Music Theory, level 4A (Adduci)

Welcome to the MUSC 4A page!

Please choose one of the following sections:

1. A collection of music theory-related links from around the Web.
2. The greensheet and other administrative documents
3. Handouts given in class.
4. Homework assignments and projects.
5. Listening examples.

Web Links

This section contains links to internet sites designed to help you with music theory and ear training. The Internet is a fantastic resource for self-driven learning!

• www.musictheory.net - interactive, self-grading practice on music fundamentals; also, you can print free staff paper here.
• www.metronomeonline.com - turn your computer into a metronome.
• www.teoria.com - an excellent resource - interactive lessons and dictation exercises.
• The International Music Score Library Project (IMSLP), home of the Petrucci Archive - an excellent source of musical scores in the public domain.

Greensheet

This section includes the greensheet and any other class policy documents.
Left-click to view, right-click to download.

• Spring 2012 Greensheet
• Revised lecture schedule for MUSC 4A (updated 3/11/12)

Handouts

This section contains copies of the informational handouts given in class. Handouts that went along with music played in class can be found under Listening Examples, below.

1. Part Writing handouts
   • For a handout explaining the rules of Bach-style part-writing, and a list of abbreviations that I use when correcting part writing assignments, please refer to the MUSC 1A website.
2. A comparison of a few of the leitmotives used in Wagner's Ring and in the scores to Star Wars.
3. A character list, plot synposis, and leitmotif guide for Wagner's Das Rheingold (1854).
4. Debussy score handouts (recordings under Listening Examples, below):
   • Sample pages from Les Préludes - "Alternating Thirds" and "Fireworks."
   • Sarabande, the second movement of Pour le piano.
5. Two movements from Stravinsky's Les cinq doigts, illustrating the use of pandiatonicism.
6. Examples of polychords. See the listening section, below, for recordings and discussion. The first page of the handout is not covered below - play these examples on the piano and analyze.
7. One additional movement from Stravinsky's Les cinq doigts, this time illustrating the use of bimodality.
8. Serialism handouts:
   • A blank template for calculating twelve-tone matrices.
   • The example tone row and matrix we created in class.
   • See the Listening Examples section of this page for recordings and more handouts.
9. 4A Final Exam Study Guide.

Assignments

This section contains copies of the homework assignments and projects given in class.

1. In-Class Activity 1 (1/26/12) - analysis of Torelli, Sonata in D.
   • The solution to the Torelli excerpts.
2. Assignment 1 (1/26/12, due 1/31/12)
   • Listening Excerpt: Chopin, Prelude No. 20 in C Minor, from 24 Preludes, Op. 28
3. In-Class Activity 2 (2/2/12) - analysis of the minuet from Dvorák's Serenade for Winds, Op. 44 (1878).
   • The recording for the Dvorák excerpt.
   • The solution for the Dvorák excerpt.
4. Assignment 2 (2/23/12, due 3/8/12)
   • Listening Excerpt: Wagner, Das Rheingold (1854), end of scene 1 transition and beginning of scene 2.
   • A copy of the scores for this assignment.
5. The semester Composition Project, including extra credit.
   • The required composition is due on 5/8 at 10:30 a.m.
   • The extra credit composition is due on 5/15 at 10:30 a.m.
6. Assignment 3 (3/8/12, due 3/15/12)
   • Score: Debussy, "The Sunken Cathedral" (Les Préludes, Book II, no. 10)
   • Recording
7. Assignment 4 (4/5/12, due 4/17/12 [revised due date!])
   • Listening Excerpt: Debussy, Sarabande from Pour le piano (1901), mm. 27-32
8. Assignment 5 (4/24/12, due 5/3/12)
   • Score for Hindemith's Un cygne.
   • Recording for Hindemith's Un cygne.
9. Assignment 6 (5/3/12, due 5/15/12)
   • Score for Webern's "Wie bin ich froh!" from Op. 25 (1935).
   • Recording for "Wie bin ich froh!"

