Tuning the Soundboard
A goal this month was to glue the soundboard to the body creating an acoustic chamber. Ordinarily, the soundboard is glued to the rim before the back is glued to the rim. There is no harm in gluing the soundboard last but it does complicate tuning.
Tuning the soundboard can be simply described as removing enough wood from the carved soundboard and its bracing (making them less stiff) in order to adjust the resonance pitch to a desired frequency. All solid objects have a resonance frequency. (like a champagne glass, a tuning fork, a suspension bridge, etc. see Tacoma Narrows Bridge collapse).
The resonance pitch is the frequency at which the soundboard resonates when tapped with your finger or the eraser end of a pencil. A microphone and a strobe tuner (like the Peterson pictured here) are also necessary to capture and record the tap tone. These electronic tuners are made for recognizing notes that are sustained, i.e. as a vibrating open string on a guitar. The soundboard tap tone is very brief and an electonic tuner may not capture it. For those with a good ear, listen to the tap tone and hum it back into the tuner. Otherwise, tap repeatedly in short bursts and observe the tuner screen
Woody's Understanding of Resonance Theory
One would think that, since many mandolin/violin melodies are played in the key of D or A, it would be helpful if the soundboard (and later the entire acoustic chamber) were tuned to a resonance pitch of D or A.
Not so much. The tone of a stringed instrument will be enhanced if the resonance pitch exactly matches a note in the 12-tone octave. If the instrument naturally resonates at the note D3 (for instance, 146.8 hz) the box will boom when that note is played. Far better to tune the box to a pitch that compliments the key note... like F#, the major 3rd and a component of the D major chord (like C#, in the A chord).
The important part is to tune the soundboard resonance to the exact frequency of one of the standard 12-tones... not sharp or flat. If the instrument's resonance pitch is a few cents sharp or flat of a particular note, it will create beats when the note is played. These are called "wolf" notes because the instrument will howl (woo-woo-woo) when that note is played. This is not good for the player. At minimum, the player will have to adjust their attack every time the wolf note is played.
The good news is that wolf notes are primarily a problem for bowed instruments where the bow allows the notes to sustain. With instruments, like the mandolin, that are plucked (picked), the problem is not so great an issue... at least for beginners. As one's ear develops, however, one becomes more acutely aware of the balance of timbre, tone and volume. The best and most expensive vintage instruments were properly tuned in their creation. That's how they became the best and most expensive.
For those who have visited Woody Strings before, I believe that the "pictures covering the text" problem has been solved (finally). Please let me know if you are having any trouble. (firstname.lastname@example.org)
Below there are 14 photos of 7 famous folk and pop singers/ song writers. Can you match the adult photo with the childhood photo? Who's who?
While all the glue is drying and my ears are still ringing from amplified frequency testing, the neck, fretboard and headstock are waiting to get some attention.
The neck needs a truss rod, the fretboard needs frets and inlays, and the peghead needs carving and drilling for Shaller tuning machines. The style of this peghead is a mild version of what is referred to as "Snake Head" because it tapers from back to front. By angling the line of tuners toward the center line of the peghead, a normal-sized peghead can accept 8 strings and tuners without them getting on top of each other.
Inlay and binding are yet to be decided.
Angles and Clearances
Tuning the soundboard is, as I have said, a matter of removing wood, i.e. reducing the stiffness of the soundboard, thus, lowering the resonance pitch until it is at exactly the frequency of one of the standard 12 notes. The exact frequency (in hertz) will impact the timbre of the tone of the instrument. Lower frequencies enhance bass response, perhaps inhibiting projection. Higher frequencies enhance the treble tones, perhaps at a loss of volume.
Knowing all of this helps tune the soundboard, the primary driver of sound waves through the acoustic chamber. The builder cannot, however, know the resonance frequency of the entire instrument until it is finally assembled. This is the true test... i.e., the resonance frequency of the assembled instrument... but tuning the soundboard and to coordinate with the backboard is the necessary place to start.
First, an acoustically symmetrical soundboard is essential to having the instrument behave efficiently. In saying "acoustic symmetry" I mean that the vibrations coming through the bridge travel across the soundboard in a symmetrically balanced pattern (like ripples in the water after a stone is dropped). Another way to say it is that the resistance to the travel of vibrations is symmetrical. This allows the entire soundboard to move in harmony with itself.
Acoustic symmetry can be tested with the following set up and observation.
Tuning the Soundboard
Closing the Box
This mandolin will be left in the natural color of the woods used, primarily maple and spruce (no stains or toners). Therefore, to provide a contrasting frame for the body, the bindings must be dark. As Woody only uses wood bindings, that means rosewood binding stock (0.250" x 0.080" x 36") which must be heated and bent... too hot and the rosewood will burn, not hot enough and rosewood will break when bent. It is satisfying to get it right. When complete, the rosewood provides a nice border between the maple rims and the spruce soundboard.
As you can see...I've been busy.
Still have a ways to go. I believe that next month at this time we will have something close to a complete mandolin.
Please come back and see.
Wooden J. Strings (aka Joe Lenzi, Luthier)
Sprinkle glitter (or saw dust, or salt, etc) over the inside surface of the soundboard. Place the soundboard on an acoustic amplifier such as a guitar amp laying on its back, as you see in the pictures below. The output of a tone generator is input into the amplifier. Then, starting about A3, raise the pitch one note at a time until a resonance frequency is hit, the soundboard will vibrate in a certain, very obvious pattern. These are called Chladni patterns, named after a German physicist (1756-1827).
As the generated notes are amplified, only the resonance notes will cause the glitter to vibrate into patterns. As other notes of the octave are played through the amplifier, the soundboard glitter just stays scattered and in place... almost motionless. At the resonance pitch the glitter jumps and bounces and finally accumulates along the nodal lines forming a distinct pattern (shown below).
The symmetry of the patterns will tell the maker a great deal about the efficiency of the soundboard in transferring vibrations across and along the grain lines of the soundboard. Symmetry is good. The absolute frequencies at which the soundboard reacts are important, especially in relation to matching the acoustic properties of the back. There is a good, general explanation of Chladni patterns in violins at this URL.
The mandolin under construction reacted to three distinct notes. The actual frequencies that generate the patterns should be noted, but it is the shape of the patterns that are most useful as guide to the luthier in the final removal of wood for the purpose of adjusting the resonance pitch of the entire soundboard.
Final Note: In the amplified set up we used here, the soundboard is only being driven by external sound vibrations from the amplifier. As a musical instrument, the mandolin soundboard will be driven by the vibration of the strings, through the bridge. The bridge, in turn, is in contact with the soundboard at only two points, the feet of the bridge, which are directly above the arms of the lower X braces. In first photo I have marked where the feet of the bridge will rest above the braces. The height of these braces directly impacts the stiffness and resonance of the soundboard.
Closing Up the Box
After flat sanding the top of the rim, the lining and the blocks into a true plane, the top is glued onto the body. Leave the soundboard an extra 2 mm over the edge of the rim all the way around. This safety margin will be routed away with the rabbet for the binding.
OK. Now we're ready. Woody was mandolin-busy in January. Below are a few pics from January, 2017.
There are a number of styles of mandolin truss rods on the market today. The version that Woody prefers is referred to as "standard welded end" (Luthier's Mercantile, Inc). This truss rod is made for mandolins. It is 7-1/2" long, 3/16" wide and requires only a 3/8" deep slot. It does not require a spline as the top welded bar is square in cross section. Bottom line: the neck can be thinner with this truss rod.
Before the soundboard can be tuned or attached to the body, the rosette is inlaid. The photo below was actually taken after the soundboard and the bindings had been installed. The rosette is a challenging inlay around the oval sound hole as the soundboard slopes both across and along the center line of the soundboard at this point.
This mandolin is being built for playing Irish/ Celtic melodies, and fiddle tunes per the preference of the owner. Note that a carved Celtic knot design was glued to the inside the tone chamber under the sound hole. This, of course, is a unique feature complimenting the owner's taste for Celtic music. The Celtic knot medallion will be an interesting surprise for those looking through the sound hole into the box.
The fretboard will get far more attention soon. A couple of weeks ago I took time out to inlay the position markers and press in the frets. The final dimensioning of the board will not take place until after it is attached to the neck. The face of the fretboard is currently covered in masking tape... so no picture this month.
Angles and Clearances
As a matter of quality check, I placed the neck onto the body, i.e. inserted the dry dovetail into the dry head block. Then I checked the break angle and height of the strings at the bridge. Standards are 18-20 mm string height at the bridge and the string break over the bridge should be 16-18 degrees. Much of this is determined by the neck angle which can only be modified very little at this point. To my gratification, all the target specs were met in this initial lay up.