1. Physics of the Blues: Music, Fourier and the Wave-Particle Duality
J. Murray Gibson
Presented at Fermilab
October 15th 2003
Not serious science – My hobby - An Amuse-Guele
Maybe not original content, but certainly unusual for Physics Colloquium, and I hope fun
Outfox Harvey Drucker talking about the new ways of war..

2. The Advanced Photon Source

3. Art and Science Art and science are intimately connected
Art is a tool for communication between scientists and laypersons

4. The Poetry of Mathematics

5. Music is excellent example…
Of all the seminar halls
In all the physics joints
In the whole world
You 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 creativity
Music can explain physical phenomena
Is there a musical particle? (quantum mechanics)
The importance of phase in imaging?

7. Overtones of a string
Fourier analysis – all shapes of a string are a sum of harmonics
Harmonic content describes difference between instruments
e.g. organ pipes have only odd harmonics..

8. Spatial Harmonics
Crystals are spatially periodic structures which exhibit integral harmonics
X-ray diffraction reveals amplitudes which gives structure inside unit cell
Unit-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 KeyboardC D E F G
1 step = semitone
2 steps = whole tone
C D E F G A

11. How to make a scale using notes with overlapping harmonics
Bflat 7/4 1 2 3 4 5 6 7 8 C
Concept of intervals – two notes sounded simultaneously which sound good together
Left 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 Melody
Harpo 1
9/8
5/4
3/2
27/16
Common to many civilizations (independent experiments?)

13. Intervals Unison (“first”) Second Third Fourth Fifth Sixth Seventh
Octave (“eighth”)
Two notes played simultaneously
Major, 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) Unison
1.0000
261.63
Minor Second
25/24 =
272.54
(C-D) Major Second
9/8 =
294.33
Minor Third
6/5 =
313.96
(C-E) Major Third
5/4 =
327.04
(C-F) Fourth
4/3 =
348.83
Diminished Fifth
45/32 =
367.93
(C-G) Fifth
3/2 =
392.45
Minor Sixth
8/5 =
418.61
(C-A) Major Sixth
5/3 =
436.06
Minor Seventh
9/5 =
470.93
(C- B) Major Seventh
15/8 =
490.56
(C-C’) Octave
2.0000
523.26

15. Diatonic Scale “Tonic” is C here C D E F G A B C
Doh, a deer
“Tonic” is C here
Doh, 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 era
And the basis of the blues, folk music etc.
Demonstrate 2 note and 3 note chords re a piece
Melody can also fill in
Mostly harmony, but also counterpoint
Disonance 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 Triad
D F A m3 P5 D Minor Triad
E G B m3 P5 E Minor Triad
F A G M3 P5 F Major Triad
G B D M3 P5 G Major Triad
A C E m3 P5 A Minor Triad
B 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 G
Dylan Folk example – blues later
e.g. Blowing in the Wind?
Gives you Edelweiss – who you cgnna impress

19. Baroque Music
Based only on diatonic chords in one key (D in this case)

20. Equal temperament scale
Note
Frequency (Hz)
Difference from Just Scale (Hz)
(Middle C) C4
261.63
C#4/Db4
277.18
4.64 D4
293.66
-0.67
D#4/Eb4
311.13
-2.83 E4
329.63
2.59 F4
349.23
0.4
F#4/Gb4
369.99
2.06 G4
392.00
-0.45
G#4/Ab4
415.30
-3.31
(Concert A) A4
440.00
3.94
A#4/Bb4
466.16
-4.77 B4
493.88
3.32 C5
523.25
Step (semitone) = 2^1/12
Pianoforte
needs multiple strings to hide beats!
The Well-Tempered Clavier

21. The Well-Tempered Clavier1 2 3 4 6 5

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

23. D dim
c.f. D min

24. Minor and Major Major and Minor on piano
Brilliant major, e.g. Beethoven, Tchaikovsky

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 7/4
Exact frequency Hz,
B flat is Hz
B is Hz
Desperately wants to resolve to the tonic (F)
B flat is not in the diatonic scale for C, but it is for F
Also heading for the “blues”

27. Circle of Fifths Allows modulation and harmonic richness
Needs equal temperament
“The Well Tempered Clavier”
Allows harmonic richness
Musical 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 root
Ambiguous and intriguing
An ability of modulate into new keys not limited by circle of fifths
And add chromatic notes
The Romantic Period was lubricated by diminished chords
Chopin’s Nocturne in E Flat
C diminished

30. Romantic music.. A flat diminished (c.f. B flat dominant 7th)2 1 3 4 5
C diminished (Fdominant 7th)

31. Beethoven’s “Moonlight” Sonata in C# Minor1 5
F# dim 9
Diminished based on C base only – very clever and foreboding…. 13
F# (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 E
E = Hz
Can be played on wind instruments, or bent on a guitar or violin. “Crushed” on a piano
12 Bar Blues - C F7 C C F7 F7 C C G7 F7 C C
The “St Louis Blues”

33. Crushed notes and the blues

34. Not quite ready for the blues
1904

35. Four-tone chords Minimum for Jazz and Contemporary Music
The Rich sounds of James Bond – For Your Eyes Only
Also classic Motown
And more: 9th, 11th s and 13th s (5,6 and 7note chords)

36. Ambiguities and Axioms
Sophisticated harmonic rules play on variation and ambiguity
Once people learn them they enjoy the ambiguity and resolution
Every 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 Mechanics
general teaching
Imaging and Phase
phase retrieval is important in lensless imaging, e.g. 4th generation x-ray lasers

38. The Wave-particle Duality
Can be expressed as fourier uncertainty relationship
Df DT ~ 2 p
2p/f DT
Demonstrated by musical notes of varying duration (demonstrated with Mathematica or synthesizer)
Wave-nature  melody
Particle-nature  percussive aspect

39. Ants Pant!
Phase-enhanced imaging
Westneat, 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 scattering
Warning, for non-periodic objects, phase, not amplitude, is most important…..

41. Fun with phases…
Helen Gibson
Margaret Gibson

42. Fourier Transforms
Helen
Marge
Amp
Phase

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 acoustics
Musician’s palette based on physics
Consonance and dissonance
Both involved in pleasure of music
Right and left brain connected?
Is aesthetics based on quantitative analysis?
Music is great for illustrating physical principles
“My Kind of Town”