I. A Brief Survey of Music Theory History
A. Chant/Plainsong--monophony
1. Around the Medieval period (Pope Gregory II) chants were being brought into existence
B. Polyphony--the discovery that two lines could be sung simultaneously; began with the prefect fifth
1. Organum--parallel motion between two voices
C. Harmony--the extension of organum
1. As voices were added, people began taking note of the congregate sounds (would become the conept of current theory in the early 18th century)
2. Much rhythmic complexity was sacrificed for harmonic complexity
D. Modes today refer basically to melodic systems, not harmonic ones; these would break down in the 16th century due to musica ficta (accidentals)
1. This was due largely to the notion that some "improvisations" (raised leading tones) just sounded better (started to lead away from modality)
2. Important to avoid the melodic tritone
3. Created leading tones
4. The concept of "major" or "minor" chord was invented by altering the chord quality with regular accidentals
5. All this happened before equal temperament and was primarily vocal
6. Chordal development created chordal progression, which finished of modality
E. Figured Bass (thoroughbass)
1. Someone came up with the idea of putting numbers under a bass line to describe the chord quality; this intensifies the idea of chord and chordal movement (vertical music reading rather than linear, or horizontal)
2. Develops the practice of "monody"
3. Polarity of outer voices
F. The 19th century
1. Beethoven and following begin pulling music back to a more melody-driven philosophy, bringing lots of accidentals into the tonal system to return to a linear philosophy of composition
2. Beethoven's use of motivic development
G. Schönberg, Wagner and the Late 19th century Modern Era
1. If we're using so many accidentals, why pretend to be in any key with key signatures?
2. Chordal mutation--linear progression of voices that comprise a chord; no longer interested in chord "progression" per se
3. Wagner introduced the concept of making opera an actual story where the drama was indispensable (he called them "music dramas")
a. If you're not going to follow the traditional Italian opera form, you have to have an endless flow to the music (avoided cadences, especially tonic ones)
b. The idea of cadencing emphasizes one chord over another; when you avoid them, you eliminate the sense of tonal center (even though the music is basically tonal)
c. If the expectation to resolve to I is never satisfied, the expectation disappears (the elimination of "functional harmony")
d. The nature of tonality is changed when the tritone as the symmetrical division of the octave is embraced (and other symmetrical divisions)
H. The Changing of Tonality in the 20th Century--Factors besides the Romantic composers
1. The interaction of cultures, beginning with the Industrial Revolution of the 19th century
2. Beethoven and Mozart used some Turkish qualities in his later music, including instruments (cymbals, triangles, etc.)
3. Debussy heard a Balinese Gamelan band at the 1889 Paris Exposition that highly influenced his latter compositions
4. Tonal (goal-directed) music gives way to goal-less music
I. Separation of Ideas--Impressionism and Serialism
1. Debussy was looking for a fresh sound; composers have to be passionate about finding new sounds and sonic combinations
2. In going back to linear composition, modes were reintroduced as a staple compositional technique (though they were not necessarily church modes)
a. "Modes"--the pitch components of a tonality
b. "Scales"--an arrangement of pitches in a mode
c. Modes typically had no leading tone; this changes harmonic thinking from "progression" (implies to a hierarchy of chords) to a "succession" (which does not)
d. Just about every 20th-century composers used modes
3. Planing--parallel motion of chord tones
a. More a matter of voicing/voice leading than harmony
b. The idea of harmony permeates everything in tonal music, but modal music is free of these constraints
4. Pandiatonicism--taking one mode and using it in a non-functional, non-traditional way
a. Primary composers
(1) Stravinsky
(2) Copland
b. Usually avoid traditional note arrangements and progressions (often with lots of arrangements of seconds and sevenths)
c. Absence of accidentals
d. Precursor to minimalism
e. Bi-modality--the use of two modes simultaneously, usually a major mode against a minor one (Stravinsky liked to put the major above the minor, but most composers do the reverse)
5. Other important scales
a. Whole-tone scale
(1) A scale of whole steps; there are by definition only two, and there is no tonal center
(2) This is a symmetrical scale, and it follows the tendency of musical symmetry in that it tends not to be "tonal"
b. Symmetrical scales
(1) Octatonic scale (or "diminished scale" to jazz players)
(2) Pitches alternate half-step/whole-step
(3) Full of lots of harmonic possibilities
J. By the end of the twentieth century, there are four collections of music:
1. Diatonic Collections
a. Major/minor scales, church modes, and anything based on them, including the pentatonic scale
