Ancient Scales of Measurement?

It would be a mistake to assume that early civilizations lacked real standards of measurement - quite the contrary. The Egyptians and Romans, for example, didn't perform their great feats of engineering and construction by "rule of thumb" so to speak - they had very precise standards of measurement. Just because a unit of measurement was called a finger (for example) does not mean to say that they actually used a finger for measurement (except for the average person making a quick and very rough check in the local rural market place perhaps).

I would agree that instruments depicted in paintings are often exaggerated (more often than not) so are not a reliable source from which to try to re create an early instrument. Artists will often work by convention or from memory or will misrepresent or omit important details like strings, frets or numbers of pegs etc..

For comparison purposes I have superimposed a half outline of the oud described by Farmer (drawn to my speculated "corrected" dimensions noted in my previous posting) over a sketch of a small bass lute by 16th C Laux Maler. The sketch of the lute is a recreation that I made many years ago based on a surviving soundboard by that maker. Both outlines are to the same scale with the bridge position as a common data point. Both instruments have a relatively long narrow 'almond shaped' body with low bridge positions. The oud also has a relatively shorter neck than the lute.

Many thanks ALAMI - what a good example of a clear document scan. I am now a bit out of my depth so will need to research a bit further before asking more questions.

Just for my information - I imagine that madmouma is plural of madmoum but how does it translate? Does it mean "double" or something similar - to make sense of the dimensions provided by Farmer?

I suppose if some units were reserved for early topographical measurement (or navigation perhaps) this might be the link to the metric scale - the metre being originally defined by triangulation surveys to determine the length of the meridian arc of the earth between the equator and North Pole - the metre being 1/10,000,000 of that distance? (Alternatively perhaps more accurate siderial measurement was used as the ancients were experts in that science?)

For information, I have updated my previous sketch comparing the profiles of the Maler lute and the Ibn Al-Tahhan oud to reflect doubling the distance of the bridge from the bottom of the bowl speculating that the original manuscript is in error. This gives a more satisfactory match than before in my opinion.
Also, it should be noted that the early Arabic writers, like Al-Khindi, and the authors of the 10th C Ikwan al-Safa and the Persian work Kanz al-tuhaf - according to Farmer's translation - gives some information about the proportional dimensions of an oud. This enables an albeit limited confirmation of the profiles of early ouds. For example that the depth of the bowl should be half the width and the length (of the bowl) should be 1 1/2 times the width with the neck length being 1/4 of the overall length. This latter ratio would fit the neck length proportions of the Doc's oud - sketch B in "Question - Big Ouds, Little Ouds" - but not the other two.

What is wrong with this Oud?

The attached image is a scale drawing of an oud described by 14th C writer Ibn al-Tahhan al-Musiqi according to the translation/interpretation of the sole surviving manuscript by Dr H.G. Farmer.
Farmer was puzzled about the low placement of the bridge (which he thought odd) but was not otherwise concerned about the size of the oud which he described as being of "considerable dimensions" and a "real archlute". He was obviously not an oud or lute player!

It is not always clear and now impossible to determine - without access to the original manuscript - what Farmer has translated word for word from the original and what is his interpretation of the text.
Farmer gives Arabic linear measurements as 'isba' = 2.25 cm and 'isba madmum' = 4.5 cm as well as 'shibr' = 27 cm but does not give the source for these assumed metric equivalents. He then goes on to give the measurements of the oud in terms of 'asabi' and 'asabi madmuma' - presumably as written in the original manuscript(?). Farmer also (strangely) gives the neck length as "= 1 shibr + 1 'aqd" giving the metric equivalent as 29.25 cm - again without clarification - from which it might be assumed that 1 shibr = 12 isba and that the neck length is then equivalent to 13 isba.
Something is not quite right here!

More to follow.

Ancient Arab and Persian Navigators
The scientists of the ancient civilisations of the Middle East were expert astronomers using their observations to develop a sophisticated analogue computer - the astrolabe - to solve problems in spherical astronomy that was used, among other things, for precise navigation. The astrolabe had to be held steady for readings to be taken so was difficult to use on board ship when at sea.

According to researchers studying early navigation methods, the ancient Arab seafarers used a technique known as latitude sailing in the Northern Hemisphere. They would sail North (or South) until they reached a required latitude and then sail East (or West) maintaining this latitude until arriving at their destination.
A latitude bearing was determined, indirectly, by estimating the angle of elevation of the Pole star above the horizon using a hand held at arm's length and counting the number of finger widths that the Pole star appeared to be above the horizon. At the equator the Pole star appears to touch the horizon (zero degrees elevation or 0 degrees latitude) whereas at the North Pole the star appears directly overhead (90 degrees elevation or 90 degrees latitude). The researchers have found that one finger unit (i.e. finger width) measured 1.875 cm subtending an angle of elevation of 1 degree 36 minutes or very close to 1.5 degrees. They also found that the physical differences between individuals - long/short arms and thin/thick fingers - tend to cancel out to produce a uniform measure.
The attached image shows a hand being used to estimate the Pole star elevation in 'fingers' - in this example measuring an elevation of 8 finger units, equivalent to 12 degrees which is the latitude bearing. So a dhow sailing to the East from the Gulf of Aden and maintaining this latitude across the Arabian Sea would eventually make land fall on the West coast of India.

Next - a more accurate and consistent way to determine latitude using 'knots'.

The Kamal or 'Guide'

According to researchers into early navigation techniques a Kamal consists of a 'sighting plate' - a small rectangle of wood or bone, measuring "about 1 inch by 2 inches" with a string attached to its centre. The string is knotted at different points along its length.

The Kamal is used to determine latitude, the sighting plate taking the place of the fingers and a knot in the string held in the teeth until the bottom of the plate appears to align with the horizon and the top of the plate with the Pole star. According to one researcher, the string on a Kamal was calibrated so that the knots on the string were spaced at intervals equivalent to an 'isba' (the width of a finger or
1 degree 3 minutes angle of altitude) with markings from 1 to 16 'isba'.

There are a number of surviving examples of Kamel in museums.
The attached image is a replica that I made with knots spaced in 'isba' units (calculated using basic trigonometry). I was only able to tie 10 knots on the string before the knot spacing became too small to be practical. Another limitation is that as the sighting plate is held closer to the eye of the observer it becomes more difficult to focus clearly on the edges of the plate as well as the horizon and Pole star - especially for us older guys with less than perfect vision.

The seafarers likely had a collection of Kamel - each dedicated to locating the latitude of a particular place - a knot tied in the string at the correct position after taking a latitude reading before leaving the home port and on arrival at the required destination.

So what has this got to do with this investigation into the
14th C Ibn al-Tahhan oud?
Well, Farmer - as previously mentioned - mysteriously refers to the Arabic word 'aqd' as a unit of linear measure equal to the length (2.25 cm) that he reckons is equivalent to a 'finger' unit (in this case an 'isba') - yet 'aqd' means 'knot'. Could it be, therefore, that Farmer is using his (or the original scribe's) interpretation of 'aqd' based upon - perhaps - a now obsolete Arab nautical term where a 'knot' on a Kamel string means
1 'isba'? Now impossible to know for sure.

The Revised Ibn al-Tahhan Geometry

The attached image is the proposed geometry of the Ibn al-Tahan oud - drawn to scale in 'finger' units - according to the corrected dimensions proposed by Curtis Bouterse and my proposed upper sound board profile, revised neck length. and assumed neck joint width of 2 'finger' units.

With the shorter neck length of 12 'finger' units (as opposed to 13 'finger' units given by Farmer) it can be seen that the neck length is then 1/3 of the string length which is the classic proportion found on ouds to this day. The radius of the arc describing the upper sound board profile increases from R = 29 'finger' units to R = 32 'finger' units. The significance of R = 32 'finger' units will become more apparent later.
It is useful, for purposes of comparison between oud/lute geometric profiles to express R in non dimensional (ND) units where the width of a sound board is divided into 4 equal parts. In this case each part is 4 'finger' units and R becomes 32/4 or 8 in ND units.

Another point to note is that if Farmer's value of 'finger' unit, equal to 2.25 cm, is applied the string length becomes 81 cm. Ibn al-Tahhan mentions that he no longer used frets on his oud which implies that a finger unit of 2.25 cm is incorrect the string length of 81 cm being practically unmanageable for a fretless oud - or even for one that is fretted.
On the other hand using a 'finger' unit of value
1.875 cm gives a string length of 67.5 cm - another significant measurement as it turns out.

This is, of course, an important observation Mahmoud. When using gut and silk strings - as were used exclusively on the oud from the 8th C (or before) until at least the 18th C (I would guess), string length is of great importance. The longer the string length the easier it is to obtain a satisfactory acoustic performance from the strings - particularly the thicker bass strings - although perhaps less of a problem for the early 4 course ouds dating to the time of Mawsili and Ziryab (8th/9th C). According to Farmer the ouds of that time were also fretted so a string length of 81 cm would have been valid for an instrument used for relatively slow vocal accompaniment.
The same parallel is found in the lute where the longest (fretted) string lengths were found on instruments like the archlute or chittarone used mainly for voice or instrumental accompaniment (continuo playing). By the end of the 17th C and beyond, the French and German 'baroque' lutes had fretted string length of around 69 to 73 cm - probably about the limit for a solo, fretted instrument. The bass strings (beyond the stopped 6th/7th course strings) were longer but were only played 'open' like harp strings.

The shorter string length, wider bodied ouds seems to have made an appearance by the 14th C judging from the familiar engraving of an oud in 'Kitab al-Adwar' (although it still has frets) that seems to match the geometry of the traditional Turkish oud quite well (so likely had a string length in the range 54 cm to 58.5 cm ?)

My current thinking is that the longer string length, narrow bodied, fretted oud continued in use until the 16th C at which time some prominent German luthiers - recognising a good thing when they heard it - used this design as the basis for their lutes, their reputation as outstanding luthiers of their time extending beyond their lifetimes as a consequence. More on this later.

The dimensions of the oud described in the 14th C 'Kanz al-Tuhaf' - like the 'Ibn al-Tahhan' oud - appear to suffer from similar scribal error. Curtis Bouterse has again proposed corrections to produce an instrument of more credible proportions. The attached image is drawn using the corrected dimensions as well as my proposed upper sound board profile assuming a neck joint width of 2 'finger' units.

Note that the length of the neck is 1/4 of the overall length of the oud - a proportion found on ouds four centuries earlier. The width of this oud is 15 'finger' units (compared to 16 for the Ibn al-Tahhan oud) yet the value for R is the same equal to 32 'finger' units.

Out of curiosity I have superimposed a geometry assuming a neck length that is 1/3 string length and find that R becomes exactly 30 'finger' units which when converted to a dimensionless number equals 8 (i.e. 30/15 x4 - as for the Ibn al-Tahhan oud with its equivalent neck proportion).

Again if Farmer's 'finger' unit of value 2.25 cm is applied, the string length is 67.5 cm. (or 56.25 cm if a 'finger' unit of
1.875 cm is used).

A third early source giving the proportions of an oud is in the risalat al-musiqi of the Rasa'il - a monumental work written by the Ikhwan al-Safa. The Ikhwan al-Safa (the Brethren of Purity) were a group of Muslim scholars located in Basra, Iraq during the
10th C. Their great contribution to humanity was in the writing of 52 volumes recording and saving for posterity all that they could of the scientific and philosophic knowledge of the Greek and Roman civilisations.

Their description of the proportions of an oud - as translated by Dr Farmer - is as follows:

" ... the lute (al-ud) of wood (khashab), its length and its width, and its depth being in the most excellent proportions. These are that its length should be half as much again as its width, and its depth should be half of it. And the neck ('unq) should be a quarter of the length."

This makes sense if the length of the bowl is 3/4 of the overall length of the oud with the neck being 1/4 of the overall length. The bowl is semi circular in section with a radius equal to half the width of the sound board. Not much to go on!
However, if it is assumed that the lower part of the sound board is a semi circle of radius 8 units and the width of the neck joint is 2 units then the arc of the upper part of the sound board is 22 units in radius. This gives a profile of credible proportions.

Note that the Kanz al-Tuhaf oud also has a neck length of 1/4 overall length but that it is proportionally more elongated than the Ikhwan al-Safa oud.

The Ikhwan al-Safa were cosmologists and numerologists to a man - believing in one divinity and the place of the human being in the universal harmony.
Their philosophy on the significance of numbers is of interest in trying to deduce a bit more about the possible geometry and dimensions of their oud.

More to follow.

The number 8 also has significance to the Ikhwan al-Safa as the primary dimensional form of a cube (2X2X2 = 8).
The attached image is a proposed developed geometry of the basic description of an oud by the Ikhwan al-Safa.
Assuming a maximum width of 16 units (8X2), the distance to the neck joint can be defined by a 3:4:5 'Pythagorean' triangle. If the neck length is extended towards the bridge by one unit, the upper sound board profile may then be defined by an arc of radius equal to 20 units. Using the same 3:4:5 triangle relationship, the first possible bridge position is defined giving a string length of 27 units (the next cubic relationship 3X3X3 = 27).

The second bridge position possibility (#2) is with the bridge mid way between the widest point and bottom of the sound board. This geometry suggests that of ALAMI's 19th C Al-Arja oud.

From this analysis my speculation is that the geometry of the oud described by the Ikhwan al-Safi, with a width of 16 units, had a bridge at position #1, string length of 27 units and sound hole 4 units in diameter the top of the sound hole touching the radius R1 =8 units.

Is it now possible to guess the dimensions of this oud? Assuming a 'finger' unit of 1.85 cm or 1.875 cm gives an instrument of string length equal to 49.94 cm or 50.63 cm respectively - probably too short for an oud strung in silk.
Alternatively if the Roman 'thumb' ( or 'unica' or 'inch') measurement is used string length becomes 54 cm for a 2cm 'thumb' unit (still a bit short), 60.75 cm for a Farmer unit of 2.25 cm or 67.5 cm for a 2.5 cm unit with sound board widths equal to 32 cm, 36 cm and 40 cm respectively.

For bridge position #2 - string length equal to 28 units, the respective length are equal to 56 cm, 63 cm and 70 cm with sound board widths of 32 cm, 36 cm and 40 cm.
If I recall correctly, the string length of ALAMI's Al Arja oud is about 63 cm with a sound board width of about 35.5 cm - suggesting that Farmer's 'thumb' unit of 2.25 cm (based upon this analysis) may perhaps have some validity? On the other hand, I previously estimated that the original string length of the Al Arja might have been about 63.5 cm (due to neck material lost in repairs). If the old Persian 'thumb' unit equal to 2.28 cm is used this would give a string length of 63.8 cm and width of 36.5 cm.