VI. Scales & Consonance Dr. Bill Pezzaglia

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Presentation transcript:

VI. Scales & Consonance Dr. Bill Pezzaglia 1 VI. Scales & Consonance Dr. Bill Pezzaglia Incomplete Rough Draft Updated April 23, 2012

Outline Musical Scales & Intervals Consonance & Dissonance 2 Outline Musical Scales & Intervals Consonance & Dissonance The Harmonic Series References

A. Musical Scales Three Basic Scales Labeling Notes Musical Intervals 3 A. Musical Scales Three Basic Scales Labeling Notes Musical Intervals

1. Three Basic Scales 4 Chromatic Scale: Octave is divided into 12 semitone steps (halfsteps) Diatonic Scale (white keys) 7 notes Pentatonic Scale (black keys) 5 notes

1b Diatonic Scales 5 You can build more (7 note) scales by starting on any of the white keys. Classic “greek” names: Soldiers should only listed to Dorian or Phrygian scales (Plato)

2. Labeling the Notes 6 Boethian Notation: white keys are labeled “A”, “B”, “C” through “G”. Sharps & Flats: black keys are notated by # or “b” Octave Numbering: C2 is octave above C1

2b Sharps and Flats 7 In modern tuning, D#=Eb, they are “enharmonic keys”, i.e. equivalent sounds.

2. The Piano 88 Keys (36 black, 52 white) Start at A0 (27.5 Hz), end at C8 (4186 Hz) Range: 7 octaves (plus 3 notes)

3. Musical Intervals 9 Label White Keys 1 through 7 CD M2 Major 2nd (Dissonant) CE M3 Major 3rd CF P4 Perfect 4th CG P5 Perfect 5th CA M6 Major 6th CB M7 Major 7th CC P8 Octave (Consonant) 1 2 3 4 5 6 7 Demonstration Link: http://www.music.sc.edu/fs/bain/atmi02/partch/index.html

C.1. Harmonic Modes 10 Daniel Bernoulli (1728?) shows string can vibrate in different modes, which are multiples of fundamental frequency (called “Harmonics” by Sauveur) n=1 f1 n=2 f2=2f1 n=3 f3=3f1 n=4 f4=4f1 n=5 f5=5f1

C.2. Harmonic Series The musical notes of harmonic series 11 Reference: http://www.music.sc.edu/fs/bain/atmi02/hs/index-audio.html Sound: http://www.music.sc.edu/fs/bain/atmi02/hs/playback/partials/hs1-12-c.mov

C.3. Pythagorean Ratios 12 Musical Intervals can be expressed as pure mathematical ratios. Lower numbers sound more consonant Bigger numbers sound more dissonant CD M2 Major 2nd 8:9 CE M3 Major 3rd 4:5 CF P4 Perfect 4th 3:4 CG P5 Perfect 5th 2:3 CA M6 Major 6th 3:5 CB M7 Major 7th 8:15 CC P8 Octave 1:2

13 D. References http://en.wikipedia.org/wiki/Consonance_and_dissonance http://www.tunesmithy.connectfree.co.uk/musical_note_intervals.htm Bugle Demo of harmonics: http://www.philtulga.com/harmonics.html