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jdowning
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Lute #36 in the Kunsthistorisches Museum, Vienna is labelled " In Padova Wendelio Venere de Leonardo Tieffenbrucker, 1582". String length 66.5 cm -
bowl 13 rib construction.
Working from a full size drawing of the instrument two bowl sections are shown - one at the clasp end (almost full width of the sound board) and the
other at the sound hole centre. From a longitudinal section of the neck joint it might be assumed that the bowl section at the neck joint is a
complete semi circle (or very close to it).
The attached images show the bowl half sections (viewed from the neck block end of the bowl) in order to demonstrate the degree of asymmetry of the
bowl section. On the treble side the bowl section is close to a complete semicircle whereas on the bass side the section is close to a flattened
semicircle. Ribs that deviate from a semicircle may be due to adjustments made by the luthier to the ribs in order to conform as closely as possible
to the bowl mold as construction proceeded? This is a distinct possibility given the 13 rib bowl construction (compared to the more accurate Venere 25
rib bowl previously posted where better control of the bowl construction would have been possible).
Lundberg provides images of this lute (front, side and back views, Photo 3 page 20 of his book) and a small thumbnail sketch of the bowl viewed from
the end of the bowl (Fig 3, page 21). This sketch may not be perfectly to scale as it represents only a slightly flattened semicircular section but no
asymmetry. Nevertheless, this might confirm that a slightly flattened semi circular bowl section was the original intent of the luthier although less
than perfect (geometrically) in its execution. Close enough perhaps as far as the maker was concerned where economies of speed of manufacture were
important?
Next to look at yet another Venere lute bowl from an earlier date.
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jdowning
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This is what now remains of an ivory lute by Wendelin Tiefenbruker, Padua, dated 1571, that I measured and drew some years ago - Cat #31 in the
Charles van Raalte Collection, Dean Castle, Kilmarnock, Scotland.
Now in rather a sorry state having been roughly converted to a German 'lute-guitar' during the 19th C, only the original bowl survives - the lute
having passed through the hands of several prominent makers for modification (see attached image of the label).
Its final modification as a lute was likely as a 13 course baroque lute - the surviving sound board bearing traces of the bridge from that conversion.
I only had time to measure and record the soundboard profile, and bowl longitudinal and cross sections. More to follow.
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jdowning
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The attached full scale drawing of the bowl half section (bass side) at the widest part of the sound board shows a semicircular profile flattened by
about 11 mm.
An overlay of the bowl longitudinal section on the sound board profile shows that the flattened profile extends for the length of the bowl - flatter
at the widest part than it is at the neck joint.
If the axis of the bowl profile is rotated relative to that of the sound board profile - as shown in the attached image - the geometry of both
surfaces matches quite closely, an indication perhaps of how the bowl mold geometry may have been determined?
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jdowning
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It is of some interest here to examine the geometry of the Dean Castle Tieffenbrucker lute soundboard.
The attached image is the proposed geometry with the assumed position and size of the original soundhole as well as the bridge - all generated with
dividers and a straightedge. The original neck joint at the sound board level would have been a little higher than shown as the lute likely had eight
courses originally.
The geometrical construction is self explanatory and is based upon arbitrary units of 4 fingers measurement. The maximum sound board width is 308 mm.
Deducting say 2 mm for total rib thickness and hence maximum mold width of 306 mm - equal to 16 fingers - gives a finger unit equivalent to 19.1 mm
for this instrument.
The relatively narrow shoulder profile of the sound board, compared to the more rounded egg shaped Paduan lute profiles of the end of the 16th C,
closely resembles the earlier geometries of the Laux Maler lutes that in turn may relate to the 14th C ouds described in the 14th C by Ibn al Tahan -
see attached images for comparison. A transitional development perhaps?
See page 3 of this thread for an example of the geometry of a later lute (1598) by another Paduan based luthier Michielle Harton.
[file]29224[/file] [file]29226[/file]
[file]29228[/file]
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jdowning
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Before leaving the Dean Castle Tiefenbruker lute it is of interest to attempt to reconstruct the original string length and the string length for its
final conversion to a 13 course German baroque lute.
