harm_X_gealtereerde_akkoorden-01

As already mentioned in the preceding section: The diminished third 'around' the fifth of the key is much more common than diminished thirds 'around' the root and the third of the key. We encounter the diminished third between #4^ en (b)6^ in the following chords:

example 8

The above chords can appear in C minor and in C major - although they are in C minor definitely 'more diatonic'... In C major they are in fact 'borrowed' from the parallel minor key: the third and the sixth are both minor (in example 6: the notes Eb en Ab).^annThe chords are these:

double diminished triad, and double diminished seventh chord on the raised IVth degree; abbrevations: #IVdv and #IVdv7
een hard diminished triad, and hard diminished seventh chord on the IInd degree; abbrevations: IIhv of IIhv7
minor-diminished seventh chord on theVIIth degree; abbrevation: VII7kv - for now, I do not discuss this last chord^ann

Maybe it is handy, when you are constructing #IVdv or IIhv yourself, to use these mnemonics:

double diminished op #IV:

in major keys: Take the IVth degree, and change it in IV of the parallel minor key
change 4^ of the key in #4^(=leading tone for V)

(in minor keys you can skip the first step...)

hard diminished onII:

in major keys: Take the IInd degree, and change it in II of the parallel minor key
change 4^ of the key in #4^(=leading tone for V)

(in minor keys you can skip the first step...)

In example 9 below, these steps are shown schematically:

example 9

augmented 6-, 6/5- and 4/3 chord

double diminished and hard diminished op #IV respectively II are most commonly used in specific inversions, namely these inversions in which the sixth of the key is in the bass. as a result, in these inversions the diminished third appearsalways inverted, as augmented sixth . In these specific inversions the chords can also be labelled as 'augmented ...chord' (in which on the position of the dots the inversion is mentioned). N.B.: This involves certainly not augmented chords, but chords in which an augmented sixth sounds between the bass and one of the higher voices. The inversions are:

augmented 6 chord: first inversion of the double diminished triad on #IV; in English this inversion as normally labelled: Italian augmented; in Dutch we can use the abbrevation ov6 (overmatig sextakkoord, augmented 6-chord), but we can equally write #IVdv6 (verhoogd IV dubbelverminderd sext, raised IV double diminished 6)
augmented 6/5 chord: first inversion van het double diminished seventh chord op #IV; in English this inversion as normally labelled: German augmented; in Dutch we can use the abbrevation ov6/5 (overmatig kwintsextakkoord, augmented 6/5-chord), but we can equally write #IVdv6/5 (verhoogd IV dubbelverminderd kwintsext, raised IV double diminished 6/5)
augmented 4/3 chord: second inversion of the hard diminished seventh chord on II; in English this inversion as normally labelled: French augmented; in Dutch we can use the abbrevation ov4/3 (overmatig tertskwartakkoord, augmented 4/3-chord), but we can equally write IIhv4/3 (II hardverminderd tertskwart, II harddiminished 4/3)^ann
augmented 6/4 chord: this chord is not so common (it is mostly used in three-part setting, as an alternative to IIhv4/3); in Dutch we can use the abbrevation IIhv6/4 (II hardverminderd kwartsext, II harddiminished 6/4); in English this chord does not have a specific (country-)name:^ann

example 10

You can listen to the examples below. In each example you first hear a short melodic fragment and the tonic triad, and then the two chords as noted in the example.

In by far most cases these 'augmented' chords (as the other inversions of #IVdv and IIhv as well) resolve to the dominant - normally V, V7 of I6/4. Functionally, #IVdv en IIhv on on the one hand are rather similar to secondary dominants (because of the leading tone to 5^); on the other hand, there are also similarities with the subdominant, in particular caused by the presence of the (minor) 6^ in both chords. Therefore they are often called: altered subdominants. I maintain that their function is somewhere in between secondary dominant and subdominant - which may also be reflected in how #IVdv and IIhv can be approached:

very common placement is: after a subdominant chord, so: between subdominant and dominant chords; the altered chord then acts as a kind of chromatic passing chord, resembling how a secondary dominant may be used; see the example in E minor below
also common: #IVdv or IIhv 'replaces' the subdominant, for example in a cadence; in this case the function of the chord could be seen as (altered) subdominant; See the example in F major below:

example 11

You can listen to the examples below:

Especially in minor keys #IVdv or IIhv after VI is well possible: we could see the altered chord then as altered subdominant as well, as we can say that #IVdv or IIhv 'replace' an 'ordinary' subdominant:

example 12

You can listen to the examples below:

Occasionally, #IVdv or IIhv is not followed by a dominant chord, but by the tonic (normally I); in that case, the altered chord is most like a subdominant chord; a progression like #IVdv6/5 --> I sounds somewhat like a plagal cadence. The augmented sixth is hereby actually resolved 'wrongly' or 'incompletely': Though #4^ moves to 5^ (as it should), 6^ leaps to 1^ (see example 11 below: G# in the soprano resolves correctly, but Bb in the bass leaps to D, instead of moving stepwise to A):

example 13

You can listen to the example below:

Some remarks about doubling and about resolutions of augmented 6-, 6/5- en 4/3-chords to the dominant:^ann

in a Italian augmented (augmented sixth chord) the only note that can be doubled is the fifth of the chord; the strong dissonance and 'direction' of the augmented sixth between the two other tones of the chord rules out doubling of the root or the third. One of the two fifths in #IVdv6 must ascend stepwise, the other has to descend stepwise; often one of the two fifths is in the upper voice; commonly then this tone descends. See example 12 a below, and compare with example 13a
the resolution of a French augmented (augmented 4/3 chord) actually speaks for itself: the augmented sixth spreads whilst resolving, and the seventh makes a stepwise descent; See example 12b below, and compare with example 13b
When resolving a German augmented (augmented 6/5 chord) to the triad of V it turns out to be impossible to avoid parallel fifths : As the lower tone of the augmented sixth, and as 6^ of the key, the bass must descend stepwise, but the seventh of the chord has to descend stepwise as well. In harmony, this parallel fifth is generally accepted, and it is relatively common in compositions. This parallel is (wrongly ..) known as Mozart fifth. See example 12 c below, and compare with example 13 c.^ann

example 14

You can listen to the example below:

example 15

000

usage of Italian, German and French augmented chords (augmented 6, 6/5 and 4/3) in a typical situation: to prepare the dominant / V( in a context that we could imagine as: end of the central section of a development section (the E at the end could mark the beginning or the dominant pedal point), or for example the end of a transitions, or a place right before another important caesura in a composition. Instead of after I6 the altered chord could equally well stand after IV6 or II4/3, or after VI.^ann

Italian augmented (augmented 6 chord /(#IVdv6):

Observe the doubled fifth, and the descent in the soprano versus the ascent in the tenor (causing the 'wrong resolution' of the augmented fourth A - D# between tenor and alto):

You can listen to the example below:

French augmented (augmented 4/3 chord /(#IIhv4/3):

the resolution is entirely 'by the book', the augmented sixth spreads when resolving, the seventh descends stepwise, and the common tone (B) stays in place:

You can listen to the example below:

German augmented (#IVdv6/5 / augmented 6/5chord ):

Resolution to V causes a parallel fifth (here between tenor and bass). The fifth is considered acceptable:

You can listen to the example below:

In compositions the parallel fifth between # IVdv6/5 and V is avoided (notwithstanding that it is permitted). The most common way is to let V be preceded by I6/4 (see example 16 a). Another, less standard trick: the seventh of #IVdv6/5 ascends to the seventh of V7 - actually the voice leading is then 'incorrect' (see example 16c).^ann

In the progression #IVdv6/5 - V in major keys the seventh of #IV is quite often notated as major sixth - see the third example in 16a. This has a reason in the voice leading: It seems logical to reach the third in I6/4 from a leading tone (in the example: B# -> C#); but as this third is in this context no more than a suspension of the fifth of V there is no reason - even with this notation - interpret the chord other than as #IV: The chord sounds just as #IV, and 'behaves' accordingly as well.^ann

example 16

a000

parallel fifth between #IVdv6/5 en V is 'bypassed' in that V is preceded by I6/4:

You can listen to the example below:

To equation: #IVdv6/5 --> V, with parallel fifth. See examples 14, 15c and example 16 c as well.

You can listen to the example below:

Especially in the 19^thcentury this is a common "trick" as well: the seventh of # IVdv6/5 ascends to the seventh of V7. Infact: 'wrong' voice leading ... ^ann

You can listen to the example below:

[continuation of this chapter]