RCM Harmony 10 Important Details to Memorize

What are the common seventh chords in Major Keys?

Common: ii7, IV7, V7, vii half-dim7

Avoid: I7, iii7, vi7

What are the common seventh chords in Minor Keys?

Common: i7, ii half-dim7, iv7, VI7

Avoid: III7, v7, VII7

What happens with the progression V4/3 - I6?

4th scale degree rises to 5th instead of falling to 3rd

“Rising Resolution”

Doubling of I, IV, V triads?

Root: RR35

First Inversion: RR35 or R355

Second Inversion: R355

Most common doubling is always the root*

Doubling of ii, iii, vi triads?

Root: RR35 or R335

First Inversion: R335 (other doublings are possible)

Most common doubling is always the root*

Doubling of VII triad?

Root in minor keys: RR35 or R335

First Inversion (vii dim6): R335

Most common doubling is always the root*

Doubling of V7 chord?

Root: R357 or RR37

First Inversion, Second Inversion, Third Inversion: R357

Doubling of ii7 chord?

Root: R357, RR37, or R337

First Inversion, Second Inversion, Third Inversion: R357

Tonal Hierarchy

Tonic, Pre-dominant, Dominant, Tonic (Authentic Cadence)

Tonic, Pre-dominant, Dominant (Half Cadence)

Tonic: I, Tonic prolongation: iii or vi (or vii dim), Pre-dominant: IV or ii, Dominant: V or vii

Plagal Cadence

IV → I

Deceptive Cadence

V → VI

Rule for seventh chord resolution?

Complete spelling (R357) → incomplete resolution and vice versa

Descending Circle of Fifths + Descending Fifths Sequence

Major: I, IV, vii dim, iii, vi, ii, V, i

Minor: i, iv, VII (natural), III, VI, ii dim, V, i (natural minor except authentic cadence)

Counterclockwise of Circle of Fifths*

Usually starts on tonic, possibly mediant (III); ends on any chord that forms a good progression (especially I, V, or ii)

Strategy for remembering: 4 steps up gives you 5 steps down (E.g., I + 4 = IV, IV - 5 = vii, vii + 4 = iii, iii - 5 = vi …)

Can be all seventh chords (vii half-dim in major, ii half-dim in minor) or can alternate between triads and seventh chords (same half-dim rules apply)

WATCH THE SOPRANO VOICE FOR DESCENDING SEQUENCE

If seventh chords are inverted: 1st inversion chords will alternate with 3rd inversion chords; 2nd inversion chords will alternate with root chords; all chords are complete (R357); seventh chords can also be alternated with triads

Pg. 28-29

Ascending Fifths Sequence

Major: I, V, ii, vi, iii, vii dim, IV, I (complete)

Minor: i, v, ii dim, VI, III, VII, iv, i (complete)

Clockwise of Circle of Fifths*

Can be partial or in different forms:

I, V, ii, vi, iii (almost always starts on tonic and ends on iii in MAJOR keys)

III, VII, iv, i, V (almost always starts on III and ends on V in MINOR keys)

3rd scale degree and 7th not favored*

Can alternate between root position and first-inversion triads

WATCH THE SOPRANO VOICE FOR ASCENDING SEQUENCE

Pg. 30-31

Ascending 5-6 Sequence

Major: I, vi6, ii, vii dim6, iii …

Minor: i, VI6, ii dim, VII6, III …

Can be partial or in different forms:

I, vi6, ii, vii dim6, iii, I6 (6 steps up gives you 5 steps down)

I(6), IV, ii, (6), V, iii(6), vi

Root-position variants:

I, vi, ii, vii, iii, I, VI (4 steps up gives you 3 steps down)

I, IV, ii, V, iii, vi

I, I6, IV, ii, ii6, V

Almost always starts on tonic and ends on I, IV, or vi

WATCH THE BASS VOICE FOR ASCENDING SEQUENCE

Pg. 31-32

Descending 5-6 Sequence

Major: I, V6, vi, iii6, IV, I6

Minor: i, v6, VI, III6, iv, i6

I, V(6), vi, iii(6), IV, I(6)

I, V, vi, iii, IV, I (5 steps up gives you 7 steps down)

Starts on any stable chord and ends on any other stable chord that forms a strong progression

WATCH BASS VOICE FOR DESCENDING SEQUENCE

Pg. 32-33

Diminished and half-diminished 7th chords in major and minor keys

Major: Half-diminished 7th chord + diminished 7th chord (lowered 6 scale degree)

Minor: Diminished 7th chord (raised 7 scale degree)

Half-diminished chord vs diminished chord?

Half: dim 5 and min 7; min 3 min 3 maj 3

Full: dim 5 and dim 7; min 3 min 3 min 3

Full dim is sometimes used in a half cadence

Tonic prolongation

I(6) → vii half/full dim7 → I

7th of the chord (4th scale degree; highest note) resolves down by step

Leading tone 7th chords are spelled as R357

Passing and Neighbour Chord Idiom

Passing → only dim allowed (E.g., I, vii dim6/5, I6)

Neighbour → half-dim allowed (E.g., I6, vii half-dim6/5, I6)

Dominant prolongation

Leading-tone 7th chords alternate with dominant 7th chords to prolong the dominant harmony

(E.g., V, vii half-dim, V and vii dim7, V, vii dim7)

Voice leading of leading-tone 7th chords

The leading tone must resolve up to the tonic (7th scale degree rises to 1st)

Seventh of the chord must resolve down by step (6th scale degree falls to 5th)

4th scale degree falls to 3rd

Dominant-function chord resolution (vii half-dim7 and vii dim7)

Always precedes (goes before) I or V:

vii half-dim7 and vii dim7 resolve to I

vii dim6/5 resolves to I or I6

vii half-dim6/5 resolves to I6

vii half-dim4/3 and vii dim4/3 resolves to I6

vii half-dim4/2 and vii dim4/2 resolve to V, V7, V6/4 → 5/3, V8/6/4 → 7/5/3

Applied chords in major keys

Applied chord (home keys) serve as temporary tonic; serves pre-dominant function in tonal hierarchy

ii: V, V7, vii dim6, vii dim7

iii: Same as ii

IV: V(7), vii dim6, vii half-dim7, vii dim7

V: Same as IV

vi: Same as ii and iii

V, V6, V7 (and inversions), vii dim6, vii half-dim 7 (and inversions), vii dim7 (and inversions)

Applied chords in minor keys

Applied chord (home keys) serve as temporary tonic; serves pre-dominant function in tonal hierarchy

III: V(7), vii dim6, vii half-dim7, vii dim7

iv: V, V7, vii dim6, vii dim7

V (always major): Same as iv

VI: V(7), vii dim6, vii half-dim7, vii dim(7)

VII: Same as III

V, V6, V7 (and inversions), vii dim6, vii half-dim 7 (and inversions), vii dim7 (and inversions)

Resolution of applied chords

Applied chords (temporary tonic) must resolve to the tonic equivalent (its own dominant-function chord); different variations and inversions are acceptable (E.g., V/ii → ii6 and V7/V → V7)

Do NOT double the temporary leading tone of the applied chord (E.g., vii dim6/ii → R335)

Applied chords can span over 2 notes (E.g., V7 and vi/IV or V-4/2 / IV

Keyboard style: RR35 (mostly) or R355; otherwise same principles to SATB style

One chord spelled complete and the other incomplete to avoid parallel fifths UNLESS inner voice (alto or tenor) falls 7th scale degree to 5th, then both chords must be complete

Pg. 74-76

*When V/V occurs at a cadential point (end of phrase), it assumes pre-dominant function

Four-part writing of applied chords

V7/ … can be spelled as R357 or RR37 (avoid doubling root in 7th chords)

Inversions of V7 are spelled as R357

vii dim6 is spelled as R335 or R355

vii half-dim7 and vii dim7 are spelled as R357

Pg. 77

Chromatic descending fifths sequence

Chain of applied chords; voices move down in a chromatic movement (alto and tenor voices in SATB instead of rising)

E.g., V7/iii → V7/vi → V7/ii → V7/V → V7 → V7/IV → IV …

Extra accidentals

When using chain of applied V7 chords:

the inner voices of SATB do not rise but rather descend in chromatic motion (Of each chord: 7th → 3rd and 3rd → 7th)

If all V7 chords are in root position, alternate R357 and RR37

Pg. 78-79

Modulation to closely related keys

Different from tonicization (one instance), changes key for a bit using pivod chord

For more detail, refer to Harmony 9 page 148

Modulation key options:

1) relative major/minor

2) add an accidental

3) relative key of added accidental

4) remove an accidental

5) relative key of removed accidental

Major: ii, iii, IV, V, vi

Minor: III, iv, v, VI, VII

*In C major you can add a # or b because there is no accidental

Main pivot chords (major):

I → IV, iii → vi, V → I, vi → ii

Pg. 115

V13 chord

V → scale degree 1 (R), 3, 7, 13 (5, 9, and 11 are dispensible)

13 is ALWAYS in the soprano (highest note/voice)

V13 is only used in ROOT POSITION

E.g., F major: C E Bb A (7th interval from 7 to 13)

True 13th = V13 (solid chord that goes directly to I or vi) 9scale degree 3 to 1)

App 13th = Soprano voice stepwise note in between V13 and I (E.g., V763 → V-5-) (Scale degree 3 to 2 to 1)

Ech 13th = Soprano voice echarpe movement (step up, skip down) (E.g., V7 → V13 or V753 → V-6-) (Scale degree 2 to 3 to 1)

Resolution to I:

3rd scale degree drops to 1st

4th scale degree drop to 3rd

7th scale degree (LT) rises to 1st

5th scale degree rises OR drops to 1st

Resolution to vi (deceptive cadence):

3rd scale degree drops to 1st

4th scale degree drops to 3rd

7th scale degree (LT) rises to 1st

5th scale degree ONLY rises to 6th

*Only V13 chord can be used for deceptive cadence; not V9

Move in contrary motion

Same LT exception as V7: LT may fall to 5th scale degree if it is inner voice (alto or tenor)

Pg. 117

V9 chord

V → scale degree 1 (R) 3 7 9 (5th note is dispensible but not 3rd)

E.g., Ab Major: Eb G Db F

True 9th: solid chord that resolves directly to I

App 9th: separated like grace note with note between V9 and I (e.g., V97 → V8-)

The 9th is ALWAYS in the soprano voice (highest note)

Only used in ROOT POSITION

CANNOT be used for deceptive cadence (V → vi)

NOT used as a FINAL authentic cadence

Resolution to I:

6th scale degree drops to 5th

4th scale degree drops to 3rd

7th scale degree (LT) rises to the 1st

5th scale degree can rise OR drop to the 1st

Perfect authentic cadence vs imperfect authentic cadence

PAC: When V → I, the 1st scale degree (tonic) is in the soprano voice in I; both chords need to be in ROOT position

IAC: when the 1st scale degree isn’t in the soprano voice (highest) in I

Characteristics of a chorale

Modulate only between closely related keys (adding/removing one accidental)

Follow T-PD-D or T-PD-D-T tonal hierarchy

Harmonic idioms → allow for tonic prolongation (E.g., I → vii dim6 → I6)

• Leading tone 7th chord can be used as a passing chord to achieve tonic prolongation OR can be used as an applied chord

Non-chord tones cannot happen on strong beat

Fermata indicated phrase endings (cadence)

4/4 timing (sometimes 3/4)

Rhythm changes every quarter-note beat (*sometimes 8th note beat but use non-chord tone when possible)

Stepwise motion with occasional leaps

Construct a bass line than complements the soprano (do this first) (root position, 1st inversion, non-chord tones)

What are the 5 popular baroque dances and what are the characteristics of baroque melodies?

Menuet, Sarabande, Gigue, Bourree, Gavotte

Follow antecedent-consequent (question-answer) phrase construction

Four-measure phrases

Effective tonal hierarchy models:

• T-PD-D

• T- T Prolongation (E.g., I, vii dim6, I6)-PD-D

• T-PD-D-T

• T-T Prolongation-PD-D-T

Melodic span does NOT exceed an octave or tenth

16-measure Baroque dance is typically in binary or rounded binary form

Common melody-writing techniques: repetition, transposition, variation, inversion

Menuet

moderately fast

triple meter (3/4 time signature)

phrases may begin with a pickup note (upbeat)

Sarabande

slow

triple meter (3/4 time signature)

stressed/prolonged second beat (E.g., ♩ ♩. ♪ | ♩ half note)

no pickup, starts on 1st beat (downbeat)

Gigue

Also called giga or jig

Compound time (any time signature with 6,9, or 12 as TOP number)

phrases may begin with a pickup note (upbeat)

contrapuntal texture*

Bourree

moderately fast / fast

usually in 2/2 time (can be 4/4)

phrases begin with a quarter-measure pickup (one quarter note / two eighth notes)

Gavotte

moderately fast

usually in 2/2 (sometimes 4/4)

phrases begin with half-measure pickup

Period structure

antecedent-consequent phrase

Period = 2 phrases of 4-measures (half of composition generally)

Antecedent → weak cadence (HC, IAC)

Consequent → complete period with strong cadence (PAC)

Parallel period → antecedent and consequent use the same material

contrasting period → consequent material is different from antecedent

*Check the shape, span, and general direction of bass part

Choose a rhythm that is consistent with the opening (don’t change too drastically)

Phrygian cadence

IV6 → V

common Baroque idiom

Common melody-writing techniques

repetition: exact repetition of previous notes

variation: different; like a sequence with more notes; can go in opposite direction)

fragmentation: take little parts of subject and making it into sequences

inversion: notes going opposite direction

transposition: same pattern of notes at a different pitch (another level)

“RV FIT”

*Canon, Melodic Inversion (extra)

AVOID using a copy-and-paste approach by using these techniques (exception: return of A in ROUNDED BINARY)

Antecedent-consequent pickup rule

When the antecedent (in phrase 1) begins with a pickup, the consequent (in phrase 2) preserves the pickup

What are the binary and ternary forms?

Simple Binary, Rounded Binary, Balanced Binary, Ternary Form

Pg. 162

Simple Binary

repeat A repeat → repeat B repeat

Each of the two sections is usually repeated

Opening key of section B is variable, but will ALWAYS end with a PAC in the home key

Section A ends with HC in the home key (*occasionally PAC in the dominant/relative major key or home key)

Section B is different from section A

Rounded Binary

repeat A repeat → repeat B A repeat

Opening key of section B is variable; arrives at dominant before the return of A and ends with a PAC in the home key

Section A ends with HC in the home key (occasionally PAC in the dominant/relative major key or home key)

Section B contains a brief return of the beginning of section A (usually 1-2 measures, up to 4)

Balanced Binary

repeat A (*) repeat → repeat B (*) repeat

Section A ends with PAC in the dominant or relative major key (occasionally in the home key)

Section B contains a brief return of the last portion of section A (usually 2+ measures) and ends with a PAC in the home key

Ternary Form

(repeat) A (repeat) Fine → (repeat) B (repeat) D.C. al Fine

Each section is self-contained and may be repeated (not always the case)

Section A ends with PAC in the home key

Section B offers contrast (different key, thematic material, etc.)

return of section A (EXACTLY SAME) may be indicated with da capo, written out in full, or written out with some variation?

What are the bigger forms?

Compound ternary form, five-part rondo form, sonata form

Compound Ternary Form

Compound form → larger constructions of basic forms (binary, ternary)

3 sections separated by double bar line (ABA)

Also known as Menuet and Trio or Scherzo and Trio form; most common type of compound form in classical music

Often includes a transition (modulate from home key to new key, or a retransition (foreign key back to home key; dominant pedal/dominant preparation*)

Some pieces end with coda (tail) → concluding section drawing on previous motives to conclude the work

Section A (Menuet or Scherzo):

• binary or rounded binary form with internal repeats

• begins and ends in the same key; contrasting material (b) may modulate or end on the dominant

• often ends with double bar line or repeat sign

Section B (Trio):

• binary or rounded binary form with internal repeats

• in the same meter (time signature) as section A

• contrasting material from A; typically less active in a key closely related to A (+- accidental)

• often ends with D.C. (da capo) to indicate return to section A

• sometimes the end of B doesn’t have a definite cadence but rather dissolves into a connecting passage that leads back to the repeat of section A

Section A (return of Menuet or Scherzo):

• repeat signs can be written out sections instead with variation*

• use lowercase letters to indicate internal sections (binary form) and use uppercase letter to indicate main sections of the form

Example on pg. 165

Five-part Rondo Form

Chain of alternating refrains and episodes

refrain → principal theme; uses SAME/similar material throughout the movement and ALWAYS remains in the home key

episode → contrast tonally and thematically with refrains

Typical structure: ABAC…A

A = refrains (theme/bridge)

B and C = episodes (contrasting keys; different part; can be own form such as Binary and Rounded binary)

five-part rondo → ABACA or ABABA is most common (A heard 3 times; can go up to 7 parts such as ABACABA and ABABACA)

Optional coda → can be only a few measures long or quite extensive and can be based on any of the thematic ideas from before

Ways to change theme → RITV (repetition, inversion, transposition, variation)

Section A:

• ALWAYS in the home key

• same melodic/motivic material each repetition

• subsequent statements may be embellished or shortened but still recognizable upon return

• usually ends with authentic cadence

• may be a period (8 measures), a binary form, or rounded binary form with repeat signs

Section B, C, etc.:

• Usually in contrasting keys (B is usually in DOMINANT or MEDIANT while C is in the TONIC MINOR, TONIC MAJOR, SUBDOMINANT, or SUBMEDIANT with OR without a change of key signature → accidentals if no key signature)

• Contrasting melodic/motivic material from each other and from A

• often in binary or rounded binary form with repeat signs

• Can be complete in themselves with authentic cadence OR can be open ended with no obvious cadence and connecting with the return of A through retransitions

• B1 (in ABAB1A) is often a transposed version of B typically in the home key

Example on page 167

Sonata Form

Also known a sonata-allegro form (single or multi-movement)

Typically used in the first movement of multi-movement compositions (can sometimes be found in subsequent movements)

Single-movement works (E.g., overtures) can be in sonata form

Expansion of rounded binary form → 3 main sections are exposition (A), development (B), and recapitulation (return of A or exposition)

Slow introduction (head) and coda (tail) may be present

Basic structure:

Optional Introduction (prepares primary key)

Exposition: Theme 1 (primary key), Bridge (modulates to secondary key), Theme 2 (dominant or relative major key), Codetta (temporary ending of section)

Development (explores new tonal areas → contrasting)

Recapitulation: Theme 1 (returns to primary key), Bridge (REMAINS in primary key), Theme 2 (REMAINS in primary key), Codetta

Optional Coda (may include brief deviations from the primary key)

Example on pg. 171

Exposition

First part of sonata form

Main thematic material (most important melody) for the movement → two contrasting themes/theme groups connected by a bridge (theme group = more than one motive used and each concludes with a cadence; abbreviated as Th1a, Th1b, etc.)

Entire exposition is usually repeated, a retransition may appear after the codetta to return to the primary key to prepare for the repeat

Contrasting keys are central to the form (rather than contrasting thematic material)

Theme 1:

• Establishes primary key

• 1 or more thematic idea(s)

• ends with HC or AC in the primary key

Bridge (connects theme 1 and 2)

• Starts the move to the key of theme 2 smoothly using accidents (but sometimes no new accidents are present and the bridge emphasizes the dominant harmony and ends on the dominant triad) (V in primary key is I in secondary key)

• Can start by repeating opening of theme 1 before transitioning to secondary key

• can present new figuration/texture (Alberti bass)

• can sometimes start suddenly in an unexpected key (vi)

Theme 2:

• Establishes secondary key (usually dominant or relative major with an authentic cadence)

• usually but not always contrasting in material

Codetta (temporary coda):

• Begins after AC in secondary key

• reinforces the key of theme 2 with another AC

• also called “close”

Development

Second part of sonata form

Tonally unstable → starts in key where exposition ended, goes through several new tonal areas and prepares for the return of the primary key in the recapitulation (next part)

Keys not confirmed by AC in sections typically

May contain 1+ themes from the exposition that can be expanded, altered, fragmented, sequenced (same pattern in different pitch), or broken down into motives (went back to simple theme)

New material introduced sometimes

End of development often contains dominant preparation (go into dominant harmony) → emphasis on dominant harmony of primary key

• Before next key using the V chord or V7

Recapitulation

Third part of sonata form

Return of theme 1 or 2 in primary key; follows same structural patterns in the exposition (but not exactly the same)

Theme 2 appears in the primary key instead (sometimes bridge is altered to remain in the primary key as well)

Sometimes theme 2 is also altered (shortened, expanded, reworked, or varied according to earlier sections)

Followed by codetta (end of exposition or recapitulation)

Coda (in form)

Final part of sonata form IF present

Concludes the movement using thematic material from previous sections

Different from codetta; the coda is the end of the entire movement (ending with AC; final; full-stop)

Must end in home key

Refrain and episode

Refrain → principal theme; uses SAME/similar material throughout the movement and ALWAYS remains in the home key

Episode → contrast tonally and thematically with refrains

Transition and retransition

transition (modulate from home key to new key)

retransition (foreign key back to home key; dominant pedal/dominant preparation*)

Coda and codetta

Coda → concluding section drawing on previous motives to conclude the work (end of entire movement)

Codetta → temporary coda; end of exposition or recapitulation

Dominant preparation

Go into dominant harmony → emphasis on dominant harmony of primary key

• Before next key using the V chord or V7 (to pivot)

REVIEW

Fugue

Contrapuntal composition (combination of multiple voices) based on distinctive theme that is original or borrowed

3-4 voices typically

“to flee”

“to chase”

Subject

Theme’s first appearance

Presents primary thematic material

No limit in length (can be a few notes to several measures)

Can enter any voice while other voices rest

In tonic key (sometimes modulates to dominant key)

Link

Also called codetta

In some fugues

Short connecting link → connects passages between subject and answer

Can be made out of motives from the theme or countersubject (or be different)

Answer

The second statement of the principal theme (A4 → 4 voices) heard in any different voice and in dominant key

SAME theme but in dominant key

Real answer

Exact transposition of subject

Tonal answer

If one or more of the intervals of subject are altered

Required when fugue subject features dominant, near the beginning, or when it modulates to the dominant key*

Countersubject

Material that consistently accompanies the answer → has to appear accompanying subjects/answers more than once

Appears in originating voice after end of subject

Can appear in any voice

Can shift from one voice to another (E.g., treble staff to bass staff)

Can begin early or later (does not always begin precisely when the theme enters)

Not every fugue has a countersubject

Can have more than one countersubject (depending on # of voices)

Fugal exposition

Each voice gets a chance to present the same subject melody (subject or answer)

Once every voice presents the subject melody, the exposition ends

Redundant entries

Additional entries of subject and answer in expositional keys (tonic key for subject and dominant key for answer) AFTER exposition ends

Stretto

When subject and/or answer overlap (one begins before the previous finishes)

Some entries may be incomplete