Music Theory I
Handouts
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Review handouts from Music Fundamentals:
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Flashcards! Instructions: print the flashcards out, then photocopy them double-sided, cut them out, and start memorizing!
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Flashcards for reading in treble and bass clef
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Flashcards for key signatures.
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Functional Harmony handout: "The Solar System of Harmony!"
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Part-Writing handouts
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Guidelines for Bach-style part-writing
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Here is a link to an article written by Dr. Matthew Fields explaining why we avoid writing parallel P5 and parallel P8 in Bach-style SATB chorales (when the article loads, scroll to page 13).
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My key to the abbreviations I use when correcting your part writing exercises.
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A summary of the different types of non-chord tones.
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Theory I Topic List - click a link to scroll down to that section of the listening examples!
Exercises
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Practice exercises for chord inversions and harmonic analysis
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Four-part (SATB) Bach-style chorales for practicing Roman numeral analysis
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In-Class Exercise 1: Harmonic Analysis (diatonic)
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Chord analysis practice for the Midterm Exam
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In-Class Exercise 1B: harmonic analysis
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In-Class Exercise 2: find all of the part writing errors in this chorale (Includes answers)
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In-Class Exercise 3: four-part chorale analysis practice
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More analysis practice - this time for chords and cadences
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In-Class Exercise 4: four-part chorale analysis practice (including cadences and non-chord tones)
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In-Class Exercise 5: realization of figured bass (with harmonic analysis and four-part writing)
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Practice for the final exam, including complete harmonic analysis and figured bass.
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In-Class Exercise 6: realization of figured bass
Concepts and Listening Examples
Topic 1: Musical Texture
The concept of texture deals with the relationships between the different lines of music ("voices") that are coexisting within the piece. Some types of music use only one kind of texture, but for many styles all textures are possible and composers change texture as a way of introducing variety and contrast into their music. Before listening to the examples below, consider the folk song "Row, Row, Row Your Boat." It is possible to perform this song using any of the textures described below.
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Monophonic texture ("monophony"): a unison melody. All performers are doing exactly the same thing, so there is only one "voice."
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For "Row, Row, Row Your Boat," have everyone sing the melody together at the same time, with no other music.
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Examples:
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Puer natus est nobis (Gregorian chant, c. 800 AD)
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Mozart, Symphony No. 40 in G Minor, KV 550 (1788), movement 4 (development). While plainchant is one of the few musical genres that is totally monophonic, many other types of music will include sections in monophonic texture. Even a group as large as a symphony orchestra can perform monophonically.
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Polyphonic texture ("polyphony"): polyphonic texture features many independent melodic lines, each equally important (no single voice stands out as the most important melody). The most popular use of this texture is in fugues and canons, where one tune is passed through many voices equally.
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For "Row, Row, Row Your Boat," sing this song "in the round," as it is usually done around the campfire. Each group of singers (a "voice") is equally as important as any other group. In this instance each voice is using the same tune, but that is not a requirement for polyphonic music.
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Examples:
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J.S. Bach, Fugue in A Minor, BWV 543 (c. 1709). A fugue is a very organized form of polyphony. The melody is called the "subject." The subject gets played by each voice, along with a countermelody (called the "countersubject") that each voice plays after it finishes the subject. For example, at the beginning of this excerpt you will hear the subject in the soprano voice; when the subject starts over in the alto voice, the soprano plays the countersubject. Sections of the piece where neither melody is being played are called "episodes," and are designed to give your ears a break and introduce new melodic material (the first episode begins near the end of this excerpt). This piece is a four-voice fugue, although the excerpt ends before all voices are deployed.
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Perotin, Sederunt principes (c. 1199) - an example of organum, a style of sacred vocal music popular around the year 1200. This example has four voices - one voice (the tenor) sustaining long notes, and three more rhythmically active voices (all four voices are not always present at the same time)
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Andrew Lloyd Webber, Phantom of the Opera (1986). Sometimes polyphonic music can sound chaotic and disorganized, particularly if the different voices are not using the same rhythms. In this excerpt, there are at least three different tunes overlapping, but all are equally important to the plot. In live performances, the characters tend to spread out on the stage and sing to different parts of the audience to avoid confusing the listeners too much.