b. Synthetic scales, made up by a composers for specific pieces
c. Pandiatonicism
2. Whole-tone Collections
3. Octatonic Collections (uses the octatonic scale)
4. Chromatic Collections (serialism, atonality, etc.)
K. Olivier Messiaen (1898-1992), The Technique of My Musical Language--describes "modes of limited transposition"--some things, when transposed, don't really produce anything new
1. Like the whole-tone and octatonic scales--they will all happen to be symmetrical scales
2. Some chords (fully diminished-seventh, augmented chords)
II. Studying Modes
A. Determining modes
1. Look for final tones
2. Observe key signature
B. Characteristics of each mode
1. Ionian--major
2. Dorian--natural minor, but sharp sixth
3. Phrygian--natural minor, but flat second
4. Lydian--major, but sharp fourth
5. Mixolydian--major, but flat seventh
6. Aeolian--natural minor
7. Locrian--mainly theoretical minor, with flat second, flat fifth
III. Change in the Music of the 20th Century--Rhythm and Meter
A. Asymmetrical meters
1. Meters that don't divide by two, but more than three (like five-four, seven-four, etc.)
2. Typically is broken down into smaller arrangements of three and two
3. Usually needs to move faster to emphasize groupings
B. Changing meters
1. Symmetrical meters that have uneven beat lengths (3+3+2 rather than 4+4)
2. Apparent in the musics of Copland, etc.
C. Metric accent
1. The prevalence of one beat per regular grouping
2. Brahms and others used this against us, then started ignoring the barline and placed the strong beats elsewhere in the measure (without changing the meter)
D. Syncopation
1. The displacement of normal accent within a meter
2. Agagic accent--emphasizing a note by virtue of its elongation
3. Swing--a jazz development, where pairs of printed straight eighth notes are actually performed as a quarter + eighth in triplet
E. Polyrhythm, polymeter--completely different rhythm patterns are juxtaposed one against the other
F. Ametric music--music that has no feeling of meteric accent (not to say that there isn't one written on the page)
G. Metrical modulation--a proportional change of tempo; i.e., a way of writing out accelerandi and ritardandi by notation (American composer Elliot Carter)
IV. Extended Harmonies
A. Extended Tertian--not only does the chord consist of increased numbers of stacked thirds, but the chords are not typically harmonically functional
B. Quartal/Quintal Harmonies--often only discernable within the context of a bunch of like chords
1. History
a. Began as unresolved 4-3 suspensions
b. Used often by Paul Hindemith
2. Construction
a. So named because of placement; many can be named as tertian
b. Tend to sound very stable if spelled with perfect 4ths, but very dissonant if you augment or diminish any of them
c. Perfect fifths (quintal) tend to be attractive, but difficult to move with because of the space
C. Secundal Harmony
1. Two chords clustered together
2. First widely used by Henry Cowell
3. Tend not to progress much; really just a sonority of effect
4. Can be respelled as sevenths instead of seconds
D. Polychords/Polytonality
1. Two chords kept separate in order to keep them from sounding like secundal chords
2. The further the tonics of each chord, the more dissonant
3. Polytonal--one tonality in one voice, another tonality in another voiceo
V. Usage of Triad Harmonies--independent of key relation or tonal function
A. Step progressions
1. Moving of triads/chords consistently by step without any attempt to function or even necessarily relate a key
2. Planing occurs--parallel motion among voices
3. May take its time over measures rather than one chord right after another
B. Root Movements of Thirds
1. Moving of triads/chords consistently by major minor thirds
2. Always a cross relation of voices in adjacent chords (major involves basing a second chord on the lowered third of the previous one; minors do not need to use this technique)
C. Analysis
1. Determine what kind of chordal technique is being used--triads? Quartals?
2. Determine how the chords are relating to each other
3. Look for root movements--step or third progressions
4. Determine how the structures relate to each other intervalically
D. Usage of Extended Harmonies
1. Frequent usage of extended tertian harmony with alterations
2. In Jazz and popular music, there is frequent tonal function in the bass, but all bets are off in the other voices
3. The way chords are stacked can change the way it is heard
a. The same chord can be stacked in thirds or fourths; this can muddy the way a chord is named
b. The seventh is necessary, however, to turn added notes into ninths, elevenths, thirteenths, etc.
