Music Theory Comprehensive Complete: Parts 19, 20, & 21

Trace the shift from traditional harmony to chromaticism, set theory, and serialism, and learn seven key terms and their notation for understanding 20th-century music.

Define a pitch as a specific note; a pitch class includes its octaves, and a pitch class set groups C, D, and E, where C sharp equals D flat.

Explore the interval vector, a six-digit descriptor for pitch class sets, learn how to calculate it, and see how different sets can share the same vector through overlapping interval vectors.

Explore set class in music theory, a group of notes that includes all possible transpositions and inversions, with an interval vector that remains the same across transpositions.

this lecture defines prime form for a pitch class set, shows rotation and transposition to c, and maps to numbers to yield 0 1 3 as the prime form 013.

Explain normal order as the smallest, compact arrangement not transposed to prime form, using curly brackets for notation and comparing it to prime form with pitch-number mappings (C=0, F-sharp=6).

Explore chord sonorities without roman numeral function, naming chords by the number of notes: trichord, tetrachord, pentachord, hexachord, and relate to the chromatic scale.

Explore how Bartók blends traditional harmony with chromaticism and set theory, drawing on Hungarian folk songs, with a focused analysis of his piano excerpt 'Bulgarian Rhythm'.

Analyze the opening measures of Bartók's Bulgarian Rhythm, noting the absence of a key and frequent courtesy accidentals. Explore whole-step and half-step patterns and the five over eight tempo.

Examine pitch class sets by numbering notes, arranging in normal order, transposing to zero, and deriving prime form to compare right-hand note collections and their interval structures.

Compute interval vectors by counting interval classes: minor seconds, major seconds, minor thirds, major thirds, perfect intervals, and tritones, across note pairs, and compare vectors like 332110 and 342110.

Explain that the numbers 02345 describe a group of notes, not a one-to-one mapping, and that the ordering may be nontraditional, before examining the left hand.

Explore left-hand note groupings, identifying optimal ordering and prime forms, revealing 016 and 023 relations, tritone and half-step structures in a practical pitch-class analysis.

Explore how the 023 based sonority shapes the music's character, contrasting it with Roman numeral analysis and examining half-step and whole-step intervals to reveal the piece's sound world.

Explore interval vectors as descriptors of a set's flavor, revealing its sound world from major and minor to modes, and examine vectors for sets like 02345 and 01235.

Learn to find interval vector for a pitch-class set, using 023 to count minor seconds, major seconds, minor thirds, perfect intervals, and tritones with inversion rules, revealing a dark sound.

Explore pitch class sets 014 and 023, build a tri chord, and compare their sonorities; analyze interval content, including minor and major thirds, a minor second, and a potential tritone.

Explore the 025 example by building notes C, D, and F into triads and analyzing intervals (major second, perfect interval, minor third) to reveal three distinct, suspended, pentatonic-tinged sonorities.

Explore z-related vectors, where two different pitch class sets share the same interval vector, revealing how distinct note collections can sound similar in interval content.

Discover forte numbers, an indexing system named for Allen Fort that names each pitch-class set and shows z-related connections, with examples like 5z18 and 3-7.

Clarifies how to notate ten and eleven semitones in interval vectors by using t for ten and e for eleven, keeping pitch-class sets like 014 11 with single-digit marks.

Analyze major scales through set theory, deriving set class and interval vector, then explore minor scales and flavors like whole tone, octatonic, and chromatic scales.

Explore the C minor scale, convert to natural minor, build the interval vector from scratch, and discuss major–minor rotations, Z-related ideas, and fort numbers.

Explore the whole-tone scale, defined by all whole steps, its interval vectors with major thirds and tritones, and its dreamy sound used by Debussy to obscure the tonic.

Examine octatonic scales, alternating whole steps and half steps to blur the tonic, and apply the whole-step and half-step pattern and interval vector insights to chromatic scales.

Explore the chromatic scale and its interval vector, counting half steps, whole steps, minor and major thirds, perfect intervals, and tritones. Observe how pitch classes form this interval vector.

Delve into Webern’s highly chromatic, short pieces and early experiments before serialism, illustrated by a string quartet excerpt with each instrument’s part and careful notation.

Listen to a string quartet on grand staff, heard on piano, and analyze chromatic chords and music where there is no tonic, using set theory as the primary tool.

Explore vertical sonorities and unordered pitch-class sets, identify bubbles of pitch-class content, and analyze how stacked harmonies form tri chords and their internal pitch-class sets.

Analyze the first bar by grouping vertical sonorities and identifying set-theory ideas, including 034 trichords and an 015 sonority, with transposition to C and normal order.

Analyze the second bar's vertical sonorities and pitch-class set patterns, exploring inversion, normal order, and labels like 014, 015, and 016 to reveal underlying relationships.

Analyze the third bar's three-note chords and vertical sonorities, identifying recurring 034 and 014 patterns, with examples like f#-d-f# and c-e flat-e, concluding the passage is mostly 014 and A14.

Analyze the 014 and 034 pitch-class sets, invert to prime form, and interpret fort number three with interval vector 101100, revealing the 014 home sonority rooted in major-scale harmony.

Explore why composers pursued chromatic music after world wars, seeking new sounds beyond traditional progressions, and see how set theory is adapted to stay grounded in tonality.

Explore how a pitch class set, notably 013, grooves through a string quartet with a transparent viola line, transposes, and diatonic versus non-diatonic textures influenced by Webern.

Explore surrealism and how it locks in chromaticism by establishing definitive rules for working chromatically, then preview parts 20 and 21 in the music theory comprehensive series.

Explore the 1934 musical context, postwar life, expressionism in art, and prime forms in the example: D to B-flat to C and G to E-flat, with Luigi Nonno cited.

Use MuseScore or any notation program to input notes and hear them back, preferably on desktop; bring staff paper and graph paper to plot points on a graph for lessons.

Build on pitch-class sets—prime form, normal order, and interval vectors—as we move to a chromatic, serial approach with no key signatures and no tonic.

Download a MuseScore version three file containing all class examples, plus a PDF for non-MuseScore users, then follow along as you prepare for the listening list.

Explore a curated 20th-century listening list of seminal pieces, with guidance for deep listening and emphasis on serial and non-serial works across composers.