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Homophonic texture ("homophony"): music using homophonic texture features one prominent melody, with all other voices acting as support - providing harmony and accompaniment. The melody is the most important or most dominant voice.
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For "Row, Row, Row Your Boat," have everyone sing the melody in unison while someone plays chords on the piano to harmonize the melody.
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In homophonic music, the melody and bass are the most important voices. One way to make the music sound more interesting is to make the bass line more "active." Avoid writing bass parts that are simply sounding the root of each new chord. Use chord inversions and non-chord tones to make the bass more melodic and singable, and to give it a sense of forward motion.
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Examples:
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Fernando Sor, La Romanesca (1835). Homophonic music can be as obvious as a single solo instrument with accompaniment - in this case, oboe and harp.
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Most symphonic music is primarily homophonic, although any texture can be used in an orchestral piece. Here are two examples from symphonies by Antonín Dvořák: the fourth movement from his Symphony No. 8 in G Major, Op. 88 (1889), and the first movement from his Symphony No. 9 in E Minor, Op. 95, "From the New World" (1893).
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Bach chorales are an interesting transitional form between polyphonic and homophonic texture. They are homophonic in that the soprano line is the dominant melody and all other voices are accompanying and supporting the soprano line, but each line is also its own independent melodic line - a hold-over from the Renaissance when polyphony was the most important type of musical texture. Here are two chorale examples by J. S. Bach (accompanied by orchestra and organ): the first is from the St. John Passion, BWV 245 (1724), and the second is from the St. Matthew Passion, BWV 244 (1727).
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Heterophonic texture ("heterophony"): heterophonic music features more than one voice performing the same melody, but each voice is embellishing the tune so that the voices do not "line up" - making it sound different from simple monophony.
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"Row, Row, Row Your Boat" - to achieve heterophonic texture, each member of your group needs to sing the tune at the same time, but taking their own liberties with the melody by adding embellishments, ornaments, etc.
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Examples:
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"Lonesome Valley" from the film O Brother, Where Art Thou? (2000)
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Dixieland or New Orleans Jazz is famous for its use of heterophony, particularly at the head of the tune when different musicians improvise on the tune at the same time. This example is from "Hotter Than That" (1927), played by Louis Armstrong and His Hot Five.
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Texture Summary - When there are a lot of things going on in the music, it can be hard to determine the texture. When is it homophonic with a complicated accompaniment, and when does it become polyphonic, with each melodic line carrying equal weight? In the Quintet from Leonard Bernstein's West Side Story (1961), all four musical textures are demonstrated, showing how a composer can move freely between textures to suit their music. At the point that our excerpt starts, the Jets have just finished singing their melody as they prepare for their fight with the Sharks. Maria joins in singing the "Tonight" melody at the same time (polyphonic). While this is going on, the Sharks start singing their own version of the Jets' song, and Anita sings her own version of "Tonight" (heterophonic - there are two simultaneous variations on each song). The excerpt finishes with Tony and Maria singing "Tonight" together, the Sharks and Jets singing their tune together, and Anita singing a countermelody (polyphonic - all voices equal). They all end on a single chord together (homophonic).
Topic 2: Voice Motion
When comparing how two melodic lines ("voices") are moving against each other, we use four different terms: parallel (same direction, same interval), similar (same direction, different intervals), contrary (opposite directions), and oblique (one voice stays on the same note, one voice moves either towards or away).
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The ear is most satisfied by hearing either contrary or oblique motion between the outer voices of a composition (the "soprano" and "bass" lines). This applies to Bach chorales, and to any other style of music, even Rock 'n Roll - in the Billy Joel tune at right (The Longest Time, 1983), there is a great deal of contrary motion between the melody and the bass in the first half of the verse. In the second half (not provided), the motion becomes less contrary and more parallel, until the end of the phrase when it becomes contrary again.
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Listening exercises: here are two companion minuets, written in 1725 by J.S. Bach: the first in G Major (BWV Anh 114), and the second in G Minor (BWV Anh 115). They each have only two voices, soprano and bass. Listen carefully and try to determine the type of voice motion being used between each beat. For dictation practice, diagram out the voice motion of each piece by figuring out how many measures there are, and writing P (parallel), C (contrary), O (oblique) or S (similar) for each beat of each measure.
