Interval exploration

Thinking about how intervals can create a sense of structure

Terms: quartal harmony, all-interval chord, all-interval row, all-interval set

• Carter, E. (1960). Shop talk by an American composer. The Musical Quarterly 46:2, 189-201.
• Link, J. (1994) The composition of Elliott Carter's  Night Fantasies. Sonus 14:2, 67-89.

Interval Exploration

Interval exploration can occur vertically, horizontally or both.

Vertically – stacking or the placing of like intervals one upon the other.

*(eg.) stacked chords of 4ths and their resulting inversions

- inversion (triadic harmony) - triads

- all interval chords

"all-interval" chords Twelve notes with each of the eleven intervals occur exactly once.

 Spans five and a half octaves.

 Composer Elliott Carter (Night Fantasies) has said that he treats these chords as a repertoire of harmonic possibilities.

 Each contributes to a variety of different harmonic possibilities. BECAUSE…

 Maintains its own unique spatial arrangement of pitches distributed across the five and a half octaves.

5th and 4th Chords• Quintal harmony - Term denoting a harmonic system based on the interval of a 5th

• Quartal Harmony - Term denoting a harmonic system based on the interval of a 4th

• Composers have found that a five note chord consisting of four perfect fifths contain more types of intervals beyond the first initial fifth.

 Outer notes (bass staff) form a 9th

 When transposed by an octave, is then a 2nd

 The E in the treble staff is a 13th from the bass note and a 6th when transposed down an octave.

 Top note creates a 17th or a 3rd when transposed down two octaves.

Therefore by using quartal or quintal harmony other chords are invented though inversions of notes.

Set theory:****

• definiens sets of pitches and organises music around those sets and their various manipulations

o retrograde inversion (backwards and upside down)

o retrograde (backwards),

o Inversions (upside down)

• Sets and set classes determine the pitch only.

Pitch class is the group of any pitch and all of its octave transpositions.

Eg. If we were to use the note C, we would then use the octave to then find the equal temperament which is obviously the chromatic scale. In a chromatic scale there are twelve different pitches and therefore there are twelve pitch classes.

C =0, C#=1, D=2, D#= 3, E= 4, F= 5, F# =6, G= 7, G#= 8, A= 9, A#= 10, B= 11.

Pitch-class sets:

 Are groupings of pitch classes placed in ascending orders

 Atonal music

 Eg. 0,1,2,6 = C, C#, D, F#

 Schoenberg’s 0,1,6 “The Viennese Trichord”

(C, C#, F#)

Composers:• Arnold Schoenberg

• Anton Von Webern

• Alban Berg

Listening example: ‘Sehr Rasch’ from ‘Concerto Op.24’

• 3 note cells

All Interval set:

 Is a set of the twelve pitch classes arranged so that all eleven intervals, 1-11, are present. -(DeLone )

All Interval Row:

 Is a twelve tone row that contains not only all twelve tones, but also all eleven intervals, occurring only once, within the octave.

Normal Row could be:

C,C#,D#,D,F#,F,E,G,A,G,B,A#.

Only intervals used are minor and major 2nd and 3rd’s.

All Interval Row may be:

C,B,C#,A#,D,A,D#,G#,E,G,F,F#

Uses every interval (1-11)

Conclude

Interval exploration is about using intervals to form the structure of a composition and then finding ways to variate and manipulate it though its inversions.