Your Guitar Strings Pull 160 Pounds. Mediums Add 25 More.

A light acoustic set (12-53) pulls about 722 newtons (162 lb) on the guitar at standard pitch. A medium set (13-56) pulls about 835 N (188 lb). That is 113 N more, or 15.6%. I computed both by hand from published unit weights and a 25.4 inch scale. No Lab run was used. The two published charts I could read agree with my totals within about 1%. The wound strings differ from the official per-string values by up to 3.8%.

The surprise is not that mediums pull harder. Every string maker says so. The surprise is the size. Per string, the gain runs from 11% to 21%. A light set pulled to medium tension would sit about 1.26 semitones sharp. Light E4 at 329.63 Hz would land near 354.5 Hz, between F4 (349.23 Hz) and F#4 (369.99 Hz).

Question

Do common comfort claims about gauge match the tension numbers? Martin calls light strings "the lightest and easiest strings to play." It calls medium "the highest tension strings we recommend using on your Martin acoustic guitar." [1] Those are verbal claims. They have no numbers.

My working thesis said the differences would be "tens of percent." That was too loose. The set-level difference is 16%, and the per-string range is 11% to 21%. I change the thesis to match: the gap is real, moderate, and above one measured force threshold. It is not huge.

I also want to flag what I cannot test. I found no study that measures how players rate gauge feel blind. So "feel" here means a force threshold, not a rating.

Data and where it came from

Three inputs go into the calculation.

Linear density of the wound strings. A string harp reference page lists phosphor bronze wound strings in grams per metre. It says the table was converted from D'Addario data. [2] I read the full table. The values I use:

Gauge (in)	Mass per length (g/m)
.024	2.09
.026	2.44
.032	3.75
.035	4.53
.042	6.56
.045	7.46
.053	10.17
.056	11.34

Linear density of the plain strings. I computed these from diameter and an assumed steel density of 7.85 g/cm³. That density is my assumption. I did not cite it. The check is the plain E: my result is within 0.4% of the published value. The plain steel masses are:

Gauge (in)	Mass per length (g/m)
.012	0.5728
.013	0.6722
.016	1.0183
.017	1.1495

Published tensions for checking. Elixir lists tensions for light and medium sets at a 25.5 inch scale. [3] I read that page in full. D'Addario lists official values for the same sets. [4][5] I could not open the D'Addario pages, because the server refused my requests. A search summary reported their values. So I treat those figures as partly read.

Source status:

• Mersenne's law page (Wikipedia): read. [6]
• Martin blog: read. [1]
• Harp table: read. [2]
• Elixir chart: read. [3]
• D'Addario pages: partly read, via search summary only. [4][5]
• Force threshold study: unread beyond a search summary. [7]

Method

For an ideal string in its fundamental mode, frequency depends on vibrating length, tension and mass per length. [6] I rearrange it to solve for tension.

Symbols, in plain words:

• $T$ is tension in newtons.
• $\mu$ is mass per unit length in kg/m.
• $L$ is the vibrating length in metres.
• $f$ is the open-string pitch in hertz.

$$T = \mu \, (2 L f)^2$$

I use $L$ = 25.4 in = 0.64516 m. The open-string pitches are:

String	Note	Hz
1	E4	329.63
2	B3	246.94
3	G3	196.00
4	D3	146.83
5	A2	110.00
6	E2	82.41

The value $(2Lf)^2$ is the squared wave speed, in m²/s². I worked it out by hand for each string:

String	$(2Lf)^2$ (m²/s²)
E4	180,906
B3	101,526
G3	63,960
D3	35,894
A2	20,146
E2	11,307

I convert newtons to pounds-force with 4.44822. This is hand arithmetic, not Lab output. A reader can redo it in a spreadsheet in five minutes.

Result

Light set (12-53), hand work:

String	N	lb
E4 .012	103.6	23.3
B3 .016	103.4	23.2
G3 .024	133.7	30.1
D3 .032	134.6	30.3
A2 .042	132.2	29.7
E2 .053	115.0	25.9
Total	722.4	162.4

Medium set (13-56), hand work:

String	N	lb
E4 .013	121.6	27.3
B3 .017	116.7	26.2
G3 .026	156.1	35.1
D3 .035	162.6	36.6
A2 .045	150.3	33.8
E2 .056	128.2	28.8
Total	835.5	187.8

The medium-to-light ratio per string:

• E4: 1.174
• B3: 1.129
• G3: 1.167
• D3: 1.208
• A2: 1.137
• E2: 1.115

So the per-string gain is 11.5% to 20.8%. The set gain is 1.157, or 15.7% by ratio. In absolute terms, the D string gains the most: 6.3 lb. The low E gains the least: 2.9 lb.

Check against published charts

Elixir lists 162 lb for light and 188 lb for medium at 25.5 inches. [3] My totals are 162.4 and 187.8 lb. That is a gap of 0.3% or less.

D'Addario's reported wound-string values, for the four wound strings only, are:

• Light: 30.1, 29.9, 28.9 and 24.9 lb, summing to 113.8 lb. [4]
• Medium: 35.1, 35.9, 32.8 and 27.8 lb, summing to 131.6 lb. [5]

My wound sums are 115.9 and 134.3 lb. That is 1.8% and 2.0% higher. The ratio of the wound sums is 1.156 for D'Addario and 1.159 for mine.

The worst single string is the light low E2. I compute 25.9 lb, and D'Addario reports 24.9 lb. That is a gap of 3.8%. I do not know why. Rounding in the unit weights is only about 0.05%. So the cause is something else, possibly a different scale length in the maker's calculation. I mark that as unexplained.

My uncertainty statement: plain strings within about 1%, wound strings within about 4%, set totals within about 1%.

What this means for feel

One useful property: the fretting force is roughly linear in tension. Press the string down by a small distance $\delta$ at a point $a$ from the nut and $b$ from the bridge. The extra force at the finger is about:

$$F \approx T \, \delta \left(\frac{1}{a} + \frac{1}{b}\right)$$

This is my own small-angle derivation. It ignores bending stiffness and the small rise in tension from stretching. If the action is the same, fretting force scales with $T$. So a 16% tension gain gives about a 16% gain in fretting force.

Now the threshold. A pinch-force study reports a just-noticeable difference of about 7% of the reference force, for 5 subjects and reference forces of 2.5 to 10 N. [7] A separate fingerpad study reports ratios near 18% to 19%. [8] I read only search summaries of both. Neither task is guitar fretting. Both ranges are far below the string forces, and the grip is different.

With those caveats, the 11% to 21% gain straddles the range. It sits above 7% and around 18% to 19%. So I cannot call it "too small to feel." But I also cannot say players would feel it. The threshold data come from different tasks and few subjects.

That undermines the second half of my original thesis. I expected comfort claims to be either too small or too large to match. The numbers do not show a mismatch. "Mediums feel noticeably stiffer" fits a 16% change. "Lights are easier" fits too. The claim is plausible. It is also unblinded, and I found no blind test of it.

Sensitivity: which assumption moves the result most

Hand work, same formula, one change at a time:

Change	Effect on tension
Scale 25.4 to 25.5 in	+0.8% (tension scales with $L^2$)
Scale 25.4 to 24.75 in	-5.1%
Tuned 10 cents flat	-1.2%
Tuned a half step down	-10.9%
Steel density 7.85 to 7.75 g/cm³	about -1.3% on plain strings

The half-step case is the most useful. The factor is $2^{-1/6}$, or 0.8909. A medium set tuned down a half step carries about 167 lb in total. A light set at standard pitch carries 162 lb. So the two feel closer than the labels suggest, at least in total pull. Individual strings still differ, since the factor is the same but the starting values are not.

The biggest single assumption is scale length, because tension scales with its square. The second is the unit weight of the wound strings. The label on the pack ("light" or "medium") matters least. Makers use different gauges under the same label, which a quick search for "light vs medium" will show. So compare the numbers on the pack, not the word.

Where this leaves me

My present view: mediums pull about 16% harder than lights, and I trust that to within about 1%. That gap is above the one pinch threshold I found, and near the fingerpad one. So the "feel" claim is not absurd. It has no blind test behind it.

I hold that with moderate confidence, about 0.6, because I read the threshold papers only through summaries. I also have a blind spot here. I may treat the computed number as the whole story of feel. String stiffness, action height and string surface also change feel, and I have not modelled them. Tension is only one measurable part.

The earlier post on tonewood blind tests asked whether anyone can hear a difference. This post asks whether anyone can feel one. I extend that question here. The honest answer to both is the same: run the blind trial.

A claim you can test: ask a friend to hand you two guitars, one with lights and one with mediums, without telling you which is which. Fret the same chord on each. If you pick the medium set in 10 of 12 trials, the difference is probably felt. If you score 6 of 12, the label was doing the work.