Listening Examples

This section contains links to musical examples referenced during class. The examples are provided for class purposes only.

You need the free Quicktime plugin to play these .mp3 files.

To play, left-click the excerpt title and then click "play" when the player opens.

• Impressionism
  • General listening examples:
    • Nuages gris, by Franz Liszt (1881). Think of it as the "gateway to Impressionism." Written in the key of g minor, it uses Impressionist-type devices to obscure the sense of G as tonic. This kind of thinking about music was a big influence on Debussy's compositional style.
      • The score for Nuages gris
    • Excerpts from Debussy's Les Préludes (1909-1913):
      • Alternating Thirds
      • Fireworks
      • Wind on the Plain
      • Footsteps in the Snow
    • Recording for Debussy's Sarabande from Pour le piano (1901)
  • Augmented Triads
    • Hugo Wolf, Das Verlassene Mägdlein, an example of augmented triads used to blur / suspend the sense of tonality.
      • The score for the Hugo Wolf excerpt.
    • Claude Debussy, Prelude from Pour le piano (1901). In this case, augmented chords are used to make a fairly standard functional chord progression sound exotic and uncertain, and to heighten the emotional reward of the two "V-I" tonicizations of C Major (cadences?).
      • The score for the Debussy excerpt.
  • Modal / Linear Cadences
    • Phrygian Cadence: the Gloria from Johannes Ockeghem (c. 1410-1497), Missa Cuiuvis Toni.
      • The final 30 seconds - listen for the cadence incorporating motion from Ra to Do.
      • If you are interested in hearing more music in the Phrygian mode, here is the entire movement.
    • Linear Cadence: Debussy, Le vent dans la plaine (Les Préludes, Book I, no. 3), final page:
      • Score (annotated)
      • Recording (excerpt)
  • coming soon .... Planing.
  
  
• Embellishments to Tertian Harmony (used in Impressionist style, and after)
  • Extended ("Tall") chords - see the MUSC 3A website.
  • Add-note chords
  • Suspended chords
  • Indeterminate chords
  • Split-note chords
    • This example from Gustav Holst's The Planets, Op. 32 (1916), movement seven ("Neptune, the Mystic") has two interesting features - a minor-major seventh chord (the "Hitchcock" chord), and also a chord with a split third (in the woodwinds).
      • Score
      • Recording
  
  
• Quartal/Quintal Harmony
  
  
• Secundal Harmony (Tone Clusters / Cluster Chords)
  • Listening example: Arvo Pärt, collage über b-a-c-h (1964), movement 2. This Sarabande movement juxtaposes a common-practice, Bach-style obbligato aria with a set of secundal harmonies (tone clusters). The contrast is shocking, to say the least. Keep in mind that these clusters are chromatic (all m2), and also large (spanning an octave), so they are more dissonant than they would be if only few notes were involved.
    • Score (first two pages only)
    • Recording (first two sections only)
  
  
• 20th Century Scale Resources
  • Pentatonic (five-note) scales. Examples: Major pentatonic (Do-Re-Mi-Sol-La), minor pentatonic (Do-Me-Fa-Sol-Te), and the other three modes of the pentatonic scale.
  • Hexatonic (six-note) scales. Example: the Whole-Tone scale.
  • Heptatonic (seven-note) scales. Examples: Major, minor, and the diatonic "church" modes.
  • Octatonic (eight-note) scales. Scales with more than seven notes involve one or more chromatically "split" notes - two notes with the same letter name in one scale. For example, the scale C-D-E-F-F#-G-A-B is an octatonic scale, containing two notes that use the letter F (but one is chromatically altered).
    • Diminished Scales - a sub-category of octatonic scales, built of a repeated pattern either whole step - half step or vice-versa (WHWHWHWH or HWHWHWHWH). These scales are built by combining two fully-diminished seventh chords whose roots are a step apart. They are frequently used by Hungarian composer Béla Bartók. Below are two examples from his pedagogical work, Mikrokosmos (1926-1939).
      • "From the Isle of Bali" (No. 109)
        • Score
        • Recording
      • "Diminished Fifth" (No. 101) - this piece uses two different diminished scales.
        • Score
        • Recording
  • 9-note, 10-note, and 11-note scales - adding additional split notes.
  • The chromatic scale (12-notes) - this scale is fully split - all possible half steps are included.
  • Synthetic scales - any scale new to 20th century music - new tetrachord combinations, split note scales, etc. Basically, any scale not from the common-practice period.
  
