Charts to accompany

Mode tuning for the violin maker

by Carleen M. Hutchins and Duane Voskuil
CAS Journal vol. 2, No. 4 (Series II), Nov. 1993, pp 5 - 9

Prominent Modes of the Violin Below 600Hz

(These tuning processes are similar for violas and cellos, but the frequencies are lower.)

Mode:

Mode Definition:

To Identify Pitch:

Violin Position:

Control Frequency by:

Match:

A0
260-
290Hz

"Helmholtz," the so-called breathing mode.

Blow rather hard across f-hole on more active G string side. Both f-holes should give same blow-tone pitch on completed instrument.

C4 to open D4 string.

Cavity volume, flexibility of all cavity walls, f-hole area and f-hole edge thickness. Increase volume (larger pattern or higher ribs), thin plates and ribs, thicken f-hole edges or reduce f-hole area to lower frequency.

A0 - Do not try to change A0 frequency after violin is assembled. F-hole area does not affect A0 frequency very much.

B0
250-
300Hz

First bending of neck and slight bending of body. Nodes across lower bout, at body/neck joint and at nut. A non-radiating mode.

Hold violin vertically at widest edge of lower bout with strings damped (but not against fingerboard) and tap back of scroll, or soft mount violin horizontally at corners over plate eigenmode tester. Glitter sprinkled on end of fingerboard will move.

B3 to open D4 string.

Mass and stiffness. Add mass in moving areas (e.g., end of fingerboard, pegbox or chinrest) or remove stiffness in a bending area (e.g., fingerboard and neck between nut and body and/or underside of fingerboard close to neck) to lower frequency. Remove mass in moving area (especially end of fingerboard) or stiffen bending area (e.g., a stiffer fingerboard) to raise frequency.

B0 - Match to A0 or to Wood Prime (W). This matching adds vibrational energy and spreads out tone over a wider range (i.e., lowers Q), thus affecting whole instrument.

A1
430-
490Hz

Internal, end to end cavity mode (longitudinal standing wave) with one node across C-bout area.

Use cavity pressure testing.

Open A4 string to B4. Slightly below W, the Main Wood frequency.

Length of body cavity and flexibility of all cavity walls. Make longer pattern and more flexible plates and ribs to lower frequency. Vise versa to raise frequency.

A1 - Separate from B1 by 60-80Hz for soloists, 40-60Hz for orchestra and below 40Hz for chamber music. Hard to remove in finished violin.

B1
480-
590Hz

First prominent top plate mode of assembled instrument with some bending of ribs and back. Top is most active, especially at bridge and bassbar area.

Soft mount violin horizontally at corners over eigenmode tester. Glitter sprinkled over top plate will move, especially over bassbar.

B4-D5: Usually one to three semitones above the open A4 string.

Frequency of free plate eigenmodes (especially modes 2 and 5), stiffness of ribs, liners, post and bassbar. Thin ribs 0.1mm, install more flexible Condax type post and/or bassbar. Install stiffer bassbar and/or soundpost to raise.

B1 - See A1 separations.

B-1
145-
190Hz

A rigid motion of body and neck rocking around the node across C-bout (like a see-saw) with a hinge joint at nut. A non-radiating mode.

Soft mount violin at nut and C-bout over eigenmode tester with end of lower bout over speaker. Glitter will be most active on end of fingerboard and scroll.

D3 to open G3 string.

Mass and stiffness. Add mass in moving area (end of fingerboard, pegbox, scroll or chinrest) to lower. Remove mass in moving area (e.g., end of fingerboard, chinrest, pegs, pegbox or scroll) to raise frequency (will also affect B0 frequency).

B-1 - Not enough is known about B-1 to say what frequencies or matching it should have. One possible mode to tune the tailpiece to.

Strong Bowed Tones and "Subharmonic" Tones Based on Harmonic Reinforcement

Abbr:

Definition:

To Identify Pitch:

Violin Position:

Control Frequency by:

Match:

W
450-
550Hz

Main Wood or (A1+B1)/2 approximately (when bowed). The exact frequency of W depends on the relative strengths of A1 and B1.

Damp strings but not against fingerboard. Hum into G side f-hole and feel movement of top and back at either end of violin. Pitch heard is octave below W. W is the strongest sound on a bowed instrument within a tone above the open A string.

A4-C#5: Semitone or two above open A string. An octave above the Wood Prime (W').

Relative frequencies and strengths of A1 and B1.

W - Haunt of wolf note, therefore, it is best to have Main Wood frequency between notes if possible.

W'
or Z

Wood Prime or W/2. "Subharmonic" of W based on second harmonic reinforcement.

Hum into G side f-hole and feel movement of top and back at either end. Listen for strong tone.

Several semitones above open G string.

One half relative frequencies and strengths of A1 and B1.

A0/2

A0/2: One half A0 frequency. "Subharmonic" of A0 based on second harmonic reinforcement.

See A0.

Octave below A0; below the violin playing range.

Controlling A0.

A0/2 - One possible tone to tune the tailpiece to.

W/4

W/4: One half wood prime. "Subharmonic" of W based on fourth harmonic reinforcement.

See W and W'.

Two octaves below W. Calculated from W or W'.

Controlling W.

W/4 - One possible tone to tune the tailpiece to.

Strong Bowed Tones and "Subharmonic" Tones Based on Harmonic Reinforcement

Mode:

Definition:

To Identify Pitch:

Violin Position:

Control Frequency by:

Match:

TP
120-
150Hz

Tailpiece frequency. Vertical or twisting motion of whole tailpiece.

Tap on tailpiece with pencil eraser or put glitter on string-end of tailpiece and vibrate as to test for B0.

B2-D#3. Below playing range of violin.

Tailpiece mass, stiffness, length, weight of tuners, distance from saddle and bridge (begin with string ends between bridge and tailpiece at 1/6 string lengths). Add mass to string end of tailpiece to lower frequency, and vice versa to raise. Experiment with other parameters.

TP - Match to A0/2, W/4, B0/2 or B-1 (B-1 is unusual).

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