harm_X_gealtereerde_akkoorden-01

In example 18 you see a schematic overview of all altered chords; in the rest of this section you find further explanation of the chords, and some examples. In sections 6-9 of this chapter you find some more detailed information, and examples from existing scores.

The starting point again is (as we know already from the double and hard diminished chords on #IV and II) that each altered chord contains a diminished third, and that this diminished must resolve to 5^, 1^ or 3^ of a major or minor key^ann That said, we can construct all altered chords in minor and major keys; example 18 shows all altered chords as they may occur in the keys of C minor and C major. All altered chords can be enharmonized, either to another chord, or to another inversion of the same chord. The enharmonic equivalents are also shown in the example, always at the right, next to the relevant altered chord:^ann

example 18

a.		b.


c.		d.

Some observations in connection with the diagram above:

Most chords can occur on several degrees:

double diminished (as triad or as seventh chord) can be used on:

#IV in minor and major keys
VII in minor and major keys
#II in major keys

hard diminished (as triad or as seventh chord) can be used on:

II in minor and major keys
V in minor and major keys
VII in major keys

This means that a double diminished chord may occur in at least three keys; for example: the chord B - Db - F (- Ab) can be: #IV in F minor or F major, VII in C major or C minor, and #II in Ab major. The Same applies to hard diminished: the chord G - B - Db (-F) can be: II in F minor or F major, V in C major or C minor, and VII in Ab major. If we compare double- and hard diminished, we also see that a double diminished chord can occur in the same keys as the hard diminished chord of which the root is a major third lower than the root of the double diminished chord. The following chords then are, as it were pairs:

double diminished on #IV and hard diminished on II (associate these with the 'normal' IV en II)
double diminished on VII and hard diminished on V (associate these with the 'normal' VII en V)
double diminished op #II and hard diminished on VII

In all three cases, we see that the notes of the chords of the 'pairs' are almost entirely the same; we might say that we see in each case see a group of five notes, of which we can use up to four to form double or hard diminished:

example 19

For all double and hard diminished chords applies what has been observed in the second section at double diminished on #IV and hard diminished on II^ann: Specific inversions are by far the most common: double diminished in 6- or 6/5-position, and hard diminished in 4/3-position. In other words: normally the upper tone of the diminished third is in the bass, which also means that we then see an augmented sixth on the bass. Double and hard diminished chords on other degrees than #IV respectively II are almost always in the form of seventh chords.

Look in the following examples at the voice leading as well:

The augmented sixth nearly always resolves to an octave.^ann
As a result thereof we have to double the third in I after #IIdv or VIIhv:

example 20

You can listen to the examples below.

a.

b.

c.

d.

From Late Romanticism, the five notes from which we can 'select' to form a double or hard diminished chord sometimes appear all combined.^ann Logically, the basis of such chords is the hard diminished seventh chord, to which a minor ninth is added. This is possible on V and II; we then can label the chords as: Vhv9/7 and IIhv9/7 respectively. It is likely that the setting in which such chord occurs is five-part:^ann

example 21

You can listen to the example below:

Like double diminished and hard diminished, most other altered chords can appear on several degrees, and can be seen as forming 'pairs'. In the following subparagraphs I show how we can look at this phenomenon, and give some examples with the chords not yet discussed.^ann

The first group to mention here consists of:

hard diminished / diminished (only possible as seventh chord!) can appear on:

V in minor keys; we can label the chord as Vhv/v or as Vb7/b5
VII in major keys; we can label the chord as VIIhv/v or as VII#3/b7

diminished / double diminished / diminished (only possible as seventh chord!) can appear on:

VII in minor keys; we can label the chord as VIIv/dv/v or as VIIb3/b5
#II in major keys; we can label the chord as #IIv/dv/v or as #IIb3

augmented dominant (only possible as seventh chord!) can only appear on:

V in major keys; we can label the chord as V(7)augm.dom or as V7/#5

As you can see, with these chords less keys are possible than with double and hard diminished, and they all have a distinct place in either a major or a minor key. For example: the chord A - C#- Eb - Gb (hard diminished/diminished) can only be placed on V in D minor, and on VII in Bb major. And the chord C#- Eb - Gb - Bb (diminished/double diminished/diminished)can only be placed on VII in D minor, and on #II in Bb major. If we compare hard diminished/diminished and diminished/double diminished/diminished, we see that they again form as it were pairs (like double and hard diminished, at the distance of a major third):

hard diminished/diminished on V and diminished/double diminished/diminished on VII in minor keys
hard diminished/diminished on VII and diminished/double diminished/diminished on #II in major keys

To the last group we could add the augmented dominant seventh chord, which then stands a major third below VIIv/dv/v , and can only be used in major keys. Again, we see that the notes of the chords are almost entirely the same; we might say that we actually have a group of six notes, from which five can be used in minor keys, and all six in major keys. We have to use four notes of the group to form one of the chords: See example 22. I propose - to promote readability - to use abbreviations of the utterly impracticle chord names (see above). As these names are not part of the English music terminology I use Dutch abbreviations^ann, like with the other chords before. Of course, adding sharps and/or flats in combination with numbers is another option (see above).

example 22

Concerning the voice leading: It is not difficult to write correct resolutions of the chords in this group, as nearly all notes point to certain other notes: They contain quite some dissonant intervals which allow only a few resolutions. Only this: As the diminished third has to resolve to the prime (or: augmented sixth to the octave) it is worth noticing that, logically, when resolving to I in minor keys, the root of I has to be doubled; when resolving to I in major keys, the third of I has to be doubled though. This applies to the entire group (see the examples below).

Hard diminished/diminished is most commonly in 4/3 position, and is known (in specifcally that position) as Eulenspiegel chord, named after Richard Strauss' Till Eulenspiegels lustige Streiche, Op. 28. In that Symphonic Poem, the chord is used (in the context of the Eulenspiegel motif) on VII in F major.^ann Diminished/double diminished/diminished chords normally are in 6/5 position. We then can observe that, like with double and hard diminished, in both these typical inversions the upper note of the diminished third is in the bass, which implies that an augmented sixth stands on the bass.

Even though you can find an analysis of the beginning of Till Eulenspiegel elsewhere in this chapter^ann I would like to show the most relevant measures of the score here as well; therefore you see below a reduction of measures 38-48 of the piece. It is of course a good idea to have a look at the complete score as well:

example 23

Richard Strauss conducts 'Till Eulenspiegel' (VPO 1944)

recording by David Zinman & Zurich Tonhalle Orchestra

recording by Wilhelm Furtwängler / Berlin Philharmonic Orchestra (1950)

recording by Rudolf Kempe/ Staatskapelle Dresden (1970)

here is the complete score (pdf)

And here are some examples with the chords hv/v , v/dv/v and augm.dom.:

example 24

You can listen to the examples below.

a.

	The Eulenspiegel chord is used three times in this example, in a similar way as in Srauss' Till Eulenspiegel: On VII in a major key (even the key is the same as in Strauss..): VOETNOOT

b.

	This example is almost the same as the previous one, only the Eulenspiegel chord on VII is replaced at two spots by #IIv/dv/v:

c.

	In this example the Eulenspiegel chord is used on V in a minor key (different from Strauss, but similar to the way Franck uses the chord regularly):^ann

d.

	In this example, which is almost the same as the previous one, the Eulenspiegel chord on V is replaced by VIIv/dv/v:

e.

	An example with augmented dominant seventh chord. Clear is that the root position resolves to an incomplete I (no fifth, see measure 4; root and third are doubled), wheras other inversions resolve to a complete I, but: with doubled third (see measure7):

The second group to mention here consists of:

major / diminished (only possible as seventh chord!) can appear on:

V in minor keys; we can label the chord as Vg/v or as Vb7
VII in major keys; we can label the chord as VIIhg/v or as VII#3/#5

minor / double diminished / diminished (only possible as seventh chord!) can appear on:

VII in minor keys; we can label the chord as VIIk/dv/v or as VIIb5
#II in major keys; we can label the chord as #IIk/dv/v or as #II#3/b5

As you can see, also with these chords we have less possible keys than with double and hard diminished, and they all have their distinct places in major and minor keys. For example: the chord A - C#- E - Gb (major/diminished) can only be placed on V in D minor, and on VII in Bb major. And the chord C#- E - Gb - Bb (minor/double diminished/diminished) can only be placed on VII in D minor, and on #II in Bb major. If we compare major/diminished and minor/double diminished/diminished, we see that they again form as it were pairs (like double and hard diminished, at the distance of a major third):

major/diminished on V and minor/double diminished/diminished on VII in minor keys
major/diminished on VII and minor/double diminished/diminished on #II in major keys

Again, we see that the notes of the chords of the 'pairs' are almost entirely the same; we might say that we in fact have a group of five notes, of which we have to use four notes to form one of the chords: See example 25. Again, I propose - to promote readability - to use abbreviations of the very impracticle chord names (see above). As these names are not part of the English music terminology I use Dutch abbreviations,^ann like with the other chords before. Of course, adding sharps and/or flats in combination with numbers is another option (see above).

example 25

Concerning the voice leading: Like in the previous group, it is not difficult to write correct resolutions of these chords, as nearly all notes point to certain other notes: They contain quite some dissonant intervals which allow only a few resolutions. Only this: As the diminished third has to resolve to the prime (or: augmented sixth to the octave) it is worth noticing that, logically, when resolving to I in minor keys, the third of I has to be doubled; whereas when resolving to I in major keys, the fifth of I has to be doubled. This applies to the entire group (see the examples below). When resolving the root positions of VIIg/v there will automatically be parallel fifths: In the example above A and E of VIIg/v should move to Bb and F. Sometimes this may be acceptable (depending of the style etc.); in general though it is wise to avoid the root position of this chord on VII in major keys.

Probably the most common inversion of major/diminished is the 2 position (resolving to I6 in minor, and to I6/4 in major keys); the chord sounds then as a root position of a minor seventh chord (in the example above: F# - A - C# - E ). And probably the most common inversion of minor/double diminished/diminished is the 4/3 position; the chord sounds then as a root position of a dominant seventh chord (in the example above: F# - A# - C# - E ). We then can observe that, like with double and hard diminished, and like in the previous group of other chords VOETNOOT TERUG, in both these typical inversions the upper note of the diminished third is in the bass, which implies that an augmented sixth stands on the bass.

example 26

You can listen to the examples below.

a.

	An example with major/diminished chords on V in a minor key. Major/dim. is here mainly used as chromatic passing chord. Compare example 26c:

b.

	An example with major/diminished chords on VII in a minor key. Compare example 26d:

c.

	An example with minor/double diminished/diminished seventh chords on VII in a minor key. The chord is mainly used as chromatic [passing chord, and the example is largely the same as example 26a above - but Vg/v is replaced by VIIk/dv/v:

d.

	An example with minor/double diminished/diminished seventh chords on #II in a major key. The chord is mainly used as chromatic [passing chord, and the example is largely the same as example 26b above - but VIIg/v is replaced by #IIk/dv/v:

The last chord to mention here is probably the most famous one:

minor / diminished (only possible as seventh chord!) can only appear on

VII in minor and major keys; we can label the chord as VIIk/v or: in minor as VII7/#5, in major as VII7/#5/b7

In 2-position, and especially when resolving to V7, this chord is known as Tristan chord, ever since Wagner used it as the first sound right at the beginning of the Prelude of his opera Tristan und Isolde.^ann Even though you can find an analysis of the beginning of this piece elsewhere in this chapter^ann I would like to show the beginning of the score here as well:

example 27

recording by Wilhelm Furtwangler & Philharmonia Orchestra (1951?)

recording by Daniel Barenboim, Bayreuth Festival, 1983

recording by Leonard Bernstein /
Boston Symphony Orchestra

recording by Karl Böhm / Orchester der Bayreuther Festspiele, 1964

here is the complete score (pdf)

                                        A minor:    (implied I) VIIk/v2        V7            (implied V)
                                                               or:
                                                               suspended
                                                               IIhv4/3
                                                              (French) ?

                                                                                                          C major: (implied VII)      VIIk/v2        V7
                                                                                                                                          or:
                                                                                                                                            suspended
                                                                                                                                            IIhv4/3
                                                                                                                                           (French) ?                    (implied V --> chromaticism )

                                                                           sounds as                                                          sounds as
                                                                           root position of                                                 root position of
                                                                           half diminished                                                   half diminished

C major: II2 (?)

A minor: suspension of (V7) [repeat] V7 (+9) VI

                 sounds as
                 2 position
                 of half diminished

The minor/diminished seventh chord is the only altered chord that has just one single place in minor and major keys: VII. For example: the chord A - C- E - Gb can only occur on VII in Bb minor or Bb major, and in Bb major then b6^ is used (molldur, or mixture). ANN

If we compare minor/diminished with hard diminished and double diminished on the most common scale degrees (ie on II and #IV respectively) VOETNOOT NAAR BOVEN, we see that we can see these three chords together as a group again: #IVdv and IIhv at the distance of a major third, and VIIk/v a minor third below IIhv. We can see a group of six notes, of which we have to use three or four to form one of the chords: See example 28. I propose again to use an abbreviation, of the impracticle chord name "minor/diminished" (see above). As this name is not part of the English music terminology I use once more a Dutch abbreviation,^ann like with the other chords before (see above). Of course, adding sharps and/or flats in combination with numbers is another option (see above).

example 28

Like in the groups above, it is not difficult to write a correct resolution of VIIk/v, as nearly all notes point to certain other notes: Only a few resolutions are possible. Only this:

Normally the chord is used as a suspension or neigbouring chord in a context of a prolonged dominant (See also the excerpt from Wagner's Tristan above); it is possible though - like with #IVdv and IIhv to resolve to a tonic
When resolving to V, it is logical to assume that the fifth of the chord ascends stepwise (as it is the leading tone to 5^); it is also possible to make a chromatic descent though, to the seventh of V (realteration of #4^). Wagner uses this possibility in the Einleitung of Tristan und Isolde:

Instead of:

Bb
G#
E
C#

A
A
E
C#

we would write:

Bb
G#
E
C#

A
G

E
C#

When the chord resolves to I logically the fifth of I is doubled (as the diminished third between fifth ad seventh of VIIk/v resolves to 5^).A s both the root and the fifth of the chord normally ascend when resolving to I (as they are leading tones, to 1^ and 5^ respectively), parallel fifths lurk: When the fifth is written above the root we will in principle produce a parallel fifth, unless the root of the chord is written above the fifth. In the above example that would mean that we

instead of:

Bb
G#
E
C#

A
A
F
D

(with parallel fifth)

we would for example write:

Bb
C#
G#
E

A
D
A
F

the root higher in the chord than the fifth

Einleitung

voorbeeld 29 EXAMPLES ARE STILL INCOMPLETE ; SOUND WRONG

You can listen to the examples below.

a.

	Een voorbeeld met het Tristanakkoord / VII2k/v, oplossend naar V:

b.

	Een voorbeeld met VIIk/v, oplossend naar I:

For what it's worth: Here is an attempt to summerize all gealtereerde chords in one diagram. What becomes clear in any case through such a scheme is where in a minor or major key the various chords are possible, and how they are interrelated:

example 30

You can see or download this diagram as pdf (opens in a sepeate window)

[continuation of this chapter]