Kite Guitar Exercises and Techniques by Kite Giedraitis: Difference between revisions
→Exercises and Techniques for Players: added cross-fret barres, and harmonics |
→Exercises and Techniques for Composers and Arrangers: added a section on using dim7 chords to modulate |
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=== 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>'''. | |||
{| class="wikitable" | |||
|+using a dim7 chord to modulate in 12-equal | |||
! rowspan="2" |starting | |||
dim7 chord | |||
! colspan="2" |bolded note is lowered | |||
! colspan="2" |bolded note is raised | |||
|- | |||
!new V7 chord | |||
!new key | |||
!new IVm6 chord | |||
!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 | |||
|Ab7 = Ab C Eb Gb | |||
|Db | |||
|Ebm6 = Bb C Eb Gb | |||
|Bb | |||
|- | |||
|B#dim7 = A '''<u>B#</u>''' D# F# | |||
|B7 = A B D# F# | |||
|E | |||
|F#m6 = A C# D# F# | |||
|C# | |||
|- | |||
|D#dim7 = A C '''<u>D#</u>''' F# | |||
|D7 = A C D F# | |||
|G | |||
|Am6 = A C E F# | |||
|E | |||
|- | |||
|F#dim7 = A C Eb '''<u>F#</u>''' | |||
|F7 = A C Eb F | |||
|Bb | |||
|Cm6 = A C Eb G | |||
|G | |||
|- | |||
| | |||
| | |||
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| | |||
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|- | |||
|E#dim7 | |||
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| | |||
| | |||
| | |||
|- | |||
|G#dim7 | |||
| | |||
| | |||
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|- | |||
|Bdim7 | |||
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|- | |||
|Ddim7 | |||
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|} | |||
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. | |||
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. | |||
{| class="wikitable" | |||
|+using an updim7 chord to modulate in 41-equal | |||
! rowspan="2" |starting | |||
^d7 chord | |||
! colspan="2" |bolded note is lowered | |||
! colspan="2" |bolded note is raised | |||
|- | |||
!new V chord | |||
!new key | |||
!new IV chord | |||
!new key | |||
|- | |||
|A^d7 = '''<u>A</u>''' ^C Eb ^Gb | |||
|Ab^7 = Ab ^C Eb ^Gb | |||
|Db | |||
|Eb^m6 = Bb ^C Eb ^Gb | |||
|Bb | |||
|- | |||
|vD#^d7 = A '''<u>^C</u>''' vD# F# | |||
|Bv7 = '''<u>vA</u>''' B vD# F# | |||
Bv,7 = A B vD F# | |||
|E | |||
|F#vm6 = '''<u>vA</u>''' C# vD# F# | |||
''(F#m,v6 = A C# vD# F#)'' | |||
|C# | |||
|- | |||
|A ^C '''<u>Eb</u>''' F# | |||
|D^7 = A ^C D '''<u>^F#</u>''' | |||
''(D,^7 = A ^C D F#)'' | |||
|G | |||
|A^m6 = A ^C E '''<u>^F#</u>''' | |||
A^m,6 = A ^C E F# | |||
|D | |||
|- | |||
|A^d7 = A ^C Eb '''<u>^Gb</u>''' | |||
|^Fv7 = A ^C Eb ^F | |||
|^C | |||
|^Cvm6 = A ^C Eb ^G | |||
|^G | |||
|} | |||
A similar table for the downdim7 chord. All the non-shifting chords contain mid intervals. | |||
{| class="wikitable" | |||
|+using a downdim7 chord to modulate in 41-equal | |||
! rowspan="2" |starting | |||
vd7 chord | |||
! colspan="2" |bolded note is lowered | |||
! colspan="2" |bolded note is raised | |||
|- | |||
!new V chord | |||
!new key | |||
!new IV chord | |||
!new key | |||
|- | |||
|'''<u>^A</u>''' C ^Eb Gb | |||
|^Abv7 = ^Ab C ^Eb Gb | |||
|^Db | |||
|^Ebvm6 = ^Bb C ^Eb Gb | |||
|^Bb | |||
|- | |||
|^A '''<u>C</u>''' D# vF# | |||
|vB^7 = '''<u>A</u>''' vB D# vF# | |||
''(vB^,~7)'' | |||
|vE | |||
|vF#^m6 = '''<u>A</u>''' vC# D# vF# | |||
''(vF#~,^6)'' | |||
|vC# | |||
|- | |||
|^A C '''<u>^Eb</u>''' vF# | |||
|^Dv7 = ^A C ^D '''<u>F#</u>''' | |||
''(^D~,v7)'' | |||
|^G | |||
|^Avm6 = ^A C ^E '''<u>F#</u>''' | |||
''(^Avm,~6)'' | |||
|^E | |||
|- | |||
|'''^'''A C ^Eb '''<u>Gb</u>''' | |||
|F^7 = ^A C ^Eb F | |||
|Bb | |||
|C^m6 = ^A C ^Eb G | |||
|G | |||
|} | |||
[[Category:Kite Guitar]] | [[Category:Kite Guitar]] | ||