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Review of Harmony

The harmony section of the Graduate Music Theory Entrance Exam is divided into two separate exams:

1. Basic Harmony
2. Chromatic Harmony

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Review for the BASIC HARMONY EXAM

I: Identify the correct Roman numeral and inversion symbol for a notated chord

(This section may include triads and/or 7th chords):

Examples:
(the actual questions will be in music notation, but in this review, pitches are given from left-to-right in the following order: bass > tenor > alto > soprano)

In the key of E minor, what is the following: G > B > E > C
(answer: in the key of E minor this is VI 4/3 (the submediant 7 chord with its 5th in the bass)
[Note: This is a Cmajor7 chord with the following structure: C=root, E=3rd, G=5th, B="major 7"]

In the key of Ab major, what is the following: Db > G > Eb > Bb
(answer: in the key of Ab major this is V 4/2 (the "dominant 7" chord with its 7th in the bass)
[Note: This is an Eb7 chord with the following structure: Eb=root, G=3rd, Bb=5th, Db= "b7"]

To review for this section, review the following links on the "Harmony" section of the "Music Theory Review"
- Basic Triads
- Basic 7th chords
- Basic Functional Harmony
- Chord Inversions and Figured Bass symbols

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II. Select the best jazz/pop "lead sheet" symbol for the following chord

Examples:
(the actual questions will be in music notation, but in this review, pitches are given from left-to-right from lowest-sounding to highest-sounding pitch)

What is the best jazz/pop chord symbol for the following: D > F# > A > C > E#

Possible answers to choose from:
a) D7#9
b) D+5 7 9
c) D+5 +7 +9
d) D b7 #9

(answer: This is a D7 #9--a D7 chord with a raised 9)
[Note: This chord has the following structure: D=root, F#=3rd, A=5th, C="b7" (jazz/pop symbol for 'flatted 7" is just "7"), and #9=E#]

Review:
A jazz/pop chord symbol must be read left-to-right:

- First, identify the root of the chord (for D7#9 "D" is the root; for Db7#9 "Db" is the root)

- If the symbol says nothing else, it is a "major traiad" built on that root

- If the symbol says "m" or "mi", the 3rd of the chord is "flatted" to make it "minor" (such as Cmi or Abmi [Ab minor triad, or F#mi7 [which is F# minor 7 with the structure F#=root, A=b3rd, C#=5th, E="b7" (jazz/pop symbol for 'flatted 7" is just "7")]

- If the symbol includes "+", the 5th of chord is raised to make it "augmented": ["G+" is G =root, B=3rd, D#=#5]--["G#+7" is Gb=root, Bb=3rd, D=#5 (raised 5th), Fb="b7" (jazz/pop symbol for 'flatted 7" is just "7")

- If the symbol includes a small "o" (such as "C#o", the triad is diminished [lower both the 3rd and the 5th structurally--"b3" AND "b5"). Whe adding a 7th to a "diminished triad", the 7th should be "fully-diminished"("bb7") unless the small "o" has a slash through it which means "half-diminished 7th" (use a structual "b7" instead of a "bb7" [To review 7th-chord types, click the "Basic 7th Chords" link].

- When the symbol spells out "ma", "maj" or "major," it always refers to the type of 7th (use a "major 7th")--otherwise, if it just says "7" use a "flatted 7": "Cmajor7" is C=root, E=3rd, G=5th, B="major 7", while "C7" is C=root, E=3rd, G=5th, Bb="flatted 7" (jazz/pop symbol for 'flatted 7" is just "7")

- Extended harmonies such as 9, 11, 13 all imply the previous odd numbered pitches are included in the chord; otherwise, the word "add" is used. For example,
- "C11"= "root, 3rd, 5th, b7, 9, 11"
- "Cmajor13" = "root, 3rd, 5th, "major 7", 9, 11, 13
- "C add 9" = "root, 3rd, 5th, 9th"

- Any alteration of a chord tone is indicated by "#" [raised by 1/2 step] or "b" [lowered by 1/2 step] in front of the number it applies to

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III: Identify the diatonic name and function of a chord for a given key

Example:
- A "C#diminished" triad is the supertonic of what key?

(answer: C# dim is the supertonic of B minor)
- the "supertonic" is "step 2" of a major or minor scale
- in minor keys, the "ii" chord triad is diminished (in major keys, the "ii" chord is minor
- C# is "scale step 2" of the key of B minor

To review for this section, keep in mind that in a major or minor key
- "tonic" (scale-step 1)
- "supertonic" (scale-step 2)
- "mediant" (scale-step 3)
- "subdominant" (scale-step 4)
- "dominant" (scale-step 5)
- "submediant" (scale-step 6)
- "leading tone" (scale-step 7)

Also review the following links on the "Harmony" section of the "Music Theory Review"
- Basic Triads
- Basic 7th chords
- Basic Functional Harmony

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IV. Based on Classic harmonic practice, which chord(s) could follow a given chord?
(in other words, what chord(s) can a particular chord move to?)

Examples:

- Which of the following chord(s) could follow a "ii" chord?
(Possible answers: VII, I, III, V, vii o, VI)

Answer: In Classic harmonic practice, "ii" [which functions as a "pre-dominant" chord] can move to either a "V" or a "vii o" [which both function as "dominant" chords]

To review, keep in mind that in Classic harmonic practice, common "chord progressions" (ways to move forward) are:

- "Pre-dominants" (ii, iio, iv, IV"--and their 7th chords) lead to "Dominants"

- "Dominants ("V" or "vii o"--and their 7ths chords) resolve to the "Tonic" ("i", "I"--or to "vi" or "VI" in a "deceptive cadence")

Other common types of Classic harmonic motion include:
- Reverse-motion around the circle-of-5ths (in other words, move by P4th): root motion e > a > d > g > c > f, etc.
- Move chords stepwise: G to Ami
- Combination of both of the above: (step, then revese-circle such as "G to Ami to D"
Review: Circle of 5ths/Key Signatures

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V. Identify the cadence type in a notated example

To review for this section, know the following:
- a "Deceptive cadence" is [in major: "V to vi", "V7 to vi"] or [in minor: "V to VI" or "V7 to VI"]
- a "Plagal cadence" is "IV to I"
- a "Half cadence" ends on "V"

An "Authentic cadence" is [in major: "V to I"] or [in minor: "V to i"]
- an "Imperfect Authentic cadence" has either the V or the I chords in inverted position (root isn't in the bass)
- a "Perfect Authentic cadence" has both the V and the I chords in root position (usually with the uppermost voice of the final "I" chord also being the tonic pitch)

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VI: From a notated two-chord example, identify the "Key Quality" [is the key "major" or "minor"?] and identify the type of cadence (see cadence types above)

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VII: Label "non-harmonic tones" in a notateed music example

To review for this, click the "Review of Non-Chord Tones" link.

Practice: 3-voice piano score in F major. Each half-measure is labeled with a circled number (0-8).

Instructions: Indicate which numbered score segment contains the following items
(possible answers are 1-beat segments labeled (0) through (8) in the score:

_________: Lower neighbor tone
_________: Passing 6/4 chord
_________: Appogiatura (this term is also used for an "accented passing tone")
_________: Escape tone
_________: Anticipation
_________: 4-3 Suspension

(see the review chart for "Non-Chord Tones")

Lower neighbor tone (see review chart)

- Passing 6/4 chord (stepwise motion leads to what looks like a 6/4 chord with two dissonant weak-beat "passing tones" that resolve by step to chord tones—such as I6 – V6/4 – I)

Appogiatura (LEAP to weak-beat dissonance that resolves to a chord tone by step in the opposite direction; the term is also used for an "accented passing tone")

Escape tone (stepwise motion to a weak-beat dissonance that then LEAPS to a chord tone)

- Anticipation (stepwise motion to a weak-beat dissonance that then stays on the same note which becomes a chord tone)

- 4-3 Suspension (STRONG BEAT [accented] dissonance created by staying on the same note that becomes a dissonance when other voices move, then resolves DOWN by step to a chord tone)—so, by definition, a suspension is "An accented harmonic dissonance created by rhythmic figuration"—in other words, you can create a suspension by taking two chords and displace the rhythm of the suspended voice one half-beat later than the other chord tones—in the example on the "Non-Chord Tones" chart, if you move the "B-natural" in the soprano voice a half-beat earlier, there is no dissonance, just two consonant chords.

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VIII: Match terms to their correct definition (know the following terms):

- Cadential six-four: a "I 6/4" chord that is an unstable embellishment that always leads to a dominant.
- Period: a pair of "antecedent" + "consequent" phrases that make a complete harmonic progression.
- Diatonic: tones belonging to the key
- Suspension: an ACCENTED (strong-beat)harmonic dissonance (non-chord tone) created by rhythmic misalignment.
- Pre-dominant function: Chords which progress to a dominant
- Tonicization: harmonic emphasis of a chord through "secondary functions"
- Deceptive cadence: moving from "V" to "vi" (see cadences, above)
- Bass Arpeggiation: presenting the notes of a chord individually in succession (as a harp does)
- Figured Bass: a system representing chords by numeric intervals above the bass
- Mode Mixture (modal borrowing): the use of tones borrowed from the parallel key

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IX. Part-Writing (identify good part-writing, as well as particular errors)

Review of Voice-leading Rules:

Unacceptable voice leading:


- Voice crossing, Parallel Octaves and Parallel 5ths, Contrary 5ths
No parallel 5ths or parallel octaves (also no "contrary" 5ths or octaves--this is when consecutive 5ths or octaves are created by contrary instead of parallel motion); avoid parallel motion or similar motion in all voices (use contrary and oblique motion): in 4-part writing if there is no common tone then move upper three voices contrary to the bass.

- Retrogression (going backward in a progression, such as dominant to predominant [V7 - IV] )

- Improper Doubling (usually double either root or 5th--never double tendency tones such as a leading tone or the 3rd of a major triad because they will force parallel octaves);

- No augmented melodic intervals when in harmonic minor using scale steps 6 and 7


Acceptable voice-leading:


- Keep each voice in its proper range
    soprano=middle c' to g"
    alto= g to d'
    tenor=c to g'
    bass=G to d

- keep common tone(s) in the same voice(s) when possible

- primarily use stepwise motion in all voices

- use large leaps sparingly--a large leap in one direction is usually followed by a stepwise or other small move in the other direction

- Resolve all "tendency tones" in the same voice--
   1. A leading-tone must resolve UP by half-step to the tonic;
   2. 7ths of "dominant 7th" and "secondary dominant 7ths must resolve down by a half-step,
   3. A chromatically-raised pitch resolves up by half-step while a chromatically-lowered pitch must resolve down by half-step. 

Never double a tendency tone because this necessitates parallel octaves for both tendency tones to be resolved correctly.

Practice example:

Part-wriitng

1. Within each of these 3-measure excerpts, two of the measures have a voice-leading error—one does not.

a) Which measure contains the most acceptable voice-leading pair?

b) Identify the measure that contains the following type of voice-leading error:
- Voice Crossing (usually the alto and tenor parts switch into each other's ranges because of too large leaps)
- Contrary fifths (two consecutive 5th intervals, but created by contrary not by parallel motion)
- Retrogression (a bad [backward] harmonic progression that moves from a dominant to a predominant:  V to IV , V to ii, vii to IV, vii to ii)
- Improper doubling (don’t double a leading tone!!)
- Parallel octaves (check for parallel leaps in the same direction, often in the outer voices)

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Review for the CHROMATIC HARMONY EXAM:

I. Key relationships:

"Relative" keys share the same key signature:
- C major and A minor
- F major and D minor

"Parallel" keys share the same "tonic" and the same diatonic chord functions:
- C major and C minor
- F major and F minor

"Enharmonic" keys: sound exactly the same, but are spelled differently:
- C major and B# major
- Gb major and F# major
- Eb minor and D# minor

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II. Diatonic Pivot chords
(How to move between two keys by a chord that both keys share)

Example: Which diatonic triads in C minor could serve as a diatonic pivot chord to F minor?
(Yes or No)

___ V in C minor (No. "V of C minor" is "G", which does not belong to the key of F minor)
___ VI in C minor (Yes. "VI of C minor is "Ab", which is "III" in the key of F minor)
___ viio in C minor (No. "viio of C minor" is "B diminished", which does not belong to the key of F minor)
___ iv in C minor (Yes. "iv of C minor is "f minor", which is "i" in the key of F minor)

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III. Identifying functional chromatic chords in a score

Practice: Indicate which numbered score segment contains the following items
(possible answers are 1-beat segments labeled (0) through (8) in the score:

_________ Question 1: Diatonic pivot chord
_________ Question 2: Secondary leading-tone 7th chord
_________ Question 3: Non-dominant diatonic 7th chord
_________ Question 4: Secondary dominant 7th chord
_________ Question 5: Scalar variant chord (also "modal chromaticism"-an altered diatonic chord)
_________ Question 6: Dominant 7th chord (V7)

score identification

-Diatonic pivot chord: (a chord in the current key that also functions in another key that you tonicize or modulate to (for example a G chord can be V in C major and I in G major; in a minor key: D minor can function as a shared diatonic pivot between D minor and A minor [it's both "i of D minor" and "iv of A minor"])

-Secondary leading-tone 7th chord: (a "leading-tone chord" is a vii chord—always diminished that leads from vii to I (or i in minor). So, a "secondary leading-tone chord" is vii of some other key that you are tonicizing momentarily)

-Non-dominant diatonic 7th chord: (a "diatonic 7th chord" is ANY 7th chord that can be built on  one of the diatonic tones that occur normally in a scale/key. A "dominant 7th chord" is that type of 7th chord that is built from these diatonic pitches by building in 3rds on the dominant [V7]. Therefore, a "non-dominant diatonic 7th chord" is a 7th chord built in 3rds starting on any diatonic note BUT the dominant… In Major: ii7 [minor 7chord], iii7 [minor 7 chord], IV7 [major 7 chord], vi7 [minor 7 chord]  … In harmonic minor: iio7 [half-diminished 7 chord], III7 [major 7 chord], iv7 [minor 7 chord], VI7 [major 7 chord]

