A Survey of Music Theory for the College Classroom: Chromatic Harmony 2 and 20th Century Music

Harmony in the 20th Century

Pitch/Tonal Centers

It is common for 20th and 21st century music to be based on a central tone but to otherwise avoid the harmonic functions found in traditional tonality. Music that has a tonal center but that lacks traditional harmonic functions is called pitch-centric. Pitch-centric music may utilize a variety of scales as well as tertian and nontertian sonorities. Methods for establishing a pitch center include the following:

  • First and Last – the pitch center is used as the first and last note in a passage or piece.
  • Repetition – the pitch center is repeated.
  • Accent – the pitch center appears on metrically accented beats.
  • Length – the pitch center is written with longer note lengths in strategic places, textures, or timbres.
  • Pedal or drone – the pitch center appears as a pedal point or as a drone
  • Ostinato – the pitch center occurs as an important pitch within an ostinato.
  • Dynamic – the pitch center has a louder dynamic or is accented.
  • Register – the pitch center is placed as the most prominent note in the texture, such as the highest or lowest pitch.
  • Modal function – the pitch center is reinforced by modal voice leading relationships such as movement from a subtonic to the tonic.
  • Harmonic function – the pitch center is paired with its dominant note a P5 above or P4 below.
  • Melodic function – the pitch center is paired with a leading-tone to tonic (\(\hat{7}\)-\(\hat{1}\)), subtonic to tonic (\(\hat{7}\)-\(\hat{1}\)), or supertonic to tonic (\(\hat{2}\)-\(\hat{1}\)) melodic motion.

An example of pitch centric music that has primarily modal underpinnings is Debussy’s Sunken Cathedral. While different pitch centers and scales are explored in the piece, it clearly ends with C as the pitch center. Another example is the opening movement of Stravinsky’s Symphony of Psalms, which centers on the note E while using a variety of modal and synthetic scales.

Pandiatonicism

Pandiatonicism emerged as a response to the highly chromatic and atonal music of the late 19th and early 20th centuries and is most often associated with Neoclassicism. The term is difficult to define because practices vary widely, but characteristics or definitions of pandiatonic music can include the following:

  • The notes of the diatonic scale are used very freely and in a way that does not promote tonal harmonic progression based on the circle of fifths, tonal melodic voice-leading practices, and the conventional resolution of dissonances.
  • Chords may be tertian or nontertian in construction.
  • A tonal center may or may not be implied.
  • The scales are usually in major mode, giving the music a bright, open sound that is the opposite of atonal or other highly chromatic music.
  • Key signatures or accidentals may be used, or the music may exclusively feature the “white keys” on the piano.
  • Ostinatos are sometimes found, and these may be layered upon one another to create dissonant and rich textures. 

Examples of pandiatonicism include Alfredo Casella’s Valse Diatonique, Aaron Copeland’s Appalachian Spring, Sergei Prokofiev’s Piano Concerto No. 3, Stravinsky’s ballet Petrushka in the Russian Dance and the Shrovetide Fair tableaux. 

Extended Tertian Chords

Although relatively rare, ninth chords (Mmm and MmM) have been used since the beginning of the 19th century. It was not until the early 20th century that the use of 11th and 13th chords became common. The subsequent example illustrates several extended chords built on C as well as recommended lead-sheet symbols. This list is by no means exhaustive in scope.

extended tertian chords

These “tall chords” or “extended chords” as 9th, 11th, and 13th chords are sometimes called, can be used in functional progressions (circle of fifths) and in nonfunctional successions. In functional progressions, they can substitute for triads and seventh chords, and in nonfunctional successions of chords can be used as color chords and in planing. The next example shows a circle of fifths progression in C with 9th, 11th, and 13th chords substituting for simpler diatonic triads and seventh chords.

tall chord progression

Maurice Ravel’s Rigaudon from Le Tombeau de Couperin opens with a IVM7 – ii11 – V13 – I progression in C major in the first two measures. Gabriel Faure’s Après un Rêve features several fine examples of the use of ninth chords, and an example in the last measure of the Russian Dance from Petrushka exemplifies the use of extended chords in a tonal cadence. The progression is a ii11 (missing the third but with reinforcement of the supertonic D in the original score) – V11 – Iadd6 in C major.

Added Note Chords

Added note tertian chords are formed when a 2nd, 4th, or 6th are added above the root. Added note chords can be used to add color to an otherwise standard tonal progression to create a distinctly modern sound. Because of the strong dominant to tonic bass motion, the added 6th in the final chord in the next illustration is clearly a Iadd6 and not an inverted seventh chord.

progression with added note chords

Depending on how these chords are voiced, the effect can be that of a 9th or 11th chord with supporting thirds omitted. Because of the voicing, the Iadd2 and Iadd4 in the ensuing example could be seen as incomplete I9and I11 chords respectively, but the absence of the supporting 7th in the first example and the supporting 7th and 9th in the second example certainly weakens the sound and interpretation of these as tall chords.

added note chords

Debussy’s Canope from Preludes, Book II, includes examples of added note chords as well as other techniques discussed in this chapter.

