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jdowning
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The inside edge of the sound hole is reinforced with full depth black-white-black purfling made by 'sandwiching' plain maple veneer between maple
veneer stained black. The glued veneers - with non-stick oven paper on either side - were taped to a cardboard tube of about the same diameter as the
sound hole with the grain of the veneer running parallel to the axis of the tube. No hot bending of purfling made this way is required. The pre-formed
purfling was further reinforced with a piece of black fine silk fabric (paper would do just as well) glued on top of the 'sandwich' as a final
layer.
Once the glue had cured slices - about 4 mm wide - were cut, freehand, from the 'sandwich' using a fine tooth razor saw - the cardboard tube providing
the necessary support during the cutting process. Additional segments were cut for spares or use on another future project.
The segments, with ends trimmed square with a razor blade, were then glued and taped to the inside edge of the sound hole. Four pieces and a bit were
required - the last piece being the most difficult to fit precisely.
The excess material was trimmed using a scraper blade so that the purfling was made level with the sound board surface. A properly sharpened scraper
blade is the best (perhaps the only) tool for the job as it quickly removes fine shavings from the end grain purfling without causing grain 'tear
out'.
The soundhole iner edgehas been completed with a solid, hot bent, ebony strip to protect the vulnerable end grain purfling.
 
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jdowning
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With the neck temporarily screwed to the bowl and alignment checked the finished sound board was placed over the two braces and aligned with the bowl
centreline. Two small trigger operated clamps were then arranged - passing through the sound hole- to hold the upper brace in position. The sound
board with clamps attached was then lifted from the bowl and the outline ends of the brace marked exactly with several strips of adhesive tape to
provide positive, precise registration for the brace when being finally glued into position. This was just a 'dry run' test to check the viability of
the method. Seems pretty straight forward! The braces will be glued one at a time to ensure an optimum fit without need for further fine adjustment to
the fit of the brace ends. Hopefully this arrangement will ensure fast and perfect registration of the sound board when being glued in place.
The little clamps - made in China - cost less than a dollar each from a local 'Dollar' store. They do not provide a lot of clamping pressure but are
fine for this particular application. Clamping pressure is released with the press of a button. The clamps can also be arranged to press in the
opposite direction - rather than squeeze - if required.
 
 
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jdowning
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The first brace has been set up for gluing. The hide glue is to soak in water overnight so this brace will be glued tomorrow.
In the meantime other components are being prepared.
One great thing about this project is that the instrument only has three tuning pegs to make and fit! I have a quantity of lute pegs in stock - rough
blanks turned as a batch years ago from Brazilian 'boxwood' or Castello. This is not a true boxwood but is very similar and is often used as a
substitute for the real thing. I will use the same wood for the fingerboard.
The peg shank taper is cut with a peg shaver or cutter (a kind of giant pencil sharpener) made using my peg reamer - so ensuring the exact peg shank
taper.
My pegs are made in the style of the old lute pegs - the peg heads being simply cut flat with a chisel (not fancy curved as on a violin or on some
modern ouds). In keeping with the metal to wood theme of this project I may add a decorative 'silver' ring to each finished peg. More on that
later.
  
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rootsguitar
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looking great! You've been putting in some good hours.
I had to let you know I had the good fortune of seeing a Colascione played live last night...by musician Will Morris.
There were also two lutes & a percussionist.
Ron McFarlane's band Ayreheart at a small irish pub. Great music.
The instrument added bassier sounds in a welcome way & could see it being used in a lot of settings...
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jdowning
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The Ayreheart group have posted a number of pieces on YouTube that include a colascione. Here is one - an arrangement of the late 16th C lute
composition by John Dowland (no, not directly related although both the family names are Irish!)
https://www.youtube.com/watch?v=MzF3SVBzjCY
and another
https://www.youtube.com/watch?v=I6kHuN_0OfE
The Will Morris example of a large colascione has four(single) courses that seems to be the norm for modern performers - usually (?) with the courses
tuned either a fourth apart (like the 3rd, 4th, 5th and 6th strings of a classical guitar) or a fifth apart - G D A E for example. I am not sure if
either tuning is historically authentic as colascione performance was an oral, unwritten tradition - obsolete and forgotten since the 19th C - and
what little written evidence that survives is from observers who were not players of the instrument. However, if today it works musically 'go for it'
- although I suspect that the Italian folk instrument was originally fretted in a much more interesting manner than the (approximately) 12 tone Equal
Temperament fretting of a lute.
