Finger Piano Tuning

  1. Provide a step by step approach to tuning your instrument.
    1. Set up an electric amplifier and attached microphone in a quiet workspace.
    2. Hold the microphone against the edge of the finger piano’s resonator box opposite from the keys.
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    3. Strike a key and adjust the audio quality of the amplifier to produce the clearest possible sound.
    4. Loosen the wingnuts on the right hand side and the center of the bridges by turning them counter clockwise. This should allow the bridge to be lifted slightly.
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    5. The right side of the bridge will hold the keys that produce the higher frequencies – E3, D3#, D3, C3#, C3, and B2. Place the shortest keys underneath the right hand section of the bridge.
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    6. Adjust the length of the free section (not constrained by the bridge) of each key to match the length calculated using the general equation.
    7. Tighten the wingnuts to exert the greatest force possible on the ends of the keys (in order to restrict the motion of the ends of the keys).
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    8. Open the ClearTune app on an IPhone and place the IPhone on the resonating box between the microphone and the keys.
    9. Pluck each key (from highest to lowest) and record the frequency and note measured by the tuning app.
    10. Compare the measured frequency to the desired frequency.
      1. If the desired frequency is higher than the measured frequency, loosen the wingnuts and shorten the free section of the key. Tighten the wingnuts, strike the key, measure the frequency, and continue to adjust as necessary to reach the desired frequency.
      2. If the desired frequency is lower than the measured frequency, loosen the wingnuts and lengthen the free section of the key. Tighten the wingnuts, strike the key, measure the frequency, and continue to adjust as necessary to reach the desired frequency.
    11. Repeat steps E-J on the left hand side of the bridge using the longer keys.

How did you measure the frequencies produced by your instrument?

I amplified the sounds produced by the vibrations of the keys using a microphone and an amplifier, then used the ClearTune app for IPhone to measure the frequency produced by each key at various lengths.

Provide details on the frequency you measured versus what you calculated.

  • The frequencies on which I based my length calculations corresponded directly with the desire notes. The frequencies to which I tuned the finger piano are 10 or fewer Hertz away from the desired absolute frequencies of the notes, depending on the key.
      • How did you go about fixing the discrepancy?
        1. The discrepancies in frequency between the absolute frequency of the desired note and the frequency of the key at its calculated length were reduced by adjusting the length of the keys until the frequencies produced by striking the keys was as close as possible to those of the desired notes.
        2. The following are the calculated lengths of keys vs. the lengths of keys after adjustments to produce the correct pitch.
        3. Note f (Hz) L (m) Actual Length (adjusted) (m)
          F2 87.31 0.061345708 0.0681
          F2# 92.5 0.05959987 0.0652
          G2 98 0.057903277 0.0627
          G2# 103.83 0.056254174 0.0612
          A2 110 0.054653734 0.0599
          A2# 116.54 0.053098062 0.0589
          B2 123.47 0.051586428 0.0567
          C3 130.81 0.050118228 0.0547
          C3# 138.59 0.048691172 0.0525
          D3 146.83 0.047305189 0.0496
          D3# 155.56 0.045958644 0.0488
          E3 164.81 0.044650302 0.0476
      1. The ClearTune app was accurate enough to allow me to adjust my keys to produce the desired notes. I tested the ClearTune app against a Pitch Pipe app called Pitch Perfect (for Windows phone). A Pitch Pipe produces single, sustained notes, and I assessed the accuracy of ClearTune by playing individual notes and testing whether the note detected by ClearTune matched the note played by the pitch pipe.Did you feel that the frequency measuring device/software was accurate?  How did you validate its accuracy?

Summarize your learning:

Any future builders should be very cautious when adjusting the length of a key to ensure that they do not slightly shorten or extend any other key — even the slightest adjustment to the length of a key can drastically change its pitch.

It is essential that the wood used for the bridge is stiff (but not brittle). If the bridge is pliable, the keys in the middle of each subsection will not be held in place, allowing the portion of the key underneath the bridge to vibrate against the wood, producing an unpleasant sound. If the keys cannot vibrate underneath the bridge but are not held firmly in place, the lightest bump can jar the key and change its length, thus changing the note. To fix this, simply tape the end of the key (on the opposite side of the bridge from the free section of the key) to the box to hold the key in place.

Be sure that no keys overlap each other. Overlapping keys will restrict the vibration of said keys.

What should the next builder be cautious about when they build and when they tune? What do you wish you had known/thought of during the construction process?  In other words,  what issues cropped up during tuning that you might have avoided if you had taken care of it during building?

The resonant frequency of the resonator box is closer to that of the higher-frequency notes produced by the finger piano. When these notes are played, the latch that closes the box vibrates, producing a rattling sound that is both nearly as loud as the note itself and very unpleasant. During construction, I should have either removed or better secured the latch to avoid this sound.

For explanation of the harmonics:

Harmonics of Finger Piano

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Finger Piano: Building Proccess

Provide a step by step procedure you used to build your instrument:

1. Cut basswood into two seven-inch-long sections.

2. Cut one section of basswood to a width of 1.5 cm. and the other to a width of 2 cm.

3. Sand down all edges of the basswood. These are your bridges.

4. Mark a line down the center of each bridge (lengthwise). On this line, mark points 1/2 inch away from each end. Directly in the center of the bridge (3.5 inches from each end), mark a point.

5. Put on safety glasses and turn the operation light of a drill press. Turn on drill press and lower the bit very slowly towards the wood. At each point marked along both bridges, drill a hole. Be sure to be as close to center as possible. The holes should be roughly 3/16″ wide.

Drilling holes in the basswood bridges

Drilling holes in the basswood bridges

6. Sand the outside of each hole drilled in the bridges.

7. Clamp both bridges to the pine box with the holes facing up. The bridges should be exactly parallel to each other and the edge of the box. Place them along the side of the box parallel to the seam along which the box opens. These bridges should not be on the side of the box that holds the clasp or the side that hold the hinges.

Side of box- note position of bridge.

Side of box- note position of bridge.

8. Using the holes in the bridges as guides, gently drill through the side of the pine box so that a bolt can fit neatly through holes that run from the bridge through the wood.

Drilling holes in the bridges

Drilling holes in the bridges

Drilling the holes through the pine box (Held in place with bolts, not clamp)

Drilling the holes through the pine box (Held in place with bolts, not clamp)

9. Sand both the top and the bottom of each hole in the box.

10. Push carriage bolts through the holes in the box and bridge so that the heads of the bolts are inside the box. This should require six bolts: three bolts through the thicker bridge and three through the thinner bridge. The bolts that fit through the thicker bolts should be 4″, and the bolts through the thinner bridge should be 1″. Both sets of bolts should be 3/16″ wide (i.e. radius of 3/32″). Between the bolts should be two equal sections of bridge.

Inside of box- Note position of the heads of the bolts

Inside of box- Note position of the heads of the bolts

11. Holding the bolts from the outside of the box, pull gently to lock the bolts in place.

12. On the portion of the bolts on the outside of the box, place one washer and one wingnut (that fits with a 3/16″ bolt).

13. Placing the washer at the base of the bolt (outside of the box), spin the wingnut until it touches the washer.

Top of bridge - Note position of the washers and wingnuts on the bolts.

Top of bridge – Note position of the washers and wingnuts on the bolts.

12. To make the keys, mark the putty knives with horizontal lines 1 cm. apart. There should be six 1 cm.-wide sections per putty knife

13. Using a metal shear, cut the putty knives along the horizontal lines. The keys will differ in length. There should be twelve keys.

Metal shear and handle of putty knife after cutting

Metal shear and handle of putty knife after cutting

14. Using a metal file, file the edges and points of the keys.

15. Arrange the keys by length.

16. Lift the bridges slightly from the box. Slip the keys under both bridges so that the keys extend over the edge of the box. Leave the shortest possible length of key free on the opposite side of the bridge. The keys should be arranged by length, with six keys in each section of the bridges (delineated by the bolts).

Arrangement of keys

Arrangement of keys

17. To tune the keys, extend the free end to decrease pitch and shorten the free ends to increase pitch. To change the length of the free end of the key, push the key towards the bridge or pull the key away from the bridge.

18. Tune the piano to a range between F1 and E2. The shortest keys should play the highest notes/frequencies. The key lengths necessary to produce each note is listed below (in meters). The following values are the calculated values for length. They need to be modified.

Note

f (Hz)

L (m)

F2

87.31

0.061345708

F2#

92.5

0.05959987

G2

98

0.057903277

G2#

103.83

0.056254174

A2

110

0.054653734

A2#

116.54

0.053098062

B2

123.47

0.051586428

C3

130.81

0.050118228

C3#

138.59

0.048691172

D3

146.83

0.047305189

D3#

155.56

0.045958644

E3

164.81

0.044650302

19. Once the keys are adjusted to produce their correct notes (including adjustments), tighten the wingnuts until the bridges put enough pressure onto the keys to hold them in place.

Materials List:

Item Number Price ($)
1.5 ft. of basswood (1” x 1”) 1 Free (In woodshop)
7” x 7” x 3” Pine box w/ clasp 1 2.99
4” Carriage Bolts (3/16” wide) 3 0.20 (each)
1” Carriage Bolts (3/16” wide) 3 0.15 (each)
Wingnuts 6 0.20 (each)
Washers 6 Free (In woodshop)
Spring Steel Putty Knives 2 3.99 (each)

Adjustments:

  1. The calculated lengths for the keys relied on a variety of factors which I could not calculate exactly. First, I did not use the speed of sound in spring steel in my equation. Instead, I used the speed of sound in stainless steel, which is a slightly similar alloy. This will alter the calculated lengths of my keys very slightly.
  2. As the pitch increased, the harmonic of the vibration could have increased. Because the equation for length involves the variable m, which is equal to (2n-1) – n represents the harmonic number, the harmonic of the vibration affects the calculated lengths. It should be noted that the equation (2n-1) represents the pattern of harmonics for vibrations in bars with one free end: the harmonic number will always be odd (i.e. harmonics 1, 3, and 5 are possible, not 2 or 4).
  3. I cannot devise an equation to account for the adjustments in the lengths of the keys without a deeper understanding of the causes of the inaccuracies. Such other causes could be the width of the key, the pressure holding the key in place as exerted by the bridge, and the force with which the key is struck.

Resources:

http://www.ehow.com/how_5616221_make-thumb-piano.html (Other method)

Finger Piano Physics- Calculating Length and Building a Prototype.

1. Frequencies of desired notes and corresponding calculated lengths of keys:

Note f (Hz) L (m)
F2 87.31 0.061345708
F2# 92.5 0.05959987
G2 98 0.057903277
G2# 103.83 0.056254174
A2 110 0.054653734
A2# 116.54 0.053098062
B2 123.47 0.051586428
C3 130.81 0.050118228
C3# 138.59 0.048691172
D3 146.83 0.047305189
D3# 155.56 0.045958644
E3 164.81 0.044650302
  1. Provide a reasoning on why you selected this particular octave (middle versus higher or lower).  Perhaps due to length restrictions etc.  Show calculations showing what your minimum and maximum lengths are.

I selected this octave of a middle frequency based on the calculated lengths necessary to produce the frequencies of these notes. I have a length limit to the keys of my finger piano, with the length of my longest key with the shortest possible section held under the bridge representing the maximum length (9 cm) and the length of my shortest key with possible section held under the bridge representing the minimum (4 cm). These restrictions are simply a function of the material from which the keys were cut: the putty knives provide inherent limits on the length of the keys, because unlike wood, they are not sold in a variety of lengths. Notes of higher frequencies are more audible on these keys. Therefore, within my length limits, the 2nd and 3rd harmonics are the most audible and possible to produce.

Calculations: See attached documents.

  1. Prototype:
    1. How did you prototype your instrument without building an exact replica?
      1. Using a box of similar dimensions and of identical wood to the body of my final instrument, I attached two bridges made of maple to the side of the box adjacent to the hinges. These bridges were made of a lighter, more flexible wood than the bridges of my final instrument. The smaller of the two bridges was 1.5 cm. wide by 1 cm. tall. The larger bridge was 2 cm. wide by 2.5 cm. tall. These bridges were divided into two sections and attached to the box with three hexagonal bolts, with the head of each bolt in the interior of the box and the opposite end holding the bridge in place by a washer and a wingnut. The bridges held in place the twelve spring steel keys, with five keys per section. The keys lengths were adjusted by loosening the winguts and lifting the bridges to extend or shorten the length of the key that was free to vibrate. The space between keys and the space between bolts was greater than those on the final instrument.
    2. What design considerations were you hoping to validate with your prototype?
      1. I did not cut a hole in the resonator box in my prototype to test whether the sound would be sufficiently amplified without the hole. I also tested the importance of the pliability of the wooden bridge, and I tested whether placing the keys perpendicular to the resonating surface would sufficiently amplify the notes.
    1. What did you learn from this experience and how do you intend to change the actual design or building process?
      1. The wooden bridge on my prototype was very pliable, and the sections of bridge between the bolts bent in the center, reducing the pressure on the keys in the center of each section and allowing both ends to vibrate slightly, producing an unpleasant sound. In my final instrument, used  basswood bridges, which are much stronger than my previous maple bridge and apply pressure evenly to the ends of the keys.
      2. I initially used hexagonal bolts to fasten the bridge and apply pressure to the keys, but the hexagonal bolts do not grip the wood. Once the bolts were tightened to a certain point with the wingnuts, the bolt would turn in its hole and no more pressure could be applied. In my final instrument, I fastened the bridges with carriage bolts, which dig into the wood and hold themselves in place.
      3. The frequencies that are amplified by the resonator box without the hole are D2, D2#, and E2, which are the highest frequencies on the finger piano. I am considering whether the final instrument requires a resonator hole to amplify all notes. One possible change would involve removing the back of the box and extending the keys perpendicular to the opening to amplify all notes and leave the un-plucked ends of the keys to vibrate freely.
      4. 4. Calculation explanations:
Note f (Hz) π v (m/s) K m L (m)
F2 87.31 3.141592654 5790 0.000144509 1 0.061345708
F2# 92.5 3.141592654 5790 0.000144509 1 0.05959987
G2 98 3.141592654 5790 0.000144509 1 0.057903277
G2# 103.83 3.141592654 5790 0.000144509 1 0.056254174
A2 110 3.141592654 5790 0.000144509 1 0.054653734
A2# 116.54 3.141592654 5790 0.000144509 1 0.053098062
B2 123.47 3.141592654 5790 0.000144509 1 0.051586428
C3 130.81 3.141592654 5790 0.000144509 1 0.050118228
C3# 138.59 3.141592654 5790 0.000144509 1 0.048691172
D3 146.83 3.141592654 5790 0.000144509 1 0.047305189
D3# 155.56 3.141592654 5790 0.000144509 1 0.045958644
E3 164.81 3.141592654 5790 0.000144509 1 0.044650302

Calculations/Explanations/Nodes and Anti-nodes: See attached document.

Calculations of Minimum and Maximum Lengths

Blog Post 1

I have begun the process of building a finger piano, which will consist of eight or more bamboo or spring-steel keys laid across a bridge and extending over a resonating chamber. The finger piano (or Mbira) has two origins: The wood-keyed piano was first used 3000 years ago in West Africa, and the metal-keyed version was developed in the Zambezi River area of Southern Africa around 1,300 years ago. The finger piano is a part of the Lamellophone family, which create sound by vibrating a series of thin plates with one attached and one free end.

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The finger piano seemed to be the instrument that would require a good amount of engineering without running the risk  of sounding awful.

The finger piano is a percussion instrument in that it produces sound by being struck. Within the realm of percussion instruments, the finger piano is an Idiophone, which produce sound by striking metal bars or chimes. More specifically, it is a plucked Lamellophone, which produces sound by plucking a series of keys or tines.

The initial medium for the sound waves in this type of instrument are the metal keys. The vibration originates at the free end of the key and travels through the key and into the base on which the keys are mounted.

The nodes of the finger piano (the point at which the medium is least displaced from equilibrium) is the point at which the keys meet the bridge of the piano. The vibration passes through the key as a transverse wave, and the displacement from the equilibrium decreases as the wave moves towards the bridge. Therefore, the node is at the point at which the key can move the least — the point at which the key meets the bridge, where it is held in place. The antinode (the point at which the medium is most displaced from equilibrium) is at the free end of the key, the movement of which is least restricted by the force of the bridge. In any harmonic, a node exists at the fixed end and an antinode exists at the free end.

The materials necessary for the construction of a finger piano are:

# Material Price ($)
2 Putty Knife 3.99 (each)
1 Wood Box/Cigar Box 1.50
6 Small wood screws 0.06
1 1”x1”x1’ Wood 0.99
1 Craft Glue 1.50
1 30 cm. of Copper Wire 0.30

An alternative to the putty knives: 1 meter of Bamboo (Free).

A few sources that could give some direction on the project:

http://www.instructables.com/id/Instant-Thumb-Piano%3a-How-to-make-a-set-screw-lamel/step9/Other-Emphases/

http://makezine.com/projects/thumb-piano/

http://www.thewidgetforge.com/projects/thumb_piano/keys.html

I am still unsure how I can build a bridge that does not damp the vibration of the keys. I also cannot clearly visualize the vibration of the keys — this is largely because I do not understand pliability. I am operating under the assumption that the maximum amplitude of the vibration occurs at the free end of the key, though I cannot explain the reasoning behind my assumption.