There is a lot of confusion here.
So let me sort it out.
The source of all the confusion is very simple: There are two ways to build triads/chords.
One is to start with any note and add the appropriate thirds. For instance, start on C, add a major third (E) and then a minor third (G) and you have a major triad – called C major, because it starts on C. Start on Bb, add a major third, then a minor third: BbDF and again you have a major chord, this time Bb major since it starts in Bb. If you want a Seventh chord, start with any note, add a major third, a minor third and a minor third (or a minor 7th if you are counting from the starting note): CEGBb is C7th (because it starts on C), GBDF is G7th and so on.
If you want a diminished 7th, then you need to add to any starting note a minor third, another minor third, and yet another minor third (or a diminished 7th counting from the starting note): CEbGbBbb is the Cdim7 chord and You must build a chord using only the notes of the scale in question.
This is what faulty was suggesting and he is correct of course.
However there is another way. And that is to consider the scale from which the chords are built. Work this way, and all confusions and contradictions will disappear.
(And you will see where faulty went wrong)
Consider the C major scale. If you build triads on each note of the C major scale limiting yourself only to the notes of the C major scale, this is what you get:
Degree of the scale Note triad type chord type
I – Tonic C CEG major CEGB major 7th
II – Supertonic D DFA minor DFAC minor 7th
III – Mediant E EGB minor EGBD minor 7th
IV – Subdominant F FAC major FACE major 7th
V – Dominant G GBD major GBDF seventh
VI – Submediant A ACE minor ACEG minor 7th
VII – Leading note B BDF diminished BDFA minor 7th -5
(tritone)
If you examine this table there are three interesting observations concerning this discussion:
1. Major triads, major 7th chords and minor 7th chords can be quite easily generated from a number of notes in the scale.
2. If you limit yourself only to the notes of the major scale, you can only generate one diminished triad from the leading note, and one seventh chord from the dominant note. There is no other way to come by the diminished triad or the seventh chord using only the notes of a major scale.
3. If you are using only the notes of the major scale these are all the chords/triads you will be able to generate: major, minor, diminished triads, major 7th, minor 7th and 7th chords. This means that you cannot possibly generate a diminished 7th chord from a major scale, for instance.
Now let us do the same thing for the harmonic minor scale: (I will use A minor as an example).
Degree of the scale Note triad type chord type
I – Tonic A ACE minor ACEG minor 7th
II – Supertonic B BDF diminished BDFA minor 7th -5
III – Mediant C CEG major CEGB major 7th
IV – Subdominant D DFA minor DFAC minor 7th
V – Dominant E EG#B major EG#BD seventh
VI – Submediant F FAC major FACE major 7th
VII – Leading note G# G#BD diminished G#BDF diminished 7th
(tritone)
Sharping the leading note and changing the order of the notes has some dramatic effects on the generation of chords. Observe:
1. Now there are two ways of generating diminished triads (tritones): from the supertonic and the leading note (in the major scale only the leading note could do so).
2. The seventh chord – as in the major scale – can only be generated from the dominant.
3. A new chord – the diminished seventh – can now be generated from the leading note (and only from the leading note).
There are several other interesting observations to be made, but for the purposes of your question now we have the necessary background to clear up the confusion.
1. What is the diminished seventh arpeggio for E minor?
There are two answers to this question depending on the way you look at it. If you look at chord formation as adding thirds to an arbitrary note, the diminished seventh arpeggio for Em is going to be E – Bb – Gb – A. (Because you assume that you will be starting from E - a very wrong assumption as we will see next).
However, if you look at this question as: What is the diminished arpeggio generated by using only the notes of the E minor scale, then the answer is quite different. It is going to be D# - F# - A – C. From the above, we know that we can only generate a diminished seventh chord from the leading note of a minor scale. In the case of E minor, it is D# the leading note. Likewise it must only contain the notes present in the E minor scale, which is the case with D# - F# - A – C.
Edim7, in spite of its name is completely unrelated to E minor: E – Bb – Gb – A contains only two notes that belong to E minor. Bb and Gb are not part of it at all. If so, what is the scale that will generate the Edim7 chord? Easy. The scale which has E as its leading note (it must be a minor scale, since major scales do not have diminished 7th chords). Exactly: F minor.
At this point I must disagree with Johnnypiano that this an useless discussion. Quite the opposite. The above knowledge is fundamental in order to make a harmonic analysis of your piece, and to truly understand what is going on. It is the whole point of learning and being conversant with scales and arpeggios. Making these connections should precede any practice at the piano. When you look at an Edim7 chord you should know that the tonal centre for this chord is F minor, not E minor. Likewise, D#dim7 will have as tonal centre E minor. This is the reason why exams are set up the wasy they are. You learn the diminished 7th arpeggios in relation to their tonal centres, not in a vacuum, by themselves. Likewise you will learn the seventh chords as dominant 7ths, that is G7 has as its tonal centre C major, not G major (since the way to get a G7 chord is to build it on the dominant of C major).
Finally, the fingering:
General rule or arpeggios with black keys: Use thumb on white key. Use finger 3 and 4 on black keys (The fingering I use - which by the way is not the only possibility - is in brackets after the relevant note)
D# dim 7 arpeggio (that is, the E minor scale diminished seventh arpeggio)
RH - D# (3) – F# (4) – A (1) – C (2)
LH – D# (4) – F# (3) – A (1) – C (2)
Keep the same fingers on the same notes for the inversions.
Best wishes,
Bernhard.
Topic: IMPORTANT! Fingering for E Minor Dim 7th Arpeggios