Monday, 21 February 2011

#1.1: The Life of Strings


"How often should I change my guitar strings?" Let’s find out. We’ll put a set of brand new strings on a guitar, and see how the sound changes over time.

The first question to answer is: how are we going to measure the "freshness" of these strings? Sustain and tone. We’re going to say sustain is the time it takes for the volume to drop by 75% (-20 dB) from the loudest point. For tone, we’ll look at one particular measure of brightness: the proportion of energy in the upper frequencies (the "high end" of the sound). These are simple measures, but they’re pretty intuitive and a good place to start!


STEP 1: Collecting some data
First step complete! I put new strings on this past week, gave them a proper stretch, and before doing any playing, recorded how they sounded. Here’s an example of an open D string:

Strings were plucked (with a pick) one at a time until the unamplified sound couldn't be heard anymore; they were picked low to high and this routine was repeated three times. An American Standard Fender Telecaster was the guitar of choice and the strings were D’Addario “BRIGHT Round Wound, Regular Light Gauge (0.010–0.046).” Recording involved a M-Audio MobilePre USB interface and Reaper software. Number crunching was done in MATLAB, which was also used to make plots, with the help of MS Excel and MS Paint. NOTE: The guitar model, type of strings, instrument maintenance, climate in Toronto, and so forth will all affect the sound, but because we care about relative values—i.e., the difference in sustain and tone week-to-week—and we’re keeping our setup the same, they shouldn’t play a major role.


STEP 2: Taking a peek
Before we get to the results, let’s see how some of the data actually look. Here’s a plot of the B string's volume. We can see that after the string is plucked, the volume goes down pretty steadily until coming to a stop at around 12 seconds.

Below is the frequency content for the B string. Notice how there’s a big peak on the left: this is the fundamental frequency—it’s what makes the note a B. All the peaks on the right contribute to the tone, and we’ll use them to measure brightness. These peaks are often shorter than the fundamental frequency, and the stubbier they are, the duller the sound.



STEP 3: The results!
Now that you’ve seen what some of the data actually look like, here’s a summary of the results for Day 1. The red bars are averages over the three plucks; the blue dots are the values for each individual pluck.

Some general observations: low strings ring longer than high strings; also, there's a bigger difference in sustain among the wound strings (Low E, A, D) than among the plain strings (G, B, High E).

One thing that really pops out here is the brightness of the two E strings. Why are they so bright? There are several possibilities, but this question deserves its own investigation...



Let’s play these new strings for a week, and then see how things look!

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