Topic 3: Cadences
A cadence is a musical punctuation mark, used to give a sense of flow and pacing to music. The strength of a punctuation mark (like a comma versus an exclamation point) communicates to the reader whether the idea is complete or if the writer is just pausing for emphasis. Just like a run-on sentence, music written without cadences can sound breathless, hurried and panicky. Consider these points about how cadences are used:
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A cadence only occurs at the end of a musical phrase.
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A cadence is an event involving the final two chords or harmonies of a phrase. Chord quality does not matter - only function. In the examples below, you will see Arabic numbers (1,2,3) instead of Roman numerals (I, ii, iii). This is to show that, for example, if a cadence uses the "Five" chord (dominant), it doesn't matter if it is Major V or minor v - only that it is "5."
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When phrases are paired together (into a musical "period"), the first (antecedent) phrase usually ends with a weak cadence, and the second (consequent) phrase usually ends with a strong cadence. When thinking about periodic structure in music, think of the antecedent as a question, and the consequent as the answer. The question does not make sense unless it is immediately followed by an answer. Using a weak cadence tells the listener that the answer is coming.
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Using written English as an example, which of these two statements makes the most sense?
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I woke up! And went to school,
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I woke up, and went to school.
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In the first example, the presence of a strong punctuation mark in the middle of the statement disrupts the flow of the argument. The lack of a strong ending to the statement leaves the listener wondering what has been left out. The second example is correctly punctuated - the first clause is a complete statement in itself, but it is not the entire argument so it ends with a comma to tell the reader to expect more afterward.
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Like written language, music needs to have a meaningful balance of motion and rest for it to be understandable to the listener. Cadences are one important way for the composer to communicate clearly with the audience.
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In music of the Common Practice era (approximately 1600-1900), there are four main types of cadences. Music written before and after this period has additional types of cadences. Theory 1A concentrates on Common Practice music; the four primary cadence types are listed below with examples.
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Authentic Cadence. The most common and most obvious type of cadence; in an authentic cadence, the harmony moves from dominant-function (5 or 7) to tonic (1). There are two varieties:
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Perfect Authentic Cadence (PAC) - for an authentic cadence to be perfect, three things must be true. If all three of these requirements are not met, the cadence is not a PAC:
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The harmony moves from 5 to 1.
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The bass voice leaps from Sol to Do (up or down).
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The soprano voice ends on Do.
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Imperfect Authentic Cadence (IAC) - the harmony moves either 5 to 1 or 7 to 1. No other requirements are needed.
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Example 1: the final phrase of the fourth movement of Felix Mendelssohn's Symphony No. 5, "Reformation," Op. 107 (1832) ends with a perfect authentic cadence.
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Example 2: at the beginning of the same movement, the third and fourth phrases are a period. The antecedent phrase ends with a plagal cadence (see below), and the consequent phrase ends with a perfect authentic cadence.
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Plagal Cadence (PC). The plagal cadence moves from 4 (subdominant) to 1 (tonic). This cadence is commonly called the "Amen cadence" because it is often found at the end of Protestant hymns in Major keys, accompanying the word Amen: Ah (IV) --- men (I). In classical music, the plagal cadence is often in a minor key (iv-i).
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There is some debate about the plagal cadence; some theorists maintain that, because the IV-I motion is usually preceded by a V-I gesture, the plagal motion doesn't really stand on its own. Rather than calling it a plagal cadence, they call it a plagal extension of an authentic cadence. The Brahms example below actually illustrates this very well - there are a series of V-I motions right before the final IV-I statement.
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Example 1: again in Mendelssohn's Reformation Symphony, the first movement ends with a plagal cadence in the key of D minor.
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Example 2: in Johannes Brahms's Symphony No. 4 in E Minor, Op. 98 (1885), the first movement also ends with a plagal cadence.
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Half Cadence (HC). The half cadence ends on the dominant chord, 5. Any other chord may be used in the first half of the cadence. The half cadence is a weak gesture (a musical "comma"), and so it appears at the end of an antecedent phrase of a period. A lot of Common Practice music is built using periods that arch upward to the dominant (antecedent, ending with HC) and then fall back to the tonic (consequent, ending with PAC or IAC).
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Example 1: The very first phrase of Beethoven's Symphony No. 5 in C Minor, Op. 67 (1808) ends on a half cadence.
