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

partialThird

(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

Tritones

• Tritone = augmented 4th/diminished 5th

• Partials are too close• Galileo – frequencies should be proportionate

– 1/√2 – not a simple ratio – complex = dissonance

CF#

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

• Add minor third at top of tritone• More notes?

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

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

• Adding particular notes reduces dissonance

• Order in which notes played matters

• What you hear before matters

• Tritone can be used to create more dynamic, interesting progressions