Presentation on theme: "Physics of the Blues: Music, Fourier and the Wave-Particle Duality"— Presentation transcript:
1 Physics of the Blues: Music, Fourier and the Wave-Particle Duality J. Murray GibsonPresented at FermilabOctober 15th 2003Not serious science – My hobby - An Amuse-GueleMaybe not original content, but certainly unusual for Physics Colloquium, and I hope funOutfox Harvey Drucker talking about the new ways of war..
5 Music is excellent example… Of all the seminar hallsIn all the physics jointsIn the whole worldYou had to walk into this one…
6 Outline: What determines the frequency of notes on a musical scale? What is harmony and why would fourier care?Where did the blues come from? (We' re talking the "physics of the blues", and not "the blues of physics" - that's another colloquium).Rules (axioms) and ambiguity fuel creativityMusic can explain physical phenomenaIs there a musical particle? (quantum mechanics)The importance of phase in imaging?
7 Overtones of a stringFourier analysis – all shapes of a string are a sum of harmonicsHarmonic content describes difference between instrumentse.g. organ pipes have only odd harmonics..
8 Spatial HarmonicsCrystals are spatially periodic structures which exhibit integral harmonicsX-ray diffraction reveals amplitudes which gives structure inside unit cellUnit-cell contents? (or instrument timbre?)Ribosome
9 Semiconductor Bandgaps… Standing waves in a periodic lattice (Bloch Waves) – the phase affects energy and leads to a bandgap“Bloch Waves sent my kids to college” said a solid-state physicist,” and sent them back home” said a student..
10 Familiarity with the Keyboard CDEFG1 step = semitone2 steps = whole toneC D E F G A
11 How to make a scale using notes with overlapping harmonics Bflat 7/412345678CConcept of intervals – two notes sounded simultaneously which sound good togetherLeft brain meets the right brain…Pythagoras came up with this….
12 The pentatonic scale * * * * * C D E G A 1 9/8 5/4 3/2 27/16 Demonstrate with Scotland the Brave and Chinese/Native American MelodyHarpo19/85/43/227/16Common to many civilizations (independent experiments?)
13 Intervals Unison (“first”) Second Third Fourth Fifth Sixth Seventh Octave (“eighth”)Two notes played simultaneouslyMajor, minor, perfect, diminished..Not all intervals are HARMONIC (although as time goes by there are more..Harmony is a learned skill, as Beethoven discovered when he was booed)
14 Natural Scale Ratios Interval Ratio to Fundamental in Just Scale Frequency of Upper Note based on C (Hz)(C-C) Unison1.0000261.63Minor Second25/24 =272.54(C-D) Major Second9/8 =294.33Minor Third6/5 =313.96(C-E) Major Third5/4 =327.04(C-F) Fourth4/3 =348.83Diminished Fifth45/32 =367.93(C-G) Fifth3/2 =392.45Minor Sixth8/5 =418.61(C-A) Major Sixth5/3 =436.06Minor Seventh9/5 =470.93(C- B) Major Seventh15/8 =490.56(C-C’) Octave2.0000523.26
15 Diatonic Scale “Tonic” is C here C D E F G A B C Doh, a deer“Tonic” is C hereDoh, Re, Mi, Fa, So, La, Ti, Doh….
16 Simple harmony Intervals “perfect” fifth major third minor third the harmonic triads – basis of western music until the romantic eraAnd the basis of the blues, folk music etc.Demonstrate 2 note and 3 note chords re a pieceMelody can also fill inMostly harmony, but also counterpointDisonance is also a part of the story (but limited)AMAZING GRACE?The chords are based on harmonic overlap minimum of three notes to a chord(to notes = ambiguity which is widely played e.g. by Bach)
17 The triads in the key of C C E G M3 P5 C Major TriadD F A m3 P5 D Minor TriadE G B m3 P5 E Minor TriadF A G M3 P5 F Major TriadG B D M3 P5 G Major TriadA C E m3 P5 A Minor TriadB D F m3 d5 B Diminished Triad
18 Three chords and you’re a hit! A lot of folk music, blues etc relies on chords C, F and GDylan Folk example – blues latere.g. Blowing in the Wind?Gives you Edelweiss – who you cgnna impress
19 Baroque MusicBased only on diatonic chords in one key (D in this case)
20 Equal temperament scale NoteFrequency (Hz)Difference from Just Scale (Hz)(Middle C) C4261.63C#4/Db4277.184.64D4293.66-0.67D#4/Eb4311.13-2.83E4329.632.59F4349.230.4F#4/Gb4369.992.06G4392.00-0.45G#4/Ab4415.30-3.31(Concert A) A4440.003.94A#4/Bb4466.16-4.77B4493.883.32C5523.25Step (semitone) = 2^1/12Pianoforteneeds multiple strings to hide beats!The Well-Tempered Clavier
22 Mostly Mozart From his Sonata in A Major Note erroneous corrections on manuscript preserved for centuries – Must have frustrated Mozart (stupid referees – somethings are universal)From his Sonata in A Major
26 The “Dominant 7th” The major triad PLUS the minor 7th interval E.g. B flat added to C-E-G (in the key of F)B flat is very close to the harmonic 7/4Exact frequency Hz,B flat is HzB is HzDesperately wants to resolve to the tonic (F)B flat is not in the diatonic scale for C, but it is for FAlso heading for the “blues”
27 Circle of Fifths Allows modulation and harmonic richness Needs equal temperament“The Well Tempered Clavier”Allows harmonic richnessMusical example? And circle and more notes
29 Diminished Chords A sound which is unusual All intervals the same i.e. minor 3rds, 3 semitones (just scale ratio 6/5, equal temp -1%)The diminished chord has no rootAmbiguous and intriguingAn ability of modulate into new keys not limited by circle of fifthsAnd add chromatic notesThe Romantic Period was lubricated by diminished chordsChopin’s Nocturne in E FlatC diminished
30 Romantic music.. A flat diminished (c.f. B flat dominant 7th) 21345C diminished (Fdominant 7th)
31 Beethoven’s “Moonlight” Sonata in C# Minor 15F# dim9Diminished based on C base only – very clever and foreboding….13F# (or C) dim
32 “Blue” notes Middle C = 261.83 Hz E flat = 311.13Hz Blue note = perfect harmony = 5/4 middle C = Hz – slightly flatter than EE = HzCan be played on wind instruments, or bent on a guitar or violin. “Crushed” on a piano12 Bar Blues - C F7 C C F7 F7 C C G7 F7 C CThe “St Louis Blues”
35 Four-tone chords Minimum for Jazz and Contemporary Music The Rich sounds of James Bond – For Your Eyes OnlyAlso classic MotownAnd more: 9th, 11th s and 13th s (5,6 and 7note chords)
36 Ambiguities and Axioms Sophisticated harmonic rules play on variation and ambiguityOnce people learn them they enjoy the ambiguity and resolutionEvery now and then we need new rules to keep us excited (even though we resist!)Similarity with mathematics
37 Using Music to Explain Physics Quantum Mechanicsgeneral teachingImaging and Phasephase retrieval is important in lensless imaging, e.g. 4th generation x-ray lasers
38 The Wave-particle Duality Can be expressed as fourier uncertainty relationshipDf DT ~ 2 p2p/fDTDemonstrated by musical notes of varying duration (demonstrated with Mathematica or synthesizer)Wave-nature melodyParticle-nature percussive aspect
39 Ants Pant!Phase-enhanced imagingWestneat, Lee et. al..
40 Phase Contrast and Phase Retrieval Much interest in reconstructing objects from diffraction patterns“lensless” microscopy ios being developed with x-ray and electron scatteringWarning, for non-periodic objects, phase, not amplitude, is most important…..
43 Swap phases Helen with Marge’s phases Marge with Helen’s phases Phases contain most of the information… (especially when no symmetry)
44 Sound Examples Beethoven Clapton Clapton with Beethoven’s phases Beethoven with Clapton’s Phases
45 Conclusion Music and physics and mathematics have much in common Not just acousticsMusician’s palette based on physicsConsonance and dissonanceBoth involved in pleasure of musicRight and left brain connected?Is aesthetics based on quantitative analysis?Music is great for illustrating physical principles“My Kind of Town”