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Example 2: The first two phrases of the Minuet (third movement) from Haydn's Symphony No. 6 in D Major, "Le matin," Hob. 1/6 (1761) are a contrasting period. The antecedent phrase ends with a half cadence (at around 10.5 seconds in the recording), and the consequent phrase ends with a perfect authentic cadence (V-I harmony, the flute ends on Do, and the bass leaps Sol-Do).
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Deceptive Cadence (DC). In general terms, calling something "deceptive" in music means that it almost goes where we expect it to, but not quite. In this case, when we hear a cadence beginning with V, we are conditioned to expect it to move to I - an authentic cadence. Instead, the deceptive cadence moves from 5 to 6 (usually V-vi in a Major key). This works best by having both chords in root position, and by resolving the leading tone up to tonic as it should, but then moving the bass up by step from Sol to La instead of leaping from Sol to Do. In this way, we get one of the resolutions we expect (Ti-Do), but not the other (Sol-Do) - so the result sounds like we were tricked.
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Example: The minuet from Haydn's Symphony No. 6 also has many deceptive cadences. In this particular example, after the deceptive cadence the phrase is then extended with an additional authentic cadence, but this is not a requirement.
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More on periods:
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A Parallel Period is one where the antecedent and consequent phrases start the same way. The consequent phrase can have a different ending - only the beginning of the phrase has to be the same as the antecedent. For example, the childrens' song "Mary Had a Little Lamb" has two phrases that both start with the same melody, forming a parallel period.
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Phrase One: "Mary had a little lamb, little lamb little lamb" (Mi Re Do Re Mi Mi Mi, Re Re Re, Mi Sol Sol)
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Phrase Two: "Mary had a little lamb whose fleece was white as snow" (Mi Re Do Re Mi Mi Mi Mi Re Re Mi Re Do).
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A Contrasting Period is one where the consequent phrase starts differently than the antecedent phrase.
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The antecedent phrase should end with a weak cadence: IAC, HC, or DC.
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The consequent phrase should end with a strong cadence: PAC, PC (or IAC - less common).
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Topic 4: Non-Harmonic Tones
Non-harmonic tones, or NHT (also called non-chord tones or NCT) are notes that are not part of the harmony. They are added for melodic embellishment, to make the music more intricate and interesting, or to smooth out music with a lot of leaps. When analyzing music, first figure out the chord being played, and then circle any notes that do not fit into the chord. These are the NHT. In classical music there are nine types of NHT; many of them are still used in today's compositions and in popular music as well. NHT may be accented (occurring on the beat) or unaccented (occurring off the beat).
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Passing Tone (PT): approached by step, resolved by step in the same direction.
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Neighboring Tone (NT): approached by step, resolved by step in the opposite direction (returns to starting note).
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A neighboring tone may be above the chord note (upper neighbor) or below it (lower neighbor).
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Changing Tones (CT): Also called cambiata, this is a pair of notes: one upper neighboring tone and one lower neighboring tone.
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For example, think about the beginning of the song "Some Enchanted Evening" from the musical South Pacific (1949). In this example the melody is Do-Ti-Re-Do Do Sol. The harmony during this tune is I (Do-Mi-Sol). The Ti and Re in the melody would be analyzed together as CT.
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Appoggiatura (APP): approached by leap, resolved by step (usually in the opposite direction). The appoggiatura is usually accented (occurs on the beat).
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The "formula" for an appoggiatura is to leap up then step down. This does not always have to be the case, however. In the song "Maria" from Leonard Bernstein's West Side Story, at the start of the chorus the "ri" in the word "MaRIa" is an appoggiatura on the downbeat. It leaps up by an A4, then resolves up by a m2 (Ma-ri-a = Do-Fi-Sol)
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Retardation (RET): the physical opposite of a suspension. It works in exactly the same way, except that the resolution is up by step instead of down.
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Anticipation (ANT): the temporal opposite of a suspension. In an ANT, one voice resolves early to the note it will have in the next chord. This often happens at the final cadence of a chorale, in an inner voice.
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Step one: all voices sing the first chord.
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Step two: one voice moves early (often on an eighth note) to a note from the next chord.
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Step three: all remaining voices move to the next chord.
