#1.4: The Life of Strings

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Just over a month ago, a new set of strings was put on a Tele. Since then, we've been tracking what happens to these strings over time. Does the sound become less bright? Does the sustain go down? Along the way, some interesting results have come up:

• Thicker strings ring for longer (#1.2)
• The effect of plucking location on brightness is less significant when using a fingertip versus a pick (#1.2)
• Playing closer to the bridge yields a brighter tone (#1.2)
• Playing softly results in a brighter tone, and one that drops in volume more slowly than when playing hard (#2)

When we checked in on the data last time, there wasn't anything conclusive just yet. Sustain was staying pretty much the same, and brightness had unexpectedly increased. Since those measurements, about a month and 30 hours of playing have now passed—let's check in again and see what's happened!

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UPDATE: NEW DATA!
Since the last post, there have been four new measurements—we're now up to 46 hours of playing over 46 days, coincidentally. Let's take a look:

NOTE: The first set of values that we collected back in February has been removed from these plots. That's because those measurements were made a little differently—a guitar pick was used instead of a fingertip to pluck the strings.

Nothing much has changed for sustain. Brightness is another matter: each pluck of the string has such a unique sound that it's tough to get an idea of the string's general brightness level at a given point in time (#1.2 is a good example). There's just too much variation.

So, why do the brightness values change so much between plucks? My guess is a combination of minor variations in plucking position, intensity, and how the finger interacts with the string (e.g., which part of the fingertip touches the string, how fast the string is plucked). We may need to refine either our brightness measure or our methods—or both—to get a clearer understanding of what's going on!

#3: Miking an amplifier

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Last weekend, I was helping a friend record a few songs at the lab/studio, and we decided to revisit a microphone experiment we had tried last year. This time around we compared the frequency responses of two microphones and two miking positions. Here's what we found.

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EXPERIMENT
We recorded an amplified Rhodes piano using two Shure SM57 and two Rode NT5 microphones. The first SM57/NT5 pair (placed side-by-side) was aimed directly at the centre of the amplifier's speaker cone, a few centimetres from the amp face. The second pair was placed roughly 15 cm below the speaker centre, aiming upward at about 45 degrees.

The performance was recorded with Reaper (Cockos) using all four microphones simultaneously. Each track was then fed into MATLAB to calculate the power spectrum (i.e., the power levels across different frequencies), which was then normalized (for a more straight-forward comparison) and plotted in Excel.

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RESULTS
Here are the results! Each of the four spectra is plotted twice; this way, we'll be able to see the different mic and position comparisons more easily. Now, one thing that's immediately clear is that the recorded song was in the key of A! How do we know that? Well, there are nice big peaks around 110, 220, 440, and, to a lesser extent, 880 Hz. Each of these frequencies corresponds to a different octave of the note A. (The peaks also give us four clear points of comparison.)

Microphones. First, let's look at the microphone results. Regardless of position, we see a couple trends: the upper bass range (roughly 160–250 Hz) is stronger for the SM57, whereas the NT5 is more sensitive to the low-mids (roughly everything above 250 Hz on these plots). When the mic is positioned directly at the centre, the SM57 continues its sensitivity from the upper bass range all the way down, but when angled the NT5 is more sensitive to lower frequencies.

Positions. From the plots below, we can see that for both microphones angled placement emphases the upper bass range (about 160–250 Hz) and centre placement emphases the low-mids (250 Hz and up). On the low end of things, around the 110 Hz peak, the two microphones respond differently to positioning: the sensitivity of the SM57 to low frequencies drops dramatically with angled placement. The low-range response of the NT5 is much less sensitive to changes in angle.

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SUMMARY
So, what's the verdict?

• The SM57 has stronger low-frequency response (we can say it's warmer), and the NT5 is more sensitive to higher frequencies—it gives a brighter sound.
• Angled microphone placement contributes to a warmer sound, whereas centre (i.e., "straight-on") placement produces a brighter sound.
• For the NT5, the low-end response is similar for both placements, but the SM57 experiences a significant drop in low-end response for angled placement.

#1.3: The Life of Strings

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In the last post, we looked into the differences between soft and hard picking (besides the volume!): harder sounds were slightly less bright and softer sounds had greater sustain (more steady volume). Let's now return to our first experiment: we're onto the third week for a new set of strings, and we've got some new sustain and brightness results to show for it.

Let's compare the new information to the past two weeks' results, keeping in mind that the first week's samples were played using a pick, and a finger has been used to pluck the strings since then.

We don't yet see any general trends for sustain, but we unexpectedly see an increase in brightness for most strings. The total playing time is still only at 18 hours, so let's accumulate a few more recordings and then take another look...

#2: Attack of the Guitar Pick!

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Let's say you record the same guitar part two times. The first time you play the part very softly, gently plucking the strings with every note and chord. The second time you play as hard as you can, hitting all the notes accurately, but with all of your might. Our intuition says that both recordings would sound different, even if the volumes were matched. Louder sounds louder even if isn't... OK, but how? That's what we're going to look at today: how does "playing harder" affect guitar tone?

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THE PLAN
We'll pluck the same string over and over again; sometimes we'll pick harder, other times softer. Then we'll look for differences in the sound. First, we'll look at our classic sound characteristics—brightness and sustain—for the full duration of each pluck (see first blog). Then, we'll separate each pluck into two parts: the attack and the decay. For each part, we'll determine the brightness and sustain separately.

As usual, the guitar is a Fender Telecaster (American Standard) with D'Addario regular light strings (0.010–0.046). The 3rd string (G) was used for this experiment.

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RESULTS!
> The whole signal. Brightness goes down (a little) with harder picking, and sustain drops significantly. There may be a relationship between these two trends: higher harmonics ring longer than lower harmonics ("On the sensations of tone," Part I, Chapter IV, H. Helmholtz), and if louder sounds aren't as bright, as we see here, then it would make sense that they don't ring for as long. (It may be a good time to note that these sustain values are based on a drop of -20 dB from the signal maximum. If we were just looking for the point where the signal got silent, then louder sounds would certainly ring for longer, as our intuition would suggest.)

> Attack! The brightness trend here is similar to that for the entire signal: a slight decrease in brightness for louder sounds. Because the attack region is so short (one second), an alternate method for expressing sustain was used: the volume drop across the region. There may be greater sustain (i.e., less volume drop) over the attack region for louder sounds—opposite to the effect for the entire signal—but the data in the plot below are too messy to say for sure.

> Decay... The results here are similar to those for the whole signal: louder sounds are less bright and drop faster in volume.

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CONCLUSIONS
Playing harder or softer leads to differences in sound beyond just a change in volume. A softer sound has greater sustain and is a little brighter, whereas a harder sound has a stronger fundamental frequency and decreases in volume more quickly.

#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!