+++++++++++++++++++++++++ ++ TONAL HARMONY NOTES ++ +++++++++++++++++++++++++

mood should be consistent (Wright): - major vs. minor - affinity to tonic or dominant - conjunct vs. disjunct; contour; ascending (tension) vs. descending (release) - scale (lyrical) vs. harmonic series (primordial, grand) - ethnic scales can add lots of color, e.g., pentatonic - rhythmic simplicity; tempo; strength of beat; harmonic acceleration - timbre; volume; articulation - spacing & register & doubling of chords greatly affect mood - drama is contrast: dynamics, range, chromaticism, modulations, rhythmic var. - functions in classical music: theme, transition, development, cadential

basic melodic principles: - contour: usually conjunct, shape should be clear, with a single focal point - leaps:

= avoid augmented intervals, 7ths, and intervals larger than p8
= diminished intervals may be used if the melody changes dir by step after
= intervals > P4 should be approached and left in the dir opposite to the leap
= small leaps in the same dir should outline a triad (even if chord changes)
= bigger leaps require longer note durations

- tendency tones: ^7 usually moves to ^1; ^4 usually moves to ^3 - consonant intervals include m3, M3, m6, M6, P5, P8

= P4 is dissonant if it's in the bass, otherwise it's consonant

- my own ranking of intervals

= most to least pleasant: M3, m3, M6, m6, P5, P8, P4, m7, M2, M7, m2, d5/A4

motivic development: - a motive is a salient feature of a musical idea

= advice: if you don't plan on developing something, don't make it stand out
= the rest of this section describes motivic development techniques
= take note of how each technique affects the emotional character of basic idea
= and use them accordingly in your composition

- transposition: may be exact, tonal, or sequential - variation: elaboration or simplification by adding or removing NCTs - fragmentation: utilizing only a portion of the motive - intervallic alteration: stretching or contracting the intervals of a motive - inversion: direction of the intervals are reversed (exact, tonal, or modified) - retrograde: motive stated backwards - augmentation: statement of motive with proportionally longer rhythmic values - diminution: statement of motive with proportionally shorter rhythmic values - extension: repetition of elements within the motive to make it longer - truncation: elimination of elements within the motive to make it shorter

rhythmic motives: - subdivision of the pulse - regular vs. irregular rhythm: longer notes on strong beats? - syncopation: off down beats, whole over dotted, triplets, grace notes

= cross rhythm, polyrhythm, swing (suspensions), latin (anticipations) 
= hemiola: temporarily switching from triple to duple by changing accents

- basic accompaniment ideas (besides block chords):

= oom-pah-(pah), Alberti bass, other arppeggic patterns, ostinato, walking bass
= bass riffs, bass fillers, 

-

how to make a textural reduction: - remove all non-chord tones (probably the most difficult task) - using longer note values or ties for repeated notes - transposing parts by P8 when necessary to make the lines smoother - to identify the number of voices

1. best way is to listen
2. big leaps & short note durations, or small steps and long note durations?
3. check to see if it's arpeggiating one chord or moving to different chords

functional harmonic analysis: - general rules: [iii]->[vi]->[IV /-> ii]->[viio /-> V]->[I]->[any]

= exception 1: V-vi, the deceptive progression (because you would expect V-I)
= exception 2: vi-V, skipping over predominant
= exception 3: iii-IV, harmonizing 1-7-6
= exception 4: IV-I, plagal cadence
= exception 5: I64-V, with the I64 on a strong beat, is equivalent to V

- iii is rarely used except to harmonize a 1-7-6 soprano line

= but III is commonly used in the minor as it represents the relative major

- viio is often used in tonic prolongation: I-viio6-I6 or I6-viio6-I

= it's also useful for harmonizing a 6-7-1 soprano line
= it can also precede V: viio-V-I

- IV has a variety of functions:

= plagal cadence: IV-I
= precede IV-ii-V-I
= substitute ii as the predominant: IV-V-I

- differences in minor mode:

= common triads: i, iio, III, iv, V / v6, VI, viio / VII
= III is much more commonly used than iii
= VII is sometimes used to move to III (secondary dominant), but never to i
= v6 is sometimes used to move to iv6, to harmonize a ^7-^6 melody

secondary functions: - a very brief modulation and back that emphasizes, or tonicizes, some chord

= most common types: V/X, V7/X, viio/X, viio7/X, viio'7/X,
= where X is a major or minor chord in the original key

- secondary dominant (V/X, V7/X):

= V7/X is as common as, if not more so than V/X (unlike "normal" 7th chords)
= these are the most frequently encountered form of altered chords
= remember that only major and minor triads (7th optional) can be tonicized
= in fact, secondary dominants frequently resolve to a 7th chord
= the V7/V is the most common secondary dominant, and similarly V7/V-{I64-V}
= also common is the V(7)-V/vi, to add momentum to the deceptive progression
= in the minor, VII(7)-III is common, but notate this as V(7)/III-III
= but the V/VI should be simply analyzed as III
= worth noting in major mode, V7/IV is used instead of V/IV, because V/IV = I

- recognizing secondary dominants:

= check to see that it's a major triad or major-minor seventh
= check to see that the note 5th below its root is within the original key

- using secondary dominants (suggestions, not rules):

= can be added in front of any chord in a sequence
= can sometimes be chained to another secondary dominant: e.g. V/ii-V/V-V-I
= secondary dominant can be approached by any chord a P5 higher: V-V/iv-iv
= or approached from similar chord or target chord: ii-V/V-V, vi-V/vi-V/ii
= or approached from whatever sounds good: ii-V7/IV-IV

- secondary leading tone chords aren't as popular as the secondary dominants

= but they're still more common than mode mixtures
= the viio7/X is more commonly used than viio'7/X, even if the mode is major
= tonicized chord is usually ii, IV, V, or vi in major, and in minor, iv or V

mode mixture and the Neapolitan: - commonly found in the minor:

= Picardy third: I often substitutes i as the final tonic in pre-1750 music
= Neapolitan, or bII6, or N6: see textbook for more info

- mode mixture in the major:

= most common are the b^6 chords: viio7, iv, iio'7, iio
= somewhat less common: i, bVI, iv7; least common: bIII, bVII

modulations (within movement) and key changes (between movements): - the 1st and 3rd movements of a symphony usually start and end on the same key - modulating to ii, iii, IV, vi, and V is common

= these keys are closely related as they differ by 1 accidental or less
= I-V is most common in major; i-III and i-v is most common in minor

- common chord modulation: the standard method for smooth modulation - altered chord modulation: using a secondary function or a mode mixture - sequential modulation: where a transposed melody establishes the tonal center - circle modulation: e.g., C-C7-F-F7-Bb - direct modulation: no attempt to smooth over; usually used between phrases - common tone modulation - monophonic modulation

form basics: - the idea is to hit harmonic goals (cadences) every four measures or so - PAC: V-I, V7-I, with a ^1 in the melody over the I - IAC: same as PAC, but ^3 or ^5 is in melody over the I

= inverted IAC: same as IAC, but with at least one of the chords inverted
= leading tone IAC: viio-I or some variations of this

- PC: IV-I (plagal cadence) - DC: V-vi, V-!I (deceptive cadence) - HC: any chord not containing leading tone -> V chord

= phrygian half cadence: iv6-V (minor only)

- motive: smallest identifiable musical idea; a pitch and / or rhythmic pattern

= it is developed by repetition and variation throughout the composition

- phrase: relatively complete idea that ends on a cadence

= can be extended by a DC + AC, or by repetition of the original cadence
= not every cadence indicate an ending; instead look for rests and long notes

- period: two phrases in antecedent-consequent or question-answer relationship

= first phrase should end with HC / IAC; second phrase with IAC / PAC
= parallel period: if phrase a and a' begin with similar / identical material
= contrasting period: if a and b are not similar
= three phrase period: 3 different phrases
= double period: 4 phrases in 2 pairs; cadence at second pair being stronger
= parallel double period: a(HC)b(HC)a(HC)b'(PAC) 

- sentence: a long 1-phrase theme with 2 parts: presentation + continuation

= presentation consists of motive + exact / sequence / ornamented repetition
= presentation phase establishes harmony by staying close to tonic
= continuation features fragmentation + harmonic acceleration + HC / AC
= fragmentation: the motive is broken up to smaller segments which are repeated
= harmonic acceleration: the chord change speeds up to 1 / bar or even 2 / bar

larger forms: - analysis caveats:

= sectional if 1st part ends on tonic chord of main key, else, continuous
= the two-reprise is common, e.g, |:a:||:ba:|, is a two-reprise ternary
= beware: some composers like to write out the repeats
= the individual parts need not be of equal length
= ternary or binary? each section in ternary can stand on its own
= ternary or binary? in ternary, the 1st and 3rd parts are almost identical

- binary: aa', where a' contains both continuation and contrast - ternary: aba - rounded binary: ab(1/2)a: typically, a(HC)a'(PAC)b(HC)a'(PAC) - sonata-allegro form: often used as the 1st movement, featuring tonal conflict

= |:    exposition    :||: development |  recapitulation  :| coda |
= |: P trans. S clos. :||: modulations | P trans. S clos. :|
= key: I-V or i-III/v :||:  unstable   |      I or i      :| I or i

- rondo form: often used as the final movement

= five part rondo:         A(I) B(V or i or vi) A(I) C(x) A(I)
= five part rondo variant: A(I) B(V or i or vi) A(I) B(?) A(I)
= seven part rondo:        A(I) B(V) A(I) C(x) A(I) B(I) A(I)
= sonata rondo:            A(I) B(V) A(I) C(dev.) A(I) B(I) A(I)
= where x is some key other than I or V, and "?" could be anything

part writing basic ideas: - spacing:

= no part should cross above soprano or below bass
= avoid muddiness: upper parts should be close; lower parts farther apart
= i.e. soprano, alto, and tenor should be within 1 octave apart from each other
= open or closed? open means soprano and tenor is 1 octave or more apart

- harmonic motion involving constant P5 and P8 intervals are to be avoided

= reason is to avoid having any two voices sounding like a single voice
= these rules apply especially strongly when involving soprano or bass
= likewise, P12 is not allowed, but P4 is allowed, even though it's inverted P5 
= but it's ok to double the bass line; it's also ok when chords don't change
= 5/8th by contrary motion: not allowed; so don't fix parallel 5ths this way
= unequal 5th: a dim5 to P5 movement is often avoided in the bass
= direct 5/8th: avoid outer voices leaping in similar motion into a P5 or P8
= stepping into it is ok; also ok if only the bass leaps (and soprano steps)

- 3 parts or 4 parts? these are my personal opinions:

= 3-parters showcase interesting melodic movements: singable and recognizable
= 4-parters showcase smoother and richer textures: epic yet non-intrusive

root position part writing: - the key to part writing is attention to smoothness and clarity of each voice

= exception 1: when chord is repeated, variety is more valued than smoothness
= exception 2: in final tonic, 5th is often omitted to avoid muddiness

- melody rules still apply:

= leading tones should always go to tonic even if it means two parts converge
= generally avoid intervals larger than a 3rd; esp. avoid augmented intervals

- 4-part textures:

= all members of triad usually present; final chord missing 5th, root tripled
= root usually doubled (esp. first tonic); leading tone is almost never doubled
= third is usually doubled in a V-vi or V-VI progression

- 3-part textures:

= surprisingly I find this trickier to arrange than 4-part textures
= 5th of a triad usually omitted; final chord may be only a tripled root
= note: 5th is mostly kept if we're dealing with an inverted triad
= incomplete triad usually has root doubled; leading tone is never doubled

- when a chord is repeated, its upper part should be rearranged - conventions vary depending on the interval between the consecutive chord roots

= there are 3 categories: 4/5, 3/6, and 2/7: read page 94 - 100 for details
= e.g., for V-vi or V-VI: double the 3rd of the vi instead of the root

triad inversions: - sixth chords are not unusual: most phrases include at least one

= six-four chords are less common as the P4 is historically seen as unstable

- it's unusual to omit the 5th in an inverted triad, unlike it is in root pos - first inversion uses:

= substitution of a root pos triad: to improve the contour of the bass line
= arpeggiation of a root pos triad: to add variety in a repeated / long chord
= note: in the arpeggiation case, root pos is played first, then the inversions
= to destabilize the V and I chords in order to keep the momentum going
= to avoid parallel 5ths but create parallel 4ths; e.g. IV6-iii6-ii6-I6-viio6
= historically, diminished chords were used in first inversion to avoid tritone
= passing chord sequences / parallel 6ths: arising out of passing notes

- second inversions uses:

= they're harmonically weak and so serve only embellishing functions
= base arpeggiation
= cadential 64: see below
= passing 64: harmonically weak; used only to create a stepwise bass line
= pedal 64: simply move the 3rd and 5th up and then back down, e.g. I-IV64-I
= passing and pedal 64s should be notated in braces due to harmonic weakness

- cadential 64 progression, I64-V, with the I64 on a stronger beat than V

= fulfills the same function as the dominant, e.g.: I-ii6-I64-V-I

- the III+6-V progression (rare)

= serves the same function as i64-V, but has no major key equivalent
= it's not as often used as the cadential 64; e.g.: iv-III+6-V-I

- vi6 and VI6:

= never use it after a root position V, it'll sound like a tonic gone wrong
= it is sometimes used in the I-vi6-ii progression

inverted triad part writing: - first inversion triads:

= in 3-part textures, all members of triad should be present
  but if a tone must be omitted, it is usually the 5th of the triad
= in 4-part textures, any tone can be doubled; follow the doubling rules below:
= in contrapuntal style, double the member that give the best voice leading
= in homophonic style, double the member that give the best sonority
= sonority is affected by spacing and doubling:
  an inner voice doubling the soprano is most preferred
  an inner voice doubling the bass is next preferred
  soprano doubling the bass is next preferred
  inner voices doubling each other is least preferred
  and never ever double a leading tone

- second inversion triads:

= in 3-part textures, all members of triad should be present
  but if the root or the 3rd must be omitted, make sure to double the 5th
= in 4-part textures, pretty much always double the bass (5th)

non-chord tone (NCT) categorization:

                      approached by    | left by

- passing tone (p): step | step in same direction - neighbor tone (n): step | step in opposite direction - suspension (s): same tone | step down - retardation (r): same tone | step up - appogiatura (app): leap | step (often by semitone) - escape tone (e): step | leap in opposite direction - neighbor group (n.gr): | - anticipation (ant): step or leap | same tone or leap - pedal point (ped): |

NCT basics: - NCTs are decorative; use them to breathe life into the harmonic backbone - NCTs are found frequently in chromatic forms as well as diatonic forms - passing tone(s): use one to fill an M3, or use more to fill larger intervals - neighboring tone: go above or below a main tone and back to embellish it - suspensions: used to produce an accented dissonance, which is very noticeable - retardation: same as suspension but going up, usually 7-1 - appogiatura: when leaping, first overshoot the target, and then step back - escape tone: pretends to leave but leaps back to target; short and unaccented - neighbor group: appogiatura + escape tone; either together or staggered - anticipation: step or leap into a tone in second chord, creating dissonance - petal point: a sustained tone (usually bass) which turns into NCT and back

suspensions: - basic types (named by bass to suspended interval):

= 7-6, 4-3, 9-8: common non-bass suspensions
= 2-3: common bass suspension

- variations on the basic types:

= suspension with change of base: occurs when bass is made to arpeggiate
= suspension can be made to resolve after many notes, rather than just one
= suspension can also be chained: res of one serves as prep of another

- basic guide for finding places to add suspensions:

= 2-3: find a step down in the bass, does it form a 3rd with some upper tone?
= 4-3, 7-6, 9-8: step down in an upper voice, does it form a 3rd, 6th, 8ve?

- other types are ok as long as a dissonance between voices is made and resolved

how to go nuts with embellishments: - it's usually pointless to embellish the middle voices; focus on melody & bass - add passing tones between every leap (these are the most ubiquitous NCTs)

= but generally avoid adding them on strong beats

- insert neighbor tones into long notes and inbetween repeated notes - look for places to add 2-3, 4-3, 7-6, 9-8 suspensions, and add them - arpeggiate the longer notes, esp. bass; can also be used to connect big leaps - appogiatura fits anywhere in the melody, and can really bring it to life

= there are 4 types: up down over under; they all sound very different

- if a 2-1 exists in melody, you can ornament it with an escape tone 2-3-1

= escape tones and sequences can be added anywhere but they must be short

- neighbor group is very good for embellishing a prolonged stable melodic note

= n. gr. and neighbor tones can be interpretted as secondary dominants

- anticipation is good when voice leading is nice and the note is dissonant - pedal point, doubled or single, broken or sustained; e.g. V-I64-V or I-IV64-I

= as an NCT, peds in the root can be used to strongly establish the tonic

- same idea: staggering the left and right hand so that the right hand lags - embellishments can be used to hide parallels and other voice leading errors

= but check to see it's not introducing additional voice leading errors!

- embellishing is an art in itself, so practice, and study from the old masters

7th chord general principles: - ranking by frequency of seventh chords used in major: V7, ii7, viio'7, etc - 7th of the chord almost always resolves down by step - 7th of the chord may be approached by, from most to least common:

= suspension, passing, neighbor, or appoggiatura figure

- incomplete chords must contain at least the root and the 7th - doubled tones should not be the chord 7th or the leading tone

the V7 chord: - often the 7th only occupy a portion of the chord, like an NCT: e.g., I-V-7-I - in voice leading, the 7th of the chord should be:

= approached by constant, step, rarely ascending leap, never descending leap
= always resolved by a descending step, except in V43-I6, where it steps up

- the leading tone in V7 should always resolve up when it's an outer voice - V7-I (root pos) voice leading solutions, from most to least common:

= complete V7, incomplete I: reducing the I to 3 roots and a 3rd
= complete V7, complete I: hide leading tone in inner voice, bring down by M3
= incomplete V7, complete I: omit the 5th in the V7, double the root
= complete V7, incomplete I: reducing the I to 2 roots and 2 3rds

- V7-vi voice leading guide:

= the leading tone move up by step unless its an inner voice in major mode
= the bass moves up by step; the other voices move down by step
= just like V-vi, expect the vi to have a doubled 3rd usually
= the V7 should always be complete in a 4-part texture

- in a 3-part texture, the 5th, or less commonly, the 3rd is omitted - inverted forms have weaker harmonic functions

= use them in the middle of phrases to harmonize specific melody and bass notes
= commonly used as tonic prolongation like this: V65-I, V43-I6, V43-I, V42-I6
= in voice leading, both the 7th chord and the resolution are usually complete

the ii7 and viio7 chords: - keep in mind that these chords are not very common

= they serve the same functions as their triad counterparts
= common usages and exceptional problems are discussed below

- ii7 most commonly occurs as ii65, e.g.: ii65-V7

= rarely, the ii65 is used like a ivadd6 in a plagal cadence: ii65-i

- viio'7-I: watch out for parallel 5ths in viio'7-I and viio'43-I6 resolutions - viio'7-V65 is easily resolved by taking the 7th down a step - viio'42 is never used, neither is viio'65-I

= but in the minor, viio42-V7 and viio42-i64-V7 are more common

- viio7-i: in order to resolve both tritones, the 3rd of the i is doubled

= to handle tritones, remember that +4 resolves outward, o5 resolves inward

- VII7 is used in special circle sequences only, see below for details

other 7th chords: - keep in mind these chords are very very rare

= they serve the same functions as their triad counterparts
= common usages and exceptional problems are discussed below

- iv7 or IVM7 can't move directly to V due to parallel 5ths, solutions:

= doubling the 5th of the iv7 instead of the root
= can go to the cadential 64: IVM7-I64-V
= can go to the viio instead
= iv7-iio'65 is easily achieved by moving the 7th of iv7 down a step

- IV7, though unusual, can be created in minor to harmonize a ^6-^7-^1 - vi7 or VIM7 is pretty much used like their triad counterparts - IM7 or i7 is unstable and wants to move to IV, ii, or vi - giant circle of 5th sequence containning 7th chords is a common usage:

= e.g. i-iv7-VII7-IIIM7-VIM7-iio'7-V7-i
= if all root pos: complete chords will alternative with incomplete chords
= else: either 65 will alternate with 42, or 43 will alternate with root pos
= with exception of bass line, every voice either stays the same or steps down
= the inverted chords give you a smoother bass line than all root pos sequence

part writing caveats (in other words, mistakes that I frequently make): - 4-part textures:

= write soprano and bass first; check similar leaps for direct 5ths and 8ves
= also check for consecutive 5ths and 8ths by contrary motion
= also beware of doubling any leading tones or 7ths of 7th chords
= start by voicing any 64 chords because you always know to double the 5th
= next, voice any closed root pos chords, and let these guide the rest
= if root pos chord, always try doubling the root
= next, do the 7th chords; usually they should be complete
= avoid parallel 5ths and 8ves: I tend to miss these a lot!
= try to avoid jumps bigger than a third, but don't stress out if unavoidable
= avoid jumping from ^6 to ^7 in the minor where there's an m3 
= don't forget to sharpen the leading tones in a minor key: V and viio chords
= never double the leading tone: actually makes certain chords easy to arrange
= leading tones should always move to tonic even if two parts converge
= especially watch out for any m3 jumps from ^7 to ^6 in the minor
= for spacing: S/A/T can be close, but grant healthy spacing between T/B
= don't be afraid to merge 2 voices when it's really necessary

- rhythm:

= it's tricky to know when to mirror vs. stagger the rhythm between the SATB
= in countrapuntal style, I like simple, mirrored, steady beats for all parts
= in homophonic style: S - melodic; B - steady beats; AT - liquidated melodic
= e.g., S a variety of 1/2, 1/4, and 1/8 notes; B always 1/4; AT 1/2 and 1/4

- progressions:

= never use perfect cadence V-I or V7-I unless it's the final bit of the phrase
= instead use V6-I, V-I6, VI-I, V-vi, viio-I, etc

- embellishments:

= check to see the embellishments are not introducing voice leading errors

stuff: - arpeggio bass, alberti bass, rolling octaves, melodic bass - giant circle of descending 7th chords -