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Example: this phrase from the chorale movement of J. S. Bach's cantata, Herr Christ, der einge Gottessohn, BWV 96 (1724) ends with an anticipation in the alto voice.
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Escape Tone (ET): the opposite of an appoggiatura: the escape tone is approached by step and resolved by leap. Remember: "To escape a burning building, step to the window and leap out!"
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Suspension (SUS): approached by sustaining a note from the previous chord, then resolved downward by step.
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The suspension is a three-part event, involving two chords:
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In the first chord, the note fits into the chord.
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The harmony changes for the second chord, but one voice retains the note from the first chord. This is the "suspended" note.
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While still in the second chord, the suspended note resolves down by step, once again fitting into the harmony.
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There are four types of suspension, measured by the interval distance of the suspended note above the lowest chord note. The four types are 9-8, 7-6, 4-3, and 2-3 (bass suspension). For example, in a 4-3 suspension, the suspended note is a fourth above the bass, and it resolves to a third above the bass.
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Example: J. S. Bach's Prelude in E-flat Major, BWV 998 (c. 1745) ends on a 4-3 suspension.
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Pedal Tone (PED): Also called a pedal point, this is a long-term event, not a single note. Pedal points often occur in the bass, where they used to be played on the pedals of the pipe organ. One voice, usually the bass, sustains a note for a very long time. This note is sometimes part of the harmony, and sometimes not. Pedal points are often on the dominant or tonic pitches of the key. The purpose of a pedal point is to draw the listener's attention to the dominant (after a period of harmonic uncertainty), to prepare them for the final resolution back to tonic.
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Example 1: Beethoven, Symphony No. 5 in C Minor, third movement. There is a tonic pedal in the timpani for the last minute of the movement, which helps link the third movement directly into the fourth movement.
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Example 2: Bach, Prelude in C Major, BWV 846 from The Well-Tempered Clavier (1722). In this excerpt from the end of the piece, the bassline has arrived on Sol (the pitch G, in this case), it becomes a dominant pedal for eight measures. The constant repetition of the dominant pitch (sometimes part of the harmony, sometimes not) builds tension and intensity into the piece. This tension is finally released in the ninth bar when the bass falls from Sol to Do at the beginning of the coda. The piece then ends on a C Major chord.
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The score for this excerpt.
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Topic 5: Chords in Second Inversion
While root position, first and third inversion chords may be used freely, second inversion chords fall into four general categories based on the type of voice motion being used in the bass. A chord is not put in second inversion unless it would fit into one of these four types. This applies to triads and seventh chords in second inversion. The four types of second inversion chords are:
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Passing 6/4: The bass moves by step to the 6/4 chord, and then moves away by step in the same direction (like a passing tone). This chord usually appears on a weak beat.
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Pedal 6/4: The bass stays on the same note before, during, and after the 6/4 chord. This chord usually appears on a weak beat.
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Arpeggiated 6/4: The bass moves to and away from the the 6/4 chord by leap, arpeggiating all of the notes of a triad. This type of 6/4 chord is used to embellish a single harmony, making the bass line more interesting. This chord usually appears on a weak beat.
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Cadential 6/4: This is a special type of 6/4 chord that only occurs with the tonic triad, and only right before a cadence. When the tonic triad is in second inversion, Sol is in the bass (and doubled in an upper voice), giving the chord a dominant feeling. But it also has a pre-dominant function, meaning that it must resolve to V. This is part of a standard cadential formula: I6/4 - V7 - I (AC). This formula is so strong that this is the primary way that I6/4 may be used, and whenever I6/4 is heard there is a strong expectation that V7-I will follow. Unlike the other types of second inversion, the cadential 6/4 usually appears on a strong beat.
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The I6/4-V7-I formula is exploited in concertos, to signal the start of the soloist's cadenza. The orchestra drives to the I6/4 chord, which is held with a fermata then released. After this silence the soloist performs their cadenza, ending on a dominant trill (trilling on a member of the V chord). This is the orchestra's signal to rejoin the soloist on the V chord, which then moves to I.
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Cadenza example one: Haydn, Concerto No. 1 for Cello in C Major, Hob. VIIb/1 (1765), movement 1.
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Cadenza example two: Beethoven, Concerto for Violin in D Major, Op. 61 (1806), movement 1.
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