Diminished chords

[quaver]

In our RCM exams they require the diminished 7th chord. So for B flat minor diminished 7th you would start on the A and progress in minor 3rds.  For what reason they start on the A I know not.   A diminished B flat chord would start on B flat.  So B flat D flat and E.  Now for a diminished 7th for exam purposes, why don't they just add the G to the chord.  Why start on the half step below.  I'm confused.

[diomedes]

It looks like you're confusing diminished 7ths (chords) and diminished triads. Diminished 7ths relate to a key, so that's why it's necessary to move down half a step. Diminished 7ths have 4 notes. A diminished triad starts on the stated note, so B flat d flat and e make a diminished triad, and the G is not added because a triad has only 3 notes.

[quaver]

So does that compute that the dim triad of B flat D flat and E with the added G would be the diminished 7th of B?

[1piano4joe]

Hi quaver,

In any diminished triad the 3rd and 5th are always flatted.

Since a Bb triad is Bb, D and F that makes a Bb dim have the notes Bb, Db and Fb (Not E).

The diminished 7th flats the 3rd, 5th and 7th.

What is a Bb 7 chord? And what key would you find that?

Yes, a Bb 7 is the V chord in the key of Eb major (or minor).

What is the key signature of Eb?

Yes, it's Bb, Eb and Ab.

So, a Bb 7 chord contains Bb, D, F and Ab.

Now if you flat the 3rd, 5th and 7th what would you get?

A Bb dim 7 of course, containing the notes Bb, Db, Fb and Abb. That's "A double flat" not "G".

I hope that helps, Joe.

P.S. It might be even more helpful to think of it this way. The numbers 1,3,5 and 7 are all odd numbers. The even numbers 2, 4 and 6 are skipped. Every other number is used. Well, it works the same exact way only with letters. This should make it clearer for some as to why "E" and "G" aren't used. Notice that the letters, "C, E and G" are skipped.

For HW, What is an Eb 7? What key would that be found as a V chord? What is that key's key signature? What 4 notes would that Eb 7 contain? Finally, what is a Eb dim 7?

[quaver]

I presume HW is homework.  Ok thanks for that. An E flat 7th is E flat G B flat D flat.
That would be found in the key of E flat major. Key signature is B flat E flat A flat.
An E flat dim 7th would be E flat G flat B double flat D double flat.

However the diminished 7th of E flat would start on D wouldn't it.

[diomedes]

So does that compute that the dim triad of B flat D flat and E with the added G would be the diminished 7th of B?

Sort of.... you're partially correct.

If you're looking for the diminished 7th of B, it would be represented as A sharp C sharp E G. Same notes, but placed on paper to reflect the key that it is related to. In other words, B does not have a B flat, it has an A sharp. Same goes for D flat, B doesn't have that it has C sharp.

[1piano4joe]

Hi quaver,

The notes of the chords are correct. The key and key signature are not.

This should be immediately apparent since you somehow, someway have the correct notes. Probably from stacking intervals of a minor 3rd.

But think about it, how do you account for the Db? It's not in the key signature of Eb is it?

For more HW, first take out your circle of 5ths and memorize it both forwards and backwards. Backwards is 4ths BTW. Second, correct your key and key signature.

Think about this. A C7 chord I'm sure you know is C, E, G, and Bb, right? That dominant 7th chord is found in the key of F. Look at your circle of 5ths. C is usually at the top in the 12 O' clock position by convention. F would then be at eleven, immediately adjacent to the left. So C7 is found in F major which has one flat, Bb, in the key signature which accounts for the Bb in the 7th chord doesn't it?

More HW for you. Repeat the following, "FCGDAEB" over and over and over every day. Do you know what that is?

Yes, it's the order of sharps.

Next repeat, "BEADGCF" over and over again. What is that? and Why am I asking you to do that?

Yes, it's the order of flats. Did you notice it's the order of sharps backwards?

If you knew these already then you actually know the circle of 5ths!

Finally, I don't quite understand why your starting on some funny notes. Why are you starting on A in Bb dim 7? And what about starting on D in Eb dim 7?

I have all the RCM books. If you tell me which one your looking at, I would have the context and possibly, be better equipped to explain what they're doing. Those notes are Maj. 7ths and do not belong to the diminished 7th chords.

More HW. Play a four note C7 chord in your right hand with 1245 in root position with your thumb on C. Play this a few times. Then go chromatically to the right Db7, D7, Eb7, E7, F7, Gb7, etc. all the way up to C7 an octave higher and then chromatically back down to where you started.

Repeat this with your left hand.

Now with your right hand again play C7. Move your two middle fingers (2&4) from E and G of the C7 to Eb And Gb leaving your thumb and pinkie where they are on C and Bb. That is a C dim 7! Go back and forth until its second nature.

Then chromatically up to Db7 with 1245, flat the two middle fingers (2&4) again. This is Db dim 7. Keep going. Your hands will learn what feels right and your ears will learn what sounds right. Although mentally, your totally disconnected.

Lastly, play a C dim 7, C Eb Gb Bbb with 1245 and play that "hand position" chromatically up and down so that you play all "12" dim 7 chords. Repeat with left hand of course.

I hope that helps, Joe.

P.S. Play any root position triad. Let's say a C chord. Plain old C E G with right hand fingers 135. The pinky is on the 5th G and tells you immediately G7 is the V7 chord in the key of C.

What is the V7 chord in D major? No problem, let's see D F# A. Oh, so A7 then right? Right.

HW time for you.  What are all the V7 chords? And what key are they in? You played them. Your hand knows them. Your ears know what they sound like. It's time to connect the brain. And then eventually the eyes in pieces through arpeggios, chords, Alberti bass. etc. where a good teacher tells you to "BLOCK THEM" and "NAME THEM" to make the learning easier!

I hope that helps, Joe.






 

[quaver]

Yes, Joe, thank you this is helping. You'll need to give me time to get my head around this and also to get to the piano.  Regarding the RCM I am looking at p.21 in the 2008 piano syllabus. The diminished 7th chords to start on the leading note of the minor key.  Just wondered about that.
Will get back to you when I have digested the other remains of your HW.  Thanks for your interest.

[1piano4joe]

Hi quaver,

I figured out what your confusion stems from. The RCM book. I'm pretty sure you understand it completely and the book is messing you up.

All the "classical" major and minor scales are heptatonic meaning they contain 7 notes. Consider the following: Do, Re, Me, Fa, So, La, Ti. Seven if you count them. The musical alphabet ABCDEFG, again 7 if you count them.

A triad can be built on any of the 7 scale notes.

In any harmonic minor scale, a triad built on the 7th degree of the scale, is a dimininshed triad.

In the key of Bb minor which contains 5 flats, "bead and g", the 7th degree of the scale is "A NATURAL" since in a harmonic minor scale the 7th is raised. Since the key signature indicates that "A" should be flat, accidentals are used. In this case a "natural sign".

So, in the minor key of Bb minor, the diminished 7th built on the 7th degree of the scale is in fact, "Adim7" which contains the notes, A, C, Eb and Gb. Which you could arrive at very easily by starting with A7 which containts A, C#, E and G and then just flatting 3,5 and 7! Easy peasy!

The RCM book says Bb minor but that is "ONLY" the key signature. The book than proceeds to show broken arpeggios in root position and then 1st, 2nd and 3rd inversion which are, of course, the arpeggios of "Adim7" and NOT "Bbdim7".

You are ABSOLUTELY CORRECT when you say in your first post that "Bbdim7" begins on Bb!

So, there is a distinction between a diminished 7th chord in the key of Bb minor (which is Adim7) and the chord Bbdim7 which would be in some other key entirely.

Let's make this easier, shall we?

If we take the key of "a minor", there are neither sharps, nor flats in the key signature, right?
The "a minor" harmonic minor scale requires us to raise the 7th degree of the "a natural minor" scale which contains, of course, "g natural", doesn't it?

So, in the "a harmonic minor scale" there is, in fact, an accidental placed on "G" to make it G#. This effects 3 of the 7 triads that can be built on each of the 7 scale degrees, doesn't it? Which ones?

Yes, the III chord is Augmented, the V chord is major and the vii chord is diminished.

So, what is this vii chord?

If you thought G#dim7 then you are correct! Look in the RCM book and you will find this where it says "a minor" which is ONLY the key. Confusing right?

I have to admit, I was confused myself.

Thank you, Joe.

[quaver]

Ok, thanks Joe.  Now you're going to have to give me extra time!  I think you may be helping others with this subject as well as myself.

[pianoplunker]

I presume HW is homework.  Ok thanks for that. An E flat 7th is E flat G B flat D flat.
That would be found in the key of E flat major. Key signature is B flat E flat A flat.
An E flat dim 7th would be E flat G flat B double flat D double flat.

However the diminished 7th of E flat would start on D wouldn't it.

Eb7 is not technically in Eb major but there are lots of Eb major progressions which would place an Eb7 for some type of modulation to Ab. Technically Eb7 is in Ab major as the dominant 7th.
I dont understand what you are saying about Ebdim7 starting on D. 

[keypeg]

I studied RCM theory and later went on to study with a private teacher who has given me a much more expanded view of theory in music.  If this is in rudiments, it may be that they have updated - I know that harmony theory got an overhaul between when I was studying grade 1 harmony and grade 2 harmony, with the addition of letter name chords, figured bass, and movable do solfege symbols.

Here's my take:

The RCM - maybe traditional theory as a whole - is heavy on relating everything to a diatonic model.  There is actually a fine-print "note to the teacher" in one of my theory books that states that the theory centers on the Common Practice period, and a simplified version of it at that.  One book that did not get upgraded when the syllabus changed, tried to get beyond that by giving a fuller perspective.

Everything seems to be built on functional harmony and chord degrees.  So they look at what kind of chord you will get if you use only the notes in that key.  That is what I mean by a diatonic orientation.  So if you go that route, in a major key, there is only one triad that will be diminished - the vii^o.  You will have studied this already.  So for Bb major, you want to ask yourself what the 7th degree note is (A) and what triad you'll get (ACEb), so A^o is the  vii^o in the key of Bb major.  This is the first step.

Your 7th will be a minor third above the fifth which is Eb, which we learned to call a "diminished 5th" and much of the world calls a "flat 5".  Since it's a minor 3rd above the 5th, you know that in letter names it is some kind of a G.  You can find it on the piano or work it out some other way - Eb to Gb is a minor third.  So your diminished 7 chord which is the vii^o7 chord of the key of Bb major is A C Eb Gb = A^o7. If you wanted to work out what kind of interval you have from A to Gb you'll see that it is a dim7, because A to G# = a major 7, A to G = a minor 7, so A to Gb = a dim7. But your safest bet is simply to find a minor third above the fifth that you'll have in root position.

In actual music, there will be diminished chords that have nothing to do with the 7th degree.  Composers use the dim7 to do all kinds of nifty things and they will stick it anywhere in order to make the music move in certain ways.  Another way of looking at a dim7 is to just see a minor triad where you then lower (flat) the 5, and then lower the 7 so that it is an m3 from the 5th.  So you'd ask yourself "How do I create an A^o7, or a G^o7 or whatever.

But for exam purposes you have to do this "degree" approach - the dim7 which is the 7th degree chord.

I ended up with a kind of split perspective on music -- the "how it has to be seen in formal theory in a narrower manner", and "the larger multi-sided views".  It's good to be able to see both eventually.  We can see a chord by its own characteristics just "as it is", and we can see it in terms of function meaning "which degree chord has these properties?".

[keypeg]

Rereading - if the RCM book only asks for a diminished chord in a minor key, then other information is left out.  In a minor key, the choices in composition end up being that you have a harmonic minor scale, a natural minor scale, or a melodic minor scale.  In at least some of these choices you will get a diminished triad in ii as well.