other musical traditions, Chinese music for example, have divided the octave differently and so they use different scales.

You may be thinking "OK, that's twelve notes; that still has nothing to do with the number eight", but out of those twelve notes, only eight are used in any particular major or minor scale. These are the diatonic scales, and they are the basis of most of the music we listen to.

Take a look at the piano keyboard. Only seven letter names are used to name notes: A, B, C, D, E, F, and G. (The eighth note in an octave would, of course, be the next A.) To name the other notes, the notes on the black piano keys, you have to use a "sharp" or "flat" sign.

Figure 7: The white keys are the natural notes. Black keys can only be named using sharps or flats. The pattern repeats at the eighth tone of a scale, the octave.
Keyboard
Keyboard (octaves3a.gif)

Whether it is a popular song, a classical symphony, or an old folk tune, most of the music that feels comfortable and familiar (to Western listeners) is based on either a major or minor scale. It is tonal music that mostly uses only eight of the notes in an octave: only one of the possible A's (A sharp, A natural, or A flat), one of the possible B's (B sharp, B natural, or B flat), and so on. The other notes in the chromatic scale are (usually) used sparingly to add interest or to (temporarily) change the key in the middle of the music. For more on the keys and scales that are the basis of diatonic music, see Major Keys and Scales and Minor Keys and Scales.

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