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Dominant 7th chords are played for the 5th note of the scale which makes sense as the dominant plays a strong role in classical harmony. For example in key Fmajor the dominant 7th is a D7th chord in all its inversions. The diminished chords for the minor keys are played in the 7th note of the minor scale. For exammple in E minor the diminished 7th chord is D#diminshed 7th in all its inversions . why??

There seem to be several questions there, so here are several answers.

The dominant 7th in F major is C7, not D7. It is so because the C is the fifth (dominant) scale degree in the key of F (F is the first, or tonic). (F,G,A,Bb,C).

The seventh scale degree in E minor is D or D# (it varies), because D is the seventh note after E. (E,F#,G,A,B,C,D#). When you play a triad chord on the 7th scale degree, with the upper notes of the chord still being in key, it comes out as a fully diminished chord (D#,F#,A).

If that diminished chord is a 7th chord, it is D#,F#,A,C.

Note that the term "7th" is used here in two different senses- the seventh degree of a scale is the last note before you get to the octave and start repeating in a scale. But a "seventh chord" is a chord, starting on any degree of the scale of the current key, that has the named note a seventh above the root of the chord, whatever octave it's in.

For example, with all tones in the key of C major, you can have various 7th chords:
d7 D,F,A,C
G7 G,B,D,F (the 7th chord on the dominant of C)
a7 A,C,E,G
b7 B,D,F,A (the diminished 7th chord on the 7th scale degree)

looks like Joflah got there before me, but if you want more confusion... read on...




Correction... the Dominant 7th of F major is C7, and all inversions will have the name of the dominant note, or 'C'
C-E-G-Bb (C7)
E-G-Bb-C (C7 first inversion)
G-Bb-C-E (C7 second inversion)
Bb-C-E-G (C7 third inversion)

To the chord you are speaking of in E minor...

Same with E minor, although with the example you provided the harmonic minor is used, and since the 7th degree of the scale is D#, all references to this chord (the D#º7) (with notes D# - F# - A - C )will have D# in the name - no matter the inversion - as long as the home key is e minor.

but get this... in the key of G minor (again, using the harmonic minor), the chord has the same notes, although the spelling will be different (F#-A-C-Eb) (Eb is the equivalent of D#). I will have the name F#º7 in all its inversions.

and in the key of Bb harmonic minor, the 7th chord has the same notes, but again, the spelling is different (A-C-Eb-Gb) and the chord will be referred to as "Aº7" in all its inversions.

And finally, in the Db harmonic minor scenario, the same 7th chord (enharmonically) will have the spelling (C-Eb-Gb-Bbb -doubleflat!!).... where B doubleflat is the equivalent of A, and this will be called Cº7 in all its inversions.

D#º7, F#º7, Aº7, and Cº7 are equivalent *sounding* but reference differing home keys as indicated .

Forrest

it's a mess, yes?

Do you have the theory book that the RCM uses as basis of its theory exams? (Elementary Rudiments of Music - B. Wharram) If you work through the levels of that book then some of these things will already be more clear to you. One of the first things you do is identify the 5th note (Dominant note) in any scale, and later the Dominant 7 chord. They become totally familiar.

You mention two different things: 1. Dominant 7 2. diminished chord. Let's look at each in turn.

For 1. The Dominant chord is the chord that is built on the 5th note of that key, in triads, using the notes of that key. In F major, the 5th note is C. The Dominant chord is C E G Bb, also called C7 in letter name chords. CEG is a major triad. Bb is 7 notes up from C - it is a minor 7 from C. That Bb is also a minor 3rd above the G.

The Dominant 7 is the V7 chord (Roman Numeral V = 5), and it "likes to" move to the I chord, i.e. C7 to F in F major. That is, there is a strong impulse to do so. You are asking why.

There is a natural movement of V to I that our ear expects. That is one reason. Now in CEGBb, the E is a semitone below the F and it naturally wants to move up to the F. It is called the "leading tone" because it "leads" into F. You also have a "tritone". Play E Bb together and see how that makes you feel. Do the same with BF, GDb - These are all tritones. They feel "unsettled", and "wanting to resolve. When you play C7 to F, that uncomfortable interval settles into something comfortable. Your ear feels like it has taken off tight shoes. That's why it works.

So:
V wants to move I
the leading tone (E) wants to rise to the Tonic (F)
the tritone wants to resolve

2. Diminished chords
Take your C E G Bb again. I have highlighted the top three notes that are left if you omit the root. E G Bb form a diminished triad. It is also an "unsettled" kind of chord that wants to settle. You also have the tritone in it. It will resolve in a similar way to the dom7 chord.

You can expand that diminished triad by adding another minor third above the Bb. That is Db. Now you have the diminished 7 chord. The Db is the 7th note name up from E which is why it is also called a "seventh". All the types of 7th chords involve 4-note triads. Here we have E G Bb Db (4 notes)

There are only minor thirds in a dim7:
E(min3)G(min3)Bb(min3)Db
In fact, regardless of which note you start with on the bottom, you will only get minor thirds. It is a rather magical chord.

The dim7 is also unsettled. It also contains 2 tritones:
E Bb (or Bb E which can be respelled Bb Fb or A# E for purists)
G Db (ditto)

Because it contains two tritones, it is unsettled twice over, and wants to settle. Therefore when you resolve a dim7 (Edim7 to F, or E dim to F) you have that same "take off tight shoes) feeling.

Does this go toward the kinds of things you were wondering about?

that was an outstanding explanation. basically the diminished 7th in the minor key wants to settle to the minor key 1st note hometone. the root. tritones ive heard in the past. not sure i totally understand them. im at work so i dont have a piano but certainly uve peeked my curiosity and interst. i guess im the typical adult student. i love to intellectualize this stuff. playing it is the problem!! thsnks again

itsahobbie, I've noticed that you always mentioned the minor key in discussing the dim7. I'm curious about that.

In regards to tritones and other things, play with them at the piano, listening. Try playing CF# vs. CG. Play a minor chord C Eb G. Then lower the G so that you get C Eb Gb (think of sliding to a key to the left to lower something and aiming for a lower sound, so that you can get away from intellectualizing it). Treat the intervals and chords as toys.

I'm still learning myself and doing similar things.