From the proposed sound board geometry, the 7th fret position is located at the point where the compound arc of the upper sound board profile
intersects the vertical axis of the lute. This point is a distance of 23 finger units from the front of the bridge. This distance is equivalent to 2/3
total string length. Therefore, half this distance is the distance from the nut to the 7th fret on the fingerboard.
The maximum width of the bowl (interior) is 306 mm - equivalent to 16 finger units - then a finger unit for this instrument measures 19.1 mm.
So, 23 finger units is 440 mm, half that value is 220 mm for a total string length of 660 mm.
This string length fall nicely within the range (640 to 730 mm) for a gut strung tenor lute of the late Renaissance period according to Dr. Eph.
Segerman (Northern Renaissance Instruments - article 'On Lute Sizes' May 1999).
http://www.nrinstruments.demon.co.uk/lutesize.html
Note that taking the Pythagorean ratio of 3:2 (a fifth) applied to the string length (2/3) gives a length of 440 mm - which happens to be the string
length of the little Venere Descant lute previously posted.
[file]29244[/file]
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jdowning
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The final conversion of the lute in 1726 to a 13 course German baroque lute by Hoffman entailed installing a longer (10 frets), and wider neck
extended to a second pegbox (see images for illustration) as well as a new bridge. The wider neck was fitted by re-cutting the neck joint to a more
acute angle relative to the sound board surface.
Traces of the bridge remain on the sound board so the distance from bridge to neck joint (at the sound board surface) can be determined and measures
370 mm. If a string length of 690 mm is assumed (about right for this style of lute) the distance from the nut to the 10th fret is 0.44 X 690 = 304 mm
(assuming equal temperament fret spacing). As the 10th fret cannot be tied directly over the neck joint (due to the slope of the neck joint) an
additional 16 mm must be added to the string length = 370 + 304 + 16 = 690 mm. Close enough!
This would be the minimum string length but might be made a bit longer by slightly extending the neck length and locating the 10th fret accordingly
further up the neck for a string length say within the range 691 to 715 mm found on surviving German baroque lutes from the first half of the 18th C.
The attached sketch shows - for clarity - the positioning of the 10th fret at the neck joint. The fret cannot be tied closer to the sound board than
shown.
[file]29246[/file] [file]29248[/file]
[file]29250[/file]
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jdowning
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There is only one historical source that gives the exact dimensions of early 17th C European instruments - found in 'Syntagma Musicum II, De
Organographia' 1614 - 1620, by Michael Praetorius. The standard measure (together with a printed scale) provided by Praetorius is the Brunswick 'Fuss'
(foot) divided into 12 'Zoll' (inch). The Brunswick Fuss was equal to 285.37 mm - so a Zoll was equal to 23.78 mm.
European linear measures are based upon Roman standards that were, in turn, influenced by the ancient measures of the Middle Eastern countries and
standardised in 29 BC by Agrippa. The Roman foot (Pes) measuring 296 mm was divided into 16 fingers (digitus) of value 18.5 mm. At a later period the
foot was divided into 12 inches (uncia) of value 24.6 mm. By the 16th C in Europe there was no universal standard measure - standards being set by
individual states or even cities or towns. However, the measure of commerce was the foot and inch. Interestingly, the 'finger' unit appears to only
have been used by architects, artists, craftsmen and artisans (including instrument makers?) and so may also have varied in standard dimension like
the finger units of the Middle East once did.
Curiously, Praetorius refers uniquely to the depth of a guitar also in fingers (2 or 3 fingers) - as does French lawyer Pierre Trichet in 1640
(between 3 and 4 fingers). As subdivisions of a finger are not mentioned it may be concluded that both writers were referring not to a standard finger
measure but to use of their own fingers to give a rough idea of guitar dimensions.
The early writers on the oud give only relative proportions although the 14th C sources Ibn al-Tahhan and Kanz at-Tuhaf give the relative proportions
in finger units. A standard finger unit of the region might measure anywhere between 18.5 mm to 22.8 mm - dependent upon the commercial cubit standard
in force for each region. Alternatively an oud maker may have simply used the width of his finger (or that of his customer) to determine the physical
size of a completed instrument. As the geometrical studies so far in this investigation only involve whole numbers - not fractions of fingers - then
the latter anthropometric application may well be a possibility.
This is of interest as possible confirmation of early European lute design being directly influenced by the oud - particularly via the European trade
access centres in the Venetian Republic (Venice and Padua) and those in the Ottoman Empire to the East and on the North African coast under trading
agreements with the Ottoman Turks.
The attached article provides a bit more detail on this subject matter, published in FoMRHI, July 2011
[file]29285[/file]
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jdowning
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Moving on to examine bowl profiles of some of the late 16th C lutes by the Venetian makers - again taken from full size drawings of the originals.
Venice and neighbouring Padua are only about 35 Km distance from each other so one might expect some similarity in the geometry of lutes by the Paduan
and Venetian makers (all of German origin).
The first example is an ivory lute by Marx Unverdorben in the Dean Castle Museum, Scotland, Cat.#32 - one that I measured over 30 years ago. Converted
to a 'lute-guitar' during the 19th C, the bowl and neck are original. The original string length is estimated to have been about 67 cm for an assumed
six courses.
The bowl section is 'flattened' from a perfect semi-circle with an offset of about 20.5 mm for maximum radius R.
The attached overlay of the bowl longitudinal section compared to the sound board profile shows the degree of 'flattening' of the bowl section along
the length of the bowl - becoming more or less semi-circular in section at the neck block. If the bowl profile is rotated around the neck joint, as
indicated, it closely matches the soundboard profile.
So, although the bowl section is 'flattened' compared to a full semi-circle its profile is - nevertheless - an arc of a circle radius R or very close
to it.
Interestingly, if the maximum bowl width, measured in finger units, is 16 then a finger unit originally used for this instrument would have been 20.63
mm (max. width of soundboard measures 33cm) - or very close to the radius offset of the bowl section at maximum width.
(Note that an original attempt to define the soundboard geometry of the lute was posted three years ago on page 1 of this thread. It is now thought in
hindsight that this soundboard geometry is incorrect (it is too complicated so is an unlikely solution). A simpler revised geometry is to be posted
soon)
[file]29313[/file] [file]29315[/file] [file]29317[/file]
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jdowning
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A proposed revised soundboard geometry for the Dean Castle Unverdorben lute #32 is attached for information. There are some discrepancies between the
drawing that I made 30 odd years ago and some of my measured dimensions of the instrument. This may be due to the fact that I made a tracing of the
lute outline on to card from which I made a template for transferring the soundboard profile to the drawing. This has resulted in the measured
dimension of soundboard maximum width being 330 mm whereas the width measured from the drawing is 333 mm - most likely due to an accumulation of of
slight dimensional errors in making the drawing (pencil line thicknesses etc.).
Fortunately, Canadian luthier Michael Schreiner had meaured the same instrument in October 2012 and was able to confirm the maximum soundboard width
as just over 330 mm. See here, October 2nd blog
http://schreinerlutesandguitars.blogspot.ca/search?updated-min=2012...
The proposed soundboard geometry is largely self explanatory - another version of Dürer's 'egg line' profile previously discussed on this thread. The
soundboard maximum width is assumed to be 16 finger units (1 finger unit, therefore, measuring 20.625 mm). The upper sound board profile is formed
from two conjunct arcs of radius 28 fingers and 20 fingers and the lower sound board profile from three conjunct arcs of radii R1, R3 and R4.
The bridge is located midway between the X axis and the bottom of the bowl (i.e. 4 fingers from the X axis). This gives an original string length of
687 mm. The soundhole centre might be at C1 (8 fingers from the X axis) or, alternatively, at C2 but C1 is the preferred centre position. Original
soundhole diameter might have been 4 fingers or 82.5 mm.
A finger unit of 20.625 mm may have some significance for Venetian lutes of the 16th C - to be discussed next.
[file]29390[/file]
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jdowning
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Robert Lundberg, author of 'Historical Lute Construction' died before final editing and completion of his work leaving some unresolved questions and
inconsistencies. Some of these issues are outlined in the Preface to the book by Jonathon Peterson a GAL staff member who worked with Lundberg in
compiling the publication.
One of these issues concerns the 'Venetian Inch' measure invented by Lundberg that he proposed was used uniquely by the Venetian luthiers. He gives
the metric equivalent of the 'Venetian Inch' as 'about 27.4 mm'. This dimension, however, varied within a range of just over 1 mm a discrepancy
explained as being well within the practical working parameters of a lute maker.
As far as I am aware there is no historical 'inch' measure anywhere near equivalent to 27.4 mm (± 0.5 mm).
Lundberg derived his 'Venetian Inch' by comparing the dimensions of lutes (in Brunswick inches) given by Praetorius in the early 17th C to some of the
16th C Venetian lutes that survive in unaltered condition. The Brunswick inch measured 23.78 mm, therefore, the ratio of the 'Venetian Inch' to
Brunswick Inch (or Zoll) is 1.15.
As discussed in the FoMRHI article previously posted on this thread, there was no international standard inch measure at the time of Praetorius
although the European standards were all based upon the Roman measure for a foot equivalent to 296 mm. This foot was further divided into 16 finger
units each unit equivalent to 18.5 mm or later into 12 inch units each equivalent to 24.6 mm. The latter measure became generally established as a
measure of commerce whereas the finger unit continued to be used by artists, architects, artisans and the like.
The ratio of the Brunswick inch to the Roman inch is, therefore, 23.78/24.6 = 0.97. If the Brunswick measure is given in equivalent finger units
(Praetorius does even mention finger measurement but only relating to guitars) then a 'Brunswick finger' (let's call it that) would be equivalent to
18.5 X 0.97 = 17.95 mm.
If Lundberg's 'Venetian Inch' is also converted into finger units, then a 'Venetian finger' (let's call it that) would be equivalent to 17.95 X 1.15 =
20.64 mm.
This anthropometric finger measure is well within the established range of known historical standard measures for the finger unit - based upon the
cubit - ranging from about 18.5 mm (from the Ancient Egyptian standard cubit) to 22.8 mm (from the ancient Persian Royal cubit) - 20.64 mm being
almost the mid point value.
At this point I would speculate that the Venetian luthiers were working proportionally with finger units (not inches) in the design of their lutes and
that 20.64 mm may have been the equivalent measure of their finger standard. Note that the equivalent finger measure derived from the proposed
geometry and measurement of the Dean Castle Unverdorben lute previously posted is 20.625 mm - closer than a luthier might practically
differentiate.
Alternatively, any variations observed in finger measurement derived from the dimensions of surviving lutes may be due to the actual finger width of
the luthier or his customer being used in the lute design.
More examples of surviving Venetian lutes of the must now be examined in order to help verify (or deny) these assumptions.
Note that use of actual finger widths of the human hand in design of artifacts is not so far fetched as might at first appear. For example one Middle
Eastern treatise on archery dating from the 16th C gives the dimensions of a bow in finger units. The author can not, of course, give the modern
equivalent dimension of a standard finger of his time but this is likely not particularly relevant as the size (and strength) of an archery bow must
be matched directly to the physique of an archer.
To some extent this consideration might also apply to a lute (or oud) - those with small hands generally benefiting from a smaller instrument with
shorter string length than players with larger hands.
Furthermore the author also makes reference to bow construction being a reflection of the four components of the body of man - the bow wood
corresponding to man's skeleton, horn to the flesh, sinews to arteries and glue to blood. Just like a bow, man has a back and a belly .... and there
are four types of Arab bow.
All reminiscent of the Ikhwan al Safa making reference to the human body and the magical number four in relation to the oud!
If the Venetian makers were in fact using finger units rather than inches this might indicate a surviving middle eastern luthier influence - although
by the end 16th C the design of Venetian lutes would appear, from their geometry, to have 'parted company' with any original oud traditional design.
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jdowning
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Some additional thoughts on the matter of early lute (and oud) dimensions previously posted.
Unlike commercial metrical standards where official measuring rods are necessary, no such standard rods (as far as I am aware) ever existed for a
'Venetian Inch' or a Venetian Finger' or their equivalent (although standard rods do survive for the ancient cubit measures of early societies where
the cubit was established as a standard measure of commerce).
