Stephan Paukner :: syslog

The Boss RC-2 Loop Station is a compact pedal for recording loop phrases with an electric guitar. The pedal has two bigger brothers: The RC-20XL Phrase Recorder and the spacious RC-50 Loop Station. The RC-2 is ideal for practicing and composing. It has 33 different drum patterns available and can store 11 phrases with a sum of at most 16 minutes. You can tap in the tempo of the drum patterns and even the speed of recorded phrases without changing their pitch! The pedal has an AUX IN to record phrases from an external playback device. This makes it possible to e.g. slow down guitar solos you want to learn. In this case you can use the AUTO recording mode that doesn’t start recording before an audio signal is received. Recordings can be overdubbed arbitrary times, and there’s an undo and redo function for the most recent overdub. Playback can be switched from loop to one-shot, making it possible to trigger recorded samples during a performance.

Boss must have put much brain power into the usability design of that pedal to make it possible for musicians to have a reasonable recording workflow available by just using two knobs, a single button and a single footswitch. I don’t want to go into detail here, but rather show what a typical workflow could look like (without an external footswitch):

Ibanez, my favorite guitar manufacturer, has created a model with an unusual guitar body shape which is commonly favored by heavy metal guitarists. Having Gibson’s innovative “Flying V” and “Explorer” body shapes from 1958(!) in mind, guitar companies started to release models with similar designs in the late seventies because heavy metal guitarists found that those radical body shapes match their music style and appearance on stage. Ibanez, being favored by virtuosic guitarists such as Paul Gilbert, Joe Satriani or Steve Vai, has lacked guitars of such an uncommon style so far and has finally come up with a V-shaped and an X-shaped guitar model. (I once heard that such untraditional shapes tend to bad resonance behavior, but I think that’s nonsense.) The white V-shaped one would even appeal me, as it’s not so typically “heavy metal” as the black one.

The video promoting the X-model on their website features statements of a guitar body designer and a virtuosic heavy metal guitarist from Germany. The video is underlayed with musical sequences from the guitarist’s band; extremely fast, technical and virtuosic metal music which is considered to be “neo-classical” because it tries to imitate the complex structures of traditional classical music. Unfortunately, when I saw their website and their entry on Wikipedia, they turned out to be a “technical brutal death metal” band, having “death growls” as singing voice and songs about “mutilating stillborn children” and similar. I already asked myself why they chose a name associating them with necrophilia.

Now, does this have to be? Does Ibanez really want to identify themselves with disgustingly gory necrophilic musicians who make guttural sounds while they imagine to slash rotten corpses? This is ridiculous! What do these abject topics have to do with virtuosity on the guitar? What does that have to do with classical music? I’m really agitated. Why can’t virtuosity keep being linked to virtuosic music, and be it of heavy metal style?

However, on the one hand there are awesome metal guitarists using traditional guitar body shapes, and on the other there are “ordinary” rockers such as Lenny Kravitz who use a Gibson Flying V. And companies like Dean Guitars devote themselves to radical body shapes that are appreciated by comparatively “harmless” metal giants such as Dave Mustaine or the late Dimebag Darrel. I therefore consider Ibanez’ choice of that one guitarist for their promo as an accident.

And by the way, if that guy is so keen on appearing evil on stage, why has he got that boring short hair cut?

I currently wonder what string gauge (diameter) I should use for my electric guitar. The standard is .009 (i.e. 0.009″ for the high e-string). Thinner strings allow easier string bending, but one has to play with less finger pressure to avoid detuning. As I like to tune all strings down by one halftone, the strings get even “softer”. So one should take a higher string gauge when tuning down. The question is now: Do downtuned .010’ers correspond to normally tuned .009’ers? What gauge should one use when one wants to tune down e.g. by a whole tone and have the “softness” of .009’ers? Here’s my try of a calculation:

Does a downtune by one octave correspond to a loss of half the tension? Whatever amount the tension will get, it doesn’t decrease linearly with the halftones—remember the different distances between the frets! How does one calculate this scale? You can’t just divide the half of the string length by 12 to get the steps between the frets.

Calculating the fret stepping of a guitar
For the 12th halftone, you arrive at ½ of the string length, for the 24th halftone you arrive at ¼ of the length, etc.; the 12th divides the length by 2, the 24th divides it by 4, the 36th divides it by 8, etc. Abbreviating d(n) for the divisior at halftone n, we have d(0)=1, d(12)=2, d(24)=4, d(36)=8, etc., i.e. d(12n)=2ⁿ and therefore d(n)=2^n/12. For the n-th halftone, the string length becomes

.

If you don’t believe my derivation, maybe you believe a (modified) function plot:

The blue crosses indicate the first two octaves, occurring when ½ (=50%) and ¾ (=75%) of the length are removed. The pink cross indicates the fifth fret at about ¼ (=25.085%) of the length. Every guitarist should recognize the fret stepping here!

Gauge stepping when tuning down
I found a link which explains that the relation between string diameter δ, tension t and frequency f is

,

where C is a constant depending on the material. The aforementioned scaling is still valid for the frequencies, i.e., when the frequency f is tuned down by n halftones, the resulting frequency f_n is given as

,

what can be verified for f=440Hz: The next lower tunes are 415.3Hz (n=1) and 392Hz (n=2), and the next higher tunes are 466.2Hz (n=−1) and 493.9Hz (n=−2). Replacing f by f_n in the previous equation yields that when the tension is to be kept, one has to take strings with diameter . As example, .009’er strings that are tuned down by one whole tone should be replaced by .010’ers to keep the tension of the .009’ers.

The other way round, fixing δ_n=0.010 (the taken string gauge) and δ=0.009 (the desired string gauge “feel”), one derives

what results in n=1.82 in this example, a downtune of slightly less than a whole tone. Tuning down .010’ers a “complete” whole tone corresponds to a string gauge of .0089’ers, so really almost .009’ers.

As a final rule of thumb, the steps between the string gauges correspond to tune changes of a whole tone. The following table shows how certain string gauges “feel” when they are tuned down: