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Whole-tone scale

Whole-tone scale is a science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Whole-tone scale rather than just read about it. In short: In music, a whole-tone scale is a scale in which each note is separated from its neighbors by the interval of a whole tone. In twelve-tone equal temperament, there are only two complementary whole-tone scales, both six-note or hexatonic scales.

Key takeaways

  • Whole-tone scale belongs to science; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Whole-tone scale to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Whole-tone scale from memory before moving on to harder problems.

Reference excerpt

In music, a whole-tone scale is a scale in which each note is separated from its neighbors by the interval of a whole tone. In twelve-tone equal temperament, there are only two complementary whole-tone scales, both six-note or hexatonic scales. A single whole-tone scale can also be thought of as a "six-tone equal temperament".

The whole-tone scale has no leading tone and because all tones are the same distance apart, "no single tone stands out, [and] the scale creates a blurred, indistinct effect". This effect is especially emphasised by the fact that triads built on such scale tones are all augmented triads. Indeed, all six tones of a whole-tone scale can be played simply with two augmented triads whose roots are a major second apart. Since they are symmetrical, whole-tone scales do not give a strong impression of the tonic or tonality.

Only two triads are possible, both of them augmented, and...all inversions sound alike. All 'progressions' tend to have the same tonal character. What one hears are tone centers rather than tonics, and only when they are stressed [emphasized], as by repetition or duration. It cannot be denied that the small number of possible different intervals [only even semitone intervals: 2, 4, 6, 8, 10] and nonequivalent chords available in the whole-tone scale results in a soft-edged, neutral kind of sound lacking in tonal contrast.... Since the 1930s...whole-tone harmony...has become one of the platitudes of the "Hollywood Style." The composer Olivier Messiaen called the whole-tone scale his first mode of limited transposition. The composer and music theorist George Perle calls the whole-tone scale interval cycle 2, or C2. Since there are only two possible whole-tone-scale positions (that is, the whole-tone scale can be transposed only once), it is either C20 or C21. For this reason, the whole-tone scale is also maximally even and may be considered a generated collection. Due to this symmetry, the hexachord consisting of the whole-tone scale is not distinct under inversion or more than one transposition. Thus many composers have used one of the "almost whole-tone" hexachords, whose "individual structural differences can be seen to result only from a difference in the 'location', or placement, of a semitone within the otherwise whole-tone series." Alexander Scriabin's mystic chord is a primary example, being a whole-tone scale with one note raised a semitone; this alteration allows for a greater variety of resources through transposition.

Classical music

In 1662, Johann Rudolf Ahle wrote a melody to the lyrics of Franz Joachim Burmeister's "Es ist genug" (It is enough), beginning it with four notes of the whole-tone scale on the four syllables. Johann Sebastian Bach chose the chorale to end his cantata O Ewigkeit, du Donnerwort, BWV 60, set for four parts. The first four measures are shown below.

Mozart also used the scale in his Musical Joke, for strings and horns.

In the 19th century, Russian composers went further with melodic and harmonic possibilities of the scale, often to depict the ominous; examples include the endings of the overtures to Glinka's opera Ruslan and Lyudmila and Borodin's Prince Igor, and the Commander's theme in Dargomyzhsky's The Stone Guest. Further examples can be found in the works of Rimsky-Korsakov: the sea king's music in Sadko and also in Scheherazade. Shown below is the opening theme to Scheherazade, which is "simply a descending whole-tone scale with diatonic trimmings." Notes in the whole-tone scale are highlighted.

(For some short piano pieces written completely in whole-tone scale, see Nos. 1, 6, and 7 from V.A. Rebikov's Празднество (Une fête), Op. 38, from 1907.) H. C. Colles names as the "childhood of the whole-tone scale" the music of Berlioz and Schubert in France and Austria and then Russians Glinka and Dargomyzhsky. Claude Debussy, who had been influenced by Russians, along with other impressionist composers made extensive use of whole-tone scales. Voiles, the second piece in Debussy's first book of Préludes, is almost entirely within one whole-tone scale. The opening measures are shown below.

Janáček's use of the scale in the bracing opening to the second movement of his Sinfonietta is, to quote William W. Austin, "utterly different". Austin writes, "Janáček’s free chromaticism never loses touch with a diatonic scale for long. Though the whole-tone scale is prominent in much of his music after 1905 when he encountered Debussy, it serves simply to fit the motifs over augmented chords. The same motifs return from the whole-tone to the diatonic scale without emphasizing the contrast." The first measures of the second movement of Sinfonietta are shown below.

Giacomo Puccini used whole-tone scales as well as pentatonic scales in his 1904 opera Madama Butterfly to imitate east Asian music styles. The first of Alban Berg's Seven Early Songs opens with a whole-tone passage both in the orchestral accompaniment and in the vocal line that enters a bar later. Berg also quotes the Bach chorale setting referred to above in his Violin Concerto. The last four notes of the 12-tone row Berg used are B, C♯, E♭ and F, which, together with the first note, G, comprise five of the six notes of the scale.) Béla Bartók also uses whole-tone scales in his fifth string quartet. Ferruccio Busoni used the whole-tone scale in the right hand part of the "Preludietto, Fughetta ed Esercizio" of his An die Jugend, and Franz Liszt had used the technique as early as 1831, in the Grande Fantaisie sur La clochette.

… excerpt ends here. Continue reading the full article.

Worked examples

Example 1 — a first encounter with Whole-tone scale

Start with the simplest possible case. Write down what Whole-tone scale claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Whole-tone scale before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Whole-tone scale ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Whole-tone scale

In research
Whole-tone scale appears in science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Whole-tone scale in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Whole-tone scale is common in secondary-school and first-year university syllabi. It links to neighbouring topics Anhemitonic scales, Equal temperaments, Hexatonic scales, so understanding it makes those chapters shorter.
In everyday life
Look for Whole-tone scale outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.
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How to study Whole-tone scale in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Whole-tone scale means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Whole-tone scale out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Whole-tone scale in simple terms?

In music, a whole-tone scale is a scale in which each note is separated from its neighbors by the interval of a whole tone. In twelve-tone equal temperament, there are only two complementary whole-tone scales, both six-note or hexatonic scales.

Why does Whole-tone scale matter?

Because it connects several science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Whole-tone scale?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Whole-tone scale.

Tags

  • Anhemitonic scales
  • Equal temperaments
  • Hexatonic scales
  • Musical symmetry
  • Post-tonal music theory
  • Tritonic scales

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