B Diminished

So we talked about all the diatonic C Major chords except for B Diminished. Time to cover it now.

Diminished chords are comprised of a root, its minor third, and its diminished 5th. The distance between the minor third and the diminished fifth is another minor third, so the chord is composed of 2 minor thirds and 1 diminished fifth (and their inverses).

Open Position B Diminished Triad

|-|i|-|-|-| F
|-|-|-|p|-| D
|-|-|-|-|-| x
|-|-|-|r|-| F
|-|-|m|-|-| B
|-|-|-|-|-|
 0 1 2 3 4

You'll need to use your ring finger to mute the 3rd string when you strum this chord, so you don't hear the open G string. Diminished triads tend to have pretty nasty shapes, and even vanilla B dim is no different. If it's difficult, you can drop the high F with the index finger.

Harmonic Function: Leading Chord

B dim is diatonic to the key of C Major, using its 7th scale degree as the root note. Thus, it is called the vii or vii° chord. The ° indicates diminished, but you have to be careful - we are dealing with the diminished triad here, not the diminished seventh. The Diminished 7th chord has two variations - half and full. Half is indicated with a slash through the ° symbol.

The vii chord is called the Leading Chord. Harmonically, it has a dominant function.

   C     F/C   Bdim     C
   I      IV    vii°    I
e--0------1------1------0------
b--1------1------3------1------
g--0------2------x------0------
d--2------3------3------2------
a--3------3------2------3------
e------------------------------

Full Circle Progression

  C   F   Bdim Em  Am  Dm  G   C
  I   IV  vii  iii vi  ii  V   I
e-0---1---1----0---0---1---3---0--
b-1---1---3----0---1---3---3---1--
g-0---2---x----0---2---2---0---0--
d-2---3---3----2---2---0---0---2--
a-3-------2----2---0-------2---3--
e--------------0-----------3------

Now that we know the vii chord, we can play the full circle progression in the key of C Major.

Dominant Example

Let's try it as the main dominant-function chord in a progression:

  C   F   Bdim C
  I   IV  vii  I
e-0---1---1----0--
b-1---1---3----1--
g-0---2---x----0--
d-2---3---3----2--
a-3-------2----3--
e-----------------

Rather strong resolution, especially considering the vii itself is so tense with its diminished fifth interval.

Diminished Fifth Interval

The vii chord is the only diatonic chord in any major key to contain the diminished 5th interval. Remember that the most harmonic interval (other than an octave) is the perfect fifth, represented by the simple ratio of 3:2. By contrast, the diminished 5th has a ratio is 17:12. The smaller the denominator, the more harmonic the interval. Let's see all the intervals:

Interval Name	Ratio
m2	16:15
M2	9:8
m3	6:5
M3	5:4
P4	4:3
d5	45:32
P5	3:2
m6	8:5
M6	5:3
m7	9:5
M7	15:8

Using the denominator method of analyzing intervals, we get the following order from most harmonic to least: P5, P4, M6, M3, m3, m6, 7, M2, M7, d5. The d5 is the least harmonic, and it's quite apparent when playing the B dim chord. This means the vii chord not only has tension in the context of the tonality and its placement inside a progression, but it is also quite dissonant and tense in and of itself.