This project colascione is a smaller three course instrument (Mezzo-colascione) - the early colascioni having only two or three strings - and we know
from historical record that the tuning of a three stringed colascione in the 17th C was an octave and a fifth. So this project instrument, with a 79
cm string length, will end up being tuned G g d' (A415 pitch standard).
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jdowning
Oud Junkie
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The second brace has been glued to the sound board and while the glue is left overnight to cure.
The three pegs have been shaped, fine sanded and burnished.
Each peg measures 75 mm overall in length.
Peg collars and end dots have been added as a decorative feature - made from 1.5 mm diameter soft tin wire (available from hardware stores as lead
free solder - it is actually an alloy of 96% pure tin and 4% pure silver). This metal looks like silver but does not tarnish black like silver so tin
was often used in the past for inlay work in place of silver for this reason.
Pure tin, of course, is the coating on the tin plate ribs of the project bowl.
The procedure for making and fitting these peg collars is described in an earlier project on this forum - posted here on 1-11-2010.
http://www.mikeouds.com/messageboard/viewthread.php?tid=8488&pa...
 
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jdowning
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The sound board braces have been planed to final shape and the sound board dry fitted to the bowl ready for gluing. The precise registration of the
brace ends into the pockets in the bowl liner will allow fast, correct positioning when gluing the sound board to bowl where 'speed is of the essence'
when using hot hide glue.
The neck/pegbox assembly has been shaped close to final dimensions and the neck has been aligned and glued to the neck block. The upper surface of the
neck has been planed level with the bowl sound board joint surface. Final finishing of the neck will be done after the sound board and fingerboard
have been glued in place
The fingerboard blank has been made from two butt joined pieces of Brazilian boxwood (the raw boxwood billets being only about 38 cm in length) and
has been planed flat ready for gluing to the neck. The fingerboard increases in thickness towards the nut by 1 mm.
With the neck and bowl centrelines in alignment the bridge may now be precisely positioned and glued to the sound board (to be done prior to gluing
the sound board to the bowl).
To keep things initially as plain and simple as possible (to save time in progressing the work) the usual inlay work such as sound board and
fingerboard edge banding will be omitted but will be added later after the instrument is otherwise complete. I am particularly interested to find out
how much influence the sound board edge banding may have on the overall acoustic response of the instrument - measured by 'before and after testing.
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jdowning
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With the sound board temporarily taped to the bowl, the bridge blank has been positioned with tape and the string height at the bridge determined
using a steel straight edge laid on packing at the nut position (1mm string height above the fingerboard) and 16th fret position (3.5 mm action above
the fingerboard). With string height determined the bridge blank was drilled for the three string holes and carved to shape.
In preparation for gluing the bridge, its position on the sound board has been temporarily marked with three layers of adhesive tape - an aid for
precise registration, important when working quickly with hot hide glue,
The bridge will now be finished and stained black before gluing. After gluing the bridge in place, ebony 'dots' will be added to each end of the
bridge as a plain decorative feature.
The bridge material is European Pear wood cut from a small tree in my neighbours garden many moons ago (with permission!) and air dried in small
billets for peg or bridge making. Nice close grained wood for carving and relatively low density.
  
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jdowning
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The completed bridge has been stained black with 'Indian ink' available from any stationary or office supply store. This ink is shellac based so dries
quickly and penetrates well to a dense dark black. For convenience in handling the bridge when staining and gluing a wooden 'toothpick' has been
pushed into the central string hole.
To glue the bridge strong dry granulated hide glue (Lee Valley cat#56K50.01) has been mixed with about 50% water by volume and left overnight for all
water to be absorbed. The glue - in a clean glass jar - has been heated in a pan of simmering (just boiling) water until fluid enough for use (the
glue runs off the glue brush in a steady stream). The water bath prevents overheating and so spoiling the glue and its strength.
The bloom strength of the glue is rated at 260g so it is very strong - drying to a glass hardness - but gels quickly so set up must be uncomplicated.
The set up was tested with several 'dry' runs to determine the optimum position for the spring clamps so that they do not slip and spoil the job. In
fact clamps are not essential as the bridge may be held (with great patience) in place with only finger pressure for a few minutes until the glue sets
- I prefer to use clamps particularly at the thin, flexible ends of the bridge to ensure that they lay in contact with the sound board surface. A flat
board is also temporarily positioned under the sound board as extra support during the gluing operation.
