1. Dissonance and Resolution Emily Trentacoste Math 5

2. Dissonance Partials of two notes are too close Critical bandwidth –Dissonant = partial within bandwidth –Consonant = partial outside bandwidth

3. 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

4. Major C intervals partial Third (E) Fourth (F) Sixth (A) 1CCC 2CCC 3DCC 4DCC 5DCD

5. Tritones Tritone = augmented 4 th /diminished 5 th Partials are too close Galileo – frequencies should be proportionate –1/√2 – not a simple ratio – complex = dissonance

6. C  F# F# freq. Band width lower band upper band C freq.result 37063.93338.036401.96261.626C 523.251C 739.99101.04689.471790.51784.878D 1109.99139.8571040.061179.921046.50D 1479.98180.381389.791570.171308.13C 1569.76D

7. Consonance by circumstance Add minor third to bottom of tritone Add minor third at top of tritone More notes? Abwith Cwith F# 207.65CC 415.3CC 622.95CC 830.6DC 1038.25DC 1245.9DC

8. 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

9. 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)

11. With A

12. 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