diminished chords

[clef]

well I've been looking seriously at diminished chords and scales at the moment and the more I think about it the more complicated it gets, first I noted that there are only three types of diminished chords, they all invert into each other perfectly (Co7 = Eb07...) and that a seventh chord is made up of a diminished chord with a seperate root.  (C7=Eo/C) and then I tried to comprehend more about the diminished scales and its relationship to the dominant flat 9 chord, and then things got a bit fuzzy, a clear explanation of what makes a diminshed chord and diminished scales so special in many ways would be good...

[pianistimo]

all i have is major, minor, and chromatic.  what exactly are you after?  maybe more arpeggios (because a 'diminished scale' would be like:  c d e-flat, f g-flat a-flat b-flat  which is so near the key of e-flat minor and c minor that no one would bother with the extra accidentals to make it diminished.  diminished chords are used infrequently to get their bonus sound to the minor and are used in chords more sparingly too. 

here's some arpeggios of the diminished 7th ex. in c minor:

b-natural (1) d (2) f (3) a-flat (4) ...repeat... top note b-natural (5) repeat backwards.

pick up hand = start again on d (1) f (2) a-flat (3) b-natural (4)...repeat (top d is 5) repeat backwards.

then on f and a-flat for the last two diminished arpeggios.  those are all four positions of the c minor scale with diminished seventh chords used. 

[prometheus]

Root + minor third + minor third is a diminished triad.

1 b3 b5, so a diminished fifth.

It is easy to see this triad is symmetrical. C plus minor third is Eb, Eb plus minor third is Gb, Gb plus minor third is Bbb, Bbb plus minor third is C.

4 x 3 is 12

1 b3 b5 bb7 1
C Eb Gb Bbb C

So if you start at C then you have an unique chord. If you start at C#/Db you have an unique chord. If you start at D you have an unique chord. But then you start at D#/Eb and the chord starting on C already has that note. That chord also has the C and the Gb and the A/Bbb, so it's the same chord.

Now we go the other way. We can start at B/Cb and we will have an unique chord. But this unique chord is the same chord as the unique chord starting on D.
You can start with A#/Bb but that is the same chord as the one starting on C#/Db.

So since this is symmetrical they can only start on a limited amount of notes without overlapping each other.

Leaving out the diminished seventh and you get the diminished triad.

 

[Bob]

I find it helpful to think of a diminished chords as leading to another note.  viio  I

You can build a dimished chord by taking the 7th, 2nd, and 4th step of the scale.  (I'm fuzzy on my theory on why the seventh of the dim seventh isn't in the major scale.  Either way, it would resolve down to the 5th step of the scale I would think.)

There are only three.  I had a theory person tell me.  Bravo for figuring it out yourself.

There are slash chords, but I'm not sure it's helpful to think of a dominant seventh chord as a dimished chord with an extra note as the root. 

Diminished scales are alternating whole and half tones.  There are only two -- It either starts with a whole tone or a half tone.  I'm fuzzy on this now.  I think there are also called octatonic.  The notes of the dimished chord "fit" into the diminished scale -- So you can play notes of the diminished scale over a dminished chord and they should sound good.  I think that's the basic idea.  It's more a jazz thing I think. 

Why are they special?  Because at one point it was a big deal to use dim 7th chords to modulate to different keys.  With that one chord, you have access to three other keys (major or minor), or if you use them as a viio/V, another three key areas.  Lots of possibilities.  At least that would be one reason.

[clef]

Why are they special?  Because at one point it was a big deal to use dim 7th chords to modulate to different keys.  With that one chord, you have access to three other keys (major or minor), or if you use them as a viio/V, another three key areas.  Lots of possibilities.  At least that would be one reason.

Oh yes, I see, because they are really the same chord but in different inversions, the same chord can be in several keys, therefore it can be used as a modulating chord between keys because your really in two keys, you don't leave one key until your in the next     

Diminished scales are alternating whole and half tones. There are only two -- It either starts with a whole tone or a half tone. I'm fuzzy on this now. I think there are also called octatonic. The notes of the dimished chord "fit" into the diminished scale -- So you can play notes of the diminished scale over a dminished chord and they should sound good. I think that's the basic idea. It's more a jazz thing I think.

Oh yes I remember seeing somewhere about two different diminished scales.  One goes TSTSTS... and one goes STSTST or something like that, I'm not sure, I'll have to look into it.   

Or maybe I'm getting confuzzled with the whole and half tone scales... soo many freakin scales....   

[goose]

You're right, Clef, about the diminished chord's relationship to a dominant 7th chord. Jazz musicians use the principle in creating voicings.

So a G7 (b9) chord might be voiced: F Ab B D.

Modern jazz also uses the diminished SCALE extensively in melodic improvisation, especially for playing over a V7 (b9) chord. The scales are of course symmetrical, made up of alternating half-tone and whole-tone intervals.

You'll hear jazz musicians talking about a standard diminished scale (which starts with a whole-step, or tone) and the 'auxiliary diminished scale' which starts with a half-step (semitone). The auxiliary diminished is used on V7 chords, while your standard diminished fits actual diminished chords (e.g. Bo7, often written just Bo).

The scales can be quite difficult to visualise (when improvising) until you work out a shorthand for yourself and 'see' the note groupings as you play. But, as you realised, there's only three of them to learn. It just depends what the root note is.

As Bob says diminished chords (and their related dominants) do feel strongly like the want to resolve (usually to the tonic).

best,

Goose

[lilypiano]

;

[prometheus]

(I'm fuzzy on my theory on why the seventh of the dim seventh isn't in the major scale.  Either way, it would resolve down to the 5th step of the scale I would think.

A true diminished chord is not native to any tonality. The chord on the seventh degree of the major scale is half diminished.

There are slash chords, but I'm not sure it's helpful to think of a dominant seventh chord as a dimished chord with an extra note as the root. 

Yes, it is true that the top three notes of a dom7 chords form a diminished triad. But you only use the term 'slash chord' when it is needed. When there is really a random bass note with a triad chord on top of it.

Why are they special?  Because at one point it was a big deal to use dim 7th chords to modulate to different keys.

Yes, you already yourself realised the dim7 chord is not part of any key. So this means it is a switching point to different keys. The diminished chord has a tritone that needs to be resolved. So it can be used as an easy, and maybe crude, way to jump quickly from one tonality to the next.

[silvaone]

they all invert into each other perfectly (Co7 = Eb07...)

Is this true?

I thought Cdim7 = C Eb Gb Bb

and

Ebdim7 = Eb Gb A and Db

how can they be the same?

Silva

[prometheus]

Those aren't diminished chords. They are half diminished, meaning they have a b7 and not a bb7.

The Bb should be a Bbb or A and the Db should be a Dbb, or C.

[clef]

what other modulating chords can be used to change keys?

-plays on piano for a bit-   

well using the major chord built on the supertonic of the key, such as D major in a C major can be used to modulate into the dominant (G) any other suggestions?

[prometheus]

Obviously the chords shared by the two different keys. But then the new note needs to be introduced. Plus, to establish the modulation a cadence is needed. In the case of C major to G major; D to G is the V I cadence in G major.

So first we need to have chords shared by both, then a chord with the new tone, or tones. And then a cadence to finish.


So it isn't an issue of one chord. With a diminished chord there is. But that is a very ad hoc and crude way, though very fast, of doing it.

[abell88]

what other modulating chords can be used to change keys?

This generally works:

ii, IV, or vi of the old key, followed by V7 of the new.

[ted]

Well, there can't be that many symmetric partitions of the chromatic scale can there ?  Let's see.

111111111111 - Chromatic scale, only one of those
222222 - Whole tone scale, two of those
3333 - Diminished chord, of which there are three
444 - Augmenteds, four of those
66 - Tritone, six of those
21212121 - Diminished scale, three of them
313131 - Augmented scale, four of them
211211211 - Don't know what this is called, but there are four of them
5151 - ? , six of these
4242 - Half diminished, six of those
411411 - ?, six of them
321321 - ?, two major chords a tritone apart combined - six of them
312312 - ?, two minor chords a tritone apart combined - six of them
31113111 - ?, six of them, complement of 5151
22112211 - Complement of half diminished, six of them
2111121111 - Complement of tritone, six of them

That's the lot, I think, isn't it ? The diminished 3333 far outnumbers the others in classical music, used much more than the augmented 444. I wonder why, since both of them occur in the harmonic minor scale and the augmented sounds the prettier chord in isolation to me. 321321 has turned up a lot in jazz via "substitute" chords, as has the diminished scale 21212121. But you don't hear the other permutation 312312 anywhere near as often. Again, I wonder why.

Questions like this are certainly intriguing aren't they.