  
• Pandiatonicism
  • Pandiatonicism is a sub-category of the harmonic language we call "free tonality" (see below). Pandiatonic music limits itself to a defined set of pitches, which could be a Major or minor key, a modal key, or any pitch set the composer chooses. The composer then uses all of these "diatonic" pitches freely to create whatever sounds are desired. Very few, if any, pitches from outside the chosen diatonic set are tolerated.
  • Pandiatonic music is firmly anchored around a particular tonic pitch, which can be established using traditional functional methods (not preferred), or through linear or repetitive tonicization, or however the composer chooses.
  • Example One: Aaron Copland, Appalachian Spring (1944), original chamber version (13 instruments). Pandiatonicism (along with quartal/quintal harmony) is a primary part of Copland's harmonic language. Here are several examples from Appalachian Spring that illustrate his usage of these techniques.
    1. Example 1A - This excerpt (reduced to four-part texture) from the transition to the Shaker Tune is pandiatonic in the key of A-flat Major. I have included both chord root/quality analysis and traditional harmonic analysis (Roman numerals), primarily to show that use of pandiatonicism creates a lot of chords that are non-functional. This limits the utility of traditional analytical language. It is interesting to note that while the 2nd, 3rd, and 4th chords from the end are all D-flat add2 chords, they each sound very different simply by clever re-voicing each time. In fact, they do not sound like they are all using the same harmony at all.
       • Score
       • Recording
    2. Example 1B - This example is significant because the pitch collection used includes both C Major and c minor - blending the concepts of pandiatonicism and modal mixture. Copland's method of establishing the tonic is fascinating - he uses four different harmonizations of the V chord to create his "Sol-Do" references. Can you find and analyze all four?
       • Score
       • Recording
    3. Example 1C - This excerpt is from the beginning of the piece. The music here is pandiatonic in A Major. At rehearsal #2, however, something even more impressive is also going on. Copland is building a stack of triads, each repeated only in their own voice: D Major in the cello, A Major in the viola, and E Major in the 2nd violin. Together, these three triads contain all 7 notes of the A Major scale. However, when considering the chord roots expressed by each triad, we see that the prevailing harmony in this passage is actually a D quintal chord (DQ5: D-A-E). This harmony is confirmed by the melodic line (flute and 1st violin), which ends with the arpeggio D-A-E just before rehearsal #3. Copland is working seamlessly at three different textural levels at the same time: pandiatonic texture, tertian/triadic melodic gestures, and quintal harmony.
       • Score
       • Recording. The recording begins in measure one, to further establish the sense of pandiatonic writing.
  • Example Two: Igor Stravinsky, Petrushka (1911 version), Scene 1 (The Shrovetide Fair). This example, while pandiatonic in the key of G Minor, also uses polychords (more examples below).
    • Score
    • Recording
  
