### VIDEO - L'arpa e il segreto della sua montatura: trucchi, strategie per ottimizzarla al meglio

## L'arpa e il segreto della sua montatura: trucchi, strategie per ottimizzarla al meglio Parte Prima

## L'arpa e il segreto della sua montatura: trucchi, strategie per ottimizzarla al meglio Parte Seconda

### VIDEO - Viola Da Gamba e Corde: documenti e iconografia

## Viola Da Gamba e Corde: documenti e iconografia

### VIDEO - Il segreto dell'esistenza del Liuto: il mondo dietro una lunghezza vibrante

## Il segreto dell'esistenza del Liuto: il mondo dietro una lunghezza vibrante

### VIDEO - Tra il budello intero di agnello e il nostro sintetico f- Reds: il confronto e le ragioni

## Tra il budello intero di agnello e il nostro sintetico f- Reds: il confronto e le ragioni

### Leopold mozart and his instructions on how to choose a violin’s set of strings

Leopold Mozart suggests an original method for choosing a violin’s set of strings: to hang them in pairs with two identical weights. The right diameters will be the ones that, when played empty, will give an interval of open fifth. If the interval is wider, it means that one of the two strings is too thin or the other is too big, and vice versa if the interval is narrower than a fifth. Mozart does not specify either where this gauge selection test should be performed (on a violin? on a frame?) or how much should the loads weigh.

As a matter of fact, there’s an extremely similar example found in a book by Serafino di Colco dated 1690: one could assume (but not prove) that Mozart was indeed influenced by reading this text.

What Serafino di Colco describes, however, is apparently valid… in his mind only. In fact, the author of this text has verified what he suggested in the practice, finding that it does not lead at all to the stated result: for example, two strings, calculated at the same tension – expressed in Kg – of an interval of one octave (we used the diameter of 0.60 mm and 1.20 mm), when subjected to the same kilograms by means of two equal weights, did not lead to an interval of an exact octave, as expected by Mersenne’s string law, but gave an interval than was greater than one octave.

This is the experimental demonstration:

All this happens because strings with different diameters will stretch differently when subjected to the same traction force: more for the thinner one. An elongation is nothing more than the manifestation of a reduction in diameter.

But according to Mersenne/Tyler’s string law, if a string becomes thinner (with the same density, vibrating length and tension in Kg) its frequency increases as a consequence. The 0.60 mm string, under the traction of the weight, will therefore lose a greater percentage of diameter than the 1.20 mm string: this explains why the theoretical interval of one octave is not observed in the practical verification.

As above said, strings of different diameters, put into traction by means of equal weights, lengthen differently: in Di Colco’s drawing, instead, we observe that the four equal weights lengthen the four strings of the Violin (which is strangely without neck!) of the same entity: this goes against the laws of Physics and the experimental test we performed.

It is concluded that Di Colco’s demonstration has no value, because it is physically, mathematically and experimentally wrong.

Let’s get back to Leopold Mozart. His method mentions equal weights; therefore, it seems to refer to the criterion of equal tension, but it’s not like that at all.

Let’s see why.

The first thing that can be noticed is that the choice of the diameter to be compared with the one that’s already under traction, changing the gauge until it gives the exact open fifth interval, is made when strings are already under the traction of equal weights; that is to say that both strings, due to the traction, have already lost a percentage of their original diameter, the one shown on their package.

This situation is completely different from the calculation that is made today, when speaking of equal tension settings, where all calculations are made considering the diameters of the strings still in the package, that therefore have not undergone traction yet.

As previously mentioned, putting in traction, either by means of weights or by turning the pegs, causes a certain gauge decrease which is maximum for the first string, lower for the second and almost nothing for the third and fourth (here fourth unwound string is meant). As a consequence, a setup calculated in equal tension in Kg, once installed will produce a slight inverse scaling of the tension values: the first string will have less tension than the second string; the second less tension than the third, just to mention an example.

