Scale
A collection of tones traversing the interval of the octave,
among which one tone is particularly stable.
[Example 1: Keyboard: play up and down major scale]
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A scale is a collection of tones traversing the interval of the octave, among which one tone is particularly stable. This stable tone, called the tonic, is like a "center of gravity" or "home base" for a scale, acting both as a point of departure and a place to return.
Listen again to the scale you heard at the beginning, and observe how the recurrences of the tonic, both when it repeats at the upper octave and when it returns to its point of origin, create a sense of completion and stability.
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A scale is composed of a series of "steps" which can vary both in number and in size. A step can be likened to a unit of measurement. Suppose we are given a line of a certain length. We can measure the line by inches, by centimeters, by cubits, or by any other unit of our choice. These units of measurement vary in size. Using the inch as a unit of measurement, we can traverse in six steps a distance that in centimeters would require 15 steps.
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The musical scale presents a similar case: the distance to be traversed is always that of an octave, but the unit of measurement can vary. Furthermore, just as a unit of measurement -- an inch, for example -- can be subdivided into a half, quarter, or eighth of an inch, in the same way a scale step can also be subdivided. We will therefore speak of the whole step (or whole tone), the half step (or semitone), the quarter step (or quarter tone), and so forth.
A scale is in itself an abstract structure, empty of all meaning or expression. It is simply a collection of pitches. A composer or performer will draw on this collection as a source or reservoir, in order to create melodies and harmonies that will express musical ideas. With the aid of simple diagrams for visual reference, the remainder of this entry will focus on how some commonly encountered scale patterns are put together. The basic unit of reference for the scales we will discuss is a step of a particular size, which we call the whole step, also known as the "whole tone".
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To see a simple way to derive the whole tone, click here and enter the Study Room |
The Whole-Tone scale
For our diagrams, the space of the octave will best be represented as a circle. This is because the sound of a scale reaching its upper octave gives the impression of "returning home" to a familiar tone. The starting point will be marked to the left of the circle; the scale pattern will then traverse the circle, returning to the starting point an octave higher.
Using the whole tone exclusively, we can work our way around the circle in six equal steps. (Move the cursor over the diagram to set it in motion).
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The octave traversed by six equal steps is a scale referred to as the whole-tone scale. Listen to what it sounds like:
[Ex.ample 3: Whole-Tone scale]
For further information, go to Whole-Tone Scale.
The Chromatic Scale
If we divide each of the six wedges of our diagram of the whole-tone scale in half, we will create what is known as the chromatic scale. (Pass the cursor over the diagram to activate).
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Listen to the sound of a whole step:
[Example 4 : Whole tone on piano]
Now listen to what it means in sound, to divide this whole step into two half steps (You will hear the whole tone repeated first):
[Example 5: (1) Whole step (eg. C-D); (2) Half steps (eg. C-C#-D)]
Here is a longer stretch of whole steps, followed by the same distance in half steps:
[Example 6: 1) C-D-E; (2)C-C#-D-D#-E]
And now listen to the entire scale. First, the whole-tone scale:
then the chromatic scale:
The chromatic scale, which amounts to the division of the octave into twelve equal parts, is of special significance in the Western musical system. It is even built into the structure of the piano, a typically Western instrument. You can play a chromatic scale on a piano simply by striking the white and black keys in succession from left to right (ascending) or right to left (descending).
For further information, go to Chromatic Scale
The Octatonic Scale
The twelve-part division of the octave can be used as a basis for inventing a great variety of scales. The octatonic scale is one that is frequently encountered in Western music of the late 19th and the 20th Centuries. It differs from the whole-tone and the chromatic scales in that it is made up of the alternation of two step sizes: the whole step and the half step. This pattern of alternation covers the octave in eight unequally sized steps, hence the name "octatonic." (Pass the cursor over the diagram to activate).
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Listen to what it sounds like:
[Example 9: Play scale: C# D E F G G# A# B C#]
This scale pattern has two versions. In the one we just heard, the pattern begins with a half step. But we can create an octatonic scale that begins with a whole step: (Pass the cursor over the diagram to activate)
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Fig
7: Octatonic Scale beginning with Whole Step --
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This is what the second version sounds like:
[Example 10: Play scale: C# D# E F# G A A# B# C#]
For further information go to Octatonic Scale.
The scales we have seen so far, the whole-tone, the chromatic, and the octatonic, have one characteristic in common: they are all symmetrical, that is, whatever pattern of steps is found in the first half of the scale is duplicated also in its second half.
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Scales that feature this kind of symmetry have an artificial quality, and are far more common in the music of the 20th Century, when composers began actively to search for structures that would enable them to draw out and explore new sonorities.
