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Difference between revisions of "B Diminished"

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So we talked about all the diatonic C Major chords except for B Diminished.  Time to cover it now.
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{{Top-Level Crumbs|1}}
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{{Lesson Crumbs|2}}
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{{Intermediate Lesson Crumbs|1}}
  
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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).
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In the [[Contents#Beginner|beginner lessons]] we talked about all the diatonic chords diatonic to C Major except ''B Diminished''.  Time to cover it now.
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 +
'''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 also minor third, so the chord is composed of 2 minor thirds and 1 diminished fifth. Diminished chords are often marked as using "dim" or {{dim}}, such as Bdim, B dim, or B{{dim}}.
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== PreReqs ==
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* [[C Major Chord]]
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* [[G Major Chord]]
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* [[Music Theory - Diatonic Chord Progressions]]
  
 
== Open Position B Diminished Triad ==
 
== Open Position B Diminished Triad ==
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{{crumbs|blue|1
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|B Diminished#Open Position B Diminished Triad|Open B dim
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|B Diminished#Harmonic Function: Leading Chord|Theory: Leading Chord
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|B Diminished#Full Circle Progression|Circle Prog
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|B Diminished#Diminished Fifth Interval|Dim 5th Interval}}
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'''B Diminished''' is composed of (B D F).  Here are the common voicings in or near open position:
  
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  |-|i|-|-|-| F
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{|
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  |-|-|-|p|-| D
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! Open Pos. !! 2nd Pos.
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  |-|-|-|-|-| x
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|-
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  |-|-|-|r|-| F
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|
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  |-|-|m|-|-| B
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'''F''' ||i|-|-|-|
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  |-|-|-|-|-|
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'''D''' ||-|-|p|-|
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  0 1 2 3 4
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''' '''  ||-|-|-|-|
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'''F''' ||-|-|r|-|
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'''B'''  ||-|m|-|-|
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''' ''' ||-|-|-|-|
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|
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''' '''  ||-|-|-|-|
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'''D'''  ||-|-|r|-|
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'''B'''  ||-|-|-|p|
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'''F''' ||-|-|m|-|
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'''B'''  ||-|i|-|-|
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''' ''' ||-|-|-|-|
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|}
  
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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 chords 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.
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Although B and D occur as open strings, the common open position voicing avoids using them.  The G string is typically muted, as it offers no notes from the chord until the 4th fret, which pulls us out of open position.  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.
 +
 
 +
The 2nd position shape is also a bit strange, at least in comparison to the common major and minor chords; however, it may seem a bit simpler to finger than the full open position chord.  Open position is generally preferred; however, as it includes a wider range of notes and retains open position alignment of the fingers to frets.
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 +
{{top}}
  
 
== Harmonic Function: Leading Chord ==
 
== Harmonic Function: Leading Chord ==
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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.
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{{crumbs|blue|2
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|B Diminished#Open Position B Diminished Triad|Open B dim
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|B Diminished#Harmonic Function: Leading Chord|Theory: Leading Chord
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|B Diminished#Full Circle Progression|Circle Prog
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|B Diminished#Diminished Fifth Interval|Dim 5th Interval}}
  
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The vii chord is called the ''Leading Chord''.  Harmonically, it has a dominant function.
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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{{dim}} chord''' (or vii or viio when the {{dim}} symbol cannot be made).  The {{dim}} symbol indicates diminished, but you have to be careful - we are dealing with the diminished triad here, not the [[7th Chords#Half Diminished|diminished 7th]].  The diminished 7th chord has two variations - half and full.  Half is indicated with a slash through the {{dim}} symbol (B{{hdim}}{{7}}).  Full uses the normal symbol (B{{dim}}{{7}}).
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<small>''Where the {{dim}} symbol cannot be made, such as on a standard keyboard without using special character codes, or to avoid ambiguity, you can use "dim" (ex. Bdim) to indicate the diminished quality of the chord.  Then a half diminished 7th can be written as Bm7b5''.</small>
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 +
The vii chord is called the '''leading chord'''.  Harmonically, it has a ''dominant'' function, sharing the leading tone and 2nd of the scale with the V chord (B and D in the key of C Major).
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 +
    C    F/C    Bdim    C
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    I      IV    viio    I
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E--0------1------1------0------
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B--1------1------3------1------
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G--0------2------x------0------
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D--2------3------3------2------
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A--3------3------2------3------
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E------------------------------
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{{top}}
  
 
== Full Circle Progression ==
 
== Full Circle Progression ==
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  C  F  Bdim Em  Am  Dm  G  C
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{{crumbs|blue|3
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  I  IV  vii  iii vi  ii  V  I
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|B Diminished#Open Position B Diminished Triad|Open B dim
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e-0---1---1----0---0---1---3---0--
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|B Diminished#Harmonic Function: Leading Chord|Theory: Leading Chord
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b-1---1---3----0---1---3---3---1--
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|B Diminished#Full Circle Progression|Circle Prog
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g-0---2---x----0---2---2---0---0--
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|B Diminished#Diminished Fifth Interval|Dim 5th Interval}}
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d-2---3---3----2---2---0---0---2--
 
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a-3-------2----2---0-------2---3--
 
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e--------------0-----------3------
 
  
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Now that we know the vii chord, we can play the full circle progression in the key of C Major.
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Now that we know the vii{{dim}} chord, we can play the full circle progression in the key of C Major.
  
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== Dominant Example ==
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    C    F    Bdim  Em    Am    Dm    G    C
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Let's try it as the main dominant-function chord in a progression:
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    I    IV    viio  iii  vi    ii    V    I
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E--0-----1-----1-----0-----0-----1-----3-----0--
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B--1-----1-----3-----0-----1-----3-----3-----1--
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G--0-----2-----x-----0-----2-----2-----0-----0--
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D--2-----3-----3-----2-----2-----0-----0-----2--
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A--3-----------2-----2-----0-----------2-----3--
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E--------------------0-----------------3--------
  
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  C  F  Bdim C
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{{top}}
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  I  IV  vii  I
 
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e-0---1---1----0--
 
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b-1---1---3----1--
 
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g-0---2---x----0--
 
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d-2---3---3----2--
 
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a-3-------2----3--
 
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e-----------------
 
  
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Rather strong resolution, especially considering the vii itself is so tense with its diminished fifth interval.
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== Diminished Fifth Interval ==
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{{crumbs|blue|4
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|B Diminished#Open Position B Diminished Triad|Open B dim
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|B Diminished#Harmonic Function: Leading Chord|Theory: Leading Chord
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|B Diminished#Full Circle Progression|Circle Prog
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|B Diminished#Diminished Fifth Interval|Dim 5th Interval}}
  
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== Diminished Fifth Interval ==
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The vii{{dim}} 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 45:32.  Let's see all the intervals again:
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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:
 
  
 
{|class="wikitable"
 
{|class="wikitable"
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! Interval Name !! Ratio
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! Interval Name !! Ratio  
 
|-
 
|-
 
| m2 || 16:15
 
| m2 || 16:15
 
|-
 
|-
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| M2 || 9:8
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| M2 || 9:8  
 
|-
 
|-
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| m3 || 6:5
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| m3 || 6:5  
 
|-
 
|-
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| M3 || 5:4
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| M3 || 5:4  
 
|-
 
|-
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| P4 || 4:3
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| P4 || 4:3  
 
|-
 
|-
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| d5 || 45:32
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| '''d5''' || '''45:32'''
 
|-
 
|-
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| P5 || 3:2
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| P5 || 3:2  
 
|-
 
|-
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| m6 || 8:5
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| m6 || 8:5  
 
|-
 
|-
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| M6 || 5:3
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| M6 || 5:3  
 
|-
 
|-
 
| m7 || 9:5
 
| m7 || 9:5
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|}
 
|}
  
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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.
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As you notice, the intervals closest to the root note or octave feature the larger integer numbers for their ratios and have the largest least common multiples.  As we move away from the root/octave, the ratios seem to get more and more harmonic.  Yet, the d5 is a major departure from the general trend - it appears the least harmonious of all.  (Even in an alternate tuning where its ratio is a more harmonic 7:5 variation, it is about as harmonious as the minor 3rd and 6th, far from the perfect 4th and 5th.)  As it serves as the replacement of the P5 in this chord, this immediately makes the chord quite dissonant.
 +
 
 +
It's quite apparent when playing the B{{dim}} chord.  This means the vii{{dim}} 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. Typically, we don't see diminished triads as frequently as [[7th Chords|7th]] or other [[Extended Chords|extended chords]].  Its half diminished variety (diatonic to the major, natural minor, and harmonic minor scales) actually adds consonance, which we will cover [[7th Chords#Half Diminished|later]].
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 +
{{top}}
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== Homework ==
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* Know that the diminished chord is composed of root and the m3 and d5 above.
 +
* Know that B dim consists of (B D F).
 +
* Know that the vii{{dim}} chord of a scale is a diminished chord.
 +
* Know that the vii{{dim}} chord has a dominant harmonic function.
 +
* Practice fingering and strumming B dim in open position.
 +
** Be sure to mute the G string.
 +
* Practice the I - IV - vii{{dim}} - I progression above.
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* Practice the full circle progression above.
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 +
== Q & A ==
 +
 
 +
== Related Lessons ==
 +
* [[Extended Chords]]
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* [[C Major Chord|Introduction to Chords]]
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* [[7th Chords|Seventh Chords]]
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* [[Extended Chords]]
 +
 
 +
{{top}}
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{{Intermediate Lesson Crumbs|1}}
  
 
[[Category:Guitar]]
 
[[Category:Guitar]]

Latest revision as of 22:57, 11 June 2016

In the beginner lessons we talked about all the diatonic chords diatonic to C Major except 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 also minor third, so the chord is composed of 2 minor thirds and 1 diminished fifth. Diminished chords are often marked as using "dim" or °, such as Bdim, B dim, or B°.

PreReqs

Open Position B Diminished Triad

B Diminished is composed of (B D F). Here are the common voicings in or near open position:

Open Pos. 2nd Pos. 
F  ||i|-|-|-|
D  ||-|-|p|-|
   ||-|-|-|-|
F  ||-|-|r|-|
B  ||-|m|-|-|
   ||-|-|-|-|

   ||-|-|-|-|
D  ||-|-|r|-|
B  ||-|-|-|p|
F  ||-|-|m|-|
B  ||-|i|-|-|
   ||-|-|-|-|

Although B and D occur as open strings, the common open position voicing avoids using them. The G string is typically muted, as it offers no notes from the chord until the 4th fret, which pulls us out of open position. 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.

The 2nd position shape is also a bit strange, at least in comparison to the common major and minor chords; however, it may seem a bit simpler to finger than the full open position chord. Open position is generally preferred; however, as it includes a wider range of notes and retains open position alignment of the fingers to frets.

Top

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° chord (or vii or viio when the ° symbol cannot be made). The ° symbol indicates diminished, but you have to be careful - we are dealing with the diminished triad here, not the diminished 7th. The diminished 7th chord has two variations - half and full. Half is indicated with a slash through the ° symbol (Bø7). Full uses the normal symbol (B°7).

Where the ° symbol cannot be made, such as on a standard keyboard without using special character codes, or to avoid ambiguity, you can use "dim" (ex. Bdim) to indicate the diminished quality of the chord. Then a half diminished 7th can be written as Bm7b5.

The vii chord is called the leading chord. Harmonically, it has a dominant function, sharing the leading tone and 2nd of the scale with the V chord (B and D in the key of C Major). 

   C     F/C    Bdim    C
   I      IV    viio    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------------------------------
Top

Full Circle Progression

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

   C     F     Bdim  Em    Am    Dm    G     C
   I     IV    viio  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--------
Top

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 45:32. Let's see all the intervals again:

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

As you notice, the intervals closest to the root note or octave feature the larger integer numbers for their ratios and have the largest least common multiples. As we move away from the root/octave, the ratios seem to get more and more harmonic. Yet, the d5 is a major departure from the general trend - it appears the least harmonious of all. (Even in an alternate tuning where its ratio is a more harmonic 7:5 variation, it is about as harmonious as the minor 3rd and 6th, far from the perfect 4th and 5th.) As it serves as the replacement of the P5 in this chord, this immediately makes the chord quite dissonant.

It's quite apparent when playing the B° 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. Typically, we don't see diminished triads as frequently as 7th or other extended chords. Its half diminished variety (diatonic to the major, natural minor, and harmonic minor scales) actually adds consonance, which we will cover later.

Top

Homework

  • Know that the diminished chord is composed of root and the m3 and d5 above.
  • Know that B dim consists of (B D F).
  • Know that the vii° chord of a scale is a diminished chord.
  • Know that the vii° chord has a dominant harmonic function.
  • Practice fingering and strumming B dim in open position.
    • Be sure to mute the G string.
  • Practice the I - IV - vii° - I progression above.
  • Practice the full circle progression above.

Q & A

Related Lessons

Top
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