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 muziektheorie >  harmonie  > harmonieleer  > E. Chromaticism > altered chords
Section E. is not at all complete yet. In the moment only this is available:  altered chords / sections 1-3, 5, and part of section 9
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1. general information
2. diminished third on #4^; 
score examples
3. enharmonization of the double diminished triad and seventh chord, and of the hard diminished seventh chord
 
score examples
4. #IV and IIhv in other inversions
 
score examples
5. scheme of all altered chords
6. diminished third on #4^:
score examples
7. diminished third op 7^:
score examples
8. diminished third on 2^ in minor, and on #2^ in major:
score examples
9. overview of the enharmonizations and possible modulations
10. other issues? 

 

1. general information

Before going into the actual altered chords it is useful to think about the meaning of the terms alteration and altered tone. The term 'altered', when used in the context of altered chords, is used in a pretty specific way, which is not entirely consistent with its general meaning.

An altered tone is a tone that is not diatonic in a specific key; the concept of alteration is therefore always linked with tonal or modal music: In the key of G major D# is an altered tone, as well as Ab. It should be noted that we can label some altered tones in major and minor keys in another way as well: we know the lowered sixth in a major key also asmolldur-sixth (or: b6^), and the raised sixth in a minor key as durmoll-sixth (or: #6^). These alterations are part of the so-called extended diatonicism, in which a major and parallel minor key arre 'mixed'.ann Logically, we can then speak of: mixture. For example: The tone Eb is b6 ^ in G major, and as if it were 'borrowed' from the parallel minor key; E natural in G minor is #6^, and as it were borrowed from the parallel major key. Even the use of the minor third in a major key, or the major third in a minor key sometimes can be seen as resulting from mixture, when these thirds can be seen as 'borrowed' from the parallel key.ann Sometimes even b2^ ann(in bII / Neapolitan) is seen as part of extended diatonicism. See example 1:
example 1
The fact that a chord contains one or more altered tones does not automatically mean that the chord itself is an altered chord. In most cases it is just a 'normal' chord, because, even when it does not belong to the momentary key, it can stand in one or several other keys. So, we can see it as 'borrowed' from another key. When the chord can not be explained as part of extended diatonicism, it is in miost cases a secondary dominant or secondary subdominant. For example:
example 2
  • The chord G-B-D-F is not part of the (diatonic) G major and G minor keys: in G major F is b7^ (so: alteration); in G minor B is #3^ (so: alteration as well). On the other hand the chord fits in for example C major and C minor (as V). We can explain it in G major and G minor as well, normally the chord will then act as secondary dominant:
  • The chord C-Eb-Gb-Bb is not part of the (diatonic) C major and C minor keys: in C major Eb, Gb en Bb are alterations, in C minor Gb is an alteration. On the other hand the chord fits in for example Bb minor (as II) and in Db major (als VII). We can explain it in C major and C minor as well, normally the chord will then act as secondary subdominant:

The altered chords form a separate group; this means that they share common characteristics that distinguish them from all other chords, and that we can precisely define them, as a group:

  • The most general definition of an altered chord could be: The chord is not appearing as a diatonic chord in any key. Which also implies that may chords containing an altered tone are no altered chords (see the above examples).ann
  • It is obvious that the fact that a certain chord does not belong to any diatonic key is determined by its interval structure. In other words, at least one of the intervals in the chord is not placeble in any diatonic key. If we ask ourselves which interval that could be it appears that most, even the most dissonant intervals are 'placeable' in on ore more keys. We can place a dimished seventh between 7^ and 6^ in mor (or between 7^ en 6^md in major), a dimished fifth between 7^ en 4^ in major or minot, and between 2^ en 6^ in minor. Even a diminished fourth can occur, even when only between 7^ en 3^ in minor keys:ann
 example 3
    There is one exception: the diminished third (and of course its inversion, the augmented sixth). The tones D# and F for example can not appear together in any diatonic key: when we use these notes together in A major or A minor D# is an alteration, when we use them in E minor, F is an alteration:
 example 4
This means that only chords containing a diminished third are to be considered as altered chords. The diminished third then can be between root and third, between third and fifth, or (in  seventh chords) between fifth and seventh of the chord. For example:
 example 5
In practice, altered chords occur only at certain locations in the key. Put differently: diminished thirds only can be used between specific tones in a key: Only certain tones in major and  minor keys can be raised or lowered so that a diminished third arises. Diminished thirds should shrink when resolving, and resolve to the prime (and the inversion of the diminished  third, the augmented sixth should spread when resolving, and resolve to the octave). It turns out that there are only three possible 'resolution-points' in the key:ann
  • most common: resolution to the fifth of the key; the chord to which we resolve (and that contains 5^) mostly has dominant function (and sometimes tonic function) 
  • mless often, but especially in the 19th century not uncommon: resolution to the root of the key; the chord to which we resolve (and that contains 1^) always has tonic function
  • fairly rare: resolution to the third of the key; the chord to which we resolve (and that contains 3^) always has tonic function
In the form of a diagram: These are the options (see also example 6):
in minor en major: in minor en major: in major: in minor:
(b)6^ 5^
#4^ 5^
b2^ 1^
(#)7^ 1^
4^ 3^
#2^ 3^
b4^ 3^
2^ 3^
 example 6
When a diminished third is used on #4^ a minor key is slightly more probable than a major key, as we then have to alter only one tone (namely #4^), whereas we have to alter two tones in major (namely #4^ and b6^ ) This does not mean though that chords with this diminished third cannot occur in major. When we use a diminished third on 7^ a minor key is slightly more probable than a major key as well: the lowered 2^ is in minor keys a more 'normal' phenomenon than in major keys (as lowering the 2^ in major causes an augmented second between b2^ and 3^). Again, this not mean with this diminished third cannot occur in major keys. 
The diminished third most often appears inverted in chords, as augmented sixth. And the lower tone of the augmented sixth then furthermore normally is in the bass:
 example 7
chords with the same augmented sixths then may look like this:
When you know where in major and minor keys a diminished third can be placed, you basically can find the corresponding chords yourself. Be aware of this: 
  • chords chords containing a diminished thirds either between # 4^ and (b)6^ or between (#)7^ and ^b2 are always entirely derived from the minor key, even when they are used in major. In other words: when in these chords de third or de sixth of the key occurs, these are always minor.ann
  • the diminished third that resolves to 3^ is in major at a higher pitch than in minor; logically so, as 3^ in major is a major third from the root of the key, and in minor a minor third. Otherwise said (see examples 6 en 7): the note Fb is hardly possible in C major (we would probably hear E instead); the same applies to the note D# in C minor (which we probably would hear as Eb).
In the following sections I first go into the chords associated with the diminished third between #4^ and (b)6^, because it is by far the most common. Later, the other diminished thirds, with the corresponding chords, are also discussed.

In the moment, when writing chord labels or describing chords, I always use the Dutch notation. Which means that you have to know these abbrevations:
 
abbr. means: in English:
g groot major
k klein minor
ov overmatig augmented
v verminderd diminished
dv dubbelverminderd double diminished
hv hardverminderd 'hard diminished'
ovdom overmatig dominant 'augmented dominant'
As you will see in the following sections, sometimes these abbrevations are combined to label a chord.
[continuation of this chapter]