Hello, I was just reading a thread in theory and composition about dominant 7ths, and I am about to start writing mine out to learn for my grade 7. I was just wondering before i done them all is this one right? I want the Key of A so i have the notes E, G,D and B is that correct? Secondly can anyone help in explaining how diminished 7ths are formed etc? Thankyou.

Nearly right - it's G# not G.


Just a pile of minor thirds or augmented seconds - G# B D F for example. There are only three of them, so you should be able to work out the other two.

G# is correct in the keys of A major and A minor. You could have the chord as given in G major or D.

Try the sequences

D C# D
B A- A
G E- F#
E A- D [A higher than E and D to avoid parallel motion to a perfect interval
*
and

D------- C----- B
A-. B-- G- A- G
F# G-- E- F# D
B- E-- A- D-- G [E lower than B and A; D lower than A and G
* - * --- *

The asterisks mark minor seventh chords. They resolve to their relative sub-dominant in the same way as dominants do to tonics, but now that I have checked Piston, I find that he doesn't call them secondary dominants, as I wrote in an earlier version of this post.

It is true that there are only three distinct diminished seventh chords. However, for the purpose of theory, it is important to spell them correctly using the letter names and accidentals that are appropriate for the key.

For example, if you are in the key of A minor, you should spell the diminished seventh chords as G#-B-D-F and not Ab-B-D-F.

Here is how you spell diminished seventh chords, assuming that you are using key signatures:
1) In minor keys, the leading note is the root of the chord, and then you simply stack the notes in 3rds. This gives you the fully diminished seventh chord, e.g. G#-B-D-F in A minor.

2) In major keys, the leading note is the root of the chord. Stacking the notes in 3rds gives you a half diminished seventh chord (G#-B-D-F# in A major). For a fully diminished seventh chord, you would have to lower the seventh of the chord with an accidental (change the F# into F-natural in A major).



The term "relative sub-dominant" is somewhat confusing. Walter Piston does not refer to the chords marked with asterisks as secondary dominants precisely because of their being minor seventh chords.

Only chords of dominant function can be called secondary dominants. Chords of dominant function include dominant seventh chords, half diminished seventh chords and fully diminished seventh chords.

The correct term for kenm's progression is a "descending/falling fifth progression" as the roots of the chords are descending in fifths. It looks like a III7-VI7-II7-V7-I progression in G major.

Incidentally, it is possible to turn kenm's chords into secondary dominants by adding a D# to the first chord, a G# to the second chord, and a C# to the third chord.

Thanks for the correction. If that chord occurred on the dominant in a minor key, the flat 3rd would be in the key signature, and it seems a bit strange that a 7th on the dominant can't, because of convention, be called a dominant 7th. It seems that the need for the 3rd of the chord to resolve to the tonic is the only reason for it to be sharpened in a minor key. Of course conventional resolution of the flat 3rd version would give a rising tone onto the tonic, which would sound odd, but a rising bass of dominant and tonic could combine with all other parts falling, to break no rule of which I am aware.

By minor 7th I mean the interval of four tones and two diatonic semitones, not the chord containing the minor 3rd; our usual nomenclature seems to be ambiguous here. How would you describe the chord CFGBb? It could occur with the F as an apoggiatura resolving to E, the other notes suspended.

It seems that there are variations in the systems people use to name chords, which can sometimes cause confusion. "Half-diminished" is a name I have come across only in a jazz context, but I presume you mean minor 7th, diminished 5th, minor 3rd, the diatonic 3-5-7 chord on the leading note of a major key. I couldn't find the name in Piston, though he shows the chord at the beginning of his chapter on non-dominant harmony. My ear tells me the Wagner uses it with a dominant function in the "Rhinegold" leitmotiv, but I have no score to confirm this and don't know whether a bass root to make it a 9th or a 13th is present there.

The key signature alone doesn't provide all the notes of a minor scale. In minor, the subtonic is raised to become the leading-note in order to strengthen the pull to the tonic. This can only be done by the use of an accidental.

