By Paolo Susanni
This e-book explores the internet of pitch relatives that generates the musical language of non-serialized 12-tone music and provides either the analytical fabrics and techniques worthy for analyses of an unlimited share of the 20th century musical repertoire. It does so in an easy, transparent, and systematic demeanour to advertise an simply available and international figuring out of this track. because the chromatic scale is the first resource for the pitch fabrics of 20th-century track, universal sub-collections of a few of the modes and period cycles function the foundation for his or her mutual transformation. it's accurately this peculiarity of the non-serialized 12-tone music that enables for an array of pitch family members and modal innovations hitherto perceived tough if now not very unlikely to investigate. Susanni and Antokoletz current the foundations, recommendations, and fabrics hired for research utilizing a special theoretic-analytical method of the recent musical language. The booklet encompasses a huge variety of unique analyses that discover a number of composers together with Ives, Stravinsky, Bartók, Messiaen, Cage, Debussy, Copland, and lots of extra, delivering perception into the tune of the tonal revolution of the 20 th century and contributing a massive point of view to how song works in general.
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Additional info for Music and Twentieth-Century Tonality: Harmonic Progression Based on Modality and the Interval Cycles
The total number of interval cycles consists of one cycle of minor seconds (1/11), two cyclic partitions of major seconds (2/10), three cyclic partitions of minor thirds (3/9), four cyclic partitions of major thirds (4/8), and six tritone cyclic partitions (6/6). The perfect fourth cycle (5/7)3 is unique in that it does not generate a cycle that subdivides the octave symmetrically because it must pass through several octaves before reaching the initial pitch class. Most of the interval cycles can be interpreted in more traditional terms.
19 The interval-4/8 cycles that are interlocked at the whole-tone to generate the whole tone segments can themselves be partitioned into smaller tritone or interval-6 cyclic segments. If the interval-6 cyclic segments are interloked at the minor third (interval-3) instead of the whole-tone, they will generate an interval-3/9 cyclic segment. 3 Bartók, Suite Op. 14 (mm. 1–8). Suite, SZ62, Op. 14 by Bela Bartok. © Copyright 1918 by Boosey & Hawkes, Inc. Reprinted by Permission. The Interval Cycles 33 34 Music and Twentieth-Century Tonality ↑ C–F# C–Eb–F#–A ↑ Eb–A The tritone, therefore, is directly related to both the whole-tone cycles and the interval-3/9 or minor third cycles.
6) is introduced by three grace-note dyads [D–E, Bb–D#, and A–Cb]. While at ﬁ rst it seems that only the ﬁ rst and third dyads seem to be related, both being harmonic whole-tones, it is the second and only melodic dyad that reveals the pitch relations that bind together these grace notes. The ﬁ rst harmonic E–D dyad is immediately followed by the D# of the second dyad while the Bb of the same dyad is sounded immediately before the A–Cb of the third dyad. This creates a six-note symmetry [E–D#–D–( )–( )–Cb–Bb–A] around a C/C# axis.