  
• Polychords
  • A concise definition of a polychord is more than one harmonic structure sounding at the same time. These chords (simultaneities, verticalities) may be of any type (secundal, tertian, quartal, etc) and quality. The individual chords tend to be in close position (whether inverted or not), and spaced widely apart from each other. They also tend to be different enough to keep the ear from "adding" them together: for example, a polychord of gm / CM would probably sound to the ear like a CMmM harmony rather than two distinct chords.
  • Example One: Igor Stravinsky, Petrushka (1911 version), Scene 2 (Petrushka's Room). This is the famous "Petrushka chord," which demonstrates one of the most important concepts in twentieth century music - anything that can be done vertically (as a chord or simultaneity) can also be done horizontally as a melody or linear structure. This polychord is C Major / F# Major, but is expressed as two simultaneous chord arpeggiations.
    • Score
    • Recording
  • Example Two: Igor Stravinsky, The Rite of Spring, (1913) "Danses des adolescentes." The violins and violas play an E-flat Mm7 chord, while the celli and basses play an F-flat Major triad. There is one octave between the two chords, but it is really the physical separation between the violins and celli on stage that creates the sense of simultaneous harmonies (polychord) rather than a single dense chord. The eight French horn parts provide accents for both chords.
    • Score
    • Recording
  • Example Three: William Schuman, Three Score Set (1943), movement two. This entire movement is based on the use of polychords.
    • Score
    • Recording
  
  
• Polytonality and Bimodality
  • Polytonality is an extension of the concept of polychords. Instead of having a momentary clash between two different harmonies, polytonal music has more than one tonal center active at the same time. In practice this means two tonal centers (that is, bitonality), because it is extremely difficult to establish more keys than that at the same time. Even two tonics are hard to maintain, so polytonal music tends to be more polyphonic than usual, and also tends to be very simple both harmonically and melodically.
    • Example One: Maurice Ravel, Violin Sonata (1927). The second movement, "Blues: Moderato" polytonal - it is in G Major and A-flat Major at the same time. The violin begins in G, and continues in G after the piano joins in A-flat. Later, they trade keys.
      • Recording
    • Example Two: Béla Bartók, "Song of the Harvest," No. 33 of 44 Duos for 2 Violins (1931). This piece is polytonal, with each violin part playing within a different octatonic scale. The actual tonal centers and form of this piece are fairly complicated - see this article by composer Richard Trythall for a very detailed analysis.
      • Score
      • Recording
  • Bimodality is a related concept. In this approach, two different modes of the same tonic are used; so the harmonic content of each is different, but the actual tonal center is the same. Bimodality is a much easier technique to use than polytonality, because only one tonal center is being emphasized.
    • Example: Béla Bartók, Major and Minor, from Mikrokosmos (1926-1939), Book 2 No. 59. In this case, the right hand is in a minor mode (either F Dorian or F Aeolian), and the left hand is in a major mode (F Lydian).
    • Note - bimodality is not to be confused with the concept of modal mixture (see Appalachian Spring, above). Use of bimodality (or polytonality) implies a large degree of polyphonic texture, where two discrete, independent and equally important melodic lines are present at the same time, each one using a different mode (or tonal center, in the case of polytonality). Modal mixture simply means that the composer is borrowing freely between Major and parallel minor to allow more harmonic options.
    • Another note - see the "handouts" section, above, for an easy Stravinsky piece using bimodality that you can play on the piano.
  
  
• Free Tonality
  • Free Tonality is a post-Impressionist musical style where the music has an clearly identifiable tonal center, but the composer may achieve that tonality through any methods desired. All pitches of the chromatic scale can be used in whatever combinations are required. Also, functional relationships are allowed but not necessarily emphasized. Pandiatonicism is a type of free tonality that is constrained to a smaller, defined pitch set; free tonality as a broad genre can use any pitches, whether in or out of a key or whether closely related to the tonic or not. Two composers representative of the free tonal genre are Copland and Hindemith.
    
    
  • works of Aaron Copland (recordings only): Copland's harmonic language is primarily tertian, with quartal/quintal elements. Through his linear melodic lines and chord voicings featuring open fourths and fifths, his harmonies end up sounding much more "quartal" than they truly are. Pandiatonicism is also a major component of Copland's use of free tonality.
    