With the bridge glued in place and glue 'squeeze out' cleaned up with a sharp chisel, the next operation is to glue sound board to bowl. The same
batch of glue, slightly diluted, will be used for this operation as high strength is not required or desirable for the soundboard to bowl joint.
  
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jdowning
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With relative humidity in our wood stove heated kitchen at an ideal 50% the sound board has been glued to bowl with hot hide glue. The glue has been
diluted a little to extend the time until it gels - tested on a scrap of wood. This allows maximum working time but there is still a need to work
quickly.
As counter top working space in the kitchen is restricted the pegbox has been wrapped in protective 'bubble wrap' - the long neck of the colascione
presenting some difficulty in handling without risk of knocking breakable stuff off nearby shelving. As it happens all went well without mishap.
Both joint faces were given a coat of glue brushed on and the sound board pressed in place and clamped using strong elastic adhesive tape (3M binding
tape from Lee Valley cat#25U03.30) starting with the brace end positions, then the neck block location followed by the remainder of the joint. As it
is not possible to complete the procedure before the glue starts to gel it is necessary to go over the entire joint again with a hot iron to seat
those few sections that have not closely joined. Those areas are first moistened with a little hot water applied with a small brush to soften the glue
before being re-taped - once the glue is seen to remelt with the heat application.
The instrument will be left in a warm place overnight for the glue to fully cure. After removing the tape the joint will be checked again for proper
fit and any corrections made (the glue reconstituted with heat and moisture - a benefit of hot hide glue). The sound board edges will then be trimmed
to size.
The glue pot goes into the refrigerator to prevent bacterial spoiling and the glue will be used again tomorrow for gluing the fingerboard to neck.
Reheating hide glue will cause deterioration of the glue strength but a third reheat is acceptable for this application after which the remaining glue
will be thrown out.
  
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antekboodzik
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What kind of tape do you use? Doesn't it tear small wood fibres, when removing?
Another question I would like to post, is that certain violinmaker told me, that 'used' (reheated many times) hide glue is even better that a fresh
batch. However, as he's working in a full time, he reheats (and adds dry glue or water, as he needs) almost everyday.
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jdowning
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The adhesive tape used is made by the 3M company (Scotch 233 brand) and is often used by the luthier fraternity for this application. Other 'Masking'
or painter's tapes of this type will also work but this brand is strong and will stretch before breaking so can apply a reasonable clamping force.
Another way of clamping is to quickly wrap string (or elastic rubber strip) around the bowl and sound board.
When removing the tapes they should be pulled folded back on themselves to minimise any risk of grain tear out of sound board fibres. Any micro fibres
that may be raised by the tape will be removed when the sound board surface is later finished smooth with a scraper blade.
When I attended wood working classes at school over 60 years ago only hot hide glue was used (synthetic glues were then an expensive curiosity). The
traditional cast iron glue pot was heated up in the morning and left on for as long as needed. The colour of the glue was dark brown (!) - so was not
in optimum condition for strength - but maximum strength is not required when gluing woodworking joints such as dovetails, mortice and tenon etc where
the strength is in a properly made accurate joint - the glue just holds everything together. In the class work a lot of glue was used in the course of
a day so was constantly being replaced.
The same applies to violins where maximum strength is not necessarily desirable - especially in the gluing of the top and bottom plates that may need
to be removed in future for repairs. The brittle nature of the cured glue of correct strength allows the plates to be separated without damage with
the insertion of a sharp thin knife blade into the joint.
More critical is the gluing of fixed bridges to lutes, ouds, guitars and the like so I use freshly made glue for that work and reheat the same batch
of glue for less critical applications. I am not running a commercial luthier enterprise so the glue pot is usually only in use for half an hour or so
in a day. It is then sealed air tight and put in the fridge to keep until next required - which may be a few days later as time permits. I only make
enough glue required for the work in hand (small quantities) to avoid waste.
My glue pot is a glass jar with sealed lid (the kind used for jam making) heated in a pan of hot water at just below simmering point. From experience
and previous trials with a thermometer, glue temperature is held within a range of 140 to 160°F (60 to 70°C). Above that temperature the glue will
burn and spoil.
The dry glue is placed in the glue pot and just covered with water. The glue will absorb the water in a matter of an hour or two but I usually leave
it soaking overnight for good measure. When the glue is hot and liquid I will test the gel time on a scrap of wood before use and by rubbing between
thumb and finger to test viscosity, 'tackiness' etc. All down to experience.
I do not add dry glue to the heated mix (to be avoided in my opinion) but make the glue viscous enough in the first place to require dilution by
adding small amounts of hot water as required.
After about 4 reheats any glue that is left over (small quantity) is thrown away. The remaining glue is removed from the jar by adding hot water to
dilute the glue residues. A dash of chlorine water (Javex bleach) is then added, the jar filled with fresh water, sealed and left standing for a few
days This kills any remaining organic material that is deposited as a white suspension and is poured down the drain to leave a bacterially clean jar
for the next batch of glue.
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jdowning
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The sound board and finger board edges have been trimmed to size, fingerboard levelled and neck shaped close to finished size. Pegs have been
preliminary fitted to check that there is sufficient string clearance in the peg box prior to final finishing.
Once final shaping is completed, the neck and pegbox will be stained black and clear varnished. The bowl (metal and wood components) will be clear
varnished. I had thought of applying a translucent red finish for a bit of dramatic effect but could not achieve satisfactory results on metal test
pieces.
So the colascione in its simplest and currently largely unadorned state - is almost complete.
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jdowning
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The neck has been shaped and finished to size ready for staining. I use small bronze spokeshaves for the basic shaping followed by a scraper blade
before final sanding smooth.
The shape of the neck profile is determined accurately by sight and 'feel' - I do not fuss around with templates for this class of work.
The little spokeshaves are sold as a set of three by Lee Valley (Cat# 61P10.10) and are comfortable to use.
Continuing the metal/wood theme a small solid brass knob has been fitted to the end of the bowl to serve as a button for a supporting shoulder strap.
Again this is an item that I already had in stock and so avoids me having to make one (a wide range of these small knobs are sold by Lee Valley -
listed in their Hardware Catalogue).
  
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jdowning
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The neck and peg box have been stained black and given a sealing coat of diluted oil varnish. The bowl has also been given a preliminary protective
coat of clear oil varnish. Further varnish coats will be applied so this operation could take some time to complete.
In the meantime the air resonance frequency of the bowl has been measured by tapping the bridge and recording the impulse signal at the sound hole on
a Zoom H2 digital recorder. The signal is quite strong - the air pulse being felt by my hand positioned above the sound hole.
Analysing the audio signal using 'Audacity' software, the spectrum analysis shows a pronounced air resonance frequency of 212 Hz. This value is about
three semitones higher than calculated - 179 Hz -assuming a sound hole 'dead zone' diameter of 0.67D (see previous post on page 2). It is also a
higher value than the second string pitch tuned at g 196 Hz (A440 standard) - tuning G g d' - by nearly 2 semitones.
Had this instrument been a perfect Helmholtz resonator, the calculated air resonance frequency - using the full sound hole area as 'active' - would be
240 Hz or about 3.5 semitones higher than 196Hz.
It will be interesting to see how the acoustic response turns out to be. Cutting a half depth rebate and banding around the edge of the sound board
would make the bowl/sound board combination less stiff and so would tend to lower the air resonance frequency. By how much? - hard to say without
trying.
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jdowning
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The G g d' tuning of a colascione is the early 17th C system noted by Mersenne. The later tunings varied. According to Franz Jahnel ('Die Guitar und
Ihr Bau' 1963), the number of strings on the colascione increased from two to five - the three string full size version being tuned E A d.
This implies that the half full size length of the fancy versions of mezzo-colascioni (such as the Dean Castle example) may have been tuned an octave
higher at e a d' - equivalent to the 4th, 5th and 6th strings or bass section of an equivalent 6 string guitar.
Six stringed classical guitars are designed so that the air resonance frequency of the body coincides with (or just below) the pitch of the 5th
string. Therefore, if the project colascione is tuned e165 Hz, a220 Hz, and d'294 Hz to represent the tuning of the bass section of an equivalent six
string guitar, then the measured air resonance frequency of 212Hz - being less than a semitone below the pitch of the second string (or 5th string
equivalent on a six string instrument) - should be about right for optimum bass response.
Both tuning configurations will eventually be tested to establish the optimum acoustic response for this instrument.
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jdowning
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Attempts to clear varnish the metal bowl have not been satisfactory so the bowl has been given a black 'Japanned' finish, a traditional coating for
tinware - in this case the brushed on matt black enamel will be given a protective overcoat of hard clear varnish.
The nut will be made from cow bone from stock prepared earlier from raw bone obtained from a local butcher. The two contact faces have been squared
and made flat on a sanding block. The bone has already been prepared and de-greased but will be further de-greased by immersion for a few days in
purified gasoline (the stuff sold for use in camping stoves) - just to be sure. An important step as any residual grease in the bone will eventually
leach out into the surrounding wood.
Bone preparation procedure was previously posted here:
http://www.mikeouds.com/messageboard/viewthread.php?tid=10403#pid70...
 
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jdowning
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Varnishing of the metal and wooden parts of the bowl and the neck is now complete but will be left for a few more days in a warm place to harden
fully. I have used a 'Spar' oil varnish from a local hardware store. It gives a gloss finish that I don't particularly like but the varnish should be
durable enough. The sound board is, of course, to be left unvarnished.
Stain, dust and varnish that has partially plugged the string holes in the bridge has been removed with a bit mounted in a jewellers drill.
The same procedure applies to the peg holes using a peg reamer. The stain in the wood acts as a useful indicator of the correct peg fit that should be
tighter at the peg head end of the shank than at the smaller diameter free end. This avoids risk of breaking the peg by twisting if it should stick at
the free end of the shank. The peg shank will be left extra long to accommodate any initial wear at the peg box. It remains to drill the string holes
in the shanks.
 
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jdowning
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The bone nut blank has been finally de-greased with lacquer thinner available from any hardware store and fitted in place. To ensure precise contact
with the wood of the fingerboard and pegbox all varnish and stain has been removed.
The next step will be to finally shape the nut and file and polish the string grooves before fitting the strings. At that point the nut will be held
in place with a small spot of fish glue - just so that it does not fall off and get lost at any time.
It will be interesting to see how the instrument stands up to full string tension.
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jdowning
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The colascione has now been strung and brought up to full tension to evaluate the action. No frets fitted at this stage.
Tuning is G g d' so conforms to the tuning of the tambura mentioned by Tinctoris on his visit to Naples in the late 15th C and the 17th C Colascione
described by Mersenne that was a development of the tambura.
The tonal range G to d' is the physical limit for plain gut strings at string length 79 cm.
For this test I have just used strings in stock - Pyramid 0.44PVF for d', 0.63 PVF for g and a worn wound #1017 for G. Total tension for the three
strings about 157 Newtons (or about 16Kg) - feels about right for me as a lute player. Pitch standard is A440.
First sound of the open strings is a kind of unusual powerful 'growl' - with a lot of sustain (about 20 seconds) for such a small bowl.
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jdowning
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The string tension is still stabilising but action height at the 16th fret position is about 3.5 mm treble to 4 mm bass (measured from underside of
string to surface of the fretboard). This is probably a bit on the high side even with frets installed and allowing for the amplitude of vibration of
the long bass strings.
The spectrum graph of the air resonance measured at the sound hole by tapping the bridge with the strings damped but up to full tension shows an air
resonance frequency of 197 Hz - matching the pitch of the middle string at g 196 Hz. Interestingly the air resonance test on the unfinished instrument
gave a value of 212 Hz - the only difference being the addition of the extra mass of two ebony dots on the bridge and the instrument being under full
string tension. The difference is a bit surprising so will run the test again to ensure the strings are completely damped and do not influence the
measured result. The long neck under tension may have something to do with it?
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jdowning
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I have re-run the air resonance test and the result of the spectrum analysis shows an air resonance frequency of 200 to 201 Hz - very close to the
pitch of the middle string (g 196 Hz). For this second test I made sure that there was no influencing effect from the strings by taking more care to
completely damp any string vibration - at the neck joint position and between sound hole and bridge - using cloth strips. The previous test shows some
influence of string vibration from an undamped section between the neck joint and bridge location.
This result is about a semitone lower in measured air resonance frequency from the preliminary test on the instrument when tested unstrung and without
the ebony 'dots' at the ends of the bridge. The air resonance frequency measured then was 212 Hz.
For this tuning (G g d' at A440 standard pitch) an air resonance pitch of about a semitone or two lower should provide optimum reinforcement of bass
response. This might be achieved by reducing the diameter of the sound hole slightly or by making the sound board more flexible by thinning around the
edges (or by installing a 1/2 depth binding) - modifications that will be tested in future.
Note that this instrument because of its stiff construction around the sound hole area, stiffer sound board and relatively high sound hole placement,
behaves a bit more like a true Helmholtz resonator than an oud or lute.
For purposes of calculating the air resonance frequency - the central 'dead zone' diameter of the colascione sound hole - based upon these measured
results - is about 0.56D rather than about 0.67D as it would be in the case of a single sound hole oud or lute.
For a true, perfectly rigid Helmholtz resonator with centrally positioned sound hole the whole area of the sound hole diameter D is used to compute
the air resonance frequency i.e. there is no central 'dead zone' where little air flux takes place across the sound hole area.
At this stage no changes or alterations will be made to the instrument set up and it is time to consider how the colascione should be fretted.
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jdowning
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A quick check on the calculated effect on air resonance frequency for this instrument, by reducing sound hole diameter - indicates that the sound
hole diameter would need to be reduced to about 7cm (from the current 7.8 cm diameter) to achieve about a one semitone reduction in air resonance
frequency or about 6.5 cm for a full tone reduction. These are all rough estimates as the diameter of the sound hole 'dead zone' measured from my
(albeit scientifically imperfect) sound hole acoustic trials indicate that the 'dead zone' diameter/ full sound hole diameter tends to diminish
proportionally as sound hole diameter reduces.
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jdowning
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I should mention that the air resonance test results have not been corrected for air temperature which does make some small difference. For
calculation purposes an air temperature of 20°C is assumed but house temperatures in Winter/Spring conditions may range anywhere between say 15°C
and 25°C. The speed of sound in air at 20°C is 343 m/s, at 15°C it is 340 m/s and at 25°C it is 346 m/s. So given this environment - without a
temperature measurement at the time of the test - a tolerance on the measured air resonance frequency should be taken into consideration.
The air resonance frequency is directly proportional to the speed of sound in air. So, for example, a measured frequency of 200 Hz should strictly
speaking be given a potential tolerance range of +201.7 Hz to -198.3 Hz - assuming of course that my test apparatus is of high scientific precision
(which it is not).
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jdowning
Oud Junkie
Posts: 3485
Registered: 8-2-2006
Location: Ontario, Canada
Member Is Offline
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The fingerboard has been levelled and crowned ready for fitting the frets. I suspect that these surviving fancy versions of the mid sized colascione
like the Dean Castle example may have had the courses tuned a fourth apart and fretted like a lute or guitar (i.e. more or less 12 Tone Equal
Temperament) - so that they might be played in consort with guitars, mandolins and the like. On the other hand the early full sized version of the
colascione played solo by street musicians or to accompany voice or unfretted instruments such as the fiddle may have had a somewhat more complex
fretting arrangement based upon Pythagorean scaling.
So the plan for this experimental instrument is to first fret in accordance with Pythagorean scaling just out of curiosity and to test the
practicality (or otherwise) of working with some of the close spaced fret arrangements with 18 frets to the octave on a 79 cm vibrating string length
instrument. The close spaced frets range from about 5 mm to 10 mm apart.
For convenience I have used the on line Hoffman fret calculator to establish the theoretically correct fret spacing here:
http://www.modoantiquo.com/temperatur/temperatur_en.html
The frets, of course , may be moved around to test other temperaments including the 17 fret to the octave fretting arrangement for the Tunbur
described by 10th C philosopher Abu Nasr Al-Farabi - the original text translated and analysed in detail by Chris Forster in his recent encyclopedic,
beautifully produced book 'Musical Mathematics - on the art and science of acoustic instruments', 2010, Chronicle Books, San Francisco. Contents and
excerpts here:
http://www.chrysalis-foundation.org/musical_mathematics.htm
The Al-Farabi Tunbur had two courses tuned a fourth apart so would require retuning the top string down from d' to c' on this experimental
mezzo-colascione. Interestingly the early late 15th C description by Tinctoris of a 'tambura' being played in Naples by Turkish prisoners gives the
tuning of a three stringed instrument oddly as "to the octave, fifth and fourth". Presumably Tinctoris meant that the top two strings were tuned
either a fourth or a fifth apart?
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