The early lute or oud makers created the design of their instruments according to established proportions using only a straightedge and dividers and
consistent arbitrary units to define the geometry. The design would then be given final dimensions by assigning a value to the arbitrary unit. This
value may have been the measured finger width of the luthier himself - a dimension that may not have differed that much between persons of average
build.
This would make some sense for the creative artistic mind particularly for those who believed in a Universal Harmony where the dimensions of the human
body bore great significance (for example Leonardo da Vinci, preceded by the Ikhwan al Safa and earlier still by Roman architect Vitruvius).
If this was the case then one might expect to find some dimensional differences between early lutes (or ouds) made to the same geometry by different
makers.
I am therefore coming round to the idea that the early luthiers may indeed have used the actual measured width of their finger to determine the final
dimensions of their instruments - not entirely because of considerations of matching an instrument to the physique of a player, but to create
instruments that conformed 'perfectly' in geometry and dimension to the relative proportions of the Universe ('Music of the Spheres' and all of that
good stuff, beliefs and convictions in Divine creation held by some of the greatest scientific minds and philosophers, East and West, over the
centuries).
The same guiding philosophy might also have applied to the work of other artisans like the 16th C Middle Eastern archery bow makers in order to create
a bow of perfect proportions.
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jdowning
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Another surviving Venetian lute by Marx Unverdorben is # 656 1178E in the Prague National museum. A drawing of the bowl section at maximum width is
attached. The bowl has 9 ribs of wood and is 'flattened' in longitudinal profile (very similar to the Dean Castle Unverdorben lute geometry previously
posted)
The bowl section is asymmetrical about its centre line - 'bulging' out on the treble side. On the bass side it is very close to a semicircular profile
with radius offset by about 28mm from the sound board surface. The section drawing shows the measured widths of the ribs - indicating that the luthier
was likely working quickly and was not too fussy about conforming exactly to his mold so had to make some correction on the treble side of the bowl as
construction progressed by adjustment to the rib widths.
Lack of symmetry of sound board and bowl section profile would appear to be a common feature of surviving lutes so the geometries proposed in this
thread must, of necessity, be the closest fit that is reasonable. This, of course, assumes that all measurements of the surviving instruments are
accurately recorded.
Interestingly, the measured offset of the bowl section in this case is about 28 mm - which corresponds closely to Robert Lundberg's proposed 'Venetian
Inch'. So, with a maximum soundboard width of 338 mm the width in Lundberg's 'Venetian Inch, would be 12 inches.
Therefore, more examples must be examined to see if there might be a common geometrical pattern emerging for the Venetian lute bowls.
More to follow.
[file]29524[/file]
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jdowning
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I was incorrect in earlier stating that there were no known historical inch standards approaching Lundberg's 'Venetian Inch' (equivalent to say 27 mm
to 28.1 mm).
The attached is a mid 19th C linear scale comparison, Museum of the History of Science (author ChrisO, Wikimedia Commons). It shows inch standards,
varying by country of origin, ranging from about 23.0 mm (Spanish) to 44.1 mm (Russian - but 27.7 mm for Moscow). The Turkish equivalent is about 31.3
mm. The Italian standard shown is equivalent to about 28.3 mm (divided into 8 parts) - larger than any of the other European standards.
The origin of the word 'inch' is derived from words meaning 'thumb' - for example pouce (French), tomme (Danish), pollice (Italian), pollec (Slovac).
So an 'inch' measure is the measured width of a man's thumb - but where on a thumb is the width measured?
Turning to the earliest Scottish statues for linear measure established by king David I (early 12th C) " The length of an inch is the breadth of the
thumb of a middle sized man, measured at the root of the nail (mesouret at the rut of the nayll), taking the thumbs of three men for striking the
medium".
So, as with the Turkish measure of a finger (width of the index finger measured just below the nail), the Scots used the same definition of the
position for determining the length of inch - all without reference to standard measuring rods.
Checking again my personal measurements of finger and thumb width - using dividers - I obtain about 19 mm (finger) and about 25 mm (thumb) and I am
about 'average' build. Measurements were made on my left hand. Being right handed the fingers of my left hand are less worn out after decades of use
so should give more accurate results!
From this it would seem that the luthiers using actual body measure as their 'standard' (if that is what they did - as seems quite possible) could use
either finger measure (16 fingers to the foot) or thumb (inch) measure (12 inches to the foot) as standardised by the Romans.