-Secondary dominant 7th chord: (V7 of  a different key that you are tonicizing momentarily—chords do not need to be in root position, and you could be just looking for a V7 that resolves momentarily to a chromatic chord that isn’t in the key you are in, such as "D7 to G" in D minor [which is V7 of "IV of the parallel" in D minor]). G]. In this case, G major is a "scalar variant" of iv in the key of D minor (It is major instead of minor, temporarily borrowed through mode mixture from the parallel major key of D—which is the main key of the movement)

-Scalar variant chord (also called "Modal Chromaticism", "modal borrowing" or "modal mixture")--an altered diatonic chord often borrowed from the parallel key. For example, in the key of C major using Ab [called "bVI"], Eb ["bIII"], Cmi, F mi, etc

-Dominant 7th chord: (V7 of the key you are in)—doesn't have to be in root position—in this case, you are looking for A7 in the key of D minor

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IV: Identifying chord relationships to a key

Know the following:
- Modally borrowed: borrowed from the parallel key (see above)
(such as using the chord "Cmi" in the key of C major)

- Chromatic mediant: chords/keys that are a "major 3rd" or "minor 3rd" apart, and share one common tone
(such as moving from F#mi to Ami)

- Secondary dominant: "V" or "V7" of a diatonic chord besides the tonic,
( in C major "V7 of iii" would be B7 (V7 of Emi)

- Secondary leading-tone: "viio" or "viio7" of a diatonic chord besides the tonic,
( in C major "viio of V" would be F#o (viio of G)

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V: Roman numeral analysis, including
- Secondary dominants
- Secondary leading-tone chords
- Augmented-6th chords
- Neapolitan-6th chords

The Augmented-6th chords and the Neapolitan-6th chord are fancy chromatic "Pre-dominant" Substitute Chords:

"Predominant" chords [such as ii or IV] set up the dominant [V] in a tonal progression; but there are stronger chromatic ways to move to V that use the same kinds of half-step "tendency tones" that make dominant chords resolve to I [such as V, V7, and the leading-tone diminished vii  and vii7 chords].

For clear examples, I will work in the key of C major and show you some predominant substitute chords that chromatically move to V. Here, we are trying to set up ["tonicize"] the dominant chord "G major," and that can be done by

I. Using traditional "diatonic" progressions: either "ii to V" [d minor to G], or "IV to V" [F major to G]

II. Using "secondary dominant chords", such as
-"V of V" to V [D major to G], or "V7 of V" to V [D7 to G]
-"vii of V" to V [F# diminished to G], or "vii7 of V" to V [F# fully-diminished 7 to G]

III. Using "predominant chromatic substitute" chords that lead to and tonicize V even stronger!

-Neapolitan 6 chord: ["bII"] in C major, this is a D-flat triad in first inversion

Neapolitan 6

-"Augmented 6" chords: (these all contain the interval of a "augmented 6" [in this case Ab to F#] created by using the "secondary dominant chords" shown above, but altering the A pitch to an A-flat and putting it in the bass so it is a tendency tone that leads down by half-step to the dominant root "G":

"Italian 6" chord: this is a "vii of V" with an altered Ab in the bass
- "vii of V" would be spelled "f#  a  c" [f# diminished] and resolve to G major [g b d]
(chromatic tendency tones are f# to g, and  c to b)
- "It+6" would be spelled "f# ab  c" and with the a-flat in the bass
(all three pitches are chromatic tendency tones, and two of them must resolve to the "g root" of V)

"German 6" chord: this is a "vii7 of V" with an altered Ab in the bass
- "vii7 of V" would be spelled "f#  a  c  eb" [f# fully-diminished 7] and resolve to G major [g b d]
(tendency tones are f# to g, c to b and eb to d)
- "Ger+6" would be spelled "f# ab  c  eb" and with the a-flat in the bass
(there are now four chromatic tendency tones that resolve to each note of the V chord, and two of those tendency tones must resolve to its "g" root)

"French 6" chord: this is a "V7 of V" with an altered Ab in the bass
- "V7 of V" would be spelled "d  f#  a  c" [D7] and resolve to G major [g b d]
(tendency tones are f# to g, c to b, with a common tone "d")
- "Fr+6" would be spelled "d  f# ab  c" and with the a-flat in the bass
(there are now three chromatic tendency tones and a common tone "d" that resolve to each note of the V chord, and two of those tendency tones must resolve to its "g" root)

The diagram below shows how these work in both C minor and C major, but in both keys these "augmented 6th" chords are spelled identically and resolve to the dominant [V = G].

Augmented 6th

Note that in order to avoid parallel 5ths, the "German Augmented 6" chord usually moves to a "cadential 6/4" chord [a I 6/4 chord that resolves to V]—so this is why a "cadential I 6/4" is considered a dominant chord in function [not a tonic]—it acts as an embellished dominant then resolves to V before the final cadence to a root position I chord.