The term "dominant chord" and "dominant seventh chord" means something more than just a triad or seventh chord built on the dominant scale-degree. It signifies a specific harmonic function, that of moving onto the tonic chord or a tonic substitute (e.g. VI, as in an interrupted cadence). The leading-note is absolutely necessary in any chord of dominant function.



I thought you meant a minor seventh chord, not the minor seventh interval. A minor seventh chord consists of these intervals above the root: minor 3rd, perfect 5th and minor 7th. Out of any context, the sonority C-F-G-Bb is not a chord in tonal harmony as the notes cannot be stacked in 3rds no matter how you reorder them. However, within a musical phrase, it is likely a dominant seventh chord of F major or F minor, with the note F being a suspension or appoggiatura. The note F would be expected to resolve downward by step to an E-natural.



Half diminished seventh chord and fully diminished seventh chords are found in tonal music. The half diminished seventh is used in major key only. Although the fully diminished seventh originates from the minor key, it is used in both major and minor keys.

Some theorists long before Piston (Rameau comes to my mind!) have justified both types of diminished seventh chords as dominant ninth chord with the root removed. That is why diminished seventh chords are of dominant function.

If you are serious about learning harmony, I would suggest that you put the Piston text aside and get something better. The Piston book might have been a useful resource many decades ago, but its approach is seen as rather outdated now. The main problem is that Piston looks at chords in a very literal way.

I'm not very serious about common practice harmony and I was aware that Piston was somewhat limited, because while the period he reckons to cover is "roughly the eighteenth and ninteenth centuries", he shies away from Faure and Debussy, mentioning them but not quoting from them.

What I would like to find is an elaboration of Hindemith's method of harmonic analysis, built on the psycho-acoustics of consonance and dissonance, rather than his simplistic ranking of the intervals, and avoiding his hypothesis of second-order difference tones (between ear-generated first-order difference tones), for which I know no experimental justification. It would be a huge task to construct such an edifice. The influences of timbre, register and tuning on dissonance are pretty well understood by the psycho-acoustic researchers but I'm not sure whether their investigations of voice-leading have gone as far as would be necessary to improve on traditional rules.

How about perfect 11th on C (in the key of F major) with 3rd and 9th omitted? The F appoggiatura goes to E (that's why the E is omitted) and an F triad follows.

Like I said, the problem with the Piston harmony text is his approach. There is nothing wrong with leaving out the music from the late 19th and early 20th centuries. By then, the harmonic language has become so different. In order to do full justice to the music of that time, different analytical methods must be applied. This is obviously beyond the scope of a standard-size textbook. Some textbooks like the Piston omit that music altogether. Some textbooks scratch the surface only. A separate book is needed if that repertoire is to be examined in detail.

There is a vast literature on psycho-acoustics, and music perception happens to be a fast-growing subfield in music theory. You should go to a reputable music library and browse at the latest music theory journals. You should also take a look at Hindemith's treatise, which is not difficult to find in a good library. You may even see a copy in a good music store.

I don't understand your question about an 11th chord on C with the 3rd and 9th omitted. If the F goes down a step to E, then it is a suspension or appoggiatura. There is no difference in nomenclature whether the F appears at a perfect 4th, perfect 11th or perfect 18th above the bass note C. If the F does not resolve to the E, then the F may be regarded as a pedal note, perhaps staying in the same voice when the F triad comes.

If I remember correctly, Piston mentions 11th chord in his book. But this is not a valid concept in tonal harmony (maybe valid in jazz harmony, which I know nothing about).

Dininished sevenths are formed by making up minor thirds of that key. For example, a diminished 7th in D would be-
D, F, Ab, B, D
Hope this helps,
David.

I have just re-read the copy in my own library of Part I ("Theory"), of "The Craft of Musical Composition" (which I presume is what we both mean), for the first time since I studied psycho-acoustics in the period 1997 to 2002. This is when I realised that Hindemith's excellent principles needed (moderate) emendation on the basis of more recent research and understanding.

The main point of my comment was that C, F, G, and Bb could, by raising the F by an octave, be put into a series of notes separated by thirds, all of which belong to a key, which you had stated to be impossible, and the reason that it was not a chord in tonal harmony. Do you add the criterion that the collection of notes creating the thirds must have no omissions? That would make GBDF a chord, but GBF not, even though it is used for the same dominant function. Either way, I don't yet see a rule that is both clear and helpful, but I am not particularly interested in analysis for its own sake, only to help me recreate interesting sonorities from all eras, and the nomenclature of traditional harmony sometimes seems unnecessarily rigid.

This is not 100% correct.

Diminished seventh chord is formed by stacking minor thirds, like the example driftwoord mentions: D-F-Ab-B.

However, this is a diminished seventh chord on D. It is erroneous to call this a diminished seventh chord in D. Neither the key of D major nor D minor contains all four notes; therefore, this chord does not belong to the key of D.

If you want to write a diminished seventh chord in a key-specific context, you should start from the leading note, then stack minor thirds above it. In the key of D, the chord is written as C#-E-G-Bb.

In tonal music, it is possible to write incomplete triads and chords, such as the G-B-F example that you have mentioned. The missing D is implied, of course. The concept of implied tone is perhaps the most amazing thing about tonal harmony. A note does not have to be spelled out literally, and yet its presence is understood.

The concept of implied tone is not as readily applicable in atonal harmony.

You are right in saying that it is possible to interpret the C-F-G-Bb sonority as an incomplete 11th chord, with the 3rd and 9th of the chord omitted. However, this is not a satisfactory interpretation. The biggest weakness of this interpretation is the missing 3rd. You might argue that this was done to avoid an unpleasant clash created by the E and F. But, if the E and F cannot be sounded simultaneously, then one of them must be foreign to the chord? Furthermore, without the 3rd, the quality of the chord becomes ambiguous, i.e. is this sonority closer to a dominant seventh chord or a minor seventh chord?

As I said, there is really no need to continue to stack the notes in thirds all the way up to the 11th. A more elegant way to interpret this sonority is to treat it as a dominant seventh with F being a suspension or appoggiatura or pedal note. And I bet, in all tonal repertoire, there isn't a single example of a real 11th chord, complete or incomplete!

musictheory.net

It completely augmented my knowledge of music theory prior to taking AP Music Theory back in high school (for college/university credit of course)

That's an undecidable proposition, since neither "tonal music" nor "real chord" are categories on the boundaries of which all musicians, or even all analysts, would agree.

You are right. That's the beauty about analytical discourse. We revisit something over and over again, coming up with new definitions, new understanding of old concepts, etc.

But still, I'd be interested to see any example of functional 11th chord in tonal music composed during the Baroque, Classical or Romantic periods, if you know of any. The word "functional" might be slightly better than "real".

I recommend this website for my aural skills students who wish to do extra practice on interval and chord identification.

However, I don't encourage to use the website for other purposes as some of the ideas are not quite correct. For example, the author accepts these as valid progressions for an imperfect authentic cadence: viio-I, viio6-I, V6-I.

Strictly speaking, however, all authentic cadences must have the V(7) and I chords in root position. The term perfect and imperfect denotes the melodic quality of the highest voice.

N.B. In this post, I am adopting American terminology and chord labelling.

Please will you either explain it or give examples of your chords translated into note names and registers. Keeping up with changing fashions in UK chord notation (in none of which can I recall a function for letter "o") has kept me occupied so far.

Sure. The "o" represents diminished quality. It should be written for all diminished triads and all fully-diminished seventh chords if the user adopts both uppercase and lowercase roman numerals.
The "o" is supposed to be in superscript.

The "o" is not used if the user adopts only uppercase roman numerals.

viio = the leading tone triad in root position
viio6 = the leading tone triad in first inversion
V6 = the dominant triad in first inversion

The "6" is supposed to be in superscript.

Thanks.