So, for example, the maximum soundboard width of the Prague Unverdorben lute previously mentioned is 338mm. Dividing that dimension by 16 gives a
value of about 21.1 mm for a finger unit. Dividing by 12 gives a value of about 28.2 mm for an inch unit. For the Dean Castle Unverdorben, sound board
width 330 mm the same relative values would be about 20.6 mm (finger basis) or 27.5 mm (inch basis).
So Unverdorben (if the same person) in each case when designing his lutes would not have used a 'standard ruler' to finalise the dimensions of the
instruments but would have simply set his dividers across the width of his finger or his thumb as he might choose dependent upon the geometric scale
chosen - sound board width equal to 16 for finger units or 12 for inch units (average or 'mean' size lutes - lutes at the extreme size ranges may have
different geometries and scales?). As a luthier would not be able to practically set his dividers to the equivalent of fractions of a mm we might
conclude that Unverdorben's finger width was about 21 mm and his thumb width about 28 mm - close enough for a lute design.
Next to check out some actual sound board widths of surviving lutes for further comparison.
[file]29576[/file]
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jdowning
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A special ancient application of thumb or inch appears to be to measure depth.
The earliest known reference to an inch in England dates to the 7th C where a fine for wounding another person (with knife or sword) was determined by
the depth of the cut inflicted - one inch deep, one shilling, two inches , two shillings and so on.
Today in France - 200 years after Napoleon's metrication decrees - farmers still refer to the depth of a ploughed furrow in pouces or inches!
Perhaps this might explain why Praetorius (see earlier posting) referred uniquely (and oddly) to the depth of a guitar in fingers rather than the
Brunswick inch standard that he used to dimension all other musical instruments?
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jdowning
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An interesting observation about the ancient Roman standards of measurement is that the ratio of finger to thumb widths is 3/4 or 0.75 - the Roman
standard foot being equivalent to 296 mm - a finger being 1/16 of a foot is equivalent to 18.5 mm and thumb 1/12 of a foot equivalent to 24.7 mm.
The ratio of 3:4 is a 'fourth' in the Pythagorean musical scale.
My finger width measurements of about 19 mm (index finger) and 25 mm (thumb) gives a ratio of 0.76 - close enough to 3:4. This might be a way for a
luthier - using measurements of his own finger widths to determine the dimensions of an instrument - to 'calibrate' and verify that the size of his
units of measure are properly proportioned?
So the luthier who made the Dean Castle Unverdorben lute - details of which have been previously posted - from the dimensions of the instrument was
using a finger unit equivalent to about 21 mm and thumb unit of about 28 mm, the ratio of finger to thumb width being the desired 0.75. Clearly
Unverdorben had a larger hand than mine so if I made the Dean Castle lute to the same geometry, my lute would be dimensionally about 9% smaller than
Unverdorben's. The string length of my lute would then be proportionally reduced in scale from 687 mm to 625 mm.
This observation raises another interesting possibility relating to lute sizes that - unlike the solo oud (or lute) - were made in matched sets,
intended to be played as duos, trios or quartets - tuned in unisons (1:1), fourths (3:4), fifths (2:3) or an octave (1:2) apart.
More to follow.
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jdowning
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The attached table compares the sound board width and string length dimensions of some of the surviving lutes by the Venetian and Paduan luthiers -
taken from full size drawings of the lutes that I currently have on file. Included are the 5 lutes (A,B,C,D,E), in original unaltered condition,
mentioned by Robert Lundberg in his book. These are examples of the 'standard' sizes of Renaissance lutes ranging from soprano to bass. Lundberg
compares the lutes by string length (in his 'Venetian Inches') but provides no other information concerning the precise physical dimensions of the
lutes (apart from some nice full face photographs of the instruments in question).
Based upon my work so far it would seem likely that the starting point dimension for a luthier - in order to create the geometry of a lute or oud
(using only dividers, a straightedge and the forefinger or thumb of his hand) is the width of the soundboard.
The earliest texts on the oud base the ideal proportions on this dimension - "Its length should be half as much again as its width, its depth half its
width ....." (Ikhwan al-Safa, 10th C). Other writers later provide alternative geometries with dimensions given in finger units ('isba', Arabic or
'angusht', Persian). From these descriptions it is possible to form a reasonable idea about the relative dimensions of the Medieval period oud -
including string length that is directly related to the relative proportions of the instrument.
The same cannot be said for many surviving lutes as neck length - which, in turn, dictates string length - may not relate directly to the geometry of
the rest of the instrument. For example an early 16th C lute - originally designed for 6 courses with 7 frets on the fingerboard - might during the
late 17th C, say, be re-necked to accommodate 10 courses with 10 frets on the fingerboard resulting in a lute where the body of the instrument is
proportionally smaller than ideal for the given string length. Conversely, the neck of a larger lute might be reduced in length (and hence reduced
string length from original) resulting in a body size disproportionate to string length. Examples of altered necks may be seen in lutes # 6, 7 and 9
listed in the attached table (typically the frets on lutes of the late 16th/early 17th C would be 8 in number).
Due to the amount of slope of the neck joint of a lute (the more courses, the wider the neck and more acute the neck joint angle), the working length
of the fingerboard for tied on frets is limited by the position of the neck joint at the underside of the neck (see the sketch on the attached table).
This dimension was measured from the full size drawing of each lute and the maximum possible number of tied on frets calculated from the string length
- assuming 12 tone equal temperament spacing.
More to follow.
[file]29637[/file]
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jdowning
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Lutes A, B, C, D, E noted in the previously posted table of 12 Venetian/Paduan lutes represent the 5 'standard' lute sizes of the late 16th C
according to Pythagorean string length ratios. Corresponding string lengths of the few surviving lutes in an unaltered state are 441 mm, 584 mm,
665mm, 781 mm and 937 mm although one might expect some slight variation in these dimensions - dependent upon the size of 'finger' (or inch) used.
Lute sizes B and C might represent the average size of lute comfortable for the physical size range of most men.
By way of comparison, so far these studies have indicated that the string lengths of early ouds - based upon proportions and dimensions given by the
Medieval period writers - might range from 585 mm to 675 mm.
Assuming Venetian lutes of the 16th C were of the same or similar geometry (i.e. based upon Dürer's 'Egg Shape' proposed earlier in this thread) -
the unit finger or inch dimension may be determined by dividing the sound board width into 16 Units (fingers) or 12 units (inches).
I have so far based the sound board geometries - for greater simplicity - on the width divided into four. So, each unit would be equivalent to 4
fingers or, alternatively 3 inches - so, for the same geometry the size of the lute would be the same whether or not finger units or inches are the
preferred measure.
The alternative proposed geometries of the Dean Castle Unverdorben lute are attached to illustrate this point.
There are two possible bridge positions - but which one is the most likely? I initially preferred bridge position #1 giving an original estimated
string length of 686 mm. However, bridge position #2 gives an estimated string length of 665 mm which happens to agree with that of lute C by Leonardo
Tieffenbrucker. Note that bridge position #2 is determined using a 3:4:5 Pythagorean right triangle - that 3:4 ratio again!
More to follow.
[file]29722[/file]
[file]29724[/file]
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jdowning
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Given identical lute geometries expressed in either fingers (sound board width 4 x4 fingers =16 fingers) or inches (soundboard width 4 X3 inches=12
inches) as previously posted it would then be possible for a Venetian luthier to create proportionally correct larger or smaller lutes by simply
substituting a finger unit value in the inch based geometry and inch unit value in the finger based geometry - the ratio being 3:4.
So for example given a finger unit equivalent to 18.5 mm and related inch unit equivalent to 24.7 mm, a lute sound board width would be 18.5 X 16 =
296 mm (or 24.7 x 12 = 296 mm). This size of lute would be the equivalent of example B in the previously posted table of dimensions.
For a proportionally smaller lute design of identical geometry substituting a finger value of 18.5 mm into the inch based geometry gives a soundboard
width of 18.5 x 12 = 222 mm (i.e. equivalent to the descant lute size A in the table) or a proportionally larger lute by substituting an inch value of
24.7 mm into the finger based geometry to give a sound board width of 24.7 x 16 = 395 mm (i.e. equivalent to the D size lute in the table).
The great octave bass lute E size (relative to the descant lute) would in turn be determined by doubling the finger value to 37 mm giving a soundboard
width of 37 mm x 12 = 444 mm
Whether or not the Venetian luthiers ever used this short cut technique will, of course, never be known.
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jdowning
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Robert Lundberg's 'Venetian inch'
As previously noted, one of the inconsistencies in his book that remains after his premature death is the question of the deduced 'Venetian inch'. In
the preface to 'Historical Lute Construction', Jonathon Peterson comments on some discrepancies observed in the estimated dimension of the 'Venetian
inch' and notes that Lundberg, on page 57, defines an inch Venetian as equivalent to about 27.4 mm.
Having examined the data presented in the book on the size of some surviving Venetian lutes (page 8) where the string lengths have been given in
'Venetian inches' together with their metric equivalents, I have concluded that the dimension of 'about 27.4 mm' should read 'about 28.4 mm'. This can
be verified by conversion of the lute string dimensions given as follows:
- 15.5 Venetian inches = 440 mm so 1 Venetian inch = 28.39 mm.
- 20.5 Venetian inches = 584 mm so 1 Venetian inch = 28.49 mm.
- 23.5 Venetian inches = 667 mm so 1 Venetian inch = 28.38 mm.
- 27.5 Venetian inches = 781 mm so 1 Venetian inch = 28.40 mm.
- 33.0 Venetian inches = 937 mm so 1 Venetian inch = 28.39 mm.
The average value for a 'Venetian inch' is therefore = 28.41 mm or 28.4 mm to the first decimal place.
This would in turn make my proposed 'Venetian finger' = 21.31 mm or 21.3 mm to the first decimal place.
So Lundberg's proposed Venetian inch of about 28.4 mm is, interestingly, now very close in size to the 'Itallian' inch - equivalent to about 28.3 mm -
recorded on the 19th C conversion scale previously posted.
More to follow.
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jdowning
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Most of the late 16th/early 17th C Venetian lutes appear (from this limited investigation) to be of semicircular "flattened" section - as previously
reported in the thread.
The attached image is a half section of a lute bowl by Wendelio Venere 1592 that shows almost a perfect match with a semicircular arch with radius
'flattened' or offset by about 6.5 mm.
Just to demonstrate how close this profile is to an ellipse an elliptical profile drawn on the same X Y axes has been superimposed over the full size
drawing. It can be seen that the section is not elliptical but that the match is very close - only a maximum deviation from a semicircular arc of
about 1.5 mm.
Further confirmation that the early lute makers simply used semicircular arcs to create their lute designs - using only dividers and a straight edge
as tools.
[file]30612[/file]
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jdowning
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Note that the greater the offset of the radius from the plane of the soundboard surface the greater the deviation from a pure elliptical profile -
although, for all practical purposes, not by much.
Next to re-examine the bowl profiles of some (but not all) of the earlier lute bowls by Hans Frei that have a depth that is half the sound board width
but are not semicircular in section.
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jdowning
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The bowl sections of the Warwick Frei lute, previously discussed in this thread, have been redrawn full size to compare the measured profile with an
Oval curve and an Elliptical curve - see attached images.
The bowl sections are measured at the widest part of the soundboard and bowl width is divided into 8 equal units.
The Oval curve is created from three conjunct arcs of a semicircle with radii Ra Rb and Rc with centres at A,Band C on axes X and Y as shown in the
drawing. Ra is equal to Rb.
The Elliptical curve has been generated using the '2 pin and string 'method mentioned on page 1 of this thread - the pins being positioned at A and B
as shown in the drawing. This is equivalent to the elliptical curve drawn on axes X1 and Y1 i.e. at 45° to the XY axes.
It can be seen that both the oval and elliptical curves are a close match to the actual bowl profile. Given the additional complexity of creating an
elliptical curve it is most likely that a luthier would have taken the easier route and created an oval curve - quickly and accurately - using just
dividers and a straight edge.
Note that for this particular lute, the bowl section gradually transforms into a semicircular section (with added depth) at the neck block position
(see page 4 of this thread).
[file]30620[/file] [file]30622[/file] [file]30624[/file]
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