"My" first piece - Turkish March by Mozart

[daniloperusina]

I managed to read before you edited!:)

I had to look up the definition of "triad", and it says:
three-note chord consisting of a "root" note together with the third and fifth above it

That is, the root is 1.

So, A minor is a minor triad. It doesn't matter if you call it minor triad or minor chord, as in this case it means the same thing.

A is the root (1st), C is the 3rd and E is the 5th.

E minor has E (1st) G (3rd) and B (5th)

Again, when you seem to be unsure of what you are saying, you stumble upon the correct things!:) Part of this discussion of "tricks" will namely be just that: substituting minor chords for major!:) But you'll see soon...

[daniloperusina]

Well, while you wait until you can play, you can do this theory exercise, it will be very useful:

Name all the 5ths in the C major scale!
C-G is a 5th; D-A is a 5th, etc etc

Learn them, and memorize them!

 

(I'll go off-line, be back later)

[ggpianogg]

(.....)

Now you have to play! So, first play the following chords, one after the other, in this order:
C - G7 - C

Next:
C -G7 - Am

Next:
C - G7 - Em

The ear always expects C after G7. By doing the above, you replace the expected with something else. Do you think Am and Em both sound equally well after a G7 chord?

I would say Em sounds definitely better after G7, at least for my ear! Playing Am after G7 actually sounds like a rapid change of "mood" to me.

Edit: I mistakenly named the chords, sorry I meant Am sounds better after G7.

Well, while you wait until you can play, you can do this theory exercise, it will be very useful:

Name all the 5ths in the C major scale!
C-G is a 5th; D-A is a 5th, etc etc

Learn them, and memorize them!

 

(I'll go off-line, be back later)

Will do that, thanks for the suggestion

[daniloperusina]

Yes, A minor sounds better than E minor!

That is because of the notes they contain.

E minor = E G B

What about G major?
G B D

You see? It's like you hardly leave the G major chord. They both share the G and B notes.

A minor, on the other hand, has
A C E

They don't share any notes, so the change should be very audible. In fact, A minor is very similar to C major because they both share the notes C and E.

As already said, G7 pulls strongly to C major because of the notes GBD that wants to go to the note C, and F that wants to go to the note E.

This makes A minor a very strong substitute for C major.

This similarity between G major & E minor, and also C major & A minor has been noted long ago. For this similarity they are called Parallel Chords!

Next, instead of E minor, play E major! So:
C - G7 - E

E major = E G# B

Then, E7:
C - G7 - E7

E7 = E G# B D

You hear how drastically different it becomes? Suddenly, E is not the parallel of G anymore!
More will follow...

[ggpianogg]

Confirmed

[daniloperusina]

Now play these chords:

C - G7 - Am - F - C/G* - G - C

*C/G means C major chord with G as bass, so from bass to treble: G C E


Then play these chords:

C - G7 - E7 - Am - Dm - G - C

Questions:
What is the relationship between E7 and Am?
What is the relationship beween F and Dm?

What are the intervallic relationships between the following notes?
C-G; G-D; D-A; A-E

[ggpianogg]

Now play these chords:

What is the relationship between E7 and Am?

I don't see a direct relationship between these two chords, although they do sound very well one after the other, almost as if Am was the "next" chord after E7, if you know what I mean.

What is the relationship beween F and Dm?

I would say those are Parallel chords.

What are the intervallic relationships between the following notes?
C-G; G-D; D-A; A-E

A 5th :-)

[daniloperusina]

F and Dm are indeed parallel chords!

You already answered that A-E is a fifth, which is correct (they are all fifths, so the answer is right!).

C-G is also a fifth. Gmajor is the dominant chord to Cmajor. So therefore Emajor must of course be the dominant chord to Amajor. The dominant-tonic is always a fifth apart.
The new information here is:
The Tonic can be major or minor
The Dominant is always a major chord

So, your observation "...they do sound very well one after the other, almost as if Am was the "next" chord after E7..." is very good!

Emajor, as well as E7 is the dominant chord to Aminor.
Eminor would not be defined as the dominant chord to Aminor. Sometimes it is used like that, because of the sheer fact that the two chords are a fifth apart. But in those cases, we rather call it "a weak dominant".
You have one such case here:
Am - Dm
They are a fifth apart. But because the A chord in this case is a minor chord, it's not a "real" dominant, it's a "weak dominant".

Weak dominants, that is, when it's a minor chord, is very much used. It's also just as common to add a minor 7th to that chord, as it is to add it to a real Dominant chord.