Chords with Split Thirds

A split third chord or mixed third chord includes both the major and minor third and is built on the same root, thus creating a dissonant m2. It is possible to split other members of a triad or seventh chord, but this is not as common. Examples of split third chords occur in the opening Debussy’s La Puerta del Vino. Note that the B♮ serves as the 7th of a D7 chord, and the E and F are the split thirds. 

The next example illustrates a few possibilities for voicing a split third chord.

split third chords

Polychords and Polytonality

Polychords come about when two or more distinct tertian chords (chordal units) – specifically triads and seventh chords – are sounded at the same time. Polychords can be written as vertical sonorities or in a linear manner. The “Petrushka chord” used by Stravinsky in the ballet Petrushka, consists of two triads a tritone apart. Both the vertical and linear uses of polychords can be seen in the tableau Petrushka’s Room, first in linear motion at rehearsal 49 and then as vertical sonorities at rehearsal 51 in the selected score example. A piano transcription of this tableau shows these harmonies with more visual clarity.

Polychords can be identified with lead-sheet symbols, as shown below. 

polychords

Polytonality, also called bitonality, occurs when two tonal centers are used at the same time. When this happens in a modal context, the result can be called polymodality or bimodality. Scales or modes that have little in common can be paired, or composers may select scales that have several tones in common. Different registers and timbres may be used to highlight the effect of the two tonalities sounding together. An easy and clear example occurs in Bartok’s Mikrokosmos, No. 105, Gamewhich features a pentatonic melody in different keys. A gentler example of polytonality can be found in Britten’s The Ash Grove from Folk Songs of the British Isles.

Quartal and Quintal Harmony

Quartal and quintal harmony refers to chords built of fourths and fifths, respectively. These chords came into use after the Common Practice Period as composers sought alternatives to the system of tonal harmony that uses chords built in thirds. Both quartal and quintal chords can have three or more notes, and the usual practice is for the intervals to be perfect, although augmented and diminished fourths are seen in a few quartal harmonies, including in Scriabin’s “mystic” chord. Because P4 intervals invert to P5 intervals, inverted quartal and quintal chords become indistinguishable from one another. The sonority that results includes the stable P5 with an added 2nd or 4th above the bass note, a hallmark sound of 20th century music.

quartal and quintal chords

Several examples of quartal harmony appear in Debussy’s Sunken Cathedral, wherein the composer freely uses tertianquartal, and quintal sonorities. At the opening of the second movement of Bartok’s Piano Concerto No. 2, the strings engage in a beautiful quintal passage that spans 23 measures in length.

Secundal Harmony and Tone Clusters

Secundal harmony uses 2nds and 7ths as harmonic building blocks rather than the thirds found in tertian harmony, and can be constructed in 2nds, 7ths, or in a mixture of the two. Tone clusters (cluster chords) are a type of secundal sonority that are comprised of three or more adjacent notes, and clusters containing two or more m2 intervals are more dissonant than those containing mostly M2 intervals. Tone clusters can be notated traditionally, or may be notated with solid lines and bars, as Henry Cowell did in his piano work The Tides of ManaunaunTone clusters on the piano can be played with the fingers, fist, forearm, or a block of wood or other material. Bartok made extensive use of secundal harmony and tone clusters in his Piano Concerto No. 2

The next example shows a few possibilities for notating secundal harmony and tone clusters.

secundal harmonies and tone clusters

Parallelism/Planing

Harmonic parallelism or planing is the parallel movement of two or more lines or chords. An example in a tonal environment appears in the third movement of Beethoven’s Piano Sonata Op. 2 No. 1. In the 20th century, planing is often associated with Debussy and Ravel, and its use is a feature of their styles. Both tertian (triads, seventh chords, added note chords) and nontertian sonorities (tone clusters, secundal, quartal, quintal) can be planed. Planing is categorized as diatonic, strict (real), or mixed.

Diatonic planing

diatonic planing

In diatonic planing, all voices or chord members follow the pitch classes specified in the scale or mode, as exemplified in Debussy’s Sunken Cathedral. Because only the pitches of the scale are used, vertical sonorities (triad types, etc.) change as different constructions arise within the diatonic scale. Several examples of diatonic planing also occur in Bartok’s Piano Concerto No. 2.

Strict planing

strict planing

In strict (real) planing, the voices or chord members maintain precise interval relationships, resulting in a sonority that is merely transposed after its first appearance. Debussy’s The Sounds and Fragrances Swirling Through the Evening Air features many instances of planing, including the strict use of parallel major chords.

Mixed planing

mixed planing

In mixed planing, the voices use a blend of diatonic and strict planing, as displayed in Debussy’s Dancers of Delphi.

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