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Marimba Bar and Resonator Dimensions for La Favre 5-octave instrument

Marimba bars were fabricated from African Padouk wood and tuned to A4 = 442 Hz. Bars C2 to G#3 were triple tuned (fundamental, fourth harmonic and tenth harmonic). Bars A3 to C5 were double tuned (fundamental and fourth harmonic). Bars C#5 to C7 were only tuned to the fundamental. Frequencies from C#6 to C7 were stretched by adding one cent for each step (i.e., C#6 + 1¢, C7 + 12¢). The stretch was added to the fundamental and the harmonics in this range.

The design of my marimba does not conform to a typical instrument in several aspects, some of which can be gleaned from the data below. Specifically, the bars in the bass range are considerably thicker than a typical 5-octave instrument. During the fabrication and rough tuning process, I became alarmed at the trend in the depth of the arch cut required to bring the bass bars down to the proper frequency. As I worked my way down the instrument, I could see that the center of the arch would need to be less than 1/4 inch thick. I felt that bars less than 1/4 inch thick in the center may not be strong enough to resist damage from a strong mallet blow. Therefore, I attempted to keep the bar thickness in the center of the arch to a minimum of 1/4 inch. In order to do this, I glued extra wood to the bottom of the bars at the ends (i.e., the parts of the bar that are not undercut). Bars C2 to D#3 have wood glued to their bottoms. The addition of wood to the ends of the bar increases the mass that must be moved up and down during vibration, thus reducing the vibration rate. This has an effect similar to decreasing the thickness of the bar in the center, where a thinner bar vibrates more slowly due to less stiffness in the bar. Now I am sure that some will be horrified by the notion of gluing wood together for bars. But after some thought, I decided to go this route for the reasons I have already explained. Most of the flexing in the bar occurs in the region of the arch, which does not have any glued wood in my bars. The glued wood occurs only at the ends, where the bars don't flex as much. The bars of the lowest octave have very strong overtones and the fundamental is more subdued than I like. Whether this is due to the thickness of the bars or not is not known to me at this time. I plan to experiment in the future with bars of different lengths and thicknesses, tuned to the same note, to see if there are any differences.

There is the possibility that my thicker bass bars are damped to a degree from the added mass of the glued wood. In other words, a thinner bar, with a thinner thickness in the center of the arch may vibrate to a stronger degree. If so, then there would be an increase in the volume of sound from the bar. But you need to be careful not to make the bar too thin in the center of the arch. At some point in the future I may experiment with bass bars of different thickness.

In the conventional marimba design, the bars are evenly graduated in length, which allows the cord to make a straight line path from the treble end to the bass end. In my design, I wanted to increase the length of the bass bars, something of a compromise between a bass marimba and a 5-octave instrument. Therefore, my bars increase in length at a greater rate in the range C2 to C4 than bars higher on the instrument. This required some extra work on the instrument frame to accommodate different angles in the bass region. For comparative purposes I have added two additional tables with bar dimensions taken from commercial instruments (a 5-octave marimba and a 4-octave xylophone, both with evenly graduated keyboards). If you would prefer to build an instrument with an evenly graduated keyboard, I suggest you use these tables for guidance.

Some marimba makers shape the bars in such a manner as to avoid problems with lateral and torsional modes of vibration. This is a subject that I became aware of after rough tuning my bars. I decided not to try any tuning of the lateral and torsional modes at that time because I felt it might destroy the bars. Currently (January, 2007), I am investigating these problem modes and have found certain bars on my marimba that need to be retuned due to lateral and torsional modes that vibrate close to the frequency of a tuned transverse mode. You can find more information on lateral and torsional modes and check on my progress at this page. Due to these recent findings, I am hesitant to recommend the dimensions of my bars for a building project. I believe that the bar widths I have selected in the bottom two octaves may not be the best choice due to problem lateral and torsional modes. But then again, most keyboard sets probably have challenges with lateral and torsional modes, which are addressed by various tuning techniques such as wedging. In any case, I also provide a set of bar dimensions for a commercial 5-octave marimba on this page.

 

 

Bar Dimensions for La Favre marimba

Bar Length (inches) Width (inches) Thickness (inches) Thickness at center of arch (inches) Length of arch (inches)
C2 23 3/32 3.72 1.55 0.25 15 13/16
C# 22 17/32 3.59 1.49 0.25 15 1/2
D 22 1/32 3.54 1.42 0.26 15 1/8
D# 21 9/16 3.36 1.37 0.26 14 13/16
E 21 1/16 3.36 1.36 0.26 14 3/16
F 20 9/16 3.23 1.36 0.27 14
F# 20 3/32 3.17 1.25 0.27 13 7/8
G 19 5/8 3.10 1.26 0.27 13 3/16
G# 19 3/32 3.03 1.27 0.27 12 5/8
A 18 11/16

2.92

1.26 0.27 12 1/8
A# 18 7/32 2.85 1.28 0.28 12
B 17 25/32 2.80 1.18 0.27 12
C3 17 11/32 2.70 1.14 0.27 11 1/2
C# 17 3/32 2.60 1.05 0.29 11 1/4
D 16 7/8 2.59 1.05 0.30 11 1/16
D# 16 5/8 2.49 1.01 0.31 10 5/8
E 16 3/8 2.44 0.87 0.29 10 1/4
F 16 1/8 2.38 0.88 0.30 9 3/8
F# 15 7/8 2.35 0.88 0.30 9 1/8
G 15 5/8 2.25 0.87 0.30 9
G# 15 11/32 2.19 0.87 0.32 9
A 15 5/32 2.12 0.88 0.32 8 3/8
A# 14 29/32 2.10 0.87 0.33 7 1/4
B 14 5/8 2.03 0.88 0.33 6 7/8
C4 14 7/16 1.99 0.87 0.31 6 5/8
C# 14 1/4 2.00 0.88 0.30 6 3/4
D 14 1/32 1.96 0.87 0.32 6 3/4
D# 13 13/16 1.96 0.87 0.33 6 1/4
E 13 11/16 1.96 0.87 0.34 6 1/4
F 13 1/2 1.92 0.85 0.36 6 3/8
F# 13 9/32 1.94 0.88 0.35 6 3/8
G 13 3/32 1.93 0.85 0.35 5 7/8
G# 12 15/16 1.91 0.87 0.35 6 1/16
A 12 11/16 1.90 0.88 0.36 5 5/8
A# 12 19/32 1.90 0.87 0.36 5 1/2
B 12 3/8 1.86 0.85 0.37 4 3/4
C5 12 5/32 1.87 0.88 0.36 4 5/8
C# 11 29/32 1.87 0.88 0.37 4
D 11 21/32 1.84 0.88 .037 3 3/8
D# 11 13/32 1.84 0.88 0.39 3 1/8
E 11 5/32 1.84 0.74 .039 3 1/8
F 10 15/16 1.81 0.74 0.38 3 3/8
F# 10 11/16 1.81 0.75 0.42 3 1/2
G 10 1/2 1.81 0.74 0.40 3 1/4
G# 10 5/16 1.78 0.74 0.45 3 3/8
A 10 1/16 1.78 0.75 0.42 3 1/2
A# 9 27/32 1.78 0.75 0.44 2 5/8
B 9 21/32 1.75 0.74 0.44 2 5/8
C6 9 7/16 1.75 0.75 0.45 2 3/4
C# 9 5/16 1.75 0.75 0.49 2 7/8
D 9 1/8 1.72 0.75 0.49 2 13/16
D# 9 1.72 0.74 .051 2 3/4
E 8 13/16 1.72 0.74 0.51 2 1/2
F 8 11/16 1.69 0.74 0.52 2 1/2
F# 8 17/32 1.69 0.74 0.55 2 1/2
G 8 3/8 1.68 0.74 0.55 2 3/8
G# 8 1/4 1.65 0.74 0.60 2 1/2
A 8 3/32 1.65 0.74 0.61 2 1/8
A# 7 31/32 1.65 0.75 0.62 1 7/8
B 7 13/16 1.62 0.75 0.64 1 1/2
C7 7 11/16 1.62 0.74 0.67 1 1/8

 

Bar Dimensions for an evenly graduated marimba (standard type keyboard)

 

Dimensions in this table are representative of a 5-octave marimba with rosewood bars. Please note that this table was edited on December 5, 2006. If you copied this page prior to this date, you have a set of different dimensions, which I calculated by converting the La Favre marimba to an evenly graduated keyboard. I have had correspondence with individuals who tried making bars with the calculated dimensions and found difficulties in tuning. So I decided to replace the dimensions derived by calculation with measurements taken from an existing 5-octave marimba.

For a 4-octave instrument you can also consult a book authored by Chris Banta with the title "Marimba Bar Fabrication and Tuning." Mr. Banta's book gives dimensions for a 4-octave instrument.

 

Bar Length (inches) Width (inches) Thickness (inches) Thickness at center of arch (inches)
C2
21 3/4
2 13/16
1.00
 
C#
21  3/16
     
D
21  3/16
2 5/8
0.99
 
D#
20 11/16
0.21
E
20 11/16
2 5/8
0.99
 
F
20 1/8
2 5/8
1.00
 
F#
19 5/8
 
G
19 5/8
2 1/2
0.92
 
G#
19 1/8
 
A
19 1/8
2 1/2
0.93
 
A#
18 11/16
 
B
18 11/16
2 1/2
0.91
 
C3
18  3/16
2  7/16
0.94
 
C#
17 3/4
0.26
D
17 3/4
2  7/16
0.93
 
D#
17 1/4
 
E
17 1/4
2  7/16
0.93
 
F
16 13/16
2 3/8
0.93
 
F#
16 3/8
 
G
16 3/8
2 1/4
0.93
 
G#
15 15/16
 
A
15 15/16
2 1/4
0.93
 
A#
15  7/16
 
B
15  7/16
2 1/4
0.92
 
C4
15
2 1/8
0.92
 
C#
14 5/8
0.32
D
14  9/16
2 1/8
0.94
 
D#
14 1/4
 
E
14 1/4
2   
0.94
 
F
13 3/4
2
0.93
 
F#
13 3/8
 
G
13 3/8
1 7/8
0.93
 
G#
13   
 
A
12 15/16
1 7/8
0.93
 
A#
12 5/8
 
B
12  9/16
1 7/8
0.91
 
C5
12 1/4
1 7/8
0.93
 
C#
11 7/8
0.40
D
11 7/8
1 7/8
0.93
 
D#
11  7/16
 
E
11  7/16
1 7/8
0.93
 
F
11  1/16
1 3/4
0.86
 
F#
10 3/4
 
G
10 11/16
1 3/4
0.87
 
G#
10 3/8
 
A
10  5/16
1 3/4
0.87
 
A#
10   
 
B
10
1 3/4
0.87
 
C6
9 5/8
1 3/4
0.87
 
C#
9 1/4
 
D
9 1/4
1 3/4
0.87
 
D#
8 15/16
 
E
8 15/16
1 3/4
0.87
 
F
8  9/16
1 3/4
0.87
 
F#
8  3/16
 
G
8  3/16
1 5/8
0.87
 
G#
7 7/8
 
A
7 7/8
1 5/8
0.87
 
A#
7 1/2
 
B
7 1/2
1 5/8
0.87
 
C7
7  3/16
1 5/8
0.87
 

Bar Dimensions for an evenly graduated xylophone

The dimensions in this table are from a reconditioned 4-octave Deagan xylophone..

Bar Length (inches) Width (inches) Thickness (inches) Thickness at center of arch (inches)
C3
18  5/16
2  1/2
0.96
 
C#
18  3/16
 
D
17 13/16
2  7/16
0.99
 
D#
17  9/16
0.58
E
17  1/4
2  7/16
0.94
 
F
16  5/8
2  7/16
1.01
 
F#
16  5/16
0.50
G
16     
2  3/16
1.00
 
G#
15 11/16
 
A
15  3/8
2  3/16
1.00
 
A#
15  1/8
0.56
B
14 13/16
2  3/16
1.00
 
C4
14  5/16
2  3/16
0.98
 
C#
14     
0.60
D
13 11/16
1 15/16
0.96
 
D#
13  9/16
0.60
E
13  1/4
1 15/16
0.96
 
F
12 13/16
1 15/16
0.95
 
F#
12  5/8
0.60
G
12  7/16
1 15/16
0.98
 
G#
12  3/16
 
A
12  1/16
1 15/16
0.98
 
A#
11 13/16
0.67
B
11  1/2
1 15/16
0.98
 
C5
11  1/16
1 15/16
0.97
 
C#
10  7/8
0.72
D
10  5/8
1 15/16
0.99
 
D#
10  1/2
0.72
E
10  1/8
1 15/16
0.97
 
F
9  3/4
1  7/8
0.96
 
F#
9  9/16
0.73
G
9  3/8
1  7/8
0.96
 
G#
9  1/8
 
A
8  7/8
1 15/16
0.95
 
A#
8  5/8
0.70
B
8  3/8
1 15/16
0.98
 
C6
8  3/16
1 15/16
0.95
 
C#
8  1/16
0.78
D
7  3/4
1 15/16
0.96
 
D#
7  3/4
0.76
E
7  1/2
1 15/16
0.96
 
F
7  1/4
1 15/16
0.96
 
F#
7  1/8
 
G
7     
1 15/16
0.96
 
G#
6 11/16
 
A
6  9/16
1  7/8
0.96
 
A#
6  7/16
 
B
6  1/4
1  7/8
0.96
 
C7
6  1/16
1  7/8
0.96
 

 

Below you will find data for the resonators of the La Favre marimba. The resonators were fabricated from aluminum tubing with a wall thickness of 1/16 inch. The position of the stopper in each resonator was adjusted for maximum resonance by ear while striking the bar with a mallet. Then the distance from the stopper to the open end of the tube was measured (data reported as "Air column length"). Keep in mind that this tuning was done by ear and that the stopper can be moved over a small range while still maintaining a loud resonance (in other words, don't take these measurements as absolute). The total resonator length accounts for extra length to accommodate the thickness of the stopper assembly and for tuning up to 85 degrees F. For those resonators that are mitered (not straight), the length listed is the length at the center of the tube. For mitered resonators, the length of each section is listed in the last column, starting with the section nearest the bar. All of the mitered sections were cut at an angle of 22.5 degrees so that they form a 45 degree angle at each miter when assembled. The length listed for each section is the length of the longest side of the tube (except for the third section of resonators C#2 and D#2 - which have the miters cut at a rotation of 90 degrees to each other - for this section the length is measured from the short side of the miter on one end, and the medial position of the miter on the other end).

Resonator Dimensions for La Favre marimba

Bar Tube OD (inches) Air column length - inches (72 F) Total resonator length - inches Tube shape Length of each section for mitered resonators (inches) Gap between
bottom of bar
and top of
resonator (inches)
C2 4 not measured 53 5/8 Mitered 3 sections 25, 6 3/4,
25 1/4
1
C# 4 not measured 50 11/16 Mitered 4 sections 22 9/16, 6 5/8, 7, 17 1 3/16
D 4 not measured 47 15/16 Mitered 3 sections 25, 6 3/4,
19 1/2
1
D# 4 not measured 45 3/8 Mitered 4 Sections 18 1/8, 6 5/8,
5 3/4, 17 3/8
1 1/8
E 3.5 not measured 43 1/16 Mitered 3 sections 25 1/2, 6 1/2, 14 1
F 3.5 not measured 40 3/4 Mitered 3 sections 25 1/2, 6 1/2,
11 5/8
1
F# 3.5 not measured 38 9/16 Mitered 3 sections 26 7/8, 6 1/2,
8 1/8
1
G 3.5 not measured 36 9/16 Mitered 3 sections 25 1/2, 6 1/2,
7 1/2
1
G# 3.5 not measured 34 9/16 Mitered 2 sections 21 3/4, 14 1/4 1
A 3 not measured 32 15/16 Mitered 2 sections 21 1/4, 13 7/8
A# 3 27 15/16 31 3/16 Straight not applicable 7/8
B 3 not measured 29 9/16 Mitered 2 sections 22 7/8, 8 13/16
C3 3 24 5/8 27 3/4 Straight not applicable 3/4
C# 3 23 1/4 26 1/4 Straight not applicable 3/4
D 3 22 24 7/8 Straight not applicable 3/4
D# 2.5 21 23 3/4 Straight not applicable 5/8
E 2.5 19 7/16 22 1/2 Straight not applicable 5/8
F 2.5 18 5/16 21 3/8 Straight not applicable 5/8
F# 2.5 17 3/16 20 3/16 Straight not applicable 11/16
G 2.5 16 7/16 19 3/16 Straight not applicable 5/8
G# 2.5 15 1/4 18 3/16 Straight not applicable 11/16
A 2.5 14 3/8 17 1/4 Straight not applicable 5/8
A# 2.5 13 5/8 16 3/8 Straight not applicable 11/16
B 2.25 12 7/8 15 11/16 Straight not applicable 5/8
C4 2.25 12 1/8 14 13/16 Straight not applicable 9/16
C# 2.25 11 3/16 14 1/16 Straight not applicable 5/8
D 2.25 10 5/8 13 3/8 Straight not applicable 5/8
D# 2.25 10 12 3/4 Straight not applicable 5/8
E 2.25 9 7/16 12 1/8 Straight not applicable 5/8
F 2.25 8 15/16 11 9/16 Straight not applicable 5/8
F# 2.25 8 1/4 11 Straight not applicable 5/8
G 2.25 7 15/16 10 1/2 Straight not applicable 11/16
G# 2.25 7 3/8 10 Straight not applicable 3/4
A
(442 Hz)
2.25 6 3/4 9 9/16 Straight not applicable 11/16
A# 2.25 6 1/2 9 1/8 Straight not applicable 3/4
B 2.25 5 3/4 8 11/16 Straight not applicable 11/16
C5 2.25 5 5/8 8 5/16 Straight not applicable 11/16
C# 2.25 5 1/4 7 15/16 Straight not applicable 3/4
D 2 5 7 11/16 Straight not applicable 11/16
D# 2 4 5/8 7 3/8 Straight not applicable 3/4
E 2 4 1/4 7 1/16 Straight not applicable 11/16
F 2 4 1/8 6 3/4 Straight not applicable 5/8
F# 2 3 7/8 6 1/2 Straight not applicable 3/4
G 2 3 1/2 6 1/4 Straight not applicable 5/8
G# 2 3 1/4 6 Straight not applicable 3/4
A 2 3 5 3/4 Straight not applicable 5/8
A# 2 2 3/4 5 9/16 Straight not applicable 3/4
B 2 2 11/16 5 3/8 Straight not applicable 5/8
C6 2 2 3/8 5 3/16 Straight not applicable 5/8
C# 2 not measured 5 Straight not applicable 3/4
D 2 not measured 4 7/8 Straight not applicable 5/8
D# 2 not measured 4 11/16 Straight not applicable 3/4
E 2 not measured 4 9/16 Straight not applicable 9/16
F 2 not measured 4 3/8 Straight not applicable 9/16
F# 2 not measured 4 1/4 Straight not applicable 5/8
G 2 not measured 4 1/8 Straight not applicable 9/16
G# 2 not measured 4 Straight not applicable 5/8
A 2 not measured 3 7/8 Straight not applicable 9/16
A# 2 not measured 3 13/16 Straight not applicable 9/16
B 2 not measured 3 11/16 Straight not applicable 9/16
C7 2 not measured 3 5/8 Straight not applicable 1/2

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