After struggling with my G and low E strings, which kept going out of tune after tremolo use, I sat down and looked at what would be ideal. I began buying standard sets of 10 gauge strings with a wound G string such as D'Addario EXL110W.
This helped but I had to bend that wound G string more than the other strings in order to achieve the same effect. Frustrated still, I set out to find a set of strings with similar tension on each string across the neck.
I recalled that D'Addario had printed the string tensions on the back of their string packages. I started there and went to their website where they have listed an entire chart of all of their strings already calculated for 25.5" scale guitars. Listed here:
D'Addario String Tension Chart
However, my guitar has a 25"(Martin/PRS) scale. Luckily, D'Addario also had the formulas along with the calculated tensions in the pdf. I proceeded to create the tables below for 25" scales.
I would note that there are some anomalies where a half gauge(i.e 0.0125") or an in between gauge(i.e 0.037") would be preferable, but many of these are not manufactured so I did my best to calculate on either side so that I, and now you, could make an informed choice about what tensions are readily available.
Also note that you can use the charts to create what I call "Progressive Tensioned" sets. With these the tension increases from the least tension on the high E string to the most tension on the low E string. I also included break downs of what I call "Half Sets". The idea is similar to "Heavy Bottom/Light Top" sets that you can find prepackaged from manufacturers. The difference is that each "Half Set" has it's tension closely matched. So, for instance, with the 25" scale, you could have the top three string's be 9, 12 and 15 gauge with a tension of around 12.5 lbs while the bottom 3 string's tension could center around 15 lbs for the gauges of 24, 32 and 44(or whatever tension you choose). I have "Even" and "Progressive" tensioned "Half Sets" listed so that a custom feel is possible for everyone, while the individual gauges listed let you be as specific as you wish.
This article currently only provides for 25.5" and 25" scale lengths. I plan to make a chart for 24.75"(Gibson) because my brother uses that scale on both of his guitars. Until then I hope that the included formulas and examples can help you work out your own calculations for 24.75" scales.
Note that I did not list the individual 25.5" gauges below, those are already published in the D"Addario pdf link above.
Also note that the sets listed below are intended for my own use, you may wish to use different gauges around different tensions. This is more of a guide of ideals to give an example to follow.
Last, but not least, I would acknowledge that this is not a new
concept, I simply chose to do the math and present it for everyone so
that they do not have to do the work, since I already did.
D'Addario also introduced a "Balanced Tension" set last year EXL111 (10,
13.5, 17, 24, 34, 46) which centers around 16 lbs for the top 4 strings
with the A and low E centered around 17.5 lbs.
I hope that you understand everything. If you have questions please feel free to post. I will answer as soon as I am able.
Enjoy!
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Comparison of Conventional and Even Tensioned Sets @ 25.5" Scale:
Conventional Even Tensioned Difference
Gauge Tension Gauge Tension Tension
9 13.1 9 13.1 0
11 11.0 12 13.1 2.1
16 14.7 15 12.9 -1.8
24 15.8 22 13.3 -2.5
32 15.8 30 14.0 -1.8
42 14.8 39 12.8 -2.0
10 16.2 10 16.2 0.0
13 15.4 13.5 16.6 1.2
17 16.6 17 16.6 0.0
26 18.4 24 15.8 -2.6
36 19.5 32 15.1 -4.4
46 17.5 44 15.4 -2.1
11 19.6 11 19.6 0
14 17.8 15 20.5 2.7
18 18.6 19 20.7 2.1
30 25.0 28 21.3 -3.7
42 26.3 38 21.6 -4.7
52 22.0 52 22.0 0
___________________________________________________________________
Even Tensioned String Sets
Gauges in (parentheses) are alternatives to consider when a more ideal match is not available. A (X) means that the string is not made but would most likely be ideal for the application.