4. Context often helps determine how a chord is "functioning"
5. Omissions of notes helps keep a quartal chord interesting, but it can be difficult to tell what those missing notes are
6. Polychords/Polytonality
a. Polychords have no real meaning without space between the constituent chords or some other very obvious difference (e.g., instrumentation)
b. Not all polychords are polytonal; in fact, most aren't (polytonal suggests that there are two real keys going on)
c. Most popular polytonal composer was Darius Milhaud
d. One sure-fire indication of polytonality is mixed key signatures
E. Significant Personalities in Studying Tonality
1. Paul Hindemith--theorized that all chordal transition to and from each other based on harmonic stability
2. Persichetti
3. Howard Hanson
VI. Other Developments--more historical/stylistic than theoretical; deal more with "sound" than anything else
A. Technological Advances
1. Began with the Industrial Revolution of the 19th century
2. Travel opportunities that facilitated multicultural relations
3. World War I--most historians think it was pivotal in its elimination of empirical mindsets; also contributed to a certain degree of cynicism about the "utopian" dream brought on by the Industrial Revolution
B. Musical Philosophy
1. The concepts of "beauty" are being discarded as motivation for composition
2. Futurists--a group of Italians who dispensed with typical musical composition and started calling any mundane sound "music" (sources we would consider non-musical)
a. Busoni--believed that the future of music was in some kind of electronic presentation
b. None are remembered to day
c. Honegger--"Pacific 231," a tone poem that uses an orchestra to mimic the sound of a train
d. Mossolov--"Soviet Iron Foundry," a piece that sounds like... a Soviet iron foundry
e. Anthiel--"Ballet Mechanique" for four pianos and two aircraft engines; a bit of a World War II hero for codebreaking
3. Instruments of ambiguous pitch (where pitch is not the main issue; e.g., percussion; considered primarily timbre and texture)
a. Varese--wrote "Ionisation" in the 1930s for percussion ensemble, no real pitch in the piece; considered by many as the first purely percussion piece in Western music
b. Henry Cowell--also did conventional sounding pieces along with extreme pieces and everything in between
C. Electronic Music
1. BASF Corporation in Germany invented to tape reel (analog)
2. Once it was determined that sound could be recorded, it was just the next logical step to wonder what could be done with that sound
3. Pierre Schaeffer--composed by splicing natural sounds: musique concrête, the ultimate in music based on sound (early sampling)
4. Varese--wrote "Poeme Electronique" for a pavilion at the Brussels World Fair in 1954
5. Vladimir Ussachevsky and Otto Luening--composition professors at Columbia University
a. Luening would play flute sounds in the woods
b. Ussachevsky recorded the sounds and spliced ˆ la Schaeffer
c. This got Bell Laboratories interested in processes that eventually led to digital transmission
6. Columbia and Princeton when in together to develop an "electronic music center," which gave birth to the synthesizer (the most successful attempt at electronic instruments that generate musical sounds)
a. The first synthesizer was huge, with thousands of tubes
b. Walter Karless in the early 1960s played Bach pieces on these synthesizers and sold millions of copies
7. Digital recording began replacing analog in the 1980s
D. Conventional Impression of Electronic Music--orchestral effects that simulated electronic sounds
1. Texturalism--texture is the main compositional component
2. Soundmass music--texturalism for conventional instruments used in unconventional ways
3. Not very large in "vocabulary" to remain interesting for long
4. Penderecki--"Threnody for the Victims of Hiroshima" (originally title "Study for 52 Strings")
a. All about texture and sound
b. In order to accomplish what he had in mind, he had to invent "spatial notation"
c. Indeterminacy--certain elements of the piece are left up to the perfomer; an agreement of improvisation or uncertainty
d. Aleatoric Music--an element of chance determines how a piece will be performed
5. Ligeti
a. Wrote "1000 Metronomes," 1000 metronomes that are wound up and set at different meters; finished when the last one stopped ticking
b. Wrote much of the music to "2001: A Space Odyssey"
6. John Cage
a. Cultivated the philosophy that music consists of things that people never think about
b. Studied for Schönberg, who told him he wasn't good enough to be composing in the typical way; he agreed
c. Prepared piano--music that requires manipulating the piano to eliminate its tonal components, leaving only the timbre elements
