#1.2: The Life of Strings

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It's now been a week since the first post and about 11 hours of playing. Let's start with an investigation into last week's unexpectedly bright E strings, and then look at the sustain and brightness values for this week.

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BRIGHT "E" STRINGS & PICKING LOCATION
Was the brightness of E strings last week natural, or was something weird happening during the recording? Take a look at the plots below: these graphs show the brightness when the string is plucked in different locations: over the bridge pickup, the neck pickup, and halfway between the two pickups. The small dots represent different plucks and the bar is the average.

The first thing we notice is that location makes a huge (and quite audible) difference to brightness. The closer to the bridge, the brighter the tone. So, we’re going to need to pluck the strings in the exact same place each week to keep things consistent.

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A NEW APPROACH: NO MORE PICKS!
Using a finger instead of a pick, we may be able to reduce the effect of plucking location on brightness. The graphs below show brightness when a finger (the fleshy bit) is used instead of a pick.

Now there's much more consistency between positions! This is good, as it'll make our week-to-week comparisons more accurate—they won't be thrown off by small differences in where the strings are plucked.

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RESULTS
Because of what we saw above, our methods this week have been revised: 1) strings will be plucked roughly halfway between pickups, and 2) we’ll use a finger instead of a pick (the fleshy part, not the nail). Here are this week's results:

Sustain values are similar to last week's: thicker strings ring longer. We won't do a proper week-to-week comparison just yet, as any differences we'd see would likely be due to the new methods, not string aging.

Now let's look at the brightness. Switching from a pick to a finger is likely the biggest contributor to the changes this week. We can see from these plots, and from those above, that picks give brighter tone than fingers. The E string brightness isn't as wild as last week, so our investigation paid off!

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What's on tap for next week? First, we'll have two weeks of sustain and brightness values recorded with a finger—that'll let us start comparing results over time. Also, inspired by the pick vs. finger comparison above, we'll aim to answer the question: "besides the volume, how does hard and soft playing sound different?"

#1.1: The Life of Strings

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"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!

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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.

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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.

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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...

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