Music Theory III

Franz Schubert (1797-1828) - the offical composer for Theory III

Schubert at work - accompanying his Lieder

at a salon concert

Handouts and Exercises
  • REVIEW: A packet of harmonic analysis practice exercises focusing on diatonic harmony, secondary harmony, and diatonic pivot modulations.

Theory III Topic List - click a link to scroll down to that section of the listening examples!

  1. Altered predominants

  2. Non-traditional chord resolutions

  3. Advanced forms of modulation

  4. Altered dominants

  5. Tall chords (extensions to the triad)

  6. Tritone substitution

  7. Linear chromaticism

  8. Chromatic mediants

  • REVIEW 3: Part Writing handouts

    • Guidelines for Bach-style part-writing.

    • My key to the abbreviations I use when correcting your part writing exercises.

    • Self-Test Exercise: identify as many part writing errors as you can. The solution is also provided.

Transposition Exercise 1 - Adduci
  • In-Class Activity 1: analysis of Schubert's lied, "Der Müller und der Bach" from Die schöne Müllerin, Op. 25.


  • In-Class Activity 2: How many keys does this Mm or dd seventh chord function in? (includes answer key)


Concepts and Listening Examples

Topic 1: Altered Predominants

  • Please refer to my Theory 2 page for the theoretical background for, and examples of pivot chord modulation, modal mixture, and altered predominants. More advanced examples of altered predominants (N6 and Aug6 chords) are shown below:

Advanced examples of the Neapolitan chord:

  • Tchaikovsky, theme from Swan Lake, Op. 20 (1876). This statement of the theme, in B minor, is the opening to Act 2 of the ballet (the theme appears in each act). The recording starts in measure 8; there is a prominent Neapolitan chord (CM) in measure 17.

    • Score

    • Note; the resolution of the N chord (mm. 18-19) is slightly unusual: N6 - V/V - V - i (the secondary dominant interrupts the expected N6 - V motion).

  • Bach, Passacaglia and Fugue in C Minor, BWV 582, Fugue (coda). In this example, notice the insistence on V - i motion, setting up an expectation of V on the downbeat. Bach uses the Neapolitan instead, then follows with a long pause to further emphasize this unusual chord. After the caesura, the coda resumes with the expected V chord and then the concluding section emphasizes the modal mixture of I and iv.  Also pay attention to the importance of the final tonic pedal and the imperfect authentic cadence, viio7 (fully dim.) - I (Picardy third).

    • Score (the recording starts at the last measure of the second system)

  • Bonus Example: Rachmaninov, Piano Concerto No. 2 in C Minor, Op. 18 (1901), second movement (excerpt). This is the beginning of the cadenza for the second movement, which is approached from I6/4 to N6 motion in the orchestra instead of the traditional pause on I6/4.

Swan Lake - Introduction to Act 2 - Tchaikovsky
Fugue, from Passacaglia and Fugue in C Minor, BWV 582 - Bach
Piano Concerto No. 2 in C Minor, II - Rachmaninov
  • The Augmented-sixth chord - advanced concepts:

    • The German chord, in particular, can be useful as a tool to modulate to distantly-related keys, because it sounds like a Mm7 chord. Respelling one or more notes of the German chord enharmonically can allow us to stack up a tertian Mm7, which we can then use to pivot to a new key where either that Mm7 exists, or where it is V7 of a diatonic chord.

    • The German chord contains the notes Le (b6), Do (1), Fi (#4), and Me (b3) - in C Major: Ab-C-F#-Eb. The notes with accidentals can be respelled enharmonically as follows:

Option 1: Respell Me (b3) as Ri (#2) - this changes the resolution tendency of Me, making it rise by step instead of falling by step. Me wants to fall to Re, while Ri wants to rise to Mi. This can be used to facilitate a mutation from minor to parallel major.

Option 2: Respell Fi (#4) as Se (b5) - this gives us Ab-C-Gb-Eb, which can be rearranged as AbMm: Ab-C-Eb-Gb. This chord is V7 of Db, so we can pivot to any key containing AbMm, or DbM or Dbm. This is how songs like Beyoncé's "Love on Top" (2011) can modulate up by half step after each phrase.

