Dissonance and Resolve

							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
• 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