In this last decade, the so-called equal tension setting has grown very popular among many players of historical bowed instruments, with the belief that such setting is the exact scientific interpretation of what was being done in the past (and what has been found on some historical documents, especially regarding the Lute): strings must all have the same ‘tactile sensation/equal feel’ of tension.
Physics can prove mathematically that strings that show the same deviation gradient, when an identical weight is applied at the same distance from the bridge, will also have the same tension expressed in Kg (the same deviation gradient produce also an equal feel of tension under the fingers).
What has not been considered, though, is the fact that this mathematical relationship is true only when strings are already in their final state of traction, while it proves to be false if the theorical diameters are calculated using the same value of tension in the Mersenne-Tyler string formula, like most of the equal tension supporters do nowadays.
Huggins, in the late XIX century, was already aware of this difference (just like the count Riccati in 1760).
This is what really happens: when undergoing the same weight, the thinner strings, in percentage, will experience a higher thinning as compared to the thicker ones.
In other words, once they are set into their final state of traction (i.e. intonation), each string will get thinner by a percentage that depends on the twisting ratio and how it was realized (high twist/low twist/roped etc) and expecially its Working Index into the instrument (the FL product).
Such percentage will be maximum for the high-pitched thinner strings (i.e. chantarelles), while it will be gradually lower on the thicker ones .
If the string formula is then applied to the new diameters measured once the strings reach the final tuning (and therefore they are in their final state of traction/tuning), it will be observed that tensions will follow an inverse scalar profile, and also the tactile sensation/feel of tension will necessarily feel reversed as well (minimum on thinner strings, maximum on the thicker ones).
We therefore physically performed all the tests as described by Di Colco, Mozart and Mersenne, contradicting the results that apparently seemed to confirm the “equal tension” hypothesis using the Mersenne/Tyler string formula.
Mersenne itself not only wrote that no player of his time followed his indications, but also introduced a 1/16 corrective coefficient to the string formula, without giving any explanation, and causing some criticism (for example see Daniello Bartoli, 1692).
Attanasio Kircher (“Preludium1”, 1650) provides the number of gut casings needed to make Roman Violon strings:
“Est hic Romae Chelys maior, quàm Violone vulgo vocant pentachorda, cuius maior chorda consesta est ex 200 intestinis. Secunda ex 180. Tertia ex 100. Quarta ex 50. Quinta denique ex 30. (19)
These details are very interesting and unique because they define the number of guts to be used to make the strings for this large instrument.
To verify the tension profile from other historical information we know that with three whole unsplit lamb guts we obtain an average diameter of 0.70 mm (See De Lalande and Count Riccati) . The following is obtained by simple proportion:
1: 2.21 mm (30 guts)
2: 2.85 mm (50 guts)
3: 4.04 mm (100 guts)
4: 5.42 mm (180 guts)
5: 5.71 mm (200 guts)
The Chelys Maior is tuned as follows: E, A, DD, GG, (and lastly FF)
Let’s calculate the tensions considering a ‘Roman’ pitch of 392 Hz and a vibrating length – assumed by us – of 90 cm. This is the data obtained:
1: E – 35.50 Kg
2: A – 26.31 Kg
3: D – 23.54 Kg
4: G – 18.88 Kg
5: F – 16.64 Kg
The tension profile has a scalar pattern: this is a direct example from the 17th century that demonstrates the scalarity of the tension expressed in Kg. By practical test this tension profile is also very close to an equal feel.
Unfortunately, none of today’s supporters of the equal tension, to the best of our knowledge, has ever done verification tests on what was stated on such documents, therefore trusting blindly what has been written.
As a conclusion, to recreate an “equal feel” setting, the theoretical calculation by the string formula must consider a certain degree of scalar tension.
When calculating our strings, we consider the correct scalar gradient: that’s why we are able to offer “equal feel” settings as they were used in the past, and that’s also the reason why we decided not to prepare “equal tension” settings by the string formula that have no real historical support and create disadvantages to a good musical performances, as Huggings and count Riccati already underlined in the XVIII and late XIX century.
We suggest to inform all customers about this topic, in order to finally clarify this point and avoid the practical difficulties encountered recently when calculating existent string settings.
To know more on this topic:
Vivi felice
Mimmo Peruffo