It is rather rare for music based on such scales to dwell on a single scale pattern for the length of an entire piece. Far more commonly, the music will move freely in and out of such scales, arranging the tones of the collections into melodies and harmonies that meet the expressive needs of the composer.
The most commonly used scales, however, are made of patterns which are not symmetrical, as we will see below.
If we think of symmetry as a kind of balancing of weight, so that whatever happens on one side is matched and equalized on the other, then we could think of a non-symmetrical structure as something that is weighted; something that can be made to draw more heavily in one direction than in another. In non-symmetrical scales, this unequal weight among the tones that make up the collection allows far more easily for one tone to be made to stand out from among the others as the tonic or stable tone.
The Pentatonic Scale
Pentatonic scales are by far the most frequently encountered scales in music all over the world. There is hardly a culture in the world whose folk music does not include some form of pentatonic scale.
The term pentatonic refers to a scale that divides the tonal space of the octave into five segments, usually of unequal size. The most common pentatonic scale is one made of a mixture of three whole-tone steps, and two larger steps comprised of a step and a half each. In a circular diagram this arrangement of the steps would look like this:
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The black keys of a piano are a far more familiar way to visualize this scale.
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Here is a two-octave stretch of the scale played on the piano.
[Ex.ample 11: play upwards and downwards (F# G# A# C# D# F# G# A# C# D# F#)]
Even in this neutral form, you can hear the very distinctive character of the scale.
For further information go to The Pentatonic Scale in Music Around the World: The Pentatonic Scale in Western Music
The Diatonic Scale
The term diatonic has come to us from ancient Greek music theoretical writings. The term can be loosely translated as: "proceeding mainly by whole tones." The diatonic scale is made up of seven tones. It comprises five whole, and two half steps arranged in a particular sequence. In order to visualize its makeup, we will begin with the pentatonic scale.
In a moment, you will see a whole step added after point p in the diagram below, and another whole step added after point s. Pass the cursor over the diagram now to see this.
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As you can see, there is no more room for whole steps. The distance between q and r is a half step, and the distance between t and n is also a half step. Now move the cursor over the diagram to see the pattern complete itself.
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It is this pattern, this sequence of whole and half steps, that is built into the white keys of the piano!
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Probably the most familiar form of the diatonic scale is the one that begins on the point r in our diagram, following the pattern of whole and half steps in a clockwise direction, in order as they appear.
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Because of its predominance in Western music, particularly of the 18th and 19th centuries, this form of the diatonic sequence has come to be called a scale in its own right. It is referred to as the major scale, and the starting point, point r, is the tonic.
Another scale based on the diatonic pattern of intervals, which has served as a counterpart to the major scale, is the succession of tones beginning on the letter p on our diagram. This is the basis of the minor scale, and here, the starting point p is the tonic.
The scale we just heard is frequently called the "natural minor" scale. There are two other forms of minor scale: the "harmonic minor" and the "melodic minor" scales, which will not be described here. (See Major and Minor Scales)
For further information go to Diatonic Scale, Major and Minor
Summary:
- A scale is a collection of tones traversing the interval of the octave.
- Among them, one tone, the tonic, is particularly stable.
- A scale is composed of a series of "steps" that can vary both in number and in size.
- In music, a scale is used as a collection of pitches with which to create melodies and harmonies.
- The whole-tone, chromatic, octatonic, pentatonic, and diatonic scales are examples of some commonly encountered pitch collections.
- The whole-tone scale traverses the octave in six equal whole steps.
- The chromatic scale traverses the octave in twelve equal half steps.
- The octatonic scale traverses the octave in eight unequal steps, alternating whole with half, or half with whole steps.
- The pentatonic scale traverses the octave in five unequal steps. In its most commonly encountered form, it comprises a sequence of two whole steps, one 1 1/2 step, one whole step, and another 1 1/2 step [1, 1, 1 1/2, 1, 1 1/2 ]. This scale pattern can be seen in the black notes of the piano keyboard.
- The diatonic scale is a seven note scale comprising a combination of five whole steps and two half steps, arranged in a particular order. This scale is built into the white notes of the piano keyboard, and is the basis for the major and the minor scales of Western music.
- The sequence of two whole steps, one half step, three whole steps, and one half step corresponds to the major scale.
[1, 1, 1/2, 1, 1, 1, 1/2 ]
- The same sequence of step sizes, read beginning from the sixth step of the major scale, corresponds to the natural minor scale.
[1, 1/2, 1, 1, 1/2, 1, 1]
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Visual & Sound Materials from the Gabe M. Wiener Music & Arts Library of Columbia University | |
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Scale written by:
Maryam Moshaver Recording & Mixing: Christopher Bailey |
Narration:
Annalisa Poirel Technology & Design: Maurice Matiz |