Piano Theory I

augmented

An interval a semitone larger than major, or a semitone larger than perfect, is called augmented.

ii 6

Generally doubles the third (bass) when going to V. In this very common pattern, all three upper voices descend to the closest note in the V chord- don't keep the common tone. In other contexts (not moving to V), ii 6 may double the root or third.

Second Inversion

Have intervals of 6, 4, and 3 over the bass. These are labeled as Roman numeral functions with the superscript 6 4 3, or simply 4 3: V 4 3, viiº 4 3.

French 6th "label Fr+ 6

Minor sixth scale step in bass, tonic, raised 4th and second scale degree.

Italian 6th "(label It+ 6)

Minor sixth scale step on bass, tonic aside 4th + doubling of tonic note.

passing tone

PT, approached by step, left by step, direction of resolution: same as approach.

V 7

Root is in the bass; chord goes to I. Leading tone resolves to tonic, seventh of chord steps down, fifth also steps down: resulting I chord has three roots, one thirds and no fifth.

suspension

SUS, approached by: same note or tied or repeated, left by: step, direction of resolution: usually down.

seventh chords

Using the Arabic numerals to identify intervals above the bass note, it will be seen that -7 5 3 means root position seventh chord- can also be shortened to just 7. -6 5 3 means seventh chord in first inversion-can be shortened to 6 5. -6 4 3 means seventh chord in second inversion-can be shortened to 4 3 -6 4 2 means seventh chord in third inversion-can be shortened to 4 2.

Dominant seventh chord and its inversions

V 7, V 6 5, V 4 3, V 4 3-I,V 4 3-I 6, V 4 2

dominant seventh

V chord with an added seventh. seventh typically comes about as a passing tone, falling from the doubled root of the V chord, and resolving to the third of the tonic chord.

applied dominants or transient dominants

another name for secondary dominants and they can occur at any point within the phrase. They often appear in inversion especially first inversion. Normally they resolve to the tonic chord they imply using the regular resolutions of the dominant seventh.

First Inversion

contain the interval of 6, 5, and 3 over the the bass. these are labeled with Roman numeral functions, and the superscript 6 5 3, or simply 6 5: ii 6 5, V 6 5.

c minor viiº

diminished leading tone B(♮) D F

C major viiº

diminished leading tone BDF

c minor iiº

diminished supertonic D F A♭

fifth note in scale

dominant

root position chords containing sevenths

labeled with their normal Roman numeral function followed by a superscript 7: ii 7, V 7, etc.

V 4 3-I 6

leading tone resolves to tonic, seventh of chord steps up (usually), keep common tone. Resulting I chord has a doubled fifth. If the seventh of V 4 3 descends as it does in all other resolutions of V 7, the I 6 chord will have a doubled third. This is not impossible, but is much less than the doubled fifth resolution.

seventh note in scale

leading tone* *In minor, if the seventh step is lowered, it is not a leading tone; it is often called the subtonic, lowered seventh, or natural seventh. The leading tone (raised seventh in minor) is always a half step below the tonic.

common root positions intervals

octave, third (tenth), and fifth.

Third inversion

possibility that only arise in chords with four different notes, like seventh chords. In third inversion, the seventh is in the bass, and the intervals over the bass are 6, 4, and 2. These chords are labeled with the super scripts 6 4 2, 4 2, or simply 2. For the purposes of labeling, V 6 4 2 = V 4 2 = V subscript 2.

non dominant seventh

seventh chords other than those built on V and viiº.

leading tone

should never be doubled in V or vii.

triad

three-note chord built in thirds from its lowest note. One may also think of a triad as a third and a fifth built above a starting note. The members of the triad from bottom to top are the root, the third, and the fifth.

resolution

#ii degree 7 resolves to I 6, as shown below. # vi degree 7 resolves to V 6 5. Note that the resolutions keep the common tone while the other voices move by step.

Minor Scale: Natural Minor

(corresponds to the key signature) a minor: WHWWHWW

Harmonic Minor

(variation of minor scale on which harmony is based; note the raised seventh scale step, and the one and one-half step distance between sixth and seventh scale steps) a minor: WHWWH 1.5 H

Melodic Minor

(variation of minor scale used in melodic lines; note the raised sixth and seventh in ascending form, lowered sixth and seventh in descending pattern. Descending scale is the same as natural minor). a minor ascending: WHWWWWH A B C D E F# G# A a minor descending: WWHWWHW A G♮ F♮ E D C B A

modal degrees

3, and 6 can sometimes be doubled, especially if doing so creates a good soprano line.

Half cadence

A cadence on V. Not heard as final, a half cadence creates the need for an answering full cadence.

Secondary dominant

A dominant triad or dominant 7th chord that has as its chord of resolution a triad other than I (or i) in a given key. Any major or minor triad has a dominant 7th that belongs to it, and therefore, the major or minor triad on every scale step may be preceded by its own dominant. In C major for example the primary V 7 chord is G-B-D-F but secondary V chords may be formed that resolve to other triads built on the C-major scale. For example, the ii chord in C major, D-F-A is a minor triad that has a dominant of its own. What is the dominant of D? The answer is A. The V 7 of the ii chord (D-F-A) is A-C#-E-G; the V 7 of the iii chord (E-G-B) is B-D#-F#-A; the V 7 of the IV chord (F-A-C) is C-E-G-B♭; the V7 of the V chord (G-B-D) is D-F#-A-C; the V 7 of the vi chord (A-C-E) is E-G#-B-D; note that the viiº chord does not have a secondary dominant: the viiº chord is a diminished triad, and therefore could not provide a resolution of a dominant. Following this same logic fo the triads of minor keys, one finds that III, IV, V, and VI can have secondary dominants. The iiº chord and the viiº chord are both diminished in minor keys so they cannot serve as resolutions of secondary dominants.

Major Scale

A major: WWHWWWH

Passing 6 4

A passing tone in the bass is harmonized in such a way that a 6 4 chord is created. Doubling should promote smoothness; passing 6 4 is more likely to appear on a weak beat. Remember the bass must be a passing tone-it must get to the 6 4 inversion by step and must leave it by step in the same direction.

Doubly augmented

A semitone larger than augmented.

Whole Tone Scale

All whole steps. A B C# D# F♮ G A

tonal counterpoint

Also called 18th century counterpoint or Baroque style counterpoint is related to species counterpoint but with several important differences.

diminished

An interval that is a semitone (half step) smaller than minor is called diminished.

first inversion

An inverted triad is one in which the third or fifth is in the bass voice, rather than the root. If the third is in the bass, this is called the first inversion.

dissonance

Any note that is not a member of the triadic harmony on any given beat is a nonharmonic tone. Such a note is called this.

Chromaticism-Secondary Dominants

Chromaticism may server to add color or variety to a melody or a harmonic progression, it may provide the suggestion of a harmonic shift, or it may create a complete change in tonal center. All chromaticism in harmony must be understood within the general context of tonal continuity.

V 6

Double the root or fifth, chord moves to I. Don't double the third of V, as this is the leading tone.

Neapolitan triad and Neapolitan sixth

Examples" avoid parallel 5ths as flat II 6 moves to I 6 4; don't put the fifth of flat II 6 in the top voice. Neapolitan = D flat-F-A flat: in B flat, Neapolitan= C flat-E flat-G flat in f#. Neapolitan = G-B-D etc. The Neapolitan triad in a given key has more in common with the minor mode than with the major and it is seen somewhere more frequently in minor contexts.

V 4 3

Fifth of the chord (supertonic of the key) is in the bass. Chord goes to I or I 6.

plagal cadence

IV-I can be a final cadence, coming after a V-I full cadence (the "amen" ending).

suspension cadence

If possible use a suspension on the downbeat of the bar preceding the cadence. A cadence introduced in this way is called a suspension cadence.

Alternative doublings introduce a new flexibility into voice leading

In general, whether in root position or inversion, doubling decisions (other than always-double-the root) tend to reinforce the tonal degrees of the scale. The tonal degrees are 1,2, 4, and 5. These especially 1,4, and 5, are the roots of the most key defining harmonies and are also the scale steps that are the same in both major and minor modes of a given key.

IV 6

In major tends to pass between V and V 6. All doublings are possible. In minor, fifth or root doubling is usual. A common progression in minor is iv 6-V. Called a Phrygian cadence because of its half step motion in the bass, this progression requires a doubled root or fifth in the iv 6 chord (a doubled third would move by an augmented second when iv 6 moved to V). The second example below ends with a phrygian cadence.

secondary dominant

Is a dominant triad or dominant 7th chord that has as its chord of resolution a triad other than I (or i) in a given key. What is the dominant of D? The anger is a. The V7 of the ii chord (D-F-A) is a minor triad that has a dominant of its own (Think: what is the dominant of D? The answer is A). The V7 of the ii chord (D_F-A) is A-C#-E-G; the V7 of the iii chord (E-G-B) is B-D#-F#-A; the V7 of the IV chord (F-A-C) is C-E-G-Bflat; the V7 of the V chord (G-B-D) is D-F#-A-C; the V7 of the vi chord (A-C-E) is E-G#-B-D; note that the vii degree chord does not have a secondary dominant; the vii degree chord is a diminished triad, and therefore could not provide a resolution of a dominant. Following this same logic for the triads of minor key, one finds that III, IV, V, and VI can have secondary dominants. The ii degree chord and the vii degree chord are both diminished in minor keys so they cannot serve as resolutions of secondary dominants.

iii 6

Is an unstable chord in major because of its similarity to V; doubling should promote general smoothness. In minor, III 6 is a more strongly functional chord and any doubling is possible.

I 6

Is more likely to double the root or fifth, less likely to double the third (bass), especially in major mode, unless there is good melodic reason. I 6 is a lighter version of tonic function and has many uses, but is not a final cadential goal. For full cadences, use root position.

V 6 5

Leading tone is in the bass, chord goes to I. Leading tone resolves to tonic, seventh steps down: keep the common tone. Double the root of the I chord.

V 4 3-I

Leading tone resolves to tonic, seventh steps down; keep the common tone; root of I is doubled.

German 6th label Gr+ 6

Minor sixth scale step in bass, tonic, raised 4th and minor third scale step.

v 4 2

Seventh of chord is in the bass, chord resolves to I 6. Leading tone resolves to tonic, seventh of chord steps down; keep the common tone. I 6 with doubled root results. A common variant resolves to I 6 with doubled fifth.

Cadential I 6 4

Since I 6 4-V together have a dominant function and since I 6 4 has no independent function, but is only a dissonance leading to V, many teachers prefer to label the progression V (6 4 - 5 3), with the numbers showing the voice leading. Because the sixth and fourth of I 6 4 are accented dissonances, the I 6 4 chord is accented in relation to V. Therefore cadential I 6 4 must fall on a strong beat, resolving to V on a weak beat. The sixth and fourth of cadential I 6 4, as dissonances calling for specific resolution, cannot be doubled: double the bass (the dominant).

first inversion chords

The intervals present are sixth and third (the bass could also be doubled at the octave). The interval of the sixth is characteristic of first inversion, and for this reason, Roman numerals indicating first inversion include a "6" in superscript: I 6,ii 6, etc.

doubling

The root is in the bass and another root (this is called doubling) is in one of the upper voices.

Chromatic Scale

The scale consists entirely of half steps: one octave up followed by one octave back down.

diminished seventh chords

The viiº 7 chords built up from the leading tone in ascending minor thirds. although its pitches are drawn from the minor mode, viiº 7 is used frequently in major as well as minor contexts. viiº7 is an unstable sonority that requires resolution to the tonic. Its function is comparable to that of a dominant, but weaker than a dominant for two reasons: 1.) viiº 7 is built on the diminished triad, lacks a stabilizing perfect fifth, and is symmetrical; its sonority is the same whether in root position or any inversion; and 2.) All the notes of viiº 7 act as neighbors to notes in the tonic chord, so that there is no distinctive bass pattern comparable to that of a V-I progression. IN resolving viiº7 to I, it is helpful to think of viiº7 as two paris of tritones. In the example below G#-D and B-F are the tritone pairs. IN general you should follow this rule in resolving viiº7 to I: -A diminished 5th resolves in to a third. -An augmented 4th resolves out to a sixth. -Note in the example that different voicings of viiº7 produce different intervals (d5 or A4) and therefore different voicings of the resolving i chord. Another way to think of the normal resolution-if viiº7 is spelled in order from the bottom, normally the lower two notes set up while the upper two step down. Note: (1.) All voices of viiº7 move by step into i; (2.) the resulting i chord has a doublied third; and (3) a frequently seen variation involves moving the third of viiº7 down down to the tonic to give a doubled root to the i chord (see example in bracket above).

melodic line intervals

There are no special rulers that govern intervals in the melodic line.

Arpegiatted 6 4

These may occur on weak beats as part of a textural pattern in which root position or first inversion of the same harmony is on the preceding strong beat. An arpeggiated tonic 6 4 may also come about in a V-I cadence if the upper parts resolve to I while the bass delays. Note that arpeggiated 6 4 chords have no functional independence, and usually receive no Roman numeral label in analysis.

full or authentic cadence

V-I (called perfect authentic cadence if the tonic note is in the soprano of the I chord; called imperfect authentic cadence if 3 or 5 is in the soprano of the I chord). Perfect authentic is the most final of cadences.

deceptive cadence

V-vi There are no common tones between V and vi, therefore we expect all three upper voices to move down in contrary motion to the bass. An exception occurs when the leading tone in V follows its melodic tendency to resolve up to the tonic note in the vi chord. The resulting vi chord has a doubled third instead of the usual doubled root. Note that the progression works the same way in minor mode. V-vi is not always treated as a deceptive cadence.

deceptive cadence

V-vi. Not a final cadence, prolongs the tension in a progression toward a full cadence.

Consonance and dissonance

Within the melodic line between the two parts, definitions of constance and dissonance are the same as for first, second and third species. Every weak half must be consonant. The strong half, which is tied over from the previous measure, may be either consonant or dissonant. If it is dissonant the strong half must be treated as a suspension.

chromaticism secondary dominant

chromaticism may serve to add color or variety to a melody or harmonic progression, it may provide the suggestion of a harmonic shift, or it may create a complete change.

two frequently seen diminished 7th chords that are not built on a leading tone and don't above the dominant related function that vii degree 7 chords do. There is not clear agreement on a name for these chords; some names that others use for these are

common tones diminished chords, arpeggiator diminished chords, and neighbor diminished chords.

second inversion

if the fifth is in the bass, this is called second inversion.

ii 6 5

ii 6 5 is a ii 7 chord in first inversion. ii 7 is formed by adding a minor seventh above the root of the ii triad. Note that the seventh of ii 7 is also the tonic of the key. This is true whether the ii triad is minor (in major keys) or diminished (in minor keys). ii 6 5 is used in place of ii 6 or IV, to precede V. The added senveht is treated as a suspension dissonance (whether or not the seventh is actually tied), with preparation, suspension, and resolution. As you may remember from fourth species, the rhythmic/ metric arrangement for suspension dissonance is: preparation on weak beat. Note that therefore that correct treatment of ii 6 5 involves the chords immediately before and after ii 6 5. Preparation means that the seventh in ii 6 5 must come from the same note in the same voice, in the previous chord. Since the seventh of ii 6 5 is the tonic note of the key, the chord before ii 6 5 smut contain the tonic note as a regular chord tone. This chord will normally fall on a weak beat. Suspension occurs when the harmony moves form the preparing chord to ii 6 5. The seventh of ii 6 5 is the suspension. This should occur on a strong beat. Resolution of the seventh (tonic note of key) is down by step (to the leading tone) as the harmony moves to V. The resolution normally falls on a weak beat. Note on voice leading from ii 6 5 to V: the bass steps up from ii 6 5 to V; keep the common tone; the other two upper voices step down from ii 6 5 into V.

tonicization

implies the potential for new tonic. In a tonicization a secondary dominant and its resolution form the cadence of a phrase. The scale degree of this cadence is said to be tonicized.

Triads

in figured bass, 5 or 5 3 means that the interval of a fifth, or a fifth plus a third, occurs over the given bass note. Since a fifth or fifth plus third is characteristic of root position triads, this figure tells us that the chord over the bass note is in root position. If the 5 is standing alone, 5 3 is understood. If a bass note has no figures below it, root position is usually assumed. In the same way that 5 or 5 3 indicates root position, 6 or 6 3 means first inversion. A 6 standing alone indicates first inversion and 6 3 is understood. One might think that a 6 standing alone could also suggest 6 4 or second inversion. But the interval of a fourth is essential to second inversion, and the number 4 is therefore always included in figures indicating 6 4 inversion. Therefore 6 4= second inversion.

common second inversion triad

looking at a second inversion triad one sees intervals of octave, fourth, and sixth above bass. Both the fourth and sixth are characteristic of second inversion as opposed to root position. The Roman numeral shorthand for 2nd inversion is: 6 4, I 6 4, IV 6 4, etc.

c minor V

major dominant G B♮ D

C major V

major dominant GBD

c minor III

major mediant E♭ G B♭

C major IV

major subdominant FAC

c minor VI

major submediant A♭ C E♭

C major I

major tonic: C major CEG

Doubly diminished

means a semitone smaller than diminished.

modulation

means change of key. In a modulation, all the functional relationships of the original scale are changed.

third note in scale

mediant

C major iii

minor mediant EGB

c minor iv

minor subdominant F A♭C

C major vi

minor submediant ACE

C major ii

minor supertonic DFA

c minor i

minor tonic: C E♭ G

tendency tones

note that most of the larger intervals involve tendency tones: the leading tone needs to resolve up to the tonic, and the lowered sixth scale step needs to move down to the dominant.

fourth note in scale

subdominant

sixth note in scale

submediant

second note in scale

supertonic

vii º6

tends to pass between I and I 6. Double the third or fifth, depending on the melodic context. Avoid doubling the leading tone.

Half diminished seventh

the half diminished seventh [vii circle with line through it 7] is a variant of vii degree 7 (full diminished).

diminished seventh chords

the vii degree 7 chord is built up from the leading tone in ascending minor thirds. Although its pitches are drawn from the minor mode, vii degree 7 is used freely in major as well as minor contexts. vii degree 6 5 equals first inversion of vii degree 7.. vii degree 4 3 = second inversion.. vii degree 4 2 = third inversion.

eighth

tonic

first note in scale

tonic

vi 6

unstable in major and minor because of its similarity to tonic triad; its doubling should promote smooth voice leading in its surrounding context.

Half diminished 7th

vii ø7 is a variant of vii º7 (full diminished). It is derived from the major scale and consists of a diminished triad built on the leading tone, plus a minor seventh over the root; (the full-diminished seventh consists of a diminished leading tone triad, plus a diminished seventh over the root). In Roman numeral labeling, a circle superscript with a line through it indicates half-diminished. Like full viiº7 the half diminished vii ø7 is a neighbor chord of the tonic. All voices should move by step to the resolution. The tritone should resolve as described above. Take care that the other two voices doe not move in parallel 5ths.

inversions of viiº7

viiº 6 5 = first inversion fo viiº7. viiº 4 3 = second inversion. viiº 4 2 = third inversion. Because viiº7 consists of four minor thirds (which evenly divide the octave), there is no difference in sonority between root position and inversions. In order to correctly analyze a viiº7 or its inversion, you must (1.) check the spelling and (2) check the chord of resolution. In the following example there are three viiº7 chords with different spellings. Each of these chords sounds exactly like the other two. Their key orientation can only be heard when they resolve. The spelling of each viiº7 chord uses the appropriate accidentals for the key of resolution. IN each case the voice leading follows the rule already stated: Diminished 5ths resolve in to thirds. Augmented 4ths resolve out to sixths. Here are some examples of viiº7 and inversions with normal resolutions. Tritones are resolved according to the rule stated above except in the case of viiº 6 5-i. The usual movement of the tritones would require viiº 6 5 to resolve to i 6. Quite frequently however viiº 6 5 resolves to i (root position) instead. In this case, the bass note and its tritone (diminished 5th) move in parallel motion to a perfect 5th instead of converging to a third. This diminished to perfect 5th is best avoided in outer voices, but is not considered a parallel 5th. viiº7 resolves to i or I just as V resolves to i or I. In the context of a progression we often see secondary dominants and in the same way, we can now recognize secondary diminished-7th chords. When a chord other than the tonic is preceded by its own viiº7, this is a secondary viiº7. secondary viiº7 chords (and inversions) are spelled according to the key to which they belong. They generally resolve with completely normal voice leading and resolution of tritones. A common exception to normal voice leading is viiº7/V-V. IN this case the doubled third, which is normal in the resolution of viiº7, is avoided so as not to double the leading tone in V.

pivot

whatever is shared constitutes the pivot of a modulation.