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Kite Guitar Exercises and Techniques by Kite Giedraitis: Difference between revisions

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=== Modulation via Dim7 Chords ===
=== Modulation via Dim7 Chords ===
(A work in progress)
This is analogous to 12-equal's Cdim7 --> B7 --> E (or EM7 or Em7). The idea is to lower one of the 4 notes in the dim7 chord by a semitone to transform it into a dom7 chord, then use a typical V7 - I cadence. The following table uses a single dim7 chord that is spelled 4 different ways for convenience. This starting chord is one of the three possible dim7 chords in 12-equal, thus two more tables would be needed to show all possible modulations. The note that is lowered is '''<u>bolded</u>'''.  
 
This is analogous to 12-equal's Cdim7 --> B7 --> E (or EM7 or Em7). The idea is to lower one of the 4 notes in the dim7 chord by a semitone to transform it into a dom7 chord, then use a typical V7 - I cadence. The following table uses a single dim7 chord that is spelled 4 different ways for convenience. This starting chord is one of the three possible dim7 chords in 12-equal, thus two more tables would be needed to show all possible modulations.The note that is lowered is '''<u>bolded</u>'''.
{| class="wikitable"
{| class="wikitable"
|+using a dim7 chord to modulate in 12-equal
|+using a dim7 chord to modulate in 12-equal
Line 1,133: Line 1,131:
!new IVm6 chord
!new IVm6 chord
!new key
!new key
|-
|C#dim7 = '''<u>C#</u>''' E G Bb
|C7 = C E G Bb
|F
|Gm6 = D E G Bb
|D
|-
|Edim7 = Db '''<u>E</u>''' G Bb
|Eb7 = Db Eb G Bb
|Ab
|Bbm6 = Db F G Bb
|F
|-
|Gdim7 = Db Fb '''<u>G</u>''' Bb
|Gb7 = Db Fb Gb Bb
|'''Cb'''
|C#m6 = C# E G# A#
|G#
|-
|A#dim7 = C# E G '''<u>A#</u>'''
|A7 = C# E G A
|D
|Em6 = C# E G B
|B
|-
|
|
|
|
|
|-
|-
|Adim7 = '''<u>A</u>''' C Eb Gb
|Adim7 = '''<u>A</u>''' C Eb Gb
Line 1,187: Line 1,155:
|Cm6 = A C Eb G
|Cm6 = A C Eb G
|G
|G
|-
|
|
|
|
|
|-
|E#dim7
|
|
|
|
|-
|G#dim7
|
|
|
|
|-
|Bdim7
|
|
|
|
|-
|Ddim7
|
|
|
|
|}
|}




The last two columns take this idea further. The bolded note is <u>raised</u> to make a min6 chord that resolves down a 4th to the new tonic. This IVm6 - I cadence is simply the rotation of V7 - I. Note that both cadences take you to the same 4 keys.
The last two columns take this idea further. The bolded note is <u>raised</u> to make a min6 chord that resolves down a 4th to the new tonic. This IVm6 - I cadence is simply the rotation of V7 - I. Note that both cadences take you to the same 4 keys.


In 41-equal, the dim7 chord is usually an ^dim7 or vdim7 chord, neither of which are symmetrical. So 40 more tables would be needed! How much to shift by? The bolded note has another chord note a tritone above it. The bolded note is either lowered to make that interval a perfect 5th, or raised to make a perfect 4th.  
In 41-equal, a dim7 chord is possible, but here we will focus on the ^dim7 and vdim7 chords. Neither of these are symmetrical, so 40 more tables would be needed! How much to raise/lower by? The bolded note has another chord note a tritone above it. The bolded note is either lowered to make that interval a perfect 5th, or raised to make a perfect 4th.  


Sometimes another note in the chord needs to shift by one edostep to make a low-odd-limit chord. When this happens, the shifting note is bolded in the "new chord" column. Without this shift, the new chord is more dissonant. But the down add-7 chord is a very familiar dissonance, so it's listed in the 2nd row an alternative to shifting. Furthermore the vanishing [[225/224|Ruyoyo comma]] means the 45/32 downaug 4th is really a consonant 7/5 dim 5th. The upminor add6 chord is a rotation of this, and is included as a possibility. But the other two non-shifting chords, F# minor add-down6 and D add-up7, are less plausible because of their dissonant plain 3rds.
Sometimes another note in the chord needs to shift by one edostep to make a low-odd-limit chord. When this happens, the shifting note is bolded in the "new chord" column. Without this shift, the new chord is more dissonant. But the down add-7 chord is a very familiar dissonance. Furthermore the vanishing [[225/224|Ruyoyo comma]] means the 45/32 downaug 4th is really a consonant 7/5 dim 5th. So it's listed in the 2nd row as an alternative to shifting. The upminor add6 chord is a rotation of this, and is included as a possibility. But the other two non-shifting chords, F# minor add-down6 and D add-up7, are less plausible because of their dissonant plain 3rds.
{| class="wikitable"
{| class="wikitable"
|+using an updim7 chord to modulate in 41-equal
|+using an updim7 chord to modulate in 41-equal
Line 1,243: Line 1,182:
|Bb
|Bb
|-
|-
|vD#^d7 = A '''<u>^C</u>''' vD# F#
|A^d7 = A '''<u>^C</u>''' vD# F#
|Bv7 = '''<u>vA</u>''' B vD# F#
|Bv7 = '''<u>vA</u>''' B vD# F#
Bv,7 = A B vD F#
Bv,7 = A B vD F#
Line 1,251: Line 1,190:
|C#
|C#
|-
|-
|A ^C '''<u>Eb</u>''' F#
|A^d7 = A ^C '''<u>Eb</u>''' F#
|D^7 = A ^C D '''<u>^F#</u>'''
|D^7 = A ^C D '''<u>^F#</u>'''
''(D,^7 = A ^C D F#)''
''(D,^7 = A ^C D F#)''
Line 1,278: Line 1,217:
!new key
!new key
|-
|-
|'''<u>^A</u>''' C ^Eb Gb
|^Avd7 = '''<u>^A</u>''' C ^Eb Gb
|^Abv7 = ^Ab C ^Eb Gb
|^Abv7 = ^Ab C ^Eb Gb
|^Db
|^Db
Line 1,284: Line 1,223:
|^Bb
|^Bb
|-
|-
|^A '''<u>C</u>''' D# vF#
|^Avd7 = ^A '''<u>C</u>''' D# vF#
|vB^7 = '''<u>A</u>''' vB D# vF#
|vB^7 = '''<u>A</u>''' vB D# vF#
''(vB^,~7)''
''(vB^,~7 = ^A vB D# vF#)''
|vE
|vE
|vF#^m6 = '''<u>A</u>''' vC# D# vF#
|vF#^m6 = '''<u>A</u>''' vC# D# vF#
''(vF#~,^6)''
''(vF#~,^6 = ^A vC#  D# vF#)''
|vC#
|vC#
|-
|-
|^A C '''<u>^Eb</u>''' vF#
|^Avd7 = ^A C '''<u>^Eb</u>''' vF#
|^Dv7 = ^A C ^D '''<u>F#</u>'''  
|^Dv7 = ^A C ^D '''<u>F#</u>'''  
''(^D~,v7)''
''(^D~,v7 = ^A C ^D vF#)''
|^G
|^G
|^Avm6 = ^A C ^E '''<u>F#</u>'''
|^Avm6 = ^A C ^E '''<u>F#</u>'''
''(^Avm,~6)''
''(^Avm,~6 = ^A C ^E vF#)''
|^E
|^E
|-
|-
|'''^'''A C ^Eb '''<u>Gb</u>'''
|^Avd7 = ^A C ^Eb '''<u>Gb</u>'''
|F^7 = ^A C ^Eb F
|F^7 = ^A C ^Eb F
|Bb
|Bb
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