# Presentation: 657503

## Physics of the Blues:Music, Fourier and the Wave-Particle Duality

- J. Murray Gibson
- Presented at Fermilab
- October 15th 2003

**Notes:**
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..

## The Advanced Photon Source

## Art and Science 

- Art and science are intimately connected
- Art is a tool for communication between scientists and laypersons

## The Poetry of Mathematics

## Music is excellent example...

**Notes:**
Of all the seminar halls
In all the physics joints
In the whole world
You had to walk into this one...

##  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?

## 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..

## 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?)

**Notes:**
Ribosome

## Semiconductor Bandgaps...

- Standing waves in a periodic lattice (Bloch Waves) – the phase affects energy  and leads to a bandgap

**Notes:**
“Bloch Waves sent my kids to college” said a solid-state physicist,” and sent them back home” said a student..

## Familiarity with the Keyboard

- C

- D

- E

- G

- A

- F

- B

- 1 step = semitone
- 2 steps = whole tone

- C D E F G A

## How to make a scale using notes with overlapping harmonics

- 2

- 3

- 4

- 5

- 1

- 6

- 7

- 8

- 	Pythagoras came up with this....

- Concept of intervals – two notes sounded simultaneouslywhich sound good together
- 	Left brain meets the right brain...

- C

- G3/2

- E5/4

- Bflat7/4

## The pentatonic scale

- C

- D

- E

- G

- A

- 1

- 5/4

- 3/2

- 9/8

- 27/16

*****

*****

*****

*****

*****

- Common to many civilizations (independent experiments?)

**Notes:**
Demonstrate with Scotland the Brave and Chinese/Native American Melody
Harpo

## Intervals

- Unison (“first”)
- Second
- Third
- Fourth
- Fifth
- Sixth
- Seventh
- Octave (“eighth”)

- Major, minor, perfect, diminished..

- Two notesplayed simultaneously

- Not all intervals are HARMONIC(although as time goes by there are more..
- Harmony is a learned skill, as Beethovendiscovered when he was booed)

## 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 = 1.0417 | 272.54 |
| (C-D) Major Second | 9/8 = 1.1250 | 294.33 |
| Minor Third | 6/5 = 1.2000 | 313.96 |
| (C-E) Major Third | 5/4 = 1.2500 | 327.04 |
|  (C-F) Fourth | 4/3 = 1.3333 | 348.83 |
| Diminished Fifth | 45/32 = 1.4063 | 367.93 |
| (C-G) Fifth | 3/2 = 1.5000 | 392.45 |
| Minor Sixth | 8/5 = 1.6000 | 418.61 |
| (C-A) Major Sixth | 5/3 = 1.6667 | 436.06 |
| Minor Seventh | 9/5 = 1.8000 | 470.93 |
|  (C- B) Major Seventh | 15/8 = 1.8750 | 490.56 |
| (C-C’) Octave | 2.0000 | 523.26 |

## Diatonic Scale

- C

- D

- E

- G

- A

- F

- B

- C

- Doh, Re, Mi, Fa, So, La, Ti, Doh....

- “Tonic” is C here

**Notes:**
Doh, a deer

## 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.

- The chords are based on harmonic overlapminimum of three notes to a chord
- (to notes = ambiguity which is widely played e.g. by Bach)

**Notes:**
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 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

## Three chords and you’re a hit!

- A lot of folk music, blues etc relies on chords C, F and G

**Notes:**
Dylan Folk example – blues later
e.g. Blowing in the Wind?
Gives you Edelweiss – who you cgnna impress

## Baroque Music

- Based only on diatonic chords in one key (D in this case)

## Equal temperament scale

| (Middle C) C4  | 261.63 | 0 |
| --- | --- | --- |
| 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 | 0 |

- Frequency (Hz)

- Step (semitone) = 2^1/12

*Pianoforte*
*needs**multiple**strings to hide**beats!*

- Difference from Just Scale (Hz)

- Note

**Notes:**
The Well-Tempered Clavier

## The Well-Tempered Clavier

- 1

- 2

- 3

- 4

- 5

- 6

## Mostly Mozart

- From his Sonata in A Major

**Notes:**
Note erroneous corrections on manuscript preserved for centuries – Must have frustrated Mozart (stupid referees – somethings are universal)

## D dim

- c.f. D min

## Minor and Major

**Notes:**
Major and Minor on piano
Brilliant major, e.g. Beethoven, Tchaikovsky

## Slide 25

## 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 457.85 Hz,
- B flat is 466.16 Hz
- B is 493.88 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”*

## Circle of Fifths

- Allows modulation and harmonic richness
- Needs equal temperament
- “The Well Tempered Clavier”
- Allows harmonic richness

**Notes:**
Musical example? And circle and more notes

## Slide 28

## 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

- C diminished

**Notes:**
Chopin’s Nocturne in E Flat

## Romantic music..

- A flat diminished (c.f. B flat dominant 7th)

- C diminished (Fdominant 7th)

- 1

- 2

- 3

- 4

- 5

## Beethoven’s “Moonlight” Sonata in C# Minor

- F# dim

- F# (or C) dim

- 1

- 5

- 9

- 13

**Notes:**
Diminished based on C base only – very clever and foreboding....

## “Blue” notes

- Middle C = 261.83 Hz
- E flat = 311.13Hz
- Blue note = perfect harmony = 5/4 middle C = 327.29 Hz – slightly flatter than E
- E = 329.63 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

**Notes:**
The “St Louis Blues”

## Crushed notes and the blues

## Not quite ready for the blues

**Notes:**
1904

## Four-tone chords

- Minimum for Jazz and Contemporary Music

- And more: 9th, 11th s and 13th s (5,6 and 7note chords)

**Notes:**
The Rich sounds of James Bond – For Your Eyes Only

Also classic Motown

## 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!)

**Notes:**
Similarity with mathematics

## 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

## The Wave-particle Duality

- Can be expressed as fourier uncertainty relationship
- f T ~ 2 

- Demonstrated by musical notes of varying duration (demonstrated with *Mathematica* or synthesizer)
- Wave-nature   melody
- Particle-nature  percussive aspect

- T

- 2/f

## Ants Pant!

- Phase-enhanced imaging

*Westneat, Lee et. al..*

## 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.....

## Fun with phases...

- Helen Gibson

- Margaret Gibson

## Fourier Transforms

- Helen

- Marge

- Amp

- Phase

## Swap phases

- Helen with Marge’s phases

- Marge with Helen’s phases

- Phases contain most of the information... (especially when no symmetry)

## Sound Examples

- Clapton

**Beethoven**

- Clapton with Beethoven’s phases

- Beethoven with Clapton’s Phases

## 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

**Notes:**
“My Kind of Town”