The basic tools of harmony are thetriadand theseventh chord.
Both structures are built inthirdsorskips. This process uses
theodd-numberedscale-degrees.If this process is continued past the
octave marker (scale-degree eight), with the scale being repeated
at higher registers, then the odd-numbered tones nine, eleven,
thirteen, fifteen, seventeen, nineteen, twenty-one, and
twenty-three result. These tones are calledscale extensions.scale
degree1357911131517192123
example in CCEGBDFACEGBD
applicationtriadseventhmost 7thsdim. 7ths7sus423rd
extensions
Like most chord tones, the tensions can be altered to fit the
function, applying the formula change: b, #, bb, or in the case of
23rd chord extensions,(double-sharp).The chord tones [1 - 3 - 5 -
7] and conventional tensions [9 - 11 - 13] are the typical tools of
the American Musician. 23rd chord extensions are a logical
outgrowth of the development ofchromatic harmonyin conjunction with
jazz improvisational approaches involving a linear approach to
chords [chord-tones and tensions]. This technique has been used in
classical music and by some jazz improvisers, amongst themEric
Dolphy,David Murray, andBruce
Gertz.Imaj713579#1113#15#17#19b21#23
example in CCEGBDF#AC#E#G#BbD#
applicationchord tonesconventional tensions23rd chord
extensions
IImin71b35b79#1113#15#17#192123
example in CCEbGBbDF#AC#E#G#BD
applicationchord tonestensions [ conventional 11 is natural
]23rd chord extensions
V79, 13135b79#1113#15#17#1921#23
example in CCEGBbDF#AC#E#G#BD#
applicationchord tonesconventional tensions23rd chord
extensions
IIm7b51b3b5b7911b13b151719bb21b23
example in CCEbGbBbDFAbCbEGBbbDb
applicationchord tonesconventional tensions [ can also take b9
]23rd chord extensions
Io7delayed resolution1b3b5bb7911b13b151719b21b23
example in CCEbGbBbbDFAbCbEGBbDb
applicationchord tonesconventional tensions23rd chord
extensions
V7sus4145b79#1113#1517#1921#23
example in CCFGBbDF#AC#EG#BD#
applicationchord tonesconv.23rdconv.23rdconv.23rd ext.
