#ii and #vi diminished sevenths

[netmuzik]

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What is the origin of the #ii and #vi diminished sevenths (#iio7 and #vio7)? For example, the bIII and bVI are borrowed from the parallel minor, and a secondary dominant serves to tonicize the chord that follows it (usually). So where do the #iio7 and #vio7 come from, how are they best prepared, and how do they resolve? I noticed they are enharmonically equivalent to certain secondary leading tone chords. However, they are not treated in this manner. (No, I am not mistaking these chords for other, more well-known ones. See here: http://www.musictheory.net/utilities/html/id95_en.html (http://www.musictheory.net/utilities/html/id95_en.html))

[llatham]

What is the origin of the #ii and #vi diminished sevenths (#iio7 and #vio7)? For example, the bIII and bVI are borrowed from the parallel minor, and a secondary dominant serves to tonicize the chord that follows it (usually). So where do the #iio7 and #vio7 come from, how are they best prepared, and how do they resolve? I noticed they are enharmonically equivalent to certain secondary leading tone chords. However, they are not treated in this manner. (No, I am not mistaking these chords for other, more well-known ones. See here: http://www.musictheory.net/utilities/html/id95_en.html)

In the university setting in which I teach, these chords are named "Common Tone Diminished 7ths" (Kostka/Payne "Tonal Harmony") which are labeled cto7. The differentiation is made to distinguish these from secondary chords as you mention.

For the benefit of other readers:

C-D#-F#-A in the key of C is a cto7 when it embellishes a I chord.

This chord is the same as F#o7/C - or viio7/V (or in 2nd inversion with the C in the bass) and D#o7/C - or viio7/iii (in 3rd inversion, which would be rare in classical music though because it would lead to a iii chord in 2nd inversion, which is astylistic).

But it doesn't have a secondary function (as a "leading tone chord").

Instead, its origin is as what many theorists call a "linear chord" - that is, you might want to think of it as a chord that "results" from voices moving, rather than from functional chord progressions. In fact, many texts, in addition to the different nomenclature, also put the symbol in parentheses to show it has a non-functional or embellishing raison d'etre.

So:
C - A - C
G - F# - G
E - D# - E
C - C - C

Notice how the two middle parts are chromatic lower neighbors. That's what this chord is - a "neighboring" chord. They call it a "common tone o7" because it shares a common tone with the root of the chord it embellishes. It should be noted that this chord is typically spelled as lower chromatic neighbors as above which causes it to "look like" a "II" chord - #iio7. That's why I'm not crazy about using Roman Numerals in this way. We call a D chord in C that functions as a V of the V chord "V/V" - not "II" or "II something". Likewise, I like the "cto7" or "Neighboring o7" designations - but I understand if you're trying to tell someone what notes are being used, you need some number!

BTW, often, the A above will simply be an upper neighbor of the G, rather than jumping down and up from and to the C.

Probably one of the most recognizable uses of this chord in classical music is in "The Waltz of the Flowers" from Tchaikovsky's Nutcracker Ballet.

In Jazz, one often encounters something like:
C - C
F# - G
D# - E
A - C

To make "vio7" to I (or the A may move to Bb to make I7, or to A for C6, etc.) But it's not "really" a "vi", and, from above, it's not "really" a "II" chord of some type. It's a linear embellishing chord. Jazz players don't like this though because putting "CTo7" in a chart isn't as informative as "Ao7" or "D#o7/A".

I should mention too that too many people get hung up on the spelling, and that's partly why they have a hard time understanding the origin of this chord as linear rather than "chordal".

So "#iio7" embellishes I, and #vio7" embellishes V - in C:
G - E - G
D - C# - D
B - A# - B
G - G - G

So see - it is spelled as "A#o7" so it "looks like" #vi and that's where we get the name.

But you could easily encounter this chord as Bb and Db, making it a "iiio7" which only further serves to confuse the issue. So that's why many theorists have adopted this alternate naming system, such that a cto7 could be any enharmonic spelling, just so it embellishes the chord whose root it shares.

By far - especially in classical music, cto7 to I and V are the most common and they only embellish Major triads.

As far as approaching them, the name says it all "neighboring" and "common tone".

So they either arrive at, or depart from, or, most commonly, are found in between two of the chord with which they share a root.

C-D#-F#-A is going to depart from C (I), lead to C, or be found between to C chords (or C7s etc.) typically.

The "Basie" cadence (or tag) is like this:

C - C - C
F - F# - G
D - D# - E
(A - A - A)

Or in your "country licks" that go:
C - D - D# - E
E - F - F# - G

up or down, the D# - F# (or Eb Gb) is - you guessed it, cto7:
C - D - D# - E
G - G# - A - C
E - F - F# - G
C - C - C - C

(chord 2 is like an enharmonically spelled iio7)

HTH,
Steve

[nuffink]

In jaath theory...

The following act as diatonic functioning and usually take the key of the moment...

I dim 7 resolves to I Maj 7
#I dim 7 resolves to II-7 (or V with 5th in bass)
bIII dim 7 resolves to II-7
#II dim 7 resolves to III-7 (or I with 3rd in bass)
#IV dim 7 resolves to V7
V dim 7 resolves to V7
#V dim 7 resolves to VI-7
bVI dim 7 resolves to V7

Whereas these act as non-diatonic functioning and usually take the Whole-half diminished...

bII dim 7 goes to, but does not resolve to I Maj7
bV dim 7 goes to, but does not resolve to IV Maj7
bVI dim 7 goes to, but does not resolve to V7
bVII dim 7 goes to, but does not resolve to VI-7
#VI dim 7 goes to, but does not resolve to VII-7(b5)

There are (as ever with jaath) a fair few other possible chord scales which get the odd run out by more adventurous players.

Courtesy Hiroaki Honshuku