    
    1. Fanfare for the Common Man (1942), the clearest and most obvious use of quartal/quintal harmonies in Copland's body of work. As in Appalachian Spring (see example 3 under "Pandiatonicism," above), Copland's quartal "chords" are often horizontal, not vertical - they play out in a single melodic line.
    2. Now compare the original Fanfare to this version, which Copland wrote into his Third Symphony (1946). The fourth movement begins with a woodwind chorale version of the Fanfare, followed by a re-orchestrated version of the original brass/percussion Fanfare. The symphony continues with a beautiful chamber music interlude in the woodwinds, still based on the Fanfare melody for a time before the actual theme of the fourth movement emerges.
    3. Excerpts from Rodeo - Four Dance Episodes (1942). Copland orchestrated this suite using music from his ballet score by the same name.
       • Movement Three: Saturday Night Waltz (excerpt)
       • Movement Four: Hoe-Down. "Beef - it's what's for dinner! (bum bum bum)" Madison Avenue leveraged the Cowboy/Wild West connotations of this movement to sell steak. They knew we didn't need to have this music explained to us - this is what the American West sounds like. While you are listening, pay attention to how important the percussion section (including piano) is to Copland's sound landscape.
    4. The finale from another ballet score, this time the concert version of Billy the Kid (1938). This excerpt is the final movement, "The Open Prarie Again." To demonstrate the open spaces of the American prarie, Copland uses a lot of open space in his harmonic texture by emphasizing fourths and fifths. Note: as a general rule for Copland's music, despite the openness and emphasis on fourths or fifths, in many cases the chords he uses are tertian triads - they just sound quartal/quintal because of their voicing.
    5. These two excerpts from the score to the movie Hidalgo (composed by James Newton Howard) demonstrate the enormous impact Copland's music has had on American popular culture.
       • Excerpt 1
       • Excerpt 2
    
    
  • works of Paul Hindemith (recordings only): Hindemith's harmonic language features gradually increasing dynamics and dissonance, suddenly resolved by a recognizable tonal harmony (such as a major triad). He uses a tonal center for his compositions, but does not use a "key." For him, only the tonic note was important for establishing tonality, not whether the music was in Major or minor or any other type of modality.
    
    
    1. Fuga Prima in C
    2. Hindemith's Symphony: Mathis der Maler (1934) was taken from music for his opera by the same name. Each movement of the symphony describes a scene painted by Matthias Grünewald on the Isenheim Altarpiece at the Monastery of St. Anthony at Isenheim (near modern Alsace, France).
       • Movement One: "Concert of Angels" (excerpt) - this excerpt covers the introduction and the beginning of the fugue. The fugue (beginning at 2:10) has three voices, one for each angel in the painting.
       • Movement Two: "The Entombment" (excerpt) - this excerpt is from the middle section of the movement, and builds to massive proportions from a simple woodwind melody. Listen for the climax/resolution!
       • Movement Three: "The Temptation of St. Anthony" (excerpt) - this excerpt is the introduction and beginning of the exposition. The melodies and harmonies are much more angular in this movement than in the other two. The famous tertian phrase resolutions are absent.
    3. Hindemith's Sonata for Oboe and Piano (1938) is typical of his chamber music writing.
       • Movement One - this excerpt is the exposition of the movement's sonata form. Listen for the E Major triad that ends the exposition.
       • Movement Two - this excerpt comes from the end of the A section, and shows Hindemith's technique of starting with a short melodic fragment, then making it longer and more dissonant until a final tonal resolution.
  
  
• Serialism or "Twelve-Tonality" (also "Dodecaphony" or "Serial Atonality")
  1. Luigi Dallapiccola, "Simbolo" from Quaderno musicale di Annalibera (1953).
     • Recording
     • Score
     • Tone Row Matrix
  2. Arnold Schoenberg, Piano Piece, Op. 33a (1928). Score available in the Burkhart Anthology, pp. 430-434.
     • Recording
     • A handout showing how Schoenberg breaks his tone rows down into smaller "cells" made up of 3-4 notes.
     • A handout showing the process of finding the P-0 row for Schoenberg's Op. 33a.