Violin

The violin: four strings, infinite expression. Where physics meets artistry.

The Instrument

Open Strings

The violin’s four strings in standard tuning (fifths):

String Note Frequency (Hz) Ratio to G3

IV

G3

196

1:1

III

D4

293.66

3:2 (perfect fifth)

II

A4

440

9:4 (two fifths)

I

E5

659.25

27:8 (three fifths)

The relationship between adjacent strings:

\[\frac{f_{upper}}{f_{lower}} = \frac{3}{2}\]

String Vibration

A vibrating string produces frequencies determined by:

\[f_n = \frac{n}{2L} \sqrt{\frac{T}{\mu}}\]

Where:

  • \(f_n\) = frequency of the nth harmonic

  • \(n\) = harmonic number (1, 2, 3, …​)

  • \(L\) = vibrating length of string

  • \(T\) = tension

  • \(μ\) = linear mass density

Harmonics

Natural harmonics occur at integer divisions of the string:

Node Position Interval Sounding pitch (A string)

2

1/2

Octave

A5 (880 Hz)

3

1/3, 2/3

Octave + fifth

E6 (1320 Hz)

4

1/4

2 octaves

A6 (1760 Hz)

5

1/5, 2/5

2 oct + maj 3rd

C#7 (2200 Hz)

Positions and Fingering

First Position

The foundational hand position. On the A string:

Open:   A4  (440 Hz)
1st:    B4  (493.88 Hz)  - whole step
2nd:    C5  (523.25 Hz)  - half step (low 2)
        C#5 (554.37 Hz)  - whole step (high 2)
3rd:    D5  (587.33 Hz)  - half/whole step
4th:    E5  (659.25 Hz)  - whole step

Position System

Higher positions shift the hand up the fingerboard:

Position 1st finger on A string Shift distance

1st

B4

Reference

2nd

C5

+1 half step

3rd

D5

+2 half steps

4th

E5

+3 half steps (one octave span available)

5th

F5

+4 half steps

7th

G5

+5 half steps

Scales and Intervals

The Perfect Fifth

The violin’s tuning interval. Ratio 3:2.

\[\text{cents} = 1200 \cdot \log_2\left(\frac{3}{2}\right) \approx 702\]

Just vs Equal Temperament

On violin, we can play pure intervals:

Interval Just Ratio Just (cents) Equal (cents)

Unison

1:1

0

0

Minor 2nd

16:15

112

100

Major 2nd

9:8

204

200

Minor 3rd

6:5

316

300

Major 3rd

5:4

386

400

Perfect 4th

4:3

498

500

Perfect 5th

3:2

702

700

Minor 6th

8:5

814

800

Major 6th

5:3

884

900

Minor 7th

16:9

996

1000

Major 7th

15:8

1088

1100

Octave

2:1

1200

1200

Bowing Mechanics

Tone Production

The Helmholtz motion describes ideal bowed string behavior:

  • Bow catches string (stick phase)

  • String releases and snaps back (slip phase)

  • Frequency of stick-slip cycle = pitch

Variables

Parameter Effect

Bow speed

Faster = louder, brighter

Bow pressure

More = denser tone, risk of scratch

Contact point

Near bridge = brighter; near fingerboard = softer

Hair width

Flat = full; tilted = lighter

The Bow

Pernambuco or carbon fiber stick. Horsehair ribbon.

Contact point notation:

  • Sul ponticello — near bridge (glassy, harmonic-rich)

  • Ordinario — normal position

  • Sul tasto — over fingerboard (flute-like)

Practice Methodology

Systematic Approach

  1. Scales — all keys, 2-3 octaves, varied rhythms

  2. Arpeggios — triads and seventh chords

  3. Etudes — Kreutzer, Dont, Rode, Gavinies

  4. Repertoire — isolate difficulties, slow practice

  5. Sight-reading — daily new material

Intonation Training

  • Play with drone on open string

  • Check against open strings and harmonics

  • Slow scales with tuner (understand tendencies)

  • Double-stop scales (exposed intonation)

Repertoire

Works under active study:

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