Dissonance and Resolve

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First found Jul 4, 2016

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```Dissonance and Resolution
Emily Trentacoste
Math 5
Dissonance
• Partials of two notes are too close
• Critical bandwidth
– Dissonant = partial within bandwidth
– Consonant = partial outside bandwidth
Intervals and dissonance
• Nonmusicians – major thirds, major sixths
– Imperfect consonance
• Musicians – major fourths, major fifths
– Perfect consonance
• I found musicians like upper fourths and
fifths, not always lower
• Nonmusicians prefer major sixths, nobody
likes thirds
Major C intervals
Third
(E)
Fourth
(F)
Sixth
(A)
1
C
C
C
2
C
C
C
3
D
C
C
4
D
C
C
5
D
C
D
partial
Tritones
• Tritone = augmented 4th/diminished 5th
• Partials are too close
• Galileo – frequencies should be proportionate
– 1/√2 – not a simple ratio – complex = dissonance
CF#
F# freq.
Band
width
lower
band
upper
band
C freq.
result
370
63.93
338.036
401.96
261.626
C
523.251
C
739.99
101.04
689.471
790.51
784.878
D
1109.99
139.857
1040.06
1179.92
1046.50
D
1479.98
180.38
1389.79
1570.17
1308.13
C
1569.76
D
Consonance by circumstance
• Add minor third to bottom of tritone
Ab
with C
with F#
207.65 C
C
415.3 C
C
622.95 C
C
830.6 D
C
1038.25 D
C
1245.9 D
C
• Add minor third at top of tritone
• More notes?
Relative dissonance
• Does order of notes matter?
• AbF#C, AbCF#, F#AbC, etc.
– C is worst to start
• “Priming chord”
– Includes dissonant interval – less
– Unrelated chord – more
Jazz Progression
• Tritone substitution – two chords that
share tritones can be substituted
• ii-V-I progression – ex. Dmin7-G7-Cmaj7
– G7  Db7 (Db is tritone of G)
With A
Summary