Resolving the Fully Diminished Seventh Chord

A fully-diminished seventh chord can be resolved in two general ways: (1)
so that its root is ‘ti’ leading to ‘do’ as the root in the resolution
chord, so the melody sings “ti do”, or (2) so that its fifth is ‘do’
anticipating ‘do’ in the resolution chord, so that, with the resolution,
the melody sings “amen”. The first way makes an authentic cadence, and the
second way makes a plagal cadence. Since the the fully-diminished seventh
chord is symmetrical, you can designate any one of its tones as the root.
This gives you 8 possible resolution root-tones: four tones to end the “ti
do”, and four tones to end the “amen”. The resolution chord can be either
major or minor, giving you 16 possible resolution-chords.

The tones of the fully-diminished seventh chord that aren’t singing the
first tone of “ti do” or “amen” will, on moving to the resolution chord,
fall or rise by either a minor or major second or stay the same. If you’re
harmonizing a melody, it’s good to know what chords can be used as the
resolution chord, and what tone of the resolution chord (root, third, or
fifth) will contain the melody.

I graphed out 21 melodic resolutions here:
https://archive.org/details/fully-diminished-chord-resolutions

Twelve of these resolutions are explained in the next paragraph.

* Any tone of the fully-diminished seventh chord can be resolved upward by
a minor second or downward by a major second, to the root, third, or fifth
of the minor or major resolution chord. (2x3x2=12)

Six resolutions have you to move the melody upward by a major second,
downward by a minor second, or to the same tone. They are as follows.

* Any tone of the fully-diminished seventh chord can be resolved upward by
a major second or downward by a minor second, to the third of the major
chord, fifth of the minor chord, or fifth of the major chord. (2x3=6)

Three resolutions move the melody to the same tone.

* Any tone of the fully-diminished seventh chord can be resolved to the
same tone as the root of the minor chord, root of the major chord, or third
of the minor chord. (3)

The following moves are not on that page.

You can lower any tone of the fully-diminished seventh chord by a minor
second to make the root of a dominant seventh chord. This is a softer
landing. The V7 can resolve to I, i, VI, or vi.

You can raise any tone of the fully-diminished seventh chord by a minor
second to make the minor-7th tone of a half-diminished seventh chord. This
chord can act as the iiØ7 of the targeted minor key. The 7th of the iiØ7
wants to fall back a minor second to the 3rd of the dominant chord.

--
Matt

Matt Faunce <mattfaunce@gmail.com> wrote:
> Resolving the Fully Diminished Seventh Chord
>
> A fully-diminished seventh chord can be resolved in two general ways: (1)
> so that its root is ‘ti’ leading to ‘do’ as the root in the resolution
> chord, so the melody sings “ti do”, or (2) so that its fifth is ‘do’
> anticipating ‘do’ in the resolution chord, so that, with the resolution,
> the melody sings “amen”. The first way makes an authentic cadence, and the
> second way makes a plagal cadence. Since the the fully-diminished seventh
> chord is symmetrical, you can designate any one of its tones as the root.
> This gives you 8 possible resolution root-tones: four tones to end the “ti
> do”, and four tones to end the “amen”. The resolution chord can be either
> major or minor, giving you 16 possible resolution-chords.
>
> The tones of the fully-diminished seventh chord that aren’t singing the
> first tone of “ti do” or “amen” will, on moving to the resolution chord,
> fall or rise by either a minor or major second or stay the same. If you’re
> harmonizing a melody, it’s good to know what chords can be used as the
> resolution chord, and what tone of the resolution chord (root, third, or
> fifth) will contain the melody.
>
> I graphed out 21 melodic resolutions here:
> https://archive.org/details/fully-diminished-chord-resolutions
>
> Twelve of these resolutions are explained in the next paragraph.
>
> * Any tone of the fully-diminished seventh chord can be resolved upward by
> a minor second or downward by a major second, to the root, third, or fifth
> of the minor or major resolution chord. (2x3x2=12)
>
> Six resolutions have you to move the melody upward by a major second,
> downward by a minor second, or to the same tone. They are as follows.
>
> * Any tone of the fully-diminished seventh chord can be resolved upward by
> a major second or downward by a minor second, to the third of the major
> chord, fifth of the minor chord, or fifth of the major chord. (2x3=6)
>
> Three resolutions move the melody to the same tone.
>
> * Any tone of the fully-diminished seventh chord can be resolved to the
> same tone as the root of the minor chord, root of the major chord, or third
> of the minor chord. (3)
>
> The following moves are not on that page.
>
> You can lower any tone of the fully-diminished seventh chord by a minor
> second to make the root of a dominant seventh chord. This is a softer
> landing. The V7 can resolve to I, i, VI, or vi.
>
> You can raise any tone of the fully-diminished seventh chord by a minor
> second to make the minor-7th tone of a half-diminished seventh chord. This
> chord can act as the iiØ7 of the targeted minor key. The 7th of the iiØ7
> wants to fall back a minor second to the 3rd of the dominant chord.
>

