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Easy way to calculate tension difference for tuning down to D standard?

S

shoulderpet

Sep 24, 2015
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#1
Hi all
I am thinking of dropping my tuning down to D standard on my bass, I am using a set of Rotosound 95-40 stainless steel strings at the moment which are around 146ibs of tension and I would like to keep the neck relief and string tension as close as possible.

Is there an easy way of working out how much tension I will loose if I take a set of strings and tune them to D standard?

Thanks
 
#2
shoulderpet said:
I am thinking of dropping my tuning down to D standard on my bass, I am using a set of Rotosound 95-40 stainless steel strings at the moment which are around 146ibs of tension and I would like to keep the neck relief and string tension as close as possible.

Is there an easy way of working out how much tension I will loose if I take a set of strings and tune them to D standard?
Click to expand...

I use GHS Pressurewounds on two of my basses.

40-54-76-96 in EADG = 147.2 lbs.
44-62-84-106 in DGCF = 148.5 lbs.

The 44-106 set is 187.1 lbs. in total tension when tuned to EADG. So, that's a reduction of roughly 21% going from EADG down to DGCF.

Roto RS66LD (45-65-80-105) is 181.97 lbs. in total tension. 21% off of that would be 143.76 lbs.

I realize this is probably not the most scientific way of doing it, but it at least gives you a rough idea. ;)
 
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#3
shoulderpet said:
Hi all
I am thinking of dropping my tuning down to D standard on my bass, I am using a set of Rotosound 95-40 stainless steel strings at the moment which are around 146ibs of tension and I would like to keep the neck relief and string tension as close as possible.

Is there an easy way of working out how much tension I will loose if I take a set of strings and tune them to D standard?

Thanks
Click to expand...

Yes, use the published Rotosound tension for the given pitches to calculate the unit weight, then use the unit weight to calculate the tension for the new desired pitches. The GHS String Tension Guide has all of the relevant formulas.

I've got all the math set up in a Mac spreadsheet, and could figure it out later today.
 
#5
michael_t said:
I use GHS Pressurewounds on two of my basses.

40-54-76-96 in EADG = 147.2 lbs.
44-62-84-106 in DGCF = 148.5 lbs.

The 44-106 set is 187.1 lbs. in total tension when tuned to EADG. So, that's a reduction of roughly 21% going from EADG down to DGCF.

Roto RS66LD (45-65-80-105) is 181.97 lbs. in total tension. 21% off of that would be 143.76 lbs.

I realize this is probably not the most scientific way of doing it, but it at least gives you a rough idea. ;)
Click to expand...
Thanks that is very helpful
 
#9
Rocket Queen said:
OK, here are the numbers I get for Rotosound RS66LCs:

F2 (0.040) = 31.35 lbs.
C2 (0.060) = 30.71 lbs.
G1 (0.075) = 28.16 lbs.
D1 (0.095) = 25.15 lbs.
Total = 115.36 lbs.
Click to expand...

I think @shoulderpet is looking for a set of strings for DGCF that closely matches the tension of the 40-95 set tuned to EADG.

Would you be able to recalculate the tension of the RS66LD set (45-65-80-105) for DGCF and see how close they come to the 40-95 set in EADG?
 
#10
michael_t said:
I realize this is probably not the most scientific way of doing it
Click to expand...
Well, your way is no less scientific than recalculating tensions every time with the formula, starting from unit weights: the result cannot but be the (approximate) same. Same cat to be skinned.


Want yet another way? Get tensions, or the total tension for the set, at 30.3" scale, which is the distance between 2nd fret and (nominal position of) bridge.
(Because, well, tension for E1 fretted on the second fret = tension for open D1, non?)

How do you do that? Take tension values at 34" and multiply them for the ratio of scale lengths, squared: (30.3/34)^2 = .794
~79% minus 100% = the same ~21% you got (Q.E.D.)
 
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#11
@michael_t : If you want to stay with Rotosound, the 45-105 set will be very close to the same tension...as close as you're going to get.

The 2nd string will be oddly tight, as it really should be 45-60-80-105 instead of 45-65-80-105 -- but to my knowledge, no one makes a balanced tension set of stainless steel strings, so you'll just have to live with it unless you decide the situation merits making your own set out of singles. (40-95 sets are generally quite close to balanced tension, unlike every other 'standard' set of bass strings.)
 
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#13
Tension varies as the square of the pitch, not linearly. So D standard is two half-steps or a whole step down. So you divide by that number squared, which is, of course, 4. If x is tension, than resulting y tension tuned down two half steps, E to D standard, is: x / 2^(4/12) = y. 2^(4/12) is approximately 1.26. So take the rated tension for the set of strings and divide it by 1.26. For example, the tension of a set of D'Addario XL170BT 50-120 at regular pitch, x, is averages @ 50 1/2 pounds per string, total 202 pounds. Divide that number by 1.26 and you get y @ 160 pounds for the set, or divided by 4, about 40 pounds tension per string, instead of the @ 50 1/2 pounds tension per string at regular pitch.
 
#14
michael_t said:
I use GHS Pressurewounds on two of my basses.

40-54-76-96 in EADG = 147.2 lbs.
44-62-84-106 in DGCF = 148.5 lbs.

The 44-106 set is 187.1 lbs. in total tension when tuned to EADG. So, that's a reduction of roughly 21% going from EADG down to DGCF.

Roto RS66LD (45-65-80-105) is 181.97 lbs. in total tension. 21% off of that would be 143.76 lbs.

I realize this is probably not the most scientific way of doing it, but it at least gives you a rough idea. ;)
Click to expand...

michael_t said:
Refer to page 3 of the GHS Tension Guide.
Click to expand...

HaphAsSard said:
Well, your way is no less scientific than recalculating tensions every time with the formula, starting from unit weights: the result cannot but be the (approximate) same. Same cat to be skinned.


Want yet another way? Get tensions, or the total tension for the set, at 30.3" scale, which is the distance between 2nd fret and (nominal position of) bridge.
(Because, well, tension for E1 fretted on the second fret = tension for open D1, non?)

How do you do that? Take tension values at 34" and multiply them for the ratio of scale lengths, squared: (30.3/34)^2 = .794
~79% minus 100% = the same ~21% you got (Q.E.D.)
Click to expand...

iiipopes said:
Tension varies as the square of the pitch, not linearly. So D standard is two half-steps or a whole step down. So you divide by that number squared, which is, of course, 4. If x is tension, than resulting y tension tuned down two half steps, E to D standard, is: x / 2^(4/12) = y. 2^(4/12) is approximately 1.26. So take the rated tension for the set of strings and divide it by 1.26. For example, the tension of a set of D'Addario XL170BT 50-120 at regular pitch, x, is averages @ 50 1/2 pounds per string, total 202 pounds. Divide that number by 1.26 and you get y @ 160 pounds for the set, or divided by 4, about 40 pounds tension per string, instead of the @ 50 1/2 pounds tension per string at regular pitch.
Click to expand...
.
Thanks all, everything seems to be pointing to a 21% drop in tension so I think I can be pretty confident that 21% is the magic number and with that in mind to get to 146ibs to match the current string set I would need a set of strings that is around 185ibs of tension in standard EADG tuning, as someone has now mentioned the Rotosound 105-45 set would be the closest match in D standard
 
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#15
shoulderpet said:
.
Thanks all, everything seems to be pointing to a 21% drop in tension so I think I can be pretty confident that 21% is the magic number and with that in mind to get to 146ibs to match the current string set I would need a set of strings that is around 185ibs of tension in standard EADG tuning, as someone has now mentioned the Rotosound 105-45 set would be the closest match in D standard
Click to expand...
No. 26% drop in tension. Re-do the math I set forth above.
 
#16
iiipopes said:
No. 26% drop in tension. Re-do the math I set forth above.
Click to expand...
Ahh ok, I will have a look tomorrow and see where I have gone wrong, when I take the total tension of the Rotosound 105-45 set with the 85 gauge A and divide the tension(185ibs) by 1.26 I am getting around 146ibs and when I take the 185ibs and times by 0.79 to get the value less 21% I am also getting around 146ibs, strange, is late here in the uk so I will have a look tomorrow
 
#17
shoulderpet said:
.
everything seems to be pointing to a 21% drop in tension...
Click to expand...

I once emailed Rotosound, asking them to provide the tension figures for RS77LE (Jazz Flats 50-75-95-110) in DGCF.

According to their calculation, this set is 253.01 lbs. in EADG and 200.44 lbs. in DGCF. That works out to be 20.8% reduction.

Or, to put it the other way, going from DGCF to EADG, it's 26% increase.

21% vs. 26%... It all depends on which way you're going.
 
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#18
2 half steps gives you a tension ratio of the twelfth root of 2 (the frequency ratio between successive half steps) to the fourth power - 2 half steps gives you that number squared, and the tension to frequency relationship is another squaring. That resultant ratio is a bit below 1.26. If you’re going down in frequency, you use the reciprocal - 1 divided by 1.26, which is about .79.

A simpler way to think of it is a full step up, multiply the tension by 1.26. A full step down. Divide the tension by 1.26x
 
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