E. Test Preparation
1. Section 1--five musical examples needing modal determination
2. Section 2--2-3 measure piano excerpts needing harmonic determination (secundal, quartal, triadic, etc.)
3. Section 3--five extended tertian chords that need lead sheet chord symbols
4. Section 4--ten "identify the harmonic style"
5. Section 5--25 fill-in-the-blankocta
VII. 20th-century Atonality
A. Arnold Schönberg
1. Felt there was so much modulation and key instability that tonality was irrelevant
2. Developed "pantonality," or all keys at once; now known as atonality
3. Avoids cadences or finishing phrases on strong beats
4. Avoids triadic or chord patterns of any kind
5. Minimizes pitch repetition
6. Developed Interval music (grew out of late Beethoven); later went on to 12-tone serialism (very useful for program music)
7. Alban Berg--mixed Schönberg with Romanticism
8. Webern--used the 12-tone system strictly
B. Allan Forte (Yale University)
1. 1940--published The Structure of Atonal Music
2. Did a stylistically neutral analysis; dealt strictly with pitch relationships
3. Used math ideas and "set theory" (not higher math)
4. Concepts
a. Pitch class (as opposed to a pitch)--all pitches that are octave duplications of one another
b. Fixed-zero notation--C always equals pitch class "0"
c. Movable-zero notation--any pitch class can be made "0" (like movable do)
d. Pitch-class intervals--the distance of one pitch-class to another
(1) Expressed as a whole number of half-steps, starting with 0
(2) Direction is irrelevant
e. Interval-classes--a pitch and its complement
(1) Complement--the inversion of an interval
(2) There are six interval-classes: 1-11, 2-10, 3-9, 4-8, 5-7, and 6 (tritone)
f. Any interval larger than an octave has 12 subtracted from it to compute the real interval class
g. Descending melodic notes are figured as inversions, from the first (top) note going to the second (lower); so an E followed by an Eb is not i1, but i11
h. Does not address anything but pitch (not anything else that goes on in music)
C. Stravinsky
1. A "centric" composer--he picks pitches that function as melodic centers (almost always 2, and usually a minor-3rd apart) in almost all his pieces (some call it "bifocal tonality")
2. Things that show up at the beginning, end, or great numbers of repetitions tend to have gravity and importance
3. "Unity of musical space"--no longer do we have melody and harmony functioning separately, but everything functions together
a. Pitches that are used frequently can be used either melodically or harmonically
b. Pitches can be used in melodic and rhythmic inversion
D. Milton Babbitt--American composer of highly organized serial music
1. Total, or interval serialism
2. All-interval series--the line contains one of each interval class
E. Pitch-Class Sets
1. Some kind of arrangement, melodically or harmonically, of a group of pitch-classes
2. Usually three to eight (maybe even up to ten) pitch-classes
3. Made significant by repetition (remember, music exists in time)
4. In a way, we're talking about harmonic structures that cannot necessarily be limited to major/minor triads, extended tertian chords, etc.