Topic 2: Non-Traditional Chord Resolutions

  • As the common-practice system of functional harmony began to be stretched and made increasingly chromatic, it became more common for composers to set up a chord that has an expected function, and then in some way fail to realize that function. There are two main ways to accomplish this: either the chord can resolve properly but not immediately, by inserting additional chords between the tendency chord and its chord of resolution; or the chord can resolve deceptively, that is, to a chord that has some sort of close relationship to the expected chord of resolution. Note, neither of these techniques are the same as a non-functional ("embellishing") chord, that does not resolve at all.

  • Delayed Resolutions. The best way to delay the resolution of a chord is to first resolve it to another (or more than one) chord that also has a tendency to resolve to the original destination.

    • For example, the Neapolitan chord has a tendency to resolve to the dominant. viio/V and V/V also resolves to V, and I6/4 also resolves to V. So, a composer (Mozart, in particular, liked to do this) might write the following chord progression: N6 - viio7/V - V/V - I6/4 - V. In this way, the actual resolution (to V, in this example) is strengthened by the increasingly urgent need for the ear to reach the dominant.

    • This makes good compositional sense - if you were to just insert random chords in between V/V and V, for example, when the V chord is finally reached the ear will have lost its sense of importance and arrival. This can be used deliberately to weaken a secondary dominant, usually by inserting the I chord: V/V - I - V (remember, motion to I always counts as progression in a functional harmonic system).

  • Deceptive Resolutions. A resolution counts as deceptive if the tendency chord nearly resolves to its intended destination, but not quite. This is most often done by resolving to a different chord that shares some tones in common with the intended chord, or that is chromatically altered in some way from the intended version of the chord. It sounds even more deceptive if some of the tendency notes do resolve correctly, too.

    • This is how a deceptive cadence works! The V7 chord (Sol-Ti-Re-Fa) has three tendency tones that want to resolve to I: Ti (leading tone) goes to Do, Fa (chord 7th) falls to Mi, and Sol (the dominant scale degree) falls to Do. That is a very strong set of tendencies, and this is why an authentic cadence sounds so powerful. Now, in a deceptive cadence, the harmony moves V-vi instead of V-I. But, Ti still rises to Do, and Fa still falls to Mi - the only difference is that Sol rises to La. The vi chord and the I chord share two tones in common (Do and Mi). Therefore, the resolution of V7-vi sounds shocking - your expectations are mostly met, but something important (Sol-Do) did not happen properly.

    • In the same way, this type of "almost, but not quite" resolution can be used anywhere, not just at a cadence. See the examples below!


Examples of deceptive resolution:

  • Example 1: Massenet, Thais (1894). In the "Meditation" from this opera, a very deceptive resolution occurs in measures 57-58. There is a C#Mm chord in measure 57, which is V/iii in the key of D Major. This chord should resolve to F#m (iii), but instead it resolves to DM (I). The F#m and DM triads share two tones in common - F# and A. To make this resolution even more deceptive, the melody (solo violin) actually moves from C# to F# - a correct motion to the intended chord root.

  • Example 2: Mozart, String Quartet No. 17 in B-flat Major, K. 458, "The Hunt" (1784), second movement. This excerpt, in B-flat major, arrives on an F#dd chord in measure 26. This is analyzed as viio7 / vi. As such, it should then resolve to vi (Gm). Instead of doing this, Mozart resolves to Edd, another secondary leading tone (viio7 / V) in bar 27. The Edd chord is spelled E-G-Bb-Db, which contains two of the notes of Gm (G-Bb-D). Additionally, the bass moves from F# to G, as it should if the chord were resolving correctly. The soprano also lands on Bb, which is one of the common notes between the proper resolution and the deceptive resolution. Having both of the outer voices go where they "should" makes the deception stronger.

  • Example 3: Puccini, Suor Angelica (1918). This excerpt, the last 30 seconds of the opera, sets up the expectation of a plagal cadence in C Major. Instead, IV (FM) resolves to BbMmM - a chord that contains only the C of the expected I (CM) chord. This C is resolved correctly in the soprano and the bass, giving a sense of correct resolution combined with harmonic ambiguity. After maintaining this mysterious sound for a few seconds, Puccini then resolves to I, completing the final cadence of the opera.

    • Score (includes harmonic analysis)

Meditation from Thais - Massenet
String Quartet No. 17, II - Mozart
Suor Angelica - Puccini

Topic 3 - Advanced Modulation Techniques

  • Phrase Modulation

    • A phrase modulation is a very simple way to change key: the composer ends one phrase in the original key, and starts the next phrase immediately in the new key with no pivot or preparation. This type of modulation is very common in highly sectionalized, repetitive forms such as the Minuet and Trio, where short sections of music are repeated. In a typical section of a minuet there may be a move to a new key (by pivot chord, perhaps) followed by a cadence in the new key. When the section repeats, the music is instantly back in the original key with no warning - this is a phrase modulation.

  • Example: Haydn, Symphony No. 6 in D Major, Hob. 1/6 "Le matin" (1761), third movement. This excerpt is the beginning of the Trio portion of this Minuet and Trio movement. Section one begins and ends in d minor. Section two starts immediately in F Major, via phrase modulation. During section two, the music pivots back to d minor.

Symphony No. 6, III - Haydn
  • Common Tone Modulation

    • A modification of pivot chord modulation (remember - also called common chord modulation). In this case, instead of needing an entire chord that is functional in both keys, you only need one note that exists in both keys. This allows the composer to modulate to much more distantly-related keys.

    • The formula for this type of modulation is to play a chord in its original context, then sustain one note of the chord while everything else stops. After that, give the note a new context by making it part of a new chord in the new key.  Having the islolated common note is not required, but it is very typical.

    • Because there is no preparation for this re-interpretation, common tone modulations sound more sudden/jarring than pivot modulations do. However, that doesn't mean they have to sound bad - listen to these examples!

  • Example 1: Elgar, Variations on an Original Theme, Op. 36 (1899). These are Elgar's famous "Enigma" Variations. The transition between the eighth variation and the famous ninth variation ("Nimrod") uses a modulation by common tone. Variation VIII ends in G Major. The tonic pitch, G, is sustained by the strings, and is then reinterpreted as the third of an E-flat Major chord at the beginning of variation IX, which is in E-flat Major.

  • Example 2: Françaix, Theme and Variations for Clarinet and Piano (1974). There is a common tone modulation between the end of the Theme and the beginning of Variation One. It works exactly like the Enigma Variations example does. The Theme is in D Major; a D is sustained between movements, and then Variation One begins in B-flat major on the I chord.

  • Example 3A: Beethoven, Symphony No. 9 in D Minor, Op. 125, "Choral" (1824). In the fourth movement, before the Jannissary section, the music is in D Major. There is a I-IV-V-I approach to the end of the phrase cadence, then a tonicization of the dominant: V/V - V - V/v - V. Following these four chords, the entire orchestra sustains the dominant pitch "A" by itself (with no supporting harmony). This A pitch is then placed into an F Major context under the fermata. F is V in the key of B-flat Major, the key of the Jannissary march that follows. The "common tone" is the pitch A, which is common to both the key of A Major and the key of B-flat Major. Because the common tone modulation is so powerful, your ear "believes" that the music has modulated to F Major ... it takes the insistent emphasis on the pitch Bb in the next section to convince you that you are actually in B-flat Major.

Enigma Variations - Elgar
Theme and Variations for Clarinet and Piano - Françaix
Symphony No. 9, IV - Beethoven
  • Beethoven was a tricky fellow. Remember, at a fundamental level music is a struggle between repetition and contrast. Beethoven lays the groundwork of function and expectation for the modulation described above back in the third movement of the symphony.

    • Towards the end of the third movement, Beethoven sets up a melodic pattern in the brass that involves emphasis on the dominant and the sustaining of a single tone (just like the pattern of the 4th movement modulation).

    • The first time this melody appears, there is no tonal movement at all (example 3B, below).

    • About one minute later, the same melodic pattern reappears (example 3C, below). This time, the single note in the brass becomes part of what sounds like a common tone gesture but is really just an extended tonicization of the dominant (Eb) using modal mixture (listen to the tonality shift from Eb Major to eb minor), before eventually returning to the tonic of Bb Major.

    • By repeating the same figure, Beethoven sets up an expectation of repeated harmony that he finally shatters in the fourth movement, when the common tone gesture does move to a new key. Beethoven deliberately established your harmonic expectations, 15-20 minutes in advance, before breaking those expectations in the fourth movement. This makes the modulation even more powerful when it finally arrives.

Symphony No. 9, III - example 3B - Beethoven

Example 3B: third movement; no modulation.

Symphony No. 9, III - example 3C - Beethoven

Example 3C: third movement; common tone gesture, but no modulation.

  • Example 4: Bernstein, "Tonight" from West Side Story (1957). This tune begins in A Major and moves to C Major.

    • The chord progression (mm. 73-76) leading up to the modulation is F#m, G#m, GM, CM.

      • The F#m chord is diatonic in A (vi) but not in C.

      • The G#m is not functional in either key.

      • The GM chord is diatonic in C (V) but not in A.

        • This chord does have a chromatic function in A (bVII BC), but it can't serve as a chromatic pivot chord because the previous G#m harmony is non-functional - we have already "left" the original key.

      • The CM chord is not diatonic in A, but is I in the key of C.

    • Despite these non-functional harmonies the modulation sounds smooth and uncomplicated; the ear is actually drawn to the singer's pitch (B), which is maintained throughout this section - a common tone between the keys of A and C.

      • Score (with correct and incorrect analysis of the modulation)

"Tonight" from West Side Story - Bernstein
  • Sequential Modulation
    • This technique uses a sequence to migrate away from a tonal center and establish a new key. By repeating the same melodic/harmonic pattern at different pitch levels, the original sense of "tonic" is lost. The sequential pattern can then be altered or ended to allow a pivot into the destination key.
    • Things to remember:
      • A melodic idea generally needs to appear three times in a row for it to be perceived as a sequence. Otherwise, it is just a repetition of melodic material (however, see example 1, below). Also, each statement of the sequence will be the same interval away - for example, a common technique is to sequence down by M2, where each statement of the melodic idea starts a whole step below the last statement's starting point.
      • Tonal sequence: the sequence never leaves the original key. Real sequence: the each statement of the sequence contains exactly the same melodic intervals, so accidentals will be needed. This is most useful for modulation.
      • Not every sequence becomes a sequential modulation!
  • Example 1: Bach, Minuet II from the Cello Suite in G Major, BWV 1007. This minuet is in g minor. In measure 33 Bach begins a sequence that proceeds downward by whole step. During the second repetition of the sequence, he alters the final beat (measure 36) to produce an FMm harmony, allowing a smooth pivot into the key of B-flat Major. Following this, the next phrase pivots back to g minor (not shown)

  • Example 2: Marcello, Concerto for Oboe in C Minor (1717), third movement. This excerpt begins in E-flat major, and features three overlapping sequences - 1) up by step, 2) down by step), 3) up by step. By layering these three different sequences together and changing the harmonic rhythm, Marcello keeps the passage from bogging down - the ear quickly tires of sequential patterns if they are not varied. During the transition to sequence three Marcello pivots to g minor.

  • Example 3: Dvořák, Symphony No. 8 in G Major, Op. 88 (1889), movement two (again). In addition to being an excellent example of modal mixture, this movement begins with a modulation from Eb Major to c minor, through the use and modification of a sequence and the enharmonic respelling of a German Aug6 chord. This excerpt covers measures 1-11 only.

Cello Suite in G Major - Minuet II - Bach
Concerto for Oboe in C Minor, III - Marcello
Symphony No. 8, II - Dvořák
  • Non-Diatonic Pivot Chords

    • More-advanced forms of pivot chord modulation use pivot chords that are functional, but not necessarily diatonic, in the old and/or new keys. A pivot chord may have a diatonic function, a secondary function (e.g., V/V), or some other chromatic function (eg., an augmented sixth chord). The pivot chord may be diatonic in one key and chromatic in the other, or chromatic in both keys. The important point is that the pivot chord has a function in both keys. See examples 1-4, below (under enharmonic modulation).

  • Enharmonic Modulation

    • This is a subset of pivot chord modulation that relies on enharmonic respelling of a chord to give it a function in a different key. For example, any Mm7 chord can be respelled enharmonically as a German Aug6 chord in a new key (and vice versa; the Mm7 could be "the" dominant, or a secondary dominant); any dd7 chord can be respelled enharmonically to give it a different root, making it a leading tone to a new key. Explore these possibilities on your own: take a Mm7 or a dd7 chord, and see what keys you can modulate to using it as an enharmonic pivot chord! Remember, with the surge in chromatic harmony in the late Common Practice period, pivot chords can be chromatic in one or both keys.

Examples of chromatic pivot chords, including enharmonic modulation.

  • This handout shows the scores and analyses for examples 1-4, below.

Ex. 1 - Brahms, Quintet No. 1, Op. 88
Ex. 2 - Brahms, Ballade, Op. 10 No. 4
Ex. 3 - Chopin, Mazurka, Op. 56 No. 1
Ex. 4 - Liszt, Consolation No. 2
Example 5 - Enharmonic Modulation
  • Example 5: an enharmonic respelling that allows a modulation to a distant key. This "chorale" is in F# minor. In measure 4, the E#dd chord is respelled as a Bdd chord, allowing a pivot to the key of C Major.

Topic 4: Altered Dominants

  • The pitches of the V chord may be altered, as follows:

    • The dominant triad (no seventh chords) may have a raised fifth (analysis: V#5). This typically occurs only in major keys.

    • In major or minor, the dominant seventh chord may have a lowered fifth (analysis: V7b5).

    • In major or minor, the dominant triad or seventh chord may have both a lowered third and a lowered fifth (analysis: V7b5b3). This creates a dominant that sounds as either a diminished triad or a half-diminished seventh chord.

  • When labeling altered dominants, I prefer to always use a Major Roman numeral for the dominant chord (V). Then I add figured-bass style notation to indicate the altered notes, showing how the dominant has been changed. Examples: V#5, V7b5b3 (you'll have to imagine the superscript and subscript). For me, the most important thing is that the V chord has been altered, rather than focusing on its new quality. However, it is also possible to express the Roman numeral with its new quality instead: V+, vo7, and so on (but this won't work for V7b5).

  • Altered dominants may also be secondary dominants; however, composers tend to avoid using the diminished V in this context. But, see example 3 below!

  • Example 1: Dvořák, Symphony No. 8 in G Major, Op. 88 (1889), movement two (yet again).  This movement has already been used as an example of long-term modal mixture AND sequential modulation (see above).  The beginning of the movement also contains four altered dominant chords - can you hear them?  They are the "mysterious" sounding harmonies played by the clarinets (for example, see measure 13, beat 2, and measure 16, beat 2).

    • Score (the recording starts at the pickup to rehearsal A)

  • Example 2: Schubert, String Quartet No. 13 in A Minor, D. 804 "Rosamunde" (1824), movement one. In this example, Schubert uses the V7b5 chord as a secondary dominant: V7b5 / V. This chord appears in measure 9, on beat 3.

  • Example 3: Lombardo, Concerto for Oboe (1991), measures 10-19. Two times during this phrase, the composer uses V7b5b3 (the half-diminished dominant) as a secondary dominant, and it sounds amazing! As you can see, rules are made to be broken.

    • Score and analysis (the recording starts at measure 10)

Symphony No. 8, II - Dvořák
String Quartet No. 13, I - Schubert
Concerto for Oboe in One Movement - Lombardo

Topic 5: Extended Chords ("Tall" Chords)

  • Major or minor chords may be extended by adding a 9th, 11th and/or 13th above the bass.

  • The dominant is the most commonly extended chord (either primary or secondary dominant chords).

  • Extended chords are typically in root position, with the tallest extension in the melody, treated as an appoggiatura or passing note. The extended chord usually collapses to a triad or seventh chord before resolving.

  • Example 1: Scott Joplin, The Augustine Club Waltz (1901) - examine how extensions are used to embellish a normal circle progression.
The Augustine Club Waltz - Joplin
  • Example Two: Giacomo Puccini, Aria: "Che gelida mannina" from La bohème (1896). The extended chord (V9 of V, in this case), occurs at the very end of the recording (the score shows the final two bars of the recording).

"Che gelida mannina" - Puccini

Topic 6: Tritone Substitution

  • Any chord may be replaced by a new chord whose root is a tritone away. For example, a CM chord can be replaced by an F#M or GbM chord. This new, substituted chord will function like the orignial chord.

    • The purpose of a tritone substitution is to create chords whose roots move downward by half step. This is a more interesting type of chord movement than a functional bassline that leaps by P4 or P5. When done properly, that is, substituting for a chord that is part of a circle progression (harmonic motion by P5) such as ii - V - I, you will get this smoother type of root movement.

    • The original chord and its substitute generally have the same quality (this sounds best, but is not required).

  • Mm chords are the most-often substituted chords (other chords can be replaced, but this does not sound as good). The reason that dominant-7th chords work well in tritone substitutions is that any two Mm chords that are at tritone apart actually contain the same d5 interval, enharmonically spelled. For example, AMm (A-C#-E-G) and EbMm (Eb-G-Bb-Db) contain the same tritone: C#-G (or G-Db).

    • The standard form that the tritone substitute usually takes is to replace the V7 chord in a standard ii7 - V7 - I progression. In the key of C Major, the original progression is Dmm, GMm, CM. The GMm chord is replaced with a new chord a tritone away - DbMm. This gives a new, stepwise chord progression: Dmm - DbMm - Cm. The new roman numerals are ii7 - bII7 (tts) - I. "TTS" stands for "tritone substitution". The new Roman numeral for the tritone substitute should have the correct quality, and if the root of the chord is not in the key, an accidental should be applied to the Roman numeral as shown in this example.

      • Please Note: "bII7 (tts)" should not be confused with the Neapolitan chord - the Neapolitan chord never (or rarely) has a 7th, and it resolves to V, not to I. Your analysis must be based on the chord's actual function. In other words, its identity is determined by its destination.

  • For this technique to work, the chromatic, stepwise chord root movement must be present, and the original chord progression must be obvious and functional.

  • Example: Jules Massenet, "Meditation" from Thais (1894), mm. 58-60. In this slightly unusual example, the harmony is DM - EbMm - DM. The analysis is I - bII7 (tts) - I. The example is unusual because the first chord (m. 58) would typically be ii7, not I.

    • Score (the recording starts in measure 53)

Note: there is a bonus tritone substitution here, depending on how you hear/analyze this excerpt. We have already discussed measures 57-58 as an example of a deceptive resolution (see above). However, this mysterious C#Mm chord COULD be a tritone substition for the regular IV chord (GM). If so, then Massenet's original, functional chord progression would be I - IV - I - V7 - I, or DM-GM-DM-AMm-DM (piano students everywhere recognize this). After performing two tritone substitutions, he ends up with I - VII7 (tts) - I - bII7 (tts) - I, or DM-C#Mm-DM-EbMm-DM: a much smoother, more chromatic chord progression, and a very compelling sound that does not bother our modern ears at all.

Meditation from Thais - Massenet

Topic 7: Linear Chromaticism

  • This technique, most common in the late Romantic / early 20th century repertoire, involves the gradual "mutation" of harmonies, rather than the use of functional root movements.  The goal is to create ascending or descending chromatic lines in one or more voices.  To accomplish this, the composer takes a chord and alters it, one note at a time, to create new harmonies.  The process is slow and usually involves chromatic changes.  For example, an EbMm (Eb-G-Bb-Db) chord could be mutated to Edm (E-G-Bb-Db), and then to CMm (E-G-Bb-C) by changing one note at a time.

  • Example: Chopin was a pioneer of this technique, and it appears frequently in his music (and in the music of Debussy). For example, here is an excerpt from Chopin's Prelude in E Minor, Op. 28 No. 4 (1839). See if you can hear the individual changes being made to the chords in each bar. The recording is of mm. 1-7 only.

    • Harmonic Analysis (root-and-quality analysis, only using Roman numerals at phrase endings where clear structure is evident)

    • Roman Numeral Analysis - only to show how little help this kind of analysis gives us when linear chromaticism is being used.

Prelude, Op. 28, No. 4 - Chopin

Topic 8: Chromatic Mediants

  • Chromatic mediant: take any chord, for example CEG, and add a second chord whose root is a third away (for example, EGB). This chord has two tones in common with the original chord, and has what we call a mediant (or third) relationship - meaning, the chords' roots are a third apart. Now, chromatically alter one of those common tones and re-write the second chord so that it has the same quality as the first chord (now, EG#B). This new chord is a chromatic mediant.

    • A chromatic mediant is usually related to the tonic (I) chord, and is a three-chord event: I, then the CM, then I again. Using our example, the chords would be CEG - EG#B - CEG, and the analysis would be C: I - III (CM) - I. The purpose of this sonority is to embellish / prolong the tonic.

  • A doubly-chromatic mediant has both common tones altered, so that the two chords are no longer the same quality (for example, CEG and EbGbBb). A CM - Ebm - CM chord progression in C would be analyzed as C: I - biii (DCM) - I.

  • Third relations in music become increasingly important as time goes on. The concept of a "mediant" or "chromatic mediant" can be applied to bigger structures than a single chord, as well - in the key relationships within a movement and/or the key relationships between movements of a multi-movement work, for example.

    • Compare the use of sonata form in the first movement of Beethoven's 5th Symphony, and Brahms's 3rd Symphony:

      • Beethoven 5: first theme in c minor, second theme in Eb Major. Eb is the diatonic mediant to c - that is, it is the mediant that is in the original key. The recapitulation is back in c minor, giving us the mediant motion of c - Eb - c (cmin: i - III - i).

      • Brahms 3: first theme in F Major, second theme in A Major. A Major is a chromatic mediant to F Major - FAC and AC#E contain two common tones, but the C has been raised to C# so that both chords have the same quality. The recapitulation is back in F Major, giving us the chromatic mediant motion of F - A - F (FMaj: I - III [CM] - I).

    • Consider the key relationships between movements in Beethoven's 5th Symphony, Beethoven's 9th Symphony, and Dvorak's 8th Symphony:

      • Dvorak 8: First movement in G Major, second movement in Eb Major (a chromatic mediant), which then modulates to C Major (another further chromatic mediant away from Eb).

      • Beethoven 9: First two movements in D minor, third movement in Bb Major (a diatonic mediant)

      • Beethoven 5: First movement in C minor, second movement in Eb Major (the relative major - a diatonic mediant).

Examples of chromatic mediants:

  • Example 1: Tchaikovsky, Chant sans paroles from Souvenir de Haspal, Op. 2, No. 3 (1867), measures 62-64. There are two very clear chromatic mediants here: I - bVI (CM) - I - bVI (CM) - I. The bVI chords could also be analyzed as modal borrowing from F minor, but in this case because they are surrounded by the tonic chord, it is more appropriate to analyze them as chromatic mediants.

  • Example 2: Debussy, Sarabande from Pour le piano (1901), measures 9-10.

Souvenir de Haspal - Tchaikovsky
Sarabande - Debussy
  • Sometimes in order to correctly diagnose a chromatic mediant (or any other harmony), you have to consider the different layers of music that are occurring simultaneously. For example, consider the C-Major chorale that begins in measure 17 of the finale of Saint-Saëns's Symphonie No. 3, "avec orgue" (1886).

    • Score

    • Comments:

      • The chorale is a set of four pairs of measures. The first measure of each pair is in 9/4 time, and the second measure of each pair is in 6/4 time. Each of the 9/4 measures features a diatonic chord progression in chorale texture, with a cadence that ends in the following 6/4 measure where the last chord of the progression is sustained for the entire bar. The chords in the 6/4 measures are I (CMaj), V (GMaj), III (EMaj), I (CMaj).

      • These four chords, despite being separated from each other by an entire chord progression in each 9/4 bar, are related to each other as chromatic mediants. The ear picks up on these particular chords because they are sustained for so long, and because they are the last chord of each two-bar phrase. The E Major chord in measure 22 is a chromatic mediant to the two tonic chords in measures 18 and 24.
      • This chromatic mediant relationship (CMaj: I - III [CM] - I) is interrupted by the V chord in measure 20 - this is not unusual for a chromatic mediant. However, it is interesting to note that the E Major chord is ALSO a chromatic mediant to the V chord (EG#B and GBD)!

Symphony No. 3, IV - Saint-Saëns