ed packard
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Posted 11 Feb 2006 8:44 am |
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WARNING…MORE TECH STUFF…read at your own risk…may be detrimental to your picking ability!
Staying in tune…easy said, tough to do. Ever notice the amount of frantic tweaking that happens on stage? Seems like the PSG won’t stay tuned up to suit even the big name players. What might be the reason? One of the big contributors to detuning is temperature.
Strings expand as a function of temperature. As temperature increases, they get a bit slack hence their pitch becomes flat. The rate of expansion for a material is described by a term called Thermal Coefficient of linear Expansion, or TCE for short. Different materials have different TCE values. Strings are about 10.2 parts per million per deg f, or said another way, 10.2 micro (millionths) of an inch per inch (means for each inch of length) for each deg f of temperature change.
A key head type of instrument might have string lengths that are different by as much as 6”. A keyless/gearless instrument may have string length differences less than ¼”.
There is a much worse problem than differences in string length, and that is the amount of stretch involved in getting the string up to pitch. On the BEAST, my string lengths are all within1/4” at tension, but the amount of stretch caused by the tension is 0.064” for the halftone next to in pitch for the 0.011” diameter plain string (11 gauge), and as little as 0.011” for my 0.056” (56 gauge). The 56 gauge will be MUCH more sensitive to thermal change than the 11 gauge.
By measurement on the BEAST, a 20% change in the amount of stretch for a given half tone (from temperature of mechanical flexing) is worth 30 cents of pitch shift!!! 20% on the 11 gauge is a 0.0128” change = 12.8 milli inches, or 12.8 thousandths of an inch. The same 20% for the 56 gauge is only 0.0022 “ = 2.2 thousandths of an inch = BIG difference!
Let’s see what kind of string length change we would get for a 20 deg f increase in temperature:
= TCE, times stretched string length, times deg f change = (10.2*10^-6)*31.750* 20 = about 0.0065”…that is about 10% of the 11 gauge string’s halftone stretch value, but it is over 50% of the 56 gauge string’s halftone stretch value. It produces not only an “absolute” out of tune situation, but also a “relative” out of tune situation. Larger gauge strings are the worst offenders.
All the above assumes that the body length has not changed. That may or may not have been the case. If the body is Carbon Fiber or Maple Die Board that might be the case. If the body is Maple along the grain, the TCE value might be 4 to 6 parts per million per deg f. If the body material is aluminum, the TCE value is given as 13.7 parts per million per deg f. The difference between the materials with TCE = 10.2 (strings), and the TCE = 0 body materials is 10.2; the difference between the 10.2 string TCE and the Aluminum body with a TCE = 13.7 is 3.5. The difference between the strings at a TCE of 10.2 and the Maple wood body is 4 and 6.
A lower TCE difference (string/body) value gives a lesser effect of thermal change on pitch for the common string gauges and materials.
You can run the numbers for the TCE differences and see what the various combinations give in string stretch. The TCE difference of 3.7 will give the least pitch shift, but it is still not the same for each string, and because of the body mass and the materials thermal conductivity value, there will be a time delay for the body to come up to temperature. Don’t tune during this time or be prepared to chase the tuning.
If the temperature change is slow, the low TCE difference (string/body) numbers are better. If the change is fast (a step), then the low body TCE difference values mean that you won’t have to wait as long to tune (strings come to temperature quickly), but further changes in temp’ will have a greater effect upon the tuning = tweak, tweak, tweak!
Having strings that give the same amount of stretch per cent of pitch would lead to some very large gauges, but would provide “relative” in tune conditions.
Individual string pickups and electronic pitch shift could improve the situation…so could servo tuning, but I don’t like the added weight and power consumption.
The tuning rod TCE issue and it’s effect is left to the reader “to run the numbers” … the TCE given for Titanium is between 4.9 and 7.1
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