5. May be arranged in individual order, groups, or even "chords"
6. Subsets can often be extracted from the sets (reductionist analysis)
7. Prime form--comparing the first pitch-class set in normal order with its inversion (the complement) and identifying the set with the smallest intervals, from right to left
8. Interval vector--the intervals in a set
a. Spelled in order of available intervals in a set (so [0,2,5,7] will have a vector of 021030--0: 1/11's, 2: 2/10's, 1: 3/9's, 0: 4/8's, 3: 5/7's, and 0: 6's)
b. The vector will also tell us how man common tones there will be if the set is transposed
9. Ajdacency/simultaneity--describes an arrangement of linear or simultaneous, chord-like set of pitches
10. Schönberg--"the unity of musical space," where the same pitch-class set informs both melody and harmony
11. Pitch-class regions and subsets
a. Chromatic scale [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]--has all subsets
b. Diatonic [0, 1, 3, 5, 6, 7, 10]--includes major, minor scales, church modes, pentatonic
(1) May contain a subset of [0, 1, 4], for example
c. Whole tone scale [0, 2, 4, 6, 8, 10]
d. Octatonic [0, 1, 3, 4, 6, 7, 9, 10]
(1) Major chord [0, 4, 7]
(2) Minor chord [0, 3, 7]
(3) Dominant seventh [0, 4, 7, 10]
12. Procedure
a. Arrange notes in ascending order
b. Create the inversion
c. Renumber from lowest to highest, adjusting to number first pitch
13. A transposed pitch-class set is denoted by T + number of semitones the reiteration is offset by
F. Scriabin--Synesthesia--believed in multi-sensory experiences
G. Webern
1. Pointillism--very few pitches going on simultaneously
2. A derived series--a piece where
VIII. Serialism--some element of music (pitch, rhythm, timbre, dynamics, etc.) will be arranged in a vital sequence
A. Historical Aspects
1. Schönberg discovered there were disadvantages to having no program to help avoid tonal references
2. He was looking for something to replace the structure that would invariable lead the composer to certain
3. Lasted from the 1920s to the mid-1950s (heyday was basically post-WWII)
4. Serialism tended to "even things out" in the music--anyone can write it, and everyone's music sounds like everyone else's, indicative of a "super-classical" mindset in that it means nothing besides the pitch-class
B. Twelve-tone (or dodecaphony) Analysis Procedures
1. Still looking for pitch-classes, sets, and interval vectors, but in slightly different ways
2. Twelve pitch classes will be set in a specific, non-repetitive order, or "row"
3. Compositional techniques
a. The composers makes a pre-compositional decision (not arbitrary) to put the twelve pitches in a row, or set
b. Prime set--an ordered set (appears in the same order every time) and includes every pitch
c. Not reorganized to put pitch-classes in numerical order
d. Derrived series--a tone row completely comprised of the same subclasses
4. Permutations of a row
a. P0--Prime set (the basic tone row)
b. R0--Retrograde of prime set
c. I0--Inversion of prime set
d. RI0--Retrograde-inversion of prime set
e. Changing the set number merely transposes the set to start on the pitch-class
f. As before, we compute intervals between all pitches in all sets
g. Always look for linear statements--that's where we'll likeliest find the clearest statements of the prime set
5. Joseph Hauer--worked with "tropes" (not liturgical tropes)
a. Two hexachords of the 12-tone row
b. Hexachords were grouped and mixed up within the group
c. Schönberg and Berg developed from this the "hexachord combinatoriality" (term coined by Milton Babbitt)
(1) Occurs when corresponding hexachords of two different row forms combine to from an aggregate (the first six notes of P0 plus the first six notes of I5 [a typical transposition] create an aggregate of all 12 pitch classes; the second six notes of P0 plus I5 do the same thing)
(2) Non-corresponding hexachords have the same pitch content, but not in the same order (first part of P0 and second part of I5 contain the same pitches; second part of P0 and first part of I5 also)
(3) Hauptstimme & Nebenstimme--"first voice" (most important line) and "neigbor voice" (less important line)
(4) I0 and R0 are always combinatory, as are P0 and RI0
(5) Once you know what row forms you have (P0, I0, and intervals), you can identify everything
6. Time-point System (Milton Babbitt)--the note-lengths (in 16ths usually) are derived from the tone row (the farther from 0, the longer the note)
7. Integral, or total serialism--the application of serialism to all aspects of music (playing style, dynamics, pitches, etc.)
a. Olivier Messiaen--only did one such piece, in the summer of 1948 just to show he could do it
b. Milton Babbitt--all he does; he's even incorporated Jazz into it
c. Pierre Boulez
d. Some Stockhausen