The making of my chart was inspired by this video of Kit Armstrong
explaining some aspects of Liszt’s harmony. https://youtu.be/en4qutSkmlU

--
Matt

Matt Faunce <mattfaunce@gmail.com> wrote:
> Resolving the Fully Diminished Seventh Chord
>
> A fully-diminished seventh chord can be resolved in two general ways: (1)
> so that its root is ‘ti’ leading to ‘do’ as the root in the resolution
> chord, so the melody sings “ti do”, or (2) so that its fifth is ‘do’
> anticipating ‘do’ in the resolution chord, so that, with the resolution,
> the melody sings “amen”. The first way makes an authentic cadence, and the
> second way makes a plagal cadence. Since the the fully-diminished seventh
> chord is symmetrical, you can designate any one of its tones as the root.
> This gives you 8 possible resolution root-tones: four tones to end the “ti
> do”, and four tones to end the “amen”. The resolution chord can be either
> major or minor, giving you 16 possible resolution-chords.
>
> The tones of the fully-diminished seventh chord that aren’t singing the
> first tone of “ti do” or “amen” will, on moving to the resolution chord,
> fall or rise by either a minor or major second or stay the same. If you’re
> harmonizing a melody, it’s good to know what chords can be used as the
> resolution chord, and what tone of the resolution chord (root, third, or
> fifth) will contain the melody.
>
> I graphed out 21 melodic resolutions here:
> https://archive.org/details/fully-diminished-chord-resolutions
>
> Twelve of these resolutions are explained in the next paragraph.
>
> * Any tone of the fully-diminished seventh chord can be resolved upward by
> a minor second or downward by a major second, to the root, third, or fifth
> of the minor or major resolution chord. (2x3x2=12)
>
> Six resolutions have you to move the melody upward by a major second,
> downward by a minor second, or to the same tone. >

Oops. Scratch “or to the same tone.” That comes later.

>
>They are as follows.
>
> * Any tone of the fully-diminished seventh chord can be resolved upward by
> a major second or downward by a minor second, to the third of the major
> chord, fifth of the minor chord, or fifth of the major chord. (2x3=6)
>
> Three resolutions move the melody to the same tone.
>
> * Any tone of the fully-diminished seventh chord can be resolved to the
> same tone as the root of the minor chord, root of the major chord, or third
> of the minor chord. (3)
>
> The following moves are not on that page.
>
> You can lower any tone of the fully-diminished seventh chord by a minor
> second to make the root of a dominant seventh chord. This is a softer
> landing. The V7 can resolve to I, i, VI, or vi.
>
> You can raise any tone of the fully-diminished seventh chord by a minor
> second to make the minor-7th tone of a half-diminished seventh chord. This
> chord can act as the iiØ7 of the targeted minor key. The 7th of the iiØ7
> wants to fall back a minor second to the 3rd of the dominant chord.
>

Understanding the chart is what’s important. I was worried that it wouldn’t
be self explanatory, so I wrote this introductory text despite how
laborious it might be to read.

--
Matt