Even Tensioned Full Sets
25.5" Scale
Gauge Tension
9 13.1
12 13.1
15 12.9
22 13.3
30(29) 14.0(X)
40 13.4
10 16.2
13.5 16.6
17(18w) 16.6(16.1)
24 15.8
32 15.8
44 16.1
11 19.6
15 20.5
19(20W) 20.7(19.4)
28 21.3
38 21.6
52 22.0
Even Tensioned Half Sets
Plain:
Gauge Tension
7 7.9
9.5 8.2
12 8.2
8 10.4
10.5 10.0
13.5 10.4
8.5 11.7
11.5 12.0
15(14.5) 12.9(X)
9 13.1
12 13.1
15 12.9
9.5 14.6
13(12.5) 15.4(X)
16 14.7
10 16.2
13.5 16.6
17 16.6
10.5 17.9
14 17.8
18 18.6
12 23.3
16 23.3
20 22.9
________________________
Wound:
Gauge Tension
22 13.3
30(29) 14.0(X)
40 13.4
24 15.8
32 15.8
44 16.1
28 21.3
38 21.6
52 22.0
Progressive Tensioned Half Sets
Plain:
Gauge Tension
8.5 11.7
11.5 12.0
15 12.9
10 16.2
13.5 16.6
17 16.6
10(10.5) 16.2
14 17.8
18 18.6
11 19.6
15 20.5
19 20.7
13 27.4
18(17.5) 29.5(X)
24(22) 33.0(27.7)
___________________________
Wound:
Gauge Tension
28 21.3
38 21.6
52 22.0
32 28.1
44 28.7
60(59) 30.4(29.3)
________________________________
25" Scale Calculations
T(Tension)= (UW x(2xLxF)2)/386.4
UW(unitweight)= (Tx386.4)/(2xLxF)2
UW- Unit Weight. In all the charts and formulas in the brochure, unit weight is expressed in pounds per linear inch (lb/in).
L- Scale Length. This is the vibrating length of the string. This is determined by measuring the distance from the nut to the bridge of the instrument in inches (in).
F- Frequency or pitch. This is the pitch at which you will be tuning the string expressed in cycles per second (Hertz).
On the following page are two fingerboard graphics detailing the various frequencies for the standard guitar and electric bass guitar.
Frequency @ Standard Tuning:
E 329.6 Hz
B 246.8 Hz
G 196.0 Hz
D 146.8 Hz
A 110.0 Hz
E 82.4 Hz
Here is an example:
Replace the Unit Weight(i.e .00002215 etc.) by referencing the D'Addario chart for the particular string gauge and musical note for which you wish to calculate the tension.
E T(Tension)= (.00002215 x 271590400)/386.4
B T(Tension)= (.00004037 x 152399025)/386.4
G T(Tension)= (.00006402 x 96040000)/386.4
D T(Tension)= (.00010857 x 53875600)/386.4
A T(Tension)= (.00019347 x 30250000)/386.4
E T(Tension)= (.00035182 x 16974400)/386.4
High E
7 T(Tension)= 7.626179710144928
8 T(Tension)= 9.966749151138716
8.5 T(Tension)= 11.253008033126294
9 T(Tension)= 12.609554285714286
9.5 T(Tension)= 14.050445383022774
10 T(Tension)= 15.568652587991718
10.5 T(Tension)= 17.164175900621118
11 T(Tension)= 18.837015320910973
11.5T(Tension)= 20.594199585921325
12 T(Tension)= 22.421671221532091
13 T(Tension)= 26.315591552795031
B
9 T(Tension)= 7.075669017857143
9.5 T(Tension)= 7.884204217779503
10 T(Tension)= 8.736124233307453
10.5 T(Tension)= 9.631429064440994
11 T(Tension)= 10.570118711180124
11.5 T(Tension)= 11.556137247670807
12 T(Tension)= 12.581596525621118
13 T(Tension)= 14.766613602484472
13.5 T(Tension)= 15.922227327251553
14 T(Tension)= 17.125169941770186
15 T(Tension)= 19.65726554347826
16 T(Tension)= 22.366844481754658
17 T(Tension)= 25.249962682453416
18 T(Tension)= 28.306620145574534
G
12 T(Tension)= 7.928768115942029
13 T(Tension)= 9.305739130434783
13.5 T(Tension)= 10.033992753623188
14 T(Tension)= 10.792072463768116
15 T(Tension)= 12.387768115942029
16 T(Tension)= 14.095311594202899
17 T(Tension)= 15.912217391304348
18 T(Tension)= 17.838485507246377
19 T(Tension)= 19.876601449275362
20 T(Tension)= 22.024079710144928
22 T(Tension)= 26.649608695652174
24 T(Tension)= 31.715072463768116
D
18 T(Tension)= 8.665550051759834
20 T(tension)= 10.450249016563147
22 T(Tension)= 12.805215072463768
24 T(Tension)= 15.137872391304348
25 T(Tension)= 16.40249892339545
26 T(Tension)= 17.667125455486542
28 T(Tension)= 20.448746107660455
30 T(Tension)= 24.032086997929607
32 T(Tension)= 26.97544599378882
A
24 T(Tension)= 8.499592391304348
26 T(Tension)= 9.919714026915114
28 T(Tension)= 11.481534679089027
30 T(Tension)= 13.493504140786749
32 T(Tension)= 15.146137422360248
34 T(Tension)= 16.902109213250518
36 T(Tension)= 18.760636645962733
38 T(Tension)= 20.723285455486542
40 T(Tension)= 22.955240683229814
42 T(Tension)= 25.270179865424431
Low E
32 T(Tension)= 8.49906099378882
34 T(Tension)= 9.484402070393375
36 T(Tension)= 10.527290931677019
38 T(Tension)= 11.628606169772257
39 T(Tension)= 12.27041772256729
40 T(Tension)= 12.881039254658385
42 T(Tension)= 14.180037722567288
44 T(Tension)= 15.455314202898551
45 T(Tension)= 16.12172633540373
46 T(Tension)= 16.788138467908903
48 T(Tension)= 18.178949813664596
50 T(Tension)= 20.411013126293996
52 T(Tension)= 21.134094451345756
54 T(Tension)= 23.650821614906832
56 T(Tension)= 25.30257482401656
Even Tensioned Set
Gauge Tension
7 7.6
9.5 7.9
12 7.9
18 8.7
24 8.5
32 8.5
9 12.6
12 12.6
15 12.4
22 12.8
30(29) 13.5(X)
40(39) 12.9(12.3)
10 15.6
13.5 15.9
17(18w) 15.9(15.4)
24 15.1
32 15.1
44 15.4
12(11.5) 22.4(20.6)
16 22.4
20(20w) 22.0(18.6)
28 20.4
38 20.7
50 20.4
Even Tensioned Half Sets
Bold indicates closest matched sets.
Plain:
Gauge Tension
7 7.6
9.5 7.9
12 7.9
8 10.0
10.5 9.6
13 9.3
8.5 11.3
11.5 11.6
15(14.5) 12.4(X)
9 12.6
12 12.6
15 12.4
9.5 14.1
13 14.7
16 14.1
10 15.6
13.5 15.9
17 15.9
10.5 17.1
14 17.1
18 17.8
11 18.8
15(14.5) 19.7(X)
19(18.5) 19.9(X)
12(11.5) 22.4(20.6)
16 22.4
20 22.0
13 26.3
18(17.5) 28.3(X)
22 26.6
_________________________
Wound:
Gauge Tension
18 8.7
24 8.5
32 8.5
20 10.5
26 9.9
36 10.5
22 12.8
30(29) 13.5(X)
40 12.9
24 15.1
32 15.1
44 15.4
26(25) 17.6(X)
34 16.9
46 16.8
28 20.4
38 20.7
50 20.4
Progressive Tensioned Half Sets
Plain:
Gauge Tension
8 10.0
12 12.6
16 14.1
9 12.6
13 14.7
17 15.9
9.5 14.1
13.5 15.9
18 17.8
10 15.6
14 17.1
19 19.9
10.5 17.1
15 19.7
20 22.0
11 18.8
16 22.4
22 26.6
________________________
Wound:
Gauge Tension
20 10.5
28 11.5
39 12.3
22 12.8
30 13.5
42 14.2
24 15.1
34 16.9
48 18.2
26 17.7
36 18.8
50 20.4
28 20.4
38 20.7
52 21.1
30 24.0
42 25.3
56 25.3
Never understood why the d!ckheads at all these string manufacturing companies ever came up with stupid packed sets with completely way off tensions.
ReplyDeletee.g. D'Add 8 string gauge comes with 8-10-15 in which each string's tension is way off compared to Ernie BAll 8-11-14 which has a more even tension.
It simply means these guys are indeed d!ckheads because they can manufacture and package the string sets with more even tension, without resorting to fraction gauges, but dont want to do it.
And hey it doesn't require quantum computing level of cutting edge innovation, all the technologies and string gauges were available way back.