Physics and Trigonometry laws state that when two strings have the same tension in Kg they also show the same (tactile) feel of tension (i.e. the same magnitude of lateral displacement with the same force applied acting and at a constant distance from one of the two constraints) as long as the tension in Kg is the same of the strings already in traction.

Experimental tests carried out by us have shown that the e-string by Aquila is reduced by about 5-6 %; a-string by about 2%; d-string by 0.1 %. We did not do the test with a plain gut C-string, but certainly the reduction is lower than that of d-string. The result changes little depending on how the strings are made.

So, what happens in Mozart’s case?

Let’s take the couple of e- and a-string as a reference and apply the principle of equal tension as we do today: let’s say that the first e-string is 0.620 mm; in a situation of equal Kg the a-string will be 0.93 mm and between them they will give a perfect interval of fifth but … will we still have the intervals of fifth (as calculated according to the law of the strings) even after having put them under two equal weights as Leopold Mozart suggests?

So far, we have done nothing else than apply the string formula introduced by Mersenne, and this is pure Mathematics, and Mathematics is not wrong.

But here is what happens instead: as we said before, we know that the first E-string put under weight (i.e. put in traction) reduces its diameter by about 6% while the second string reduces by about 2%.

So, once they have both been put under equal weights (let’s consider, for example, that both weights are 7.0 Kg; but nothing prevents them from being of another value) the E string will lose 6% of its diameter and thus become 0.58 mm; the A string will instead lose 2% of its diameter and become 0.91 mm.

Now let’s apply the law of the strings to this new set up of diameters (at 7.0 Kg of applied weight – which is a typical average tension of a Violin’s first string – and 0.33 meters of vibrating length) and let’s see what frequencies we get out of it:

They are 677.4 Hz for the E, and 431.7 Hz for A: but this is no longer a fifth interval!

In fact, if we start from the A string, that has 431.7 Hz, if we want a pure interval of fifth with the E string we must have 646.8 Hz and not the calculated 677.4 Hz: it is an interval greater than a fifth.

In practice, we are in the same situation as our experimental verification of Di Colco shown in our video but all in all also in the same situation mentioned by Mozart: if we obtain intervals greater than a fifth it means that the E string is still too thin or, vice versa, that the A string is too thick.

How to solve this?

First of all, in order to obtain the interval of fifth between E and A strings, when subjected to the same weight, it is necessary to start from diameters that are slightly scalar, not calculated in equal tension.

The procedure is then the following: does the E-string reduce its diameter by 6%? Then we’ll need to compensate that 6% reduction in our calculation by increasing the starting diameter accordingly. So, for example, an initial 0.62 mm diameter will become: 0.62 x 1.06 = 0.657 mm (that rounded to the nearest available diameter will be 0.66 mm).

The same logic can be applied to the A-string. Assuming that it reduces its diameter by 2%, the theoretical calculation will need to compensate that 2%. A 0.91 mm diameter will therefore become a 0.93 mm (as a result of 0.91 x 1.02 = 0.928).

When these two diameters (66 and 93) will be subjected to the same 7.0 kg tension, they will get reduced to the 0.62 and 0.91 initially expected, therefore the interval of perfect fifth will be achieved, exactly as suggested and described by Mozart (a good observer will have noticed that the diameters once in a state of traction must be exactly the ones obtained by theoretical calculation in order to have the perfect open fifth interval).

If instead, using Mersenne/Tyler’s formula, we calculate the purely theoretical tension of the ‘packed’ E string (of 0.66 mm) and the A string (of 0.93), whose diameter is measured in their ‘rest conditions’ with no strain, considering the frequency of 622.2 Hz for the E (at 415 Hz pitch) and 415 Hz for the A, we will see that the tension profile has a scalar nature: 7.58 Kg for the E of 0.66 mm and 6.74 Kg for the A of 0.93 mm.

Once again we’d like to underline that once the strings are subjected to a tensile strength, their diameters will decrease with different percentages (-6% on the E that becomes 0.62 mm thick, and -2% on the A that becomes 0.91 mm thick), and in these conditions, at the vibrating length of 0.33 m of a violin, they will both have a real tension of 6.74 Kg = equal tension = equal tactile feel of tension = open fifths; exactly what Mozart suggested.

As a conclusion, the true interpretation is that the method specified by Leopold Mozart in 1756 to determine the right gauges to be used on a violin does not concern applying a strict equal tension to the setting, as it is still believed by many today, but theoretically calculating a scalar tension setup that, once in tune, will provide an equal tension profile, expressed in Kg, that gives an exact condition of equal tactile feel of tension and will produces the open fifths: the theory we always supported.

Vivi felice

Mimmo Peruffo

### 6 AND 4 COURSES XVIII CENTURY MANDOLIN SETUP: A FEW CONSIDERATIONS

by Mimmo Peruffo

** ****Introduction**

When faced with the problem of what kind of strings were used on the 18th century Mandolins of six and four courses, the first thing that stands out is the great heterogeneity of these set up. What is really hard to understand is particularly on the 4 course Neapolitan Mandolin: here we find together gut strings; single and twisted metal wires; wound strings on gut/silk. To complete the already heterogeneous picture, for the 4^{th} course there are also two choices between unison and octave.

Here is the first question: why was it used a gut 1st and not a metal wire like the other courses, when it was then in use in the 1^{st} half of the nineteenth century?

This question is logic: the average breaking load stress (Breaking Point) of the gut is ‘only’ 34 Kg/mm2, much lower than the average of iron and bronze of the time, which easily exceeded 100 Kg/mm2.

To understand the reason, we must first start from the mechanical and acoustic behaviour of the string. In this way we will be able to try to figure out what were the guiding criteria used to determine the vibrating lengths of plucked and bowed instruments, including Mandolins.

**The strings and their characteristics**

Musical strings follow the rules that are summarized in the string equations of Taylor-Mersenne or even called Hook’s law (although the first to mention it was Vincenzo Galilei around 1580), which relates frequency, vibrating string length, diameter and density of the string.

However, when the gauge of a string increases, another thing is not included in this equation: with the increasing string diameters comes also a progressive loss of its acoustic properties until reaching the point where, over certain gauge, the string has clearly lost most of its performances. This is caused by the progressive increasing of the stiffness of the string.

This phenomenon is called Inharmonicity: before the appearance of the wound strings (on the second half of the 17th century) it was the main problem with which all the manufacturers of plucked, bowed and keyboard instruments had to deal with. (1)

The Inharmonicity clearly determines a limit to the total number of bass strings that an instrument can have, i.e. the open range. There is a second problem: a poor elasticity, i.e. a high Elastic Module, also produces an unwanted sharper frequency when pushed on the frets; this phenomenon is particularly noticeable on short vibrating length instruments (‘pitch distortion’).

The best solutions, in order to keep the Inharmonicity confined and the string sounding still ‘good’, is to limit the diameter increase by mean of some solutions (or, alternatively, keeping a thicker gauge but increasing the elasticity of the string to reduce the stiffness).

Our main interest is represented by these relationships:

-Diameter and vibrating length are inversely proportional

-Diameter and tension are inversely proportional

-Diameter and density are inversely proportional

The solutions that, at the same frequency, can contribute to reduce the diameter are the following:

1) Reduction of working tension

2) Increasing of the vibrating string length

However, there are other implementable actions:

3) Increase the elasticity of the string (does not affect the diameter reduction)

4) Increase the density of the string (affects the diameter reduction)

Point 1 is an exclusive decision of the player: according to the ancients the right string tension (better to call it the right* feel* of tension) is when the strings are not too stiff, nor too slack under the finger pressure. There is, however, a lower tension limit otherwise not only you can lose the finger control on the strings but also the acoustic power, its’ fire ‘, along with the increase of what is commonly called’ pitch distortion ‘ due to the fact that the strings are too slack and so, out of control by the performer.

Point 2 depends only by the luthier. This solution was adopted from the far past for the Arps, but latter also for the keyboards, theorboes/archlutes etc, were the vibrating string length increase, step by step, towards the bottom strings making them, step by step, thinner (proceeding in this way, the Inharmonicity is under control)

Points 3 and 4 depend only by the strings maker: the appearance of the wound strings in the middle of the seventeenth century can be considered a good example of point 4; a roped gut string/a very high twist string an example for the point 3.

At the end of the day, the point where a luthier can act is only No. 2, where vibrating length and diameter are inversely proportional (we consider that the performer has already done its job on the choice of the right feel of tension)

In the sixteen, seventieth and (maybe) the first half of the eighteenth century, the problem of string Inharmonicity was a well-known thing for luthiers: it can be seen, for example, from the still existing bowed and plucked instruments, whose vibrating string lengths are all related to the frequency of the first note and the hypothetic standard pitch: in practice we are speaking of the well knows rule of those times to tune the first string to the most acute possible just before the breakage.

In order to optimize the sound performance of a musical instrument it was therefore followed by the luthiers the rule of using the maximum vibrating length possible for that given treble note *indicated by the customer* (in other words, in which Country and its related pitch standard the instrument must be then employed) : only in that way all the strings could have the minimum gauge at the right feel of tension for the benefit of the overall acoustic performance.

However, the vibrating length cannot be increased as desired because of the limit imposed by the breaking load of the 1^{st} string: there is a limit that we call **Superior limit**

At the same time, it is not possible to increase the amount of bass strings (i.e. increasing of the open range) because there is another boundary called **Inferior limit**.

In other words, the full open range of a musical instrument is enclosed within these two borders.

The so-called Inferior limit however, using pure gut strings, begins to heavily manifest when the frequency range between the 1^{st} string and the last reach, more or less, two octaves. Only the six course Mandolin, on the two models, comes to this range. Generally speaking, the problem was, however, partially solved after the 2^{nd} mid of the 16th century by the introduction of a kind of very elastic and/or denser bass gut strings and then totally solved by the introduction of the bass wound strings in the 2nd half of the 17th century. In 2^{nd} half of the 18th century, the wound strings were probably totally in use.

**The Superior limit**

When a string of any material is progressively stretched between two fixed points (i.e., the vibrating string length), it will at some point reach a frequency where it will, instantly, break (Breaking Point)

In the case of a modern gut string, the average value of this frequency for a vibrating length of one meter is of 260 Hz (actually, after several tests, I have found that the whole range is of 250-280 Hz), which is a slightly low C.

The value of such a limit frequency, known as ‘Breaking Frequency’, is completely independent – as strange as it may seem – from the diameter and this can easily be verified both by mathematics (applying the general formula of the strings) and empirically.

By changing the diameters, the only changing parameter is the tension value always corresponding to the breaking point (i.e. the breaking frequency)

The Breaking Frequency is inversely proportional to the vibrating length at which the string is stretched.

So, if the string length is cut down to a half the frequency doubles and vice versa.

This means that the product between the vibrating length (in m) and the Breaking Frequency (in Hz) is a constant defined as ‘Breaking Index’, or more simply FL product (i.e. Vibrating length x Breaking Frequency),

By introducing the Breaking Index into the string formula considering a *unit section* of 1 mm2

(that is equal to 1.18 mm in diameter) at 1.0 m of vibrating string length, at the corresponding breaking frequency value in Hz we obtain (of course) the breaking load stress value of 34 Kg/mm2. In other terms, a string of 1.18 mm gauge, 1,3 of density, 1.0 mt scale at 34 Kg of breaking tension will reach the limit of 260 Hz.

In short: the breaking point of a modern gut string, according to our practical tests, ranges from 33 to 38 Kg mm2, which is equivalent to a breaking index of 250-280 Hz/m (mean value: 260 Hz/m). (2)

**Breaking vibrating length**

Going back to our main topic, a luthier thinks in opposition to what has been just explained; *it is the frequency of the 1 ^{st} string the first parameter to be fixed when designing a musical instrument* such as the Mandolin, Lute, etc etc.

By dividing the Breaking Index for the desired 1^{st} string’s frequency, you will obtain the theoretical vibrating length limit where the string will break when reaching the desired note (Breaking Point):

This is a simple proportion:

260: 1 meter = 1^{st} string’s frequency: X (were X is the vibrating length to be attributed in meters).

In the case of a six courses Mandolin whose first string is a G: 698.5 Hz (18th-century French chorus of 392 Hz) (3) it obtains: 260/698.5 = .37 m

This is therefore the vibrating limit length where we know that the string will break reaching the G (here we are referring to the ancient French pitch standard of 392 Hz).

The choice of vibrating ‘working’ length should therefore consider *a prudential shortening* of this limit length.

But how much? The more is shortened, more the strings are thicker with the risk of losing acoustic performance.

**Prudential Shortening or Working Index**

Examining the vibrating string lengths of the plucked and bowed instruments of the tables of Michael Praetorius (Syntagma Music, 1619) made possible to calculate their Working Index and put them in correlation to the gut breaking index. This allowed to understand the security margin adopted in those times (4) (5)

** **However, in the various calculations was (unfortunately) Ephraim Segerman taken as reference the average breaking load value -or Breaking Point- of a modern gut string *found in literature*: 32Kg mm2 (which is equivalent to a breaking index of 240 Hz/m) that is, actually, too low then the reality.

So, this value ca be placed on ‘lower quadrant’ of the range of breaking loads that we have found in today’s commercial strings during our experiments (we will here suggest the average value of a Breaking Point of 34 Kg/mm2, equal to 260 Hz/m of Breaking Index).

**Drawing from ‘Syntagma Music’ Michael Praetorius 1619**

However, comparing the breaking index of 240 Hz/m with all the other Working Index, he found that the choice of the vibrating working length of the Lute family and some Gambas (Viola Bastarda for example) was about 2-3 semitones below the Breaking Index (and hence also of the theoretical vibrating length that we calculated before).

Considering our example, therefore, the length shortening of two / three semitones would represent the real vibrating length to be adopted (corresponding to a G of 392 Hz): 32.9 / 31.1 cm, values that are included into the measures that are actually found in the six courses Mandolins of the time.

However, there is a concrete evidence of what has been said so far: we have subjected a gut string to a progressively increasing tension (Stress) and measured the related stretching (Strain).

Examining the final Stress/Strain diagram, the initial proportional variation that comes out follows the law of Hook and emerge evidently (also called Taylor / Mersenne).

At a certain point, the proportional variation stops and you reach a condition where the stretching (and therefore the corresponding tension) suddenly rises for small peg’s turns imposed to the string:

It is therefore concluded that the use of the maximum vibrating length can only work in the upper point of the linearity just before that the line start to bent up to reach the final breakage. The maximum acoustic performance (given by the maximum reduction of the diameter of all strings = maximum control on the inharmonicity) is determined by the fact that the instrument is working on the upper limit of proportionality, just before it changes, and this is exactly two to three semitones from the final exitus, as shows in the graphic.

Such behaviour of the gut string was well known even to the ancients and was therefore applied as one of the basic rules in the design / construction of musical instruments.

For Example, Marin Mersenne was avare of the right proportions that a musical instrument must have (“Harmonie Universelle” 1636, Livre Troisième, Proposition X, 129) :

Here there is what Bartoli wrote by the end of XVII century: (6) ‘*Una corda strapparsi allora che non può più allungarsi…*’ (a string breaks when it cannot stretch furthermore).

On the other hand, it is well-known to everybody the rule of those times of tuning the lute and even some bowed instruments at the highest note and stop immediately before the breakage of the first string: this is the ultimate proof of what we have already showed graphically.

**The Lute example**

The vibrating lengths that were chosen for some of the old, surviving Lutes of the past sum up valuable information.

The main problem is that in order to make an evaluation you have to use not modified instruments and instruments, whose standard pitches can be determined with a relative certainty. This is the case of some unmodified renaissance venetian lutes, German d minor baroque lutes, French baroque guitars.

Starting from an highly supposed standard pitch (thanks to their origins) and from what emerged in the study of their vibrating string lengths, the research on the various 5 course French guitars ( at the 17th French pitch standard close to 390 Hz) as well the german 13 course d minor Lutes tuned at the Kamerton of 410-420 Hz (see Baron 1727: Kammerton f note for the 1^{st}) ) and finally including even some surviving renaissance venetian lutes whose scale is of 56-58 cms probably related related to venetian standard pitch of *mezzo punto *= 460 Kz more or less, has allowed to detect a range of Working Index within 225 and 235 Hz/m with an average of 230 Hz/mt: this can be considered the Lute Working Index of the past times (theorboes generally speaking works with a bit more safety; Some Magno Graill or Buechenberg large theorbo has the vibrating string lengths around 95 cms; at the Roman pitch standard of 390 Hz/m, the related working Index range is of 210-220 Hz/m) .

We are very close to what we calculated for example from Segerman: 210 Hz/m

If we consider true that the Working Index of these examined original instruments present a safety margin of two or three semitones from the Breaking Point (how we have seen in our Stress/Strain graphic), it is even therefore possible to estimate the average Breaking Point -in Kg- of the Lute 1^{st} strings of those centuries. This can be obtained by increasing the working index that we have deducted of two or three semitones.From this simple reverse calculation, it is possible to determine that the average breaking load of the gut chanterelles of the 16, 17 and 18th century would be between 33.7-35.1 Kg/mm2 (that correspond to Breaking Index range of 256-268 Hz/m) __in the case of two semitones of safety__ margin and 35.7-37.3 Kg/mm2 (Breaking Index 273-285 Hz/m__) if the safety margin was instead of three semitones__.

How we can see, he range of all these values is perfectly in line with that of the current treble Lute gut strings of .36-.46 mm gauge (34-38 Kg / mm2).

Going back to the six-courses Mandolin with a 1^{st} string = G, a prudential shortening of two semitones on the average value of the Breaking Index of 260 Hz/m determines a vibrating length of 32.9 cms; it will be 31.1 cms if we are considering three semitones down of a safety margin: these are the typical vibrating lengths found in the surviving instruments.

The range of Working Index (the product between the frequency of the first-string x vibrating length in meters) is as follows:

Sol ( at the standard pitch 392 Hz); 32.9 cm 31.1 cm

230 Hz/m 217 Hz/m

Sol (at the standard pitch of 415 Hz); 32.9 cm 31.1 cm

244 Hz/m 230 Hz/m

As can be seen, a 6-courses Mandolin exceeds the typical Working Index of the surviving Lutes & 5 course Guitars only if the safety margin is two semitones whose pitch standard is of 415 Hz.

In the case of the 4 course Neapolitan Mandolin with a vibrating length of 33 cm (the one typical of the Violin) the following is obtained:

Mi (392 Hz reference pitch); 33.0 cm

194 Hz/m

Mi (415 Hz reference pitch); 33.0 cm

205 Hz/m

The conclusion is that both these Working Index are included within the Breaking Index of the gut treble, the 6-courses mandolin in particular works exactly like a Lute while the 4-courses Neapolitan has a lower tension condition on the first string, just like for Violin. The plausible explanation is as follows: while in the 6-courses mandolin the frequency excursion between the first and the last string is two octaves (24 semitones), in the 4 courses this excursion is reduced to 18 semitones. Consequently, in the second case, it is not strictly necessary for the strings working at the highest possible acoustic performance) i.e. close to the Breaking Point like happens on those instruments that has an open range of two full octaves like the Lute, in order to preserve the acoustic performance of the bottom strings.

However, the starting point is still unsolved: why was not used a metal treble whose sound would be much brighter and more readily available, would have had less wear and tear and even a higher breaking load than the gut? (7)

The breaking load stress of a XVIII century Iron for the Harpsichord can reach up to 100 Kg / mm2. For the old Brass this value is lower but always much higher than the average breaking load stress of the gut.

The explanation is that the highest note is certainly directly proportional to the breaking load but also inversely proportional to the specific weight of the material, which is very high in metals: 7.0 gr / cm3 for iron, 8.5 gr / cm3 for Brass; 1.3g / cm3 only for gut.

From simple calculations, taking into account both the ancient pieces of wire for keyboard instruments discussed on some essays of those times, we can list a series of Breaking Index:

Mersenne (8)

*Silver: 155 Hz/m*

*Iron: 160 Hz/m*

*Brass: 150 Hz/m*

The typical high density of metals affects quite strongly the limit of the Breaking Index: an “ancient” steel string with a breaking load of 100 Kg/mm2 for example (which is one of the higher values found among the absolute values of old strings for keyboards pieces), however, has a breaking index of just 178 Hz/m.

This clearly explains why the Battente guitar, fitted with robust metal strings, instead, have a vibrant length limited to only 55-58 cm, while those with the least strong gut strings can reach 68-73 cm (with the same reference chorus). (9)

There has been found a lot of metal strings breaking load stress of the past (10)

Here are some breaking indices found in old metal strings of Spinetta or Harpsichord:

*‘Old’ harpsicord iron: 158-188 Hz/m; mean 173 Hz/m. *(11)

*‘Old’ spinet and harpsicord iron: 164-187 Hz/m; mean 175 Hz/m. *(12)

*Old’ spinet iron from the second half of the 17 ^{th} century: 159-195 Hz/m; mean 177 Hz/m. *(13)

* *

Other metals:

*‘Old’ copper alloys: 112-138 Hz/m; media 125 Hz/m. *(14)

*‘Old’ brass: 101-155 Hz/m; media 128 Hz/m. *(15)

*‘Old’ brass: 148-153 Hz/m; media 150 Hz/m. *(16)

Considering the Iron (the metal with the highest breaking index) this would correspond to a breaking load of 145-160 Kg / mm2.

The evidence of the use of gut trebles on the Mandolin is a clear demonstration that strong metal strings were not available, in the course of the XVIII century and even for the first decades of the XIX. A metallic wire with these values would have been employed immediately, as it actually happened between the 16th and 17th centuries and after the 1830. (17)

The Mandolin was therefore inevitably forced to use gut string for the 1^{st} course due to lack of alternatives.

**Historical sources**

** **There are few historical sources of XVIII century containing information regarding the string setups of 4 or 6 courses Mandolin; these few are, at the end of the day, only Fouchetti and Corrette. (18) (19)

Let’s see what they wrote and what can be deducted:

Fouchetti

What Fouchetti wrote about the 4-courses Neapolitan mandolin setup, generally speaking, is considered unreliable, if not quite imaginative. A set of strings like those he described appears to be the most bizarre and heterogeneous among those of all the plucked and bowed instruments of his time.

In fact we find, mix together in a just four courses set, gut string, brass wires, twisted brass wires, wound gut/silk strings.

Indeed, this degree of heterogeneity is absolutely amazing. By looking more closely and by making some calculations, we realize that this set include in itself almost the utmost perfection possible for that time both from the mechanical point of view and from the acoustic point of view with very few other possibilities of choice, if we consider what was available in those times, to make strings.

Let’s see why (keeping in mind that the most wanted feature for this instrument was the brightness and the promptness of emission, as it had to imitate the harpsichord): (20)

Here is the set for the Neapolitan 4 courses Mandolin (Fouchetti says nothing about the 6 courses one):

- use a Pardessus gut treble
- a harpsichord gauge 5 yellow brass
- two harpsicord gauges 6 yellow brass twisted together
- a light G Violin wound fourth. The core can also be silk. As octave pair you can use a 5-gauge yellow brass like those of the second course. Sometimes the fourth course are installed in unison.

### VIDEO: Le montature di corda per chitarra del nuovo modello torres tra il 1880 e il 1945

## VIDEO: Le montature di corda per chitarra del nuovo modello torres tra il 1880 e il 1945

Nothing found.