Equal tension, equal feel and scaled tension
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This test was done just to verify if the Serafino di Colco’s description about the equal tension profile actually work: the answer is in this video
Serafino Di colco 1691 wrote that under the same weigth, at the same string length and twice gauge there is an interval of an octave between the strings (the equal tension’s idea, the same explained by Marin Mersenne 1636 and in different way by Mozart’s father). Unfortunately this is not true. How you can see in this test, to obtain an intervall of an octave need to push the second fret of the thicker string.
Why this hapen? Which is the explanation?
The explanation is that under the same weigth two strings of different gauges has different degree of elongation (or stretching). thinner the gauge longer the stretching.
At the end of the history, the thinner string became thinner, in percentage, than the thicker string. One thing is to have, say, 5 Kg on a 1 mm gauge and one thing is to have the same weight on a .50 mm gauge.
But from the string formula a thinner string produce an higher frequency.
The conclusion is that it is not possible to obtain the interval of the octave as propugned by Mersenne & Di Colco and today by some scholars.
The solution? Easy. it need to calculate by the string formula a scaled tension instead equal tension.
When the strings are under the weight the thinner string will stretch more and so it reduce its own gauge to the right one. Under this condition the interval of an octave will be done properly.
In conclusion the modern concept of equal tension for period instruments is a misunderstanding and deserve to be fixed.
Di Colco & Mersenne done a certain degree of confusion: unfortunately they has never considered what really hapen when the strings are put in tune and under tension.
Here is an indipendent contribution