Is It Multiscale or Fanned Fret?

Guitars and basses using compound scale lengths have exploded in popularity over the last two decades. Originally the province of boutique luthiers such as Ralph Novak, Ormsby Guitars, Conklin Guitars & Basses, blackmachine, Dingwall, .strandberg* (plus too many others to list) with several luthiers here on ProjectGuitar.com having designed and built their own, the last few years have seen compound scale length instruments become a mainstream feature.

How and why would we incorporate more than one scale into an instrument? What advantages or differences do they actually offer? What are the most common misunderstandings or misconceptions? Why are terms being used incorrectly or interchangably? We'll cover a brief history of compound scale instruments, explore the theory and demonstrate how they're designed including their strengths/flaws....

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Obligatory boring history lesson

The concept of a strung instrument utilising different lengths per string is not a new one, the most obvious and recognisable example being a grand piano or instruments such as harps, lyres, psalterys, hammered dulcimers, etc.

Grand pianos commonly have over 200 strings with similar length/tension/pitch relationships

This arrangement of using longer strings for the lower notes and shorter ones in the upper range is part of a greater relationship; the fundamental frequency of a vibrating string is a function of the free vibrating length, the tension within the string and physical mass by length ("gauge"). We don't need to go into the exact mathematics behind this relationship (more can be found through the virtues of Google, however this is very good, as is this) it can be summarised as:

• Higher pitches require....
  • short vibrating string length
  • higher string tension
  • lighter string gauge
• Lower pitches require....
  • long vibrating string length
  • lower string tension
  • heavier string gauge

This is true for the most part. As this is simply a relationship, not all of these have to be true at the same time, however the other components of the relationship need to compensate.

Okay, this has probably lost a few people already who just want to see the weird-looking instruments. At least we're not looking at the math!

Simply, a lower pitch can still be produced by a lighter string gauge, however an even lower tension and/or longer string length will be required to make up. Harps, et alia. leveraged the parts of the relationship the best that they could given the limited string material engineering capabilities of the times; high tensions and gauges simply weren't possible. This placed greater emphasis on long string lengths for lower string tunings with the reverse for higher ones; a naturally-evolved solution for instruments covering a wide range of octaves.

The Spanish guitar - the blueprint for what we might recognise as guitars - covered barely 3-1/2 octaves. String-making was such that it could meet the relatively modest demands of six strings over such a small range; string tension and mass by length were more than sufficient in the relationship to produce required tunings; a simple single scale across the entire instrument worked perfectly well. The model established by the Spanish guitar carried itself through to steel-strung acoustics, Hawaiian steel guitars, archtops, solidbody guitars, basses, etc. without the underlying single-scale architecture altering. Hold a Les Paul next to an original Torres (good luck with that) and the DNA is clearly apparent.

Disadvantages of single scale instruments

Standard guitars and basses sit on the cusp of practicality when it comes to the string pitch/mass/length/tension relationship. Many modern solidbody guitar/bass designs feature more than the "normal" number of strings and utilise tunings significantly beyond standard. Such "extended range" guitars and basses fly beyond the limits of our calm island of 6/4-string standard-E safety.

This fundamental shift highlighted the inadequacies of a single-scale arrangement; adding strings to a standard scale produces flabby lower strings with insufficient string tension, requiring excessively-heavy gauges to compensate. Increasing scale length to compensate increases string tension over the higher strings requiring super-low gauges for playability!

Accompanying alterations in the number of string courses and scale lengths is a shift in timbre around the instrument; baritone scale lengths with longer strings tensioned higher than usual emphasises the fundamental, lower and uppermost harmonic overtones becoming (appropriately) "piano-like" in timbre. Much of the softer tonality generally preferred in the upper ranges easily becomes strident, harsh and less "musical".

It was only a matter of time before these limitations in single scale lengths had to evolve in the same direction as other wide octave range instruments.

Enter the compound scale instrument

At its simplest, a compound scale instrument features two or more scales. This can be as simple as having a hybrid extension beyond the nut (not entirely unrelated to a plectrum banjo)....

Amfisound Hellbass

.... or more commonly, non-parallel frets....

Ormsby Guitars GTR TX Production Model

Advantages of compound scale instruments

Having full access to the relationship between pitch/length/tension/gauge opens up design possibilities both as a luthier and as a musician. Single scale instruments only allow us to leverage gauge and tension within a limited range before playability, tonality and practicality become too significant to ignore. We don't want cheesecutter high strings simply because we extended scale length for the benefit of the lower notes. We don't want flubby nu-metal low notes simply to keep expressive bendier high ones. Compound scales allow us to pick and choose what works best for us. A 24" 1st string and 27" 6th string? Do-able. A 16" 1st string and 30" 22nd string? Strange, but theoretically workable.

A welcome (but not strictly deliberate) side effect of introducing non-parallel frets in compound scales is a more ergonomic feel; as a 5-string bassist I can attest strongly that parallel frets require a degree of compromise and automatic playing adjustment....potentially with painful hand/wrist problems. That the architecture of your instrument starts affecting how easily you play the thing is a Big Thing.

In the playing position, the wrist and elbow (even the shoulder) have mutually comfortable ranges of movement. Parallel frets on a single-scale instrument (especially those with longer, wider necks and many high frets or for players that barre like crazy) can often pretzel your arm out of an optimally relaxed playing position.

Some say that Hendrix himself played behind his head thanks to the limitations of single scale guitars and that Eddie Van Halen jumped around simply to get himself into a playing positions. All we know is....

....compound scales tend to angle the fretting hand more naturally from the lowest notes to the highest. Even designing in an additional 1" to the lowest scale of a standard 6-string guitar produces a more organic feel with non-parallel frets. In addition to this natural arc, instrument designers commonly specify a "perpendicular" fret or position; a single point on the fingerboard where the fret (or proportional relation between scales if not actually a fret) is perpendicular to the centreline between outer scales. This aspect of a compound scale is highly personal, being affected by playing style, personal physical differences and also those of the instrument. What is comfortable for one person may be different for another. This point is most commonly found anywhere from the 5th fret to the 9th, however in theory it can exist anywhere on the neck; even between frets or beyond the nut or saddles!

The advantages of compound scales to instruments are distinct; they unlock design aspects which are otherwise constrained through habit and tradition, plus they allowing instruments to be voiced more fairly from the lowest to the highest registers.

The Novax® Fanned-Fret® System

In spite of a fretted compound scale instruments existing hundreds of years ago, Ralph Novak patented the idea (more accurately, the process) for a compound scale guitar in 1989: the Fanned-Fret® system. The patent itself has expired, however Ralph continues to enforce intellectual property rights over the system and its trademark, licencing its use to luthiers selling their instruments within the US.

Unlike a single-scale instrument where frets are parallel to each other, the Fanned-Fret® system arranges frets according to a geometric pattern whereby the straight line paths of each fret (plus the nut and theoretical bridge witness line) converge on a single point in 2D space, not entirely dissimilar to representing depth within single-point perspective. As a simple method of producing compound scales across several strings, it is elegant and very easy to implement:

Generalised layout of a Fanned-Fret® system

It does however possess one crucial flaw; the system only truly works if all of the strings are parallel to the reference scale. As with most things, taking an idea to a logical extreme serves to highlight fundamental issues. Consider a convergence point way off to one side with respect to the centre of the reference scale:

(zoom to embiggenate) Theoretical extreme of a Fanned-Fret® system on a seven-string instrument

As can be seen from the (n^th root of 2) reference scales transposed onto outer string paths, a Fanned-Fret® system fret placement would leave bass strings progressively flatter further up the fingerboard and treble strings progressively sharper; so much so, that the 24th fret is approximately one semitone sharp!

Plotting true n^th root of 2 fret locations along each string path demonstrates that the usefulness of fret placement from a single convergent point in space is poor at best unless one wants to work with no string taper. Whilst discrepancies in a real-world Fanned-Fret® system implementation will be in the order of a few cents, the theoretical basis of the system is not truly a sound one; those cent errors add up. A reliable system for producing compound scales should be fit for purpose as opposed to being merely simplistic, clever-sounding, approximate and trademarked.

Extending out true n^th root of 2 fret placements disproves the convergent point idea

Regardless of these yawning chasms, the Fanned-Fret® system introduced compound scale instruments into the consciousness of guitarists and luthiers, and is an important milestone to recognise in compound scale instrument design.

Languagewise, it is important not to confuse the term "fanned frets" with anything but the Novax® Fanned-Fret® System. Not all non-parallel/compound scale instruments are "fanned frets". The Fanned-Fret® System is a distinctive and specific enough method that the term is not a catch-all for non-parallel fret design. Whenever you hear the term "fanned fret" used, ask if it's actually Fanned-Fret® or not.

Interