Multiscaling

Regarding this technique

Many times, new manufacturing techniques are invented to fill up where traditional techniques fail to deliver.

Multiscaling though is not a novelty, at least, not anymore. It’s been around for the last 100 years or more and we know so, from the literature for this field.

We know from physics, that a stretched string, produces a soundwave when struck. Let’s assume that we look for a specific frequency from a stretched string, physical characteristics of which,we vary in order to experiment…

At first let’s experiment with the diameter of the string. By keeping the active length steady and increasing the diameter, we notice that we need a bigger tensile strength to achieve the same fundamental frequency. In addition to that, the dynamic range of the product frequency, is reduced. Of course, at some point, we expect the string to break when we exceed the tension limit.

In the next phase of this experiment, we keep constant the diameter of the string and we vary the active length. At this point, we realise that, the longer the string gets, the bigger the tensile strength becomes. Therefore, the more tension needs to produce the same fundamental frequency and vice versa. Of course, until we reach the physical and/or the material limits. The dynamic range in this case, shows a linear variation too.

The purpose of this post is not Physics as a subject, so we can sum it up as follow:

• In order to keep the fundamental frequency constant, the pairs:
• length-width have to function: conversely
• length-tension have to function: accordingly
• width-tension have to function: accordingly
• The string’s oscillation amplitude, is what defines the dynamic range of that frequency.
• The bigger the amplitude, the bigger the energy transfer.
• The thicker the string, the more mass in motion
• The larger the string, same as the above, the more mass in motion
• The more mass in motion, the more energy transfer we have and the greater the momentum.

All the above, affects the stringed instrument (in this case the guitar) as follows:

• If we increase the active length of the string in order to keep the tension constant, we have to reduce the width.
• If we want a bigger dynamic range from a string (stronger signal), we have to increase the oscillation. However, by increasing the oscillating width, we create greater momentum, therefore, a longer period until the complete damping of this string, also known as sustain. When we play polyphonies/chords, this creates a problem. For that reason, Hard Rock especially guitarists, came into playing power chords, two note chords, instead of the full chord. In that way, we ended up having less notes producing harmonies, while damping on their own. Therefore, a tighter and cleaner signal, that can have the desired clarity and presence when played through an overdriven amp. Here’s where we can see many guitarists with not enough experience on their gear, to be unable to achieve the ‘’BIG’’ sound they want, despite having spend a lot, to buy the most aggressive overdrive pedal or the highest gain amplifier, because eventually the problem may lie in their instrument or within their instrument’s setup.
• By widening the strings, we increase their mass, therefore their momentum, consequently they require a greater striking force (picking), in order for them to start oscillating. When they acquire kinetic energy though,they tend to maintain due to momentum. This energy is transferred to the body of the instrument and among others, creates sympathetic oscillations to the other strings. This is a condition, that we look for until some point, because exceeding that, we end up with a very problematic signal.

‘Previously I mentioned guitar’s body and its role as energy storage. Due to this being a huge topic all on it’s own and because it also affects what we have already discuss even more, I will come back to it with a dedicated post, as well as for the distinctive differences between construction methods, bolt-on, set-neck, neck-through.’

• By increasing the active length of the strings, so happens to their total mass and everything we talked previously, apply now too. Only now, the string has more oscillating length, next to the fretboard of course, therefore, more chances for the strings to hit the frets, known as buzzing and in the worst scenario we have a dead note. A huge problem which, of course, nobody likes. Sometimes though, some guitarists tend to use buzzing as a mean of expression on the instrument and they incorporate it to their playing.

‘A small reference, with extensive analysis to be posted another time, to my dear bouzouki players where, almost entirely, all their instruments buzz’

• We come to a conclusion. That the parameters from which we achieve our desired sound with instruments, are vast in number let alone, they interact with each other.

Let’s talk Hi Gain…

Let’s now talk about our friendly metalheads, who have the tendency to tune low, sometimes excessively, without them being the only ones to do so. Traditional instruments are not built to support such needs, driving the players to tweak their guitars with thicker strings to be able to tune low, while keeping the desired clarity. Something like that afflicts the instrument by creating some conditions. Those conditions are not always or entirely bad and undesirable. Let’s try to understand them.

By going back in time, before metal was a big thing (rock, hard rock, punk etc), we see that the classic guitar sound was moulded by the two dominated scales, the Fender’s 25.5 inches and the Gibson’s 24.75 inches. A more thorough look into these scales, reveals that the sound produced by each of them, is very distinctive and very different from the other. Let’s consider for a moment, that low tunings at that period were rare and very few used to tune low. Taking a leap forward from that period, we reach the metal era and the low tuning domination, however the guitars remaining the same as before, as so happens to the scales. The sound produced from both those scales, remain different from one another and very distinctive as well. However, we notice a great change in the characteristics of the Hi-frequencies of the guitars, with greater the lack of presence, in addition the mid frequency range filled up with dynamic harmonics, that lead to a muddy sound with no clarity. Guitarists started experimenting with different string widths so a great topic of conversation and experimentation was born.

‘I ask myself, what was that that defined the modern metal sound? Was it the ‘’old’’ guitars and their scales? Is that true? The only thing we can be straight of, is that those guitars imprisoned the sound within their characteristic’s limits.

At this point I have to say that my reference is for the guitar as an instrument. I don’t incorporate the effect on the final sound, of pick-ups, amplifiers, processors, playing techniques etc. I will elaborate that extensively in different posts.

Here is where, in my opinion, multiscaling can be a novelty, not by eradicating all the existing problems, but by broaden the limits of traditional guitars.

Until now, we have look at the way, the characteristics of a string affects its performance on the instrument. By combing all those characteristics, we try to achieve the desired outcome (playability and sound). There is no standard recipe, you have to experiment. In any case, the preference in sound is individual as any of us, therefore we have to experiment to find our own.

By using the same scale on all the strings of an instrument, you’re losing the ability to alter one of the most important characteristics, the length of the string. What should we do in that case? In my opinion, when we find out which parameter on the instrument averts us from achieving the desired outcome, by being depleted while adjusting, then we procced in building a multiscale instrument that extends the adjustability of that parameter.

Multiscale ergonomics.

I would not like to exclude the advantage of a multiscale fretboard over a standard one, regarding the finger placement. By having a closer look at our hands, we notice that our fingers, are growing radially from the palm to the outside and not parallel to one another. Precisely like the frets on a multiscale fretboard. In that way, placing the fingers on a fretboard, becomes easier and more effortless. Unfortunately, until now, there is no range on multiscale guitars on the market and that, is because the only available models, have a difference of mostly 2 inches, between the highest and lowest strings and vertical fret is usually in the middle area (8^th-12^th). Furthermore, the most important parameter, which is the differentiation of the scales, is once more restricted or limited by industry’s standards. A multiscale instrument has to be built, around the player, serving his specific needs. By designing and building a multiscale instrument you’ve given almost unlimited options tweaking the parameters. Only the builder has to build according to the customers unique specification. Having said that, we realise that building a multiscale instrument, benefits us, the builders, as well.

Bending on a multiscale guitar

Bending, is one of the most important guitar playing techniques. Even on your first venture on the instrument, bending a string, any time soon trying to mimic your favourite guitarists, is a safe bet. What is happening though, when we bent 1 string? Here is a catch, because it is not just one parameter that is altered. At first, we increase the tension, therefore the note and also, we increase the length, therefore the scale. Both those conditions, work against each other defining that rate of what we experience as a note change. More specifically, they define the curve of the frequency increase. If so happens on a standard scale guitar, the outcome is known to every guitar player.

On a multiscale guitar, things getting interesting as the effect of bending is not the same, as it varies, depending on which fret and string, you’re attempting a bending and which is the vertical fret. Now let’s see what exactly happens. We assume our vertical fret is the 7^th and we bend the b string on that fret. The feeling we get is very well known, as is the sound, form a standard guitar. Now, let’s move to the 11^th fret and repeat the bending on the string, the feeling now is completely different from bending the same string on the same fret on a standard guitar.

If we experiment by bending the strings on the highest frets (close to the body) we immediately notice a significant difference on the feeling and on the sound, compared to that of a standard guitar. To avoid extensive mathematical analysis that may confuse, I will present my annotations in a more descriptive way. On a multiscale fretboard, the angle of the frets, moving along the fretboard from the vertical fret towards the body of the instrument, affects the rate of the string elongation during bending, by reducing it, compared to the constant rate of the standard guitar. Depending on what the min/max scales of the instrument and on which fret and string the bend, this rate may show very radical changes.The frequency raises due to added tension is dominant in this case too, though the curve of that raise on the diagram (force-frequency), is actually steeper and faster, meaning faster response and more sensitive bending. In the case of bending in the area lower to the vertical fret (towards the headstock) everything we talked above comes the other way around, because of the opposite angle of the frets. All the above apply when we bent positively (upwards), in the case of negative bending (downwards), everything comes the other way around.

Looking through maths:

• Bending on a standard guitar: Increase in the frequency by increasing the tension minus the abatement in frequency because of the string elongation ΔF = Δf_t + Δf_l

where: 

ΔF = functional derivative of the wanted frequency

Δf_t = functional derivative of the frequency due to adding tensile strength

Δf_l = functional derivative of the frequency due to elongation/shortening

• Bending on a multiscale guitar: We have the same equation, only now the length derivation is smaller on the higher frets and bigger on the lower, therefore we need less effort when we bent on the higher frets (higher than the vertical) and greater effort on the lower frets (lower that the vertical) to achieve the same result as a standard guitar.

Everything we discussed in this topic, is not massively noticeable, especially for the inexperienced, however we can notice a significant difference if playing for longer periods or if we record and thoroughly hear the same lead part, played by both a standard and a multiscale guitar.

I will not by any means say that one instrument is better than the other, because for me that is not the point. Multiscaling gives us plenty of options and I find extremely tempting investing time and research to thoroughly understand those instruments.

I strongly believe that multiscale guitars can have a leading role in creating the sound of tomorrow. However now it’s nothing more than a trend, a new way of the industry to sell a novelty, without any serious R&D on the subject and without multiscaling being such a thing.