Tonal Harmony - Dominants | このままでいいから

$\text{V}^7$

$\text{V}^7$ is less stable than $\text{V}$. It contains a leading tone and a chordal 7th.

leading tone: tends to resolve up by step (do not have to if in inner voices)
chordal 7th: resolve down (no matter inner or outer)

it’s less suited for a half cadence (HC) than triad V; try to avoid it

omitting the 5th

in $\text{V}^7-\text{I}$

omitting the 5th (of either chord) to avoid voice leading problems when the leading tone is the top voice
double the root of the chord with omitted note
never omit the 3rd

$\text{V}^7-\text{V}$ should be avoided because the chordal 7th would not resolve
$\text{V}-\text{V}^7$ common, labeled as $\text{V}^{8-7}$, usually resulted from adding the chordal 7th to an existing $\text{V}$

figured bass notation

$\text{V}^6$

dominant, like $\text{V}$
typically appear in beginning/mid phrase
in $\text{V}^6-\text{I}$, the bass moves in step and the upper voices move smoothly

$\text{V}^6-\text{V}$, $\text{V}^6-\text{V}^7$, $\text{V}-\text{V}^6$ are common
$\text{V}^7-\text{V}^6$ is bad

$\text{I}^6-\text{V}^6$ is common
$\text{V}^6-\text{I}^6$ is bad because the leading tone in $\text{V}^6$ bass is not resolved in a step (voice leading rule: in outer voices leading tone should step to tonic)

$\text{V}^6$ should not be the final chord in half cadence
$\text{V}^6$ should not be the dominant chord in perfect authentic cadence
dominant chord must be in root position at cadence

double any note but the bass (leading tone)

$\text{V}^6-\text{I}$ movement is smooth in all upper voices

$\text{V}_5^6$ and $\text{V}_2^4$

both $\text{V}_5^6$ and $\text{V}_2^4$ have tendency note in the bass

dominants
$\text{V}_5^6-\text{I}$: good
$\text{V}_5^6-\text{I}^6$: bad (bass leading tone should not leap)
$\text{V}_2^4-\text{I}$: bad (bass chordal 7th must step down)
$\text{V}_2^4-\text{I}^6$: good
$\text{I},\text{I}^6,\text{V},\text{V}^6,\text{V}^7$ could be followed by $\text{V}_5^6$

$\text{V}_5^6$ could lead to $\text{V}^7$ and its inversion
$\text{V}_5^6-\text{V}$, $\text{V}_5^6-\text{V}^6$ are bad because chordal 7th is not resolved down

$\text{I},\text{I}^6,\text{V},\text{V}^6,\text{V}^7$ could be followed by $\text{V}_2^4$
$\text{V}-\text{V}_2^4$ is common
$\text{V}_2^4-\text{V}$ is bad (chordal 7th is not resolved); $\text{V}_2^4-\text{V}^7$ also bad
$\text{V}_2^4-\text{I}^6$ is the way

$\text{V}_5^6$ could embellish $\text{I}$
$\text{V}_2^4$ could embellish $\text{I}^6$

use inversions to promote variety

voice leading

$\text{V}_2^4$ figured bass

$\text{V}_3^4$ and $\text{vii}^{\circ 6}$

$\text{V}_3^4$ and $\text{vii}^{\circ 6}$ are dominant
$\widehat{2}$ is the bass
moves to $\text{I}/\text{I}^6$ with step in bass
tend to embellish, do not show up at cadences

$\text{I}-\text{V}_3^4-\text{I}^6$ and $\text{I}^6-\text{V}_3^4-\text{I}$

$\text{I}-\text{V}_3^4-\text{I}$

$\text{V}_3^4$/$\text{vii}^{\circ 6}$-$\text{I}/\text{I}^6$ could be used alternating with other D-T progression

$\text{V}_3^4-\text{V}^7/\text{V}_5^6/\text{V}_2^4$

voice leading

usually smooth, each voice either step or repeat
do not double the leading tone in $\text{vii}^{\circ 6}$

mi-fa-sol melody
$\text{I}-\text{V}_3^4-\text{I}^6$ and $\text{I}-\text{vii}^{\circ 6}-\text{I}^6$ could be used with special exceptions

bass and top move in parallel 10ths
in this case it’s ok to move from diminished 5 to perfect 5
in $\text{V}_3^4-\text{I}^6$ the chordal 7th (at top voice) in $\text{V}_3^4$ could move up instead of step down

Cadential $_4^6$

has the same note as the tonic in second inversion
despite having the GCE notes it’s dominant

progressions

cadential $_4^6$ - $\text{V}/\text{V}^7$ (root position, not inversions)

tonic/subdominant - cadential $_4^6$: ok
dominant - cadential $_4^6$: bad

more voice leading

double the bass;
do not double the 4th above bass (for example, in GCE, double G, not C)

the 4th above bass is dissonant, should down by the step
the 6th above bass is not dissonant, usually moves down

figured bass

$_{4-3}^{6-5}$ to indicate cadential $_4^6$ - dominant
$_4^6-\text{V}$ is labeled as $\text{V}_{4-3}^{6-5}$
$_4^6-\text{V}^7$ is labeled as $\text{V}\underset{\text{4-3}}{\overset{\text{8-7}}{\Tiny{\text{6-5}}}}$

placement

at cadence as part of half cadence and perfect authentic cadence
other places in the phrase
on stronger beat

cadential $_4^6$ should be placed at stronger beat

$\text{vii}^{\circ 7}$

dominants
leading to $\text{I}/\text{I}^6$

a minor: $\text{V}^7$ is E#GBD, $\text{vii}^{\circ 7}$ is #GBDF

$\text{vii}^{\circ 7}$ used more in minor keys
share three notes with $\text{V}^7$
more dissonant than $\text{V}^7$
may appear in root position or inversion, unlike $\text{vii}^{\circ}$
mostly treated like $\text{V}^7$ (inversions) with the same bass tone

$\text{vii}_2^4$ does not share bass tone with $\text{V}^7$’s inversions
does not lead to $\text{I}/\text{I}^6$
less common than other inversions of $\text{vii}^{\circ 7}$
the chordal 7th must step down but $\text{vii}_2^4-\text{I}_4^6$ is unusual (because both are dominants)

$\text{vii}_2^4-\text{V}^7$ and $\text{V}^7-\text{vii}_2^4$

can move back and forth
only one note needs to move because of the shared notes

more voice leading

chordal 7th must resolve down by step
root leading tone must resolve up by step
be careful with parallel 5th (double the 3rd of the tonic rather than root)

$\text{vii}^{\varnothing 7}$

found only in major
similar to $\text{vii}^{\circ 7}$
dominants

could appear in root or inversion
voice leading similar to $\text{vii}^{\circ 7}$

Applied dominants

$\text{V/V}$

applied $\text{V}$ of $\text{V}$
a major triad with root 5th above $\text{V}$ with raised $\widehat{4}$
example: CEG(I), GBD(V), D#FA(V/V)
in the above example, #F is the secondary leading tone
moves to $\text{V}$: $\text{V/V}-\text{V}$, just as $\text{V}-\text{I}$
comes from any chord that can precede $\text{V}$

the secondary leading tone steps up like leading tone
do not double it
normally resolves up

$\text{V}^6/\text{V}$

first inversion
leads to root position $\text{V}$, just as $\text{V}^6-\text{I}$
example: #FAD - GBD

$\text{V}^7/\text{V}$

dominant seventh
chordal 7th needs to resolve down
may be in inversions

$\text{V}_2^4/\text{V}-\text{V}^6$ similar to $\text{V}_2^4-\text{I}^6$
$\text{V}_5^6/\text{V}-\text{V}$ similar to $\text{V}_5^6-\text{I}$
$\text{V}_3^4/\text{V}-\text{V}/\text{V}^6$ similar to $\text{V}_3^4-\text{I}/\text{I}^6$

$\text{V/V}$ in minor

two accidentals
raised $\widehat{4},\widehat{6}$ (example: B#D#F for a minor)

other resolutions

$_4^6$ decoration before $\text{V}$

could also lead to $\text{V}^7$ instead of triad $\text{V}$
leading tone raised $\widehat{4}$ usually goes to $\widehat{5}$
raised $\widehat{4}$ may also go down to $\widehat{4}$

Other applied chords

all applied chord tonicize the chord to which they are applied
function as dominants
leads to the chord to which they are applied
momentarily departs from the main key
in both major and minor: could be find by forming a triad on the note that’s “sol” then the note being tonicized is treated as “do”

do not double the leading tone of the applied chord

in major keys

$\text{ii},\text{iii},\text{IV},\text{V},\text{vi}$ could be preceded by an applied dominant
$\text{vii}^{\circ}$ cannot be tonicized by an applied dominant because a diminished triad cannot be the tonic
the third functions as the leading tone
applied triad may appear in root or first inversion
applied seventh may appear in any inversion

sound

sound1, sound2

in minor keys

$\text{III},\text{iv},\text{V},\text{VI},\text{VII}$(not raised $\widehat{7}$, just plain $\widehat{7}$) triads could be preceded by an applied dominant
$\text{ii}^{\circ}$ cannot because it’s diminished