# Dissonance and Resolve

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8/27/2012
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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    Fourth   Sixth
partial      (E)     (F)       (A)

1      C        C        C

2      C        C        C

3      D        C        C

4      D        C        C

5      D        C        D
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#
Band      lower     upper
F# freq.                                 C freq.   result
width     band      band
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
dissonance
• Order in which notes played matters
• What you hear before matters
• Tritone can be used to create more
dynamic, interesting progressions

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