So in the example above, one can also try playing
C - G7 - E7 - Am7 - Dm7* - G - C

* I added the 7th to Dm as well, becasue D-G is also a fifth, and Dm is thus the weak dominant to G

Am7 = A C E G
Dm7 = D F A C


Also notice how in the first example in the post above, F follows Am, but in the second example Dm follows Am. F and Dm are parallel chords, and that is exactly how parallel chords are used:
where you expect the one, the other can "surprisingly" be thrown in...

Follow this far?  

[ggpianogg]

Crystal clear!

On a side note; the reason I didn't notice that E7 and Am (your post number #55) has a tonic-dominant relationship, is because my thought pattern was kind of 'restricted' to thinking the tonic-dominant relationship only applies in an 'ascending' motion on the keyboard/piano. So when I saw E7 and THEN Am, I failed to notice the relationship, because Am is only a 4th 'AFTER' E7 Your post made reminded me that this relationship is replicable throughout the entire piano in both directions (I think you already pointed this out at the beginning of our lessons). Thanks a lot

[daniloperusina]

Very good!
And your way of reasoning is very good!
And much of what you say is actually correct!

Intervals are always counted ascending! So, when we say a fifth, we mean the fifth we find when we acend the scale! We must do so, otherwise we'd never know which note or chord we are talking about...

Look at this:
Start on C. Ascend a 5th. Which is the note? G, of course.
Start on C. Descend a 4th. Which is the note? Well, G again...

This proves that the 4th and the 5th is the same interval turned upside-down!

Remember that the discussion about the Subdominant showed that the Tonic-Subdominant is actually an upside-down Dominant-Tonic relationship!

You observed that the E7-Am is a 4th. This gives us two possible answers:
Am is the Subdominant to E7 (IV & I)
E7 is the Dominant to Am (V & I)

Just like you concluded that F is the Subdominant to C, but also that C would be the Dominant to F, if F is the Tonic.

I think this is the time to clarify what your teacher said, quoted in post 25...

[daniloperusina]

He said "...the dominant SHOULD contain the 7th..."

Let's clarify this statement!

If our Tonic chord is C major, then the G major chord is the Dominant chord.

C E G = tonic
G B D = dominant

Period!

If we add a minor 7th, we say so!
So, G7 is called the Dominant seventh chord to the tonic C major.

C E G = tonic
G B D F = dominant 7th

With roman numbers:
C E G = I
G B D = V
G B D F = V7

Period again!:)

The Dominant seventh has been much more popular throughout the centuries than just the plain Dominant, so you'll find much more references to the dominant seventh in the literature than just the dominant!

Further, a plain triad is considered to be a stable chord in itself. A chord with an added minor 7th is not considered to be stable!

This is easy to hear. Sit down on your keyboard and play a G major chord. It will not sound as if it has to move anywhere. Do something else for a while until you have cleared your ears of the sound of that chord. Than sit down again and play a G7 chord. You'll hear that now the music immediately wants to move, it sounds very unstable!

What happens is that G7 wants to move four steps up to C major or C minor, just like E7 wants to move four steps up to A major or A minor.

This very phenomenon gives us two very solid definitions:
A dominant chord does not have to have an added minor 7th
A major chord with an added minor 7th per definition becomes a dominant chord

For this reason, when we see the two chords E7 - Am in the middle of a chord-progression like the one a few posts above, we tend to focus on the Dominant character of E7, rather then the subdominant character of A minor that follows.

Therefore, the better answer of the two is
E7 and Am relate as Dominant 7th to Tonic, rather than tonic with added seventh going to it's subdominant.

We always choose to focus on the more important event! In this case, E7

[ggpianogg]

Hi Danilo,

Everything is clear I think, although I do have a question regarding your last post:

(...)
This very phenomenon gives us two very solid definitions:
A dominant chord does not have to have an added minor 7th
A major chord with an added minor 7th per definition becomes a dominant chord
(...)

Isn't point 2 in a way contrary to point 1? Since in point one we state that a dominant chord does not need to have an added minor 7th. Then in point 2 we state that adding a 7th to a major chord makes the chord dominant. Can't we actually assume that any regular major chord (a triad), without an added 7th, is dominant in relation to the chord a distance of a 5th below it?

[daniloperusina]

Excellent question!
I have to run, so to be continued...

No, in a sense we can't do that, because as shown, a major chord can be very stable-sounding when it appears. When it is stable, it doesn't force the music to go anywhere. When it has the function of being stable, it is not really thought of as a dominant.
Take C major in our chord-sequence, for example. It's not "dominant" they way it appears here.

However, play this:

C - G7 - Am - F - C/G - G - C - C7

By suddenly adding a minor 7th to even the tonic, it suddenly becomes very unstable, and is suddenly a dominant chord (the dominant of F, which is what we want to hear after C7).

Also, the G chord before C at the end is not a G7, but because it appears where it does, it is a real dominant (because the whole chord-sequence has C as it's tonic)

So, again:
A major chord with an added minor 7th per definition becomes a dominant chord


This is something that will return again and again, as it could be said to be the very foundation of western classical music!

[ggpianogg]

Ah, all clear now, thanks

So basically, for a chord to actually be named (I'm just speaking about the terminology here) the dominant of another, it HAS to be unstable, correct?

Oh and one "side question" in here. Quoting:

(...)
However, play this:

C - G7 - Am - F - C/G - G - C - C7

(....)

Also, the G chord before C at the end is not a G7, but because it appears where it does, it is a real dominant (because the whole chord-sequence has C as it's tonic)
(...)

Just to make sure: do we call C the tonic because all of the other chords in this progression are based on the notes in the C scale, or is there some other reason for it? What, for example, if the chords in a progression were based on the notes F G A C D E? Those notes are as well a part of C, as they are a part of F. Which one would be the tonic, and how would the difference affect us? Sorry for the side question, please feel free to ignore this question if it digresses too much from the matter at hand (we can simply get back to it later if you prefer)

[daniloperusina]

On the contrary, that is exactly what needs to be explained next!

The Key

In the chord sequence
C - G7 - E7 - Am - Dm - G - C

you did notice that there was another dominant (apart from G7) which is E7.
If there is a dominant, then there is a tonic. The tonic is Am. But the tonic is already C major, so what is this? Two tonics?

The answer is
C major is the "key" of the chord sequence, the "main tonic"!
With E7-Am, there suddenly appears another tonic, but we are still in the key of C major. We can throw in as many other dominant-tonics as we want, C major will still be the key!

In the key of C major, there is only one dominant; G or G7. To create another, temporary, dominant, we have to change the scale. E7 needs the note G#, so we have to raise G temporarily. C7 needs the note Bb, so we temporarily have to lower B.

It is also clear that by temporarily changing one of the notes in the scale, we enter another "harmonic area". If you create a C7, which then acts as a dominant to F, you lower B to Bb, As it happens, the F major scale looks like this:

F G A Bb C D E

Do you see how we by lowering the B to Bb to make the chord C7, we also enter the "sound-world" of F major?

As stated, you can do this a lot, and still have C major as your "main tonic". That is, we do not leave the key of C major. These will just be very brief temporary tonics. In the chord-sequence above, Am is very briefly a tonic, but we can't stop there, we have to continue back to C major.

You can also do this much more firmly; you can actually change the key, and thus create a "new" main-tonic! When that happens, we say that "the music modulates to another key"!

Basically all classical music do these modulations! In fact, it's one of the basic ingredients in classical composition, and one of the reasons for why it's such complex music!

Typically, the piece will start in one key, say C major, then modulate to other keys (other main-tonics), and then at the end of the piece bring it all back to C major again!

And yes, I think it's fair to say that a dominant chord must be un-stable. (G7 is of course un-stable, but G is only unstable if the surrounding chords forces it to be, like in the chord-sequence above!)

[ggpianogg]

Hi Danilo!

Thanks for your answers As always, your post is very insightful and easy for me to understand! Allow me to ask a one or two questions regarding the last post (I'm leaving work in 10 minutes, but it should be enough):

1. So basically, it is how much time we spend in a given scale (well, not so much the scale itself as the notes of that scale) compared to the other scales, that determines the KEY, correct?

2. Another thing that got me thinking: in the chord sequence you give at the beginning of your last post:

C - G7 - E7 - Am - Dm - G - C

G7 is creating tension, which is later release by C. However, in the middle (before the tension from G7 is released) we technically have another "tension-release" being introduced, by E7-Am. How does this 'feel' in practice? If we create tension, and then before releasing it we create and release a DIFFERENT tension, then does this somehow affect the first tension built (in this case G7)? Or am I looking at it the wrong way?

Thanks in advance

[daniloperusina]

Excellent questions!

I'll start with nr 2:
No, the basic tension C-G7-C will remain as an "over-all tension", no matter how many temporary dominants you'll throw in. It will not be affected. It will be proven by the fact that it will not sound finished until you return to C again.

Try playing this, and you'll see:

C - B7 - E7 - A7 - D7 - G7 - C

B7 = B D# F#
A7 = A C# E
D7 = D F# A

This sequence contains no less than five dominants. Try resolving the tension at any point, like:
B7 - Emajor
E7 - Amajor
A7 - Dmajor
D7 - Gmajor

That is, take away the minor 7ths from either E7, A7, D7 or G7, but keep the minor 7th in the chord preceding it, then stop right there. It will sound unfinished, the tension is not resolved. This way you'll discover that the tension will not be released until you come all the way back to C major again.

Even when the music modulates (leaves the main-tonic and enters another main-tonic) to another key, the overall tension will remain.

In Rondo Alla Turca, for example, Mozart sets off in the key of A minor, but ends the movement in the key of A major. Those are not the same keys. So what makes it sound like it's finished?
Well, the Sonata starts in A major in the first movement. About 25 minutes later Mozart finishes the whole sonata in A major. This over-all tension of the basic key of the composition can easily remain for even such a long duration of time! It will be apparent to the listener as well, even if he doesn't know music-theory, he/she will just "feel" it in the air.

For this reason, playing Rondo Alla Turca on it's own will not be the same experience as playing the whole sonata with Rondo Alla Turca as the last movement. Mozart was extremely sensitive to this kind of over-all tension and release.

Question nr 1:

No. First, there's a hierarchy. The basic key of the composition will remain the same! This is what you'll see already in many titles: "Sonata in A major", "Waltz in C# minor" etc.

Next, to leave the basic key to enter another, temporary key, there are almost as many solutions as there are compositions!

Two examples:
Beethoven's Sonata in G major Opus 31 nr 1
He starts the first movement in G major, but within a few seconds he modulates to D major. So very quickly we have a new "main tonic", a new key. But this lasts even shorter. Hardly has he arrived at the new key when he suddenly and drastically changes the key to F major! The time spent at each key is so short to not really being an issue here, but still it really does move to those other keys. But most of all, since G major was introduced at the beginning, this will remain as the over-all key, and the movement will end in G major after maybe ten minutes, as will the whole sonata after maybe 25 minutes!

Robert Schumann's Fantasie in C major, never even starts properly in C major, but the whole first movement slowly modulates towards it. By incredible magic he "establishes" C major as the over-all key, but doesn't really arrive there until the movement finishes after maybe ten minutes. In a sense, this is the opposite of the Beethoven example above, because he takes such a long time to get to the main tonic, but has somehow mysteriously managed to establish it already from the beginning. So, if the Beethoven is extremely short-time, the Schumann can be thought of as extremely long-time.

This is of course not so easy to understand. I don't think it should be "understood" in written words primarily, but rather by playing and finding out with one's ears on a keyboard.


In short, the main key is established from the beginning, and will never be abandoned!
Temporary keys can be established slowly or quickly!

I'll see if I can come up with playable examples...

[ggpianogg]

Great post Danilo, it left no doubt in my mind No questions at this point!

[daniloperusina]

I think you should do some exercises now!

First, can you give the roman numbers to the chord sequence?
C - G7 - E7 - Am - Dm -G -C

C is I, G7 V7 etc...

Next, how does G major scale go?

Next, can you do the corresponding chord-sequence in G major instead of C major?

Looking forward to your answers!
& Good luck!

[ggpianogg]

I think you should do some exercises now!

First, can you give the roman numbers to the chord sequence?
C - G7 - E7 - Am - Dm -G -C

C is I, G7 V7 etc...

I  - V7  -  III7 - VIm - IIm - V - I

(not sure about the "m" in case of Minors, is it correct? ).

Next, how does G major scale go?

G A B C D E F# (G)

Next, can you do the corresponding chord-sequence in G major instead of C major?

G - D7 - B7 - Em - Am - D - G

Looking forward to your answers!
& Good luck!

Thanks!

(I got an automatic alert thing enabled to inform me when submit a new post, it sends a nodge to my cellphone )

[daniloperusina]

All answers correct!

I've seen a few variants about the roman numbering system.
For example, minor chords with small letters:
I - V7 - III7 - vi - ii - V - I

Also, it's common to indicate when a chord that is minor if one keeps to the scale, like E, that would be E minor if keeping to the C major scale, gets a # sign because of the raised note it contains. Thus:
III7(#)

So,
I - V7 - III7(#) - vi - ii - V - I

Next assignment:
Can you give the chords that are formed naturally from the scale in roman numbers, using capital and small letters, respectively?

Again, looking forward to the answer, and good luck!

[ggpianogg]

Hi

Next assignment:
Can you give the chords that are formed naturally from the scale in roman numbers, using capital and small letters, respectively?

Again, looking forward to the answer, and good luck!

Do you mean the G scale, or some other scale?

Also, what are "naturally formed" chords? Does it mean chords that only include the pitches that are in a given scale? Sorry if you explained this before, I might have missed it!

P.s. I will use this post to ask a bit of an off-topic question:

Since I'm still stuck with my keyboard (I had to postpone purchasing a piano at least until the end of february), and the fact that it has only 4 scales, I find it impossible to fully learn the pieces I've tackeled so far (not enough space on the keyboard). Are there any well sounding pieces that you know of, that I could play having access to only 4 scales? I realize how newbe-ish this sounds, but I have no choice, I'm sure you will understand Oh and regarding the difficulty level - I would say something around grade 4, or maybe 5 (not sure if I'm not aiming higher than I can handle.. I've seen the syllabuses for ABRSM Grade 5 and the few pieces I've listened to seemed quite simple, but I might be mistaken).

[daniloperusina]

"..Does it mean chords that only include the pitches that are in a given scale?.."

Yes!

Do it in C major for now! Also, remember I asked you to learn all the fifths in the C major scale?

I'd like you to give the chords from C major scale (I think we've done that before) with names and roman letters, also the fifths, like "C-G" "D-A" etc.. there's a discrepancy that needs to be pointed out. Can you find the discrepancy?

Well, right off my head, I'm thinking about Johann Sebastian Bach, Prelude in C major.
What you mean to say, I assume, is that your keyboard has four octaves. That's how we put it. In this case, we refer to an octave as, for example, C to C, and between those two C:s there are 12 notes all in all, counting both whites and blacks.

Which is your lowest note? Which is the highest? How many octaves are do you have, like exactly four, or three-and-a-half, or something like that?

[daniloperusina]

This should fit your keyboard:
(might be edited to include more suggestions if I find any)
Franz Schubert: Moment Musicaux nr 3 in F minor
Johann Sebastian Bach: Two-part inventions nr 1 (Cmajor), nr 4 (Dminor), nr 8 (Fmajor)

[ggpianogg]

Thanks for the post

I will do the exercise later tonight since I have to leave very soon

Yes I meant octave, sorry - I've been in the world of scales so much the last few days it's all I see right now )

Lowest note is C, highest note is C, so I would say it's exactly 4 ocataves long (49 keys).

And thanks a million for the suggestions! I will review the sheets first thing tomorrow morning. I must say, I really appreciate your help with all this, it's been extremely valuable. I hope you are also benifiting from teaching as much as I am from being taught

[daniloperusina]

And thank you! I do benefit a lot from this!

Look again at post #25, and see if we haven't been able to sort out most of those things by now!:)

Two distinctions could be made at this point:
Chordal analysis = the names of the chords, A major, G7, Em7 or whatever...
Functional analysis = Tonic, Subdominant etc & I, V7, ii etc..

"Harmonic function" would translate to Functional Analysis. I think. I'm not a native english-speaker either, so...

[daniloperusina]

And two more exercises...

C - G7 - E7 - am - dm - G - C

Transpose this to A major, and Db major!
Transpose = move the same thing to another key.

I'm very curious too see how well you manage with these tasks now!

If you have the time, also write down
*A major scale
* What notes the corresponding chords in the sequence will contain

This will also show how well you grasp the "spelling" by now, that is "is this note F# or Gb?" etc..

Much joy with it, and looking forward to see your answers!

[ggpianogg]

Good day Danilo

Let's go!

(...)
Next assignment:
Can you give the chords that are formed naturally from the scale [C scale - added by ggpianogg] in roman numbers, using capital and small letters, respectively?
(...)

I - ii - iii - IV - V - vi - vii° (I had to look up in google how to write down a diminished chord )

respectively:

C - Dm - Em - F - G - Am - Bdim

(...)
also the fifths, like "C-G" "D-A" etc.. there's a discrepancy that needs to be pointed out. Can you find the discrepancy?
(...)

C-G, D-A, E-B, F-C, G-D, A-E, B-F#

I'm assuming the discrepancy you're speaking of is with the B-F# (contains a pitch not naturally occuring in the C scale)? So The B chord is the only natural C scale chord which does not include a (perfect) 5th.

And two more exercises...

C - G7 - E7 - Am - Dm - G - C

Transpose this to A major, and Db major!
(...)
If you have the time, also write down
*A major scale
* What notes the corresponding chords in the sequence will contain
(...)

The roman notations would be:

I - V7 - III7 - vi - ii - V - I

A major is:

A - B  - C# - D - E - F# - G# - (A)

Transposing to A major, we get:

A (A C# E) - E7 (E G# B D) - C#7 (C# E# G# B) - F#m (F# A C#) - Bm (B D F#) - E (E G# B) - A (A C# E)

Db major is:

Db - Eb - F - Gb - Ab - Bb - C - (Db)

Transposing to Db major, we get:

Db (Db F Ab) - Ab7 (Ab C Eb Gb) - F7 (F A C Eb) - Bbm (Bb Db F) - Ebm (Eb Gb Bb) - Ab (Ab C Eb) - Db (Db F Ab)


Ahh, that's it I think! I had a really great time doing those If I missed an exercise, let me know, I'll take care of it

[daniloperusina]

Very very good!!
You should buy yourself a drink now and celebrate what progress you've made!

Regarding the 7th step in the scale, yes it's the only step where a regular chord (major or minor) cannot be formed. And the fifth you get with B-F is a flattened 5th. Very good!!

Sometimes, confusion can arise at places like this, because different countries might have adopted different points of view.
B-D-F is indeed diminished. When one lowers the fifth, one writes -5. So it could also be called Bm-5.

A "fully diminished" chord adds one more note. Then it is a chord consisting of three minor thirds: B-D-F-Ab.

This is a very special chord! For Beethoven, for example, it could almost be said to be his signature chord!

It's a very dominant-sounding chord. Further, only three basic combinations are possible:
B-D-F-Ab; C-Eb-Gb-A; C#-E-G-Bb

because to go another half-step up, you get D-F-Ab-B, which has the same notes as the first one. How to "spell" the individual notes they contain is another matter, and it will be apparent from the harmonic situation where it appears.

It functions as a dominant. In many cases, where you'd want a dominant chord, you can "replace" it with it's appropriate diminished equivalent instead!

So, to try it, replace the E7 in our chord sequence with the B-D-F-Ab. But re-spell it so that the notes are called B-D-F-G#.

Question: Why G# and not Ab?

Question: If one would add the note F to a E7 chord, what number would we have to add? (just like we add the number 7 when we add the note D to a E chord)

[ggpianogg]

Hey

Regarding question 2; hmm, you mean a 5 note chord here right? I'd guess that we would call it C9, perhaps?

As for question 1; before I can answer it, I need to ask for a bit further explanation regarding the fully diminished chords. From your last post:

(...)
In many cases, where you'd want a dominant chord, you can "replace" it with it's appropriate diminished equivalent instead!

So, to try it, replace the E7 in our chord sequence with the B-D-F-Ab. But re-spell it so that the notes are called B-D-F-G#.
(...)

Question for you here: what is it that makes B-D-F-G# the equivelant of the E7? I can see that B D G# pitches are shared, but doesn't it have to also share the E note for it to be the equivelant? Or are we basing this equivelancy on the fact that F pulls to E? I'm not sure, thanks in advance for explaining

[daniloperusina]

In a hurry, have to run...
Yes, C9 is correct!! But we mean E9, of course! F is the 9th to the E chord. It's not called 2nd, because it's usual placement is more than an octave above the lowest E in the chord!

More, the "normal" 9th is always a whole-tone up. That is, E9 has F#, not F. This is regardless of what key it appears in. So, to add an F to an E chord, we have to call it E with flattened 9th. Eb9! with b referring to the 9th, not to the E.

Q1: the proof of the equivalence is to play them. You hear that our diminished chord pulls towards Am as strongly as E7 does. It replaces E7 as a dominant! The deduction one makes from this is that this diminished chord is a E7 (E G# B D) with flattened 9th (E G# B D F) and without the root-note E (G# B D F).

Do you follow this?

If you do, try to do the same with our "transposed" chord sequences!
A major: replace C#7 with C#7b9 without root-note
Db major: replace F7 with F7b9 without root-note

Best of luck! If it's incomprehensible, I'll explain further later!

And play all these things! No explanation is as good as hearing how they sound!
Now I'm off (I have to go to teach, imagine:))

[ggpianogg]

You must really love your job

Do you teach privately at your student's homes or do you teach at a sort of music school?

As for your post - crystal clear!  It took some playing around on the keyboard but it's so evident you can't really miss it

[daniloperusina]

I do both, and also play concerts. Kinda' busy...
But how could I not love it?

I forgot to tell you, good & clever student, that it was supposed to be an assignement in there, namely:

In A major and Db major, how will those "replacement" chords, those diminished chords, be spelled? What will the notes that they contained be called? Can you spell them correctly?

 

[ggpianogg]

Hi Danilo!

I thought about it for some time and I'm not sure if this isn't in a way a trick question? Going back to post #78 for a bit:

(...)
So, to try it, replace the E7 in our chord sequence with the B-D-F-Ab. But re-spell it so that the notes are called B-D-F-G#.

Question: Why G# and not Ab?
(...)

Shouldn't it actually be spelled with the Ab instead of G#? I mean, it's supposed to be a seventh after all, so it would make sense to have an interval of B-A rather than B-G (with the proper accidentals)? It's either a trick question or I'm missing something big!

Hmm or maybe actually this is the point; since we are 'replacing' the dominant with the diminished chord, we want to point out that this is a replacement by using G# instead of Ab, as it's enharmonic equivelant? <scratching head> ;-)

[daniloperusina]

[Edit]
No, it wasn't a trick question!
On the other hand it got me thinking...
I have to go to the books, 'cause I might have gone a bit astray here.
So you might be right, and I might have been wrong!

I'll keep you updated.

[ggpianogg]

Hi Danilo!

Yesterday my ISP had some issues and I had no access to the internet, I managed to read your post before you edited it but it was hard to grasp on my relatively small cellphone window! I was looking forward to the lecture this morning Good luck over there, I'll read around about the Fully Diminished Chords too, might find something out as well

[daniloperusina]

I caught myself in a trap!
Do see what you can find out elsewhere.
In the meantime, I haven't found anything that contradicts neither of us.
So, at least for now, you decide for yourself!

We have two options here, and both seem to be valid.
#1 View it as the diminished seventh chord on the vii step in the scale.
Then it will be B-D-F-Ab.
#2 View it as the Dominant flattened 9th without root to A minor.
Then it will be B-D-F-G#. (=formed from E7b9 w/o root)

(On a side-note: I have avoided so far talking about minor scales and harmony, because they are more complex than major scales, but the a-minor harmonic scale goes like this:
A-B-C-D-E-F-G#. The vii7 of that scale would be G#-B-D-F, so there's yet another view-point!)

From a learning-point-of-view, I think we can use this to our advantage! We have two cases, both of which can be argued for: a viib7 (diminished 7th on vii step) as well as a dominant7b9 w/o root (from the iii step, but the note iii is left out) leading to vi (a-minor here).

Can you do the same two deductions in the A major and the Db major examples above?
You should be able to come up with two possible spellings there as well!

[smj9195]

WOW, a lot of replys here,
anyhow,
before trying to play the piece, try to listen to some good players in the internet and understand the piece.

[daniloperusina]

And the most important thing from the post I erased is:
The diminished 7th chord is a rare bird in the world of harmony!
It's a totally symmetrical chord. That is, the intervals between the four notes it consists of are exactly the same! = minor3rd + minor3rd + minor3rd.

The book I consulted just now basically explains that it is sometimes difficult to exactly determine what function it is actually performing in a specific chord-sequence. And the spelling is therefore not always apparent.

It is a very dominant-sounding chord, that requires a "tonic" to follow.
(To use a more proper language: The chord is strongly dissonant and requires resolution)

The interesting thing is how it can be resolved! A dominant chord, say E7, basically only wants to resolve into a A minor or A major chord. But the diminished 7th, because of it's perfectly symmetrical shape, will resolve into no less than eight "tonics".

To understand this perfectly, we just concluded above that it can be viewed as the viib7 chord in a major scale or the vii7 in a harmonic-minor scale. But since it is perfectly symmetrical, any of it's four notes could be the vii step in any major or harmonic-minor scale.

B is vii in C major and C minor
D is vii in Eb major and Eb minor
F is vii in Gb major and Gb minor*
G# is vii in A major and A minor

Sit down and play this chord followed by any of the above, and you'll see!

*Gb minor is rarely used. Instead, it's enharmonic equivalent, F# minor, is more common. Then the note F would be re-spelled E# to be the vii step in the F# harmonic-minor scale.

(To hear it as clearly as possible: when resolving into C, play bass-treble BDFAb; to resolve into Eb, play bass-treble DFAbB; to resolve into Gb (or F#), play bass-treble FAbCb*Ebb* etc..

*another re-spelling, judged by the harmonic context )

[sashaco]

The C Major Invention was mentioned above as a good learning piece for some of these principles, and indeed, there is probably no better.  Notice that it moves to G from C, stays there a good long while, and instead of returning to C moves to a minor (which of course is C in another guise.)  From there though, it moves to to C in a 4 chord sequence only to move immediately to F major!  Although it returns fully to C only in the last bar and a half, we are nonetheless entirely at home there, because the key of F major has, in effect, taken us "a little too far."  Bach overshoots the return to C and that gives us a balanced feeling when we return to to it completely.  Pretty cool, no?

[dss62467]

Looks to me like you are just pretending to play as the "demo" is going.   

[daniloperusina]

Looks to me like you are just pretending to play as the "demo" is going.  

What an incredibly stupid remark...

[ggpianogg]

Hi guys,
Hi Danilo!

I apologize for my slightly lowered participation today and yesterday, my ISP still hasn't established my internet connection back so my ability to use the forum is very limited. Everything will be back to normal tomorrow evening hopefully (cellphone at the moment).

I have printed the last two pages so I can read them without internet connection and I have a question which I hope you may be able to clarify for me (this is directly related to your last 'assignment' in a sort of way):  

say we have E7. We add flattened 9, then remove the tonic. What we are left with is G#-B-D-F. And my question is: why do we turn it and call it B-D-F-G# (moving the G# to the front)? I was sure I understood it before but now I'm not positive anymore (sorry I'm not going into more detail to explain my doubts, it takes me a looong time to write this post!). Thanks in advance and have a good night!!

[daniloperusina]

Don't worry, your doubt is very clear and well justified!

First, in a sense it doesn't matter if we give the notes as
B D F G#
D F G# B
F G# B D
G# B D F

because, as with any chord, it's the "same" chord as long as those four notes are played together.

Second, we can't give a good argument for any specific order we'd like them to be in, bass to treble, without looking at the specific composition we are talking about at the moment, and what comes right before and right after we play this chord. It could be an instance where the order, bass to treble, G# B D F will lead us better to whatever comes after, than any of the other orders.

At your keyboard, play the chord sequence and try for yourself which one you like best! It will also depend on how exactly you play your G7 and A minor chords that surround it.
For example, a G7 chord can be, bass to treble
G B D F
B D F G
D F G B
etc

They are all G7. For clarification, we indicate the bass note with: "name of chord"/bass note. That is,
B D F G
we call G7/B, so that we know that the note B is the lowest note.
G7 (or any other chord) does not have to have the "root" note (G in this case) as the bass-note.

In one of the chord-sequences above, I gave you the chord C/G. That is, C major chord with the note G in the bass. That is a very special case, and we'll go into that very soon!

Does it make it any clearer?
 

[daniloperusina]

How about this:
Play the chords like this, bass-treble:

CEG - BDFG - BDFG# - ACEA

and then

CEG - GBDF - G#BDF - ACE

We have here two different voice-leadings.
The first example lets the note G# as the top treble voice lead to the note A a semi-tone up.
The bass goes from B down a whole-tone to A.

The second example lets the bass move up a semi-tone from G# to A, while the treble moves down a semi-tone from F to E.

Any clarification?

[ggpianogg]

Morning! (still cellphone)

Your post number 93 is crystal clear in itself, thanks for clarifying/crystalizing :-) it has, however, presented a new dilemma for me:

Let's take the case where we spell B D F Ab instead of G#. We have E7 (E G# B D). We add a diminished 7th on top of the vii step in the scale (so in this case, the vii step would be G# - A major scale). F would be the diminished 7th here, so we've got G# B D F. Everything is looking fine, but when we ''move'' the G# to the front, making it B D F G#, suddenly we no longer have an obvious 7th over here (the distance between B and G would technically be a 6th). To ''see'' the seventh, we sort of have to 'count' starting from G# and move up to F. So in this case, aren't we complicating things? Or is there something I'm missing out on?

I have noticed your post #94 and will get back to it soon, gotta run to work! :-) (I love my job too )

[EDIT] P.S. I realize that depending on the harmonic function of the chord in some cases it might be necessary to move the G# to the front (invert it, tha's what we would call it?). In this case, however, I'm only speaking about the spelling of the chord when there is no real function taken under consideration.

[ggpianogg]

How about this:
Play the chords like this, bass-treble:

CEG - BDFG - BDFG# - ACEA

and then

CEG - GBDF - G#BDF - ACE

We have here two different voice-leadings.
The first example lets the note G# as the top treble voice lead to the note A a semi-tone up.
The bass goes from B down a whole-tone to A.

The second example lets the bass move up a semi-tone from G# to A, while the treble moves down a semi-tone from F to E.

Any clarification?

Yes, this post has been very helpful. I can see now that the way we arrange pitches in a given chord will have an impact on how a chord progression is going to sound. I don't have my keyboard at hand at the moment unfortunately to check this in pratice but I can 'hear' the difference more or less in my head. The top and bottom pitches definitely seem to be the most defining to how everything is going to sound

[daniloperusina]

Yes, this post has been very helpful. I can see now that the way we arrange pitches in a given chord will have an impact on how a chord progression is going to sound. I don't have my keyboard at hand at the moment unfortunately to check this in pratice but I can 'hear' the difference more or less in my head. The top and bottom pitches definitely seem to be the most defining to how everything is going to sound

There's two excellent observations!
The sentence "....the way we arrange pitches in a given chord..." is absolutely true!
While I would not swear by "The top and bottom [...] seem to be the most defining..", it's at least true enough to be a valid statement! (I mean, the middle voices will mean a lot too)

To give you a practical example, a supreme one, of the latter statement, look, listen and try your hand at the three Bach "Two-part Inventions" suggested above. They contain only two voices, so they are only top and bottom.

[jcabraham]

I'd like to thank the OP for *not* having gone straight to a music teacher in the first place. This has been a very educational thread!

[ggpianogg]

Haha, yes I'm also glad I didn't have these issues explained by a teacher

Unfortunately, I had to choose between: taking piano lessons and not buying a decent piano for some time now (and keep playing my 4-octave 50$ keyboard with no weighted keys, on a shaky stand), or get a decent piano (even if digital for now) and wait at least a few more months before getting a teacher. I opted for option 2) Should have the piano in around 2 weeks!