Other Scales

A black and white photograph of a jazz combo performing. From left to right: Tommy Potter playing string bass, Charlie Parker playing alto saxophone, Miles Davis playing trumpet, and Duke Jordan playing piano. Max Roach, playing drum set, is behind Parker, with only part of his face visible in the photograph. The men are all wearing suits and ties. American performers and composers Charlie Parker, saxophone, and Miles Davis, trumpet, play at the 3 Deuces jazz club in New York City in 1947, accompanied by Tommy Potter on bass, Duke Jordan on piano and Max Roach on drums. Jazz musicians often use scales beyond major and minor when improvising solos.
(William P. Gottlieb/Ira and Leonore S. Gershwin Fund Collection, Music Division, Library of Congress)

Even when we limit ourselves to twelve-tone equal temperament, there are thousands of possible scales. Some are based upon traditional tunings of particular instruments within specific cultures, and others have widespread use across many different genres and eras.

Identifying Scales

The scale of a musical passage can be determined simply by collecting and organizing the notes being used. For a short passage, all notes played might be considered; for a longer passage, certain notes might be considered chromatic exceptions to the broader overall tonality.

Measures three through five of the first piano part of Three Fantastic Variations for Two Pianos on Lilliburlero, by Madeleine Dring, which features a low melodic passage, doubled in octaves. Below the excerpt the scale Dring uses in these measures is shown: C, C sharp, D, E, F, G, G sharp, A, B, C.
Figure 1: Three Fantastic Variations for Two Pianos by English composer Madeleine Dring. An excerpt of the Piano I part, and a diagram showing the enneatonic scale used in the passage.

While major and minor scales are all based around a specific tonal center, not all scales, or usages of scales in practice, center upon a specific tonic. Scales may also contain more than one inflection of a particular notes (a scale may contain both an A# and an A natural, for example).

Cardinality

A simple method of classifying scales is by how many notes they contain.

Number of pitches Name
2 ditonic
3 tritonic
4 tetratonic
5 pentatonic
6 hexatonic
7 heptatonic
8 octatonic
9 enneatonic
10 decatonic
11 hendecatonic
12 dodecatonic

The major and minor scales are heptatonic, because they contain seven different tones. Theorists generally do not think of collections of four or fewer notes as scales, but rather as intervals (ditonic) or chords (tritonic and tetratonic). The dodecatonic scale, which includes all twelve tones, is more commonly called the chromatic scale.

Transposibility

A scale's transposibility is determined by how many times it can be transposed to yield a different set of notes. A major scale, for example, has twelve transpositions, because starting the scale on every chromatic pitch will yield a different set of notes in the scale. Other scales, like the scale in Figure 2, might have fewer than twelve transpositions — the same set of notes might arise when starting on two or more different notes.

A scale with fewer than twelve transposition. The original eight-note scale is transposed up by half-step two times to create three different sets of notes. The fourth time it is transposed, it yields the same set of notes as the original, with a different note as tonic.
Figure 2: A scale with three possible transpositions. After moving up two half-steps, a subsequent transposition yields the same notes as the original scale.

French composer Olivier Messiaen cataloged several scales which have a transposibility of less than twelve, which he called "Modes of Limited Transposition," shown in Figure 3. He used many of these scales in his own compositions as a means of de-emphasizing a strong tonal center.

Messian's seven modes of limited transposition. Each mode is shown, starting on C, with text identifying each mode by number.
Figure 4: Olivier Messiaen's Modes of Limited Transposition. Each of these modes have fewer than 12 transpositions.

Common Scales

Using twelve-tone equal temperament, there are 2048 possible scales. While heptatonic scales like major and minor are ubiquitous in western music, there are other specific scales which have widespread use or which are common in specific styles and genres.

The Pentatonic Scale

Many types of pentatonic scales are possible, but a commonly used arrangement is one created by removing the fourth and seventh scale degrees from the major scale.

A scale consisting of C, D, E, G, and A.
Figure 5: The major pentatonic scale.

This scale, the major pentatonic scale, is anhemitonic, meaning that it lacks any half-steps. As a result, the scale is relatively free of dissonance. It is an extremely common scale across many different styles and cultures which use twelve-tone equal temperament.

German composer and pedagogue Carl Orff made use of this scale in his system for early childhood music education. In his curriculum, young students are given diatonic xylophones (commonly called Orff Instruments) with the F and B bars removed and given the opportunity to improvise freely. Because they are using the anhemitonic pentatonic scale, there are no unresolved half-steps, and all melodies sound consonant and pleasant.

A large assortment of instruments, including drums of various types, diatonic xylophones and metallophones of various sizes including three large single-bar xylophones, a set of maracas, a guiro, a cymbal and a psaltery.
Figure 7: A large assortment of instruments, many of which are designed specifically for use with Carl Orff's Schulwerk curriculum for early childhood education. Most mallet instruments here have easily removable bars which may be swapped out for chromatic alternates.
(Société Studio 49 | CC BY-SA 4.0)

Another common anhemitonic pentatonic scale, the minor pentatonic scale, can be created by removing the fourth and seventh scale degrees from the natural minor scale.

The Whole-Tone Scale

The whole-tone scale is a hexatonic scale containing only whole-tone intervals. Whole-tone scales feature a large amount of chromatic diversity, and can be effective in suspending traditional tonality.

A scale consisting of C, D, E, F sharp, G sharp, and A sharp.
Figure 8: The whole-tone scale.

The whole-tone scale has a very limited transposibility; there are only two variations of the scale.

The whole-tone scale starting on C and C sharp, showing it's two possible transpositions.
Figure 9: The two possible transpositions of the whole-tone scale.
Measures 1 through 4 of Stevie Wonder's `You Are the Sunshine of My Life, showing a repeated jazz chord for the first two measures and an ascending figure drawn from the whole-tone scale in the second two measures.
Figure 10: Measures 1–4 of American singer/songwriter Stevie Wonder's 1973 song You Are the Sunshine of My Life. The third and fourth measures of the introduction are drawn from the whole-tone scale.

Blues Scales

Jazz music tends to use a much greater chromatic diversity, both in pre-composed music and improvisations. Jazz often uses blues scales — chromatically rich scales that feature a higher degree of dissonance than traditional major or minor scales. A particular common blues scale consists of a minor pentatonic scale with an added #4.

A scale consisting of C, E flat, F, F sharp, G, and B flat.
Figure 11: The hexatonic blues scale.

In practice, blue scales are often played using blue notes — specific scale degrees which are played slightly higher or lower in pitch than their standard tunings.

A black and white photograph of Ma Rainey posing with her five-person band in front of a grand piano, with a drum set, saxophone, trumpet and trombone on the floor in front of them.
Figure 12: American singer/songwriter "Ma" Rainey posing with her band — Ed Pollack, Albert Wynn, Thomas A. Dorsey, Dave Nelson, and Gabriel Washington — in 1923. Rainey's original songs, like Prove It On Me Blues, made extensive use of blues scales.
(Image: Michael Ochs Archives | Public Domain; Audio: Columbia Records | Public Domain)

Other Tuning Systems

The scales listed in this chapter are all based in twelve-tone equal temperament, but of course other tuning systems present a gamut of new scale possibilities. These concepts are discussed separately in Microtonality.

Other Scales: Summary

  • Theorists can analyze music for scale by collecting and organizing the pitches used in that span of music.
    • Determining the scale of a short passage might include all the pitches used.
    • Determining the scale of a longer passage of music might include the most common notes used, acknowledging the presence of non-diatonic notes.
  • Some scales, like major and minor, have a clear tonic, but many scales do not.
  • A scale's cardinality indicates how many notes are in the scale.
    • Theorists generally focus on scales as containing five or more notes.
  • Some scales have limited transposibility, meaning that some transpositions of the scale will result in the same set of notes as the original.
    • Composer Olivier Messiaen cataloged the seven possible scales in the twelve-tone equal temperament system which have less than twelve transposition.
  • There are 2048 possible scales, but some are used much more commonly than others.
    • The major pentatonic scale is a very common across many cultures and styles.
      • This scale is anhemitonic, meaning that it contains no half-steps.
      • Because the scale lacks half-steps, it contains no unresolved dissonances, making it especially suitable for improvisation, especially among early learners.
    • The whole-tone scale is created using only whole-tones, and is an effective way of suspending tonality in a piece.
      • The whole-tone scale has only two possible transpositions.
    • Blues scales are chromatically rich and often include blue notes, which are scale degrees intended to be played slightly out of tune with the twelve-tone equal temperament system.

Exercises

Exercise 1: Analyzing Bela Bartók's Mikrokosmos, no. 136

Exercise 2: Analyzing Bela Bartók's Mikrokosmos, no. 101

Exercise 3: Analyzing Meshuggah's Do Not Look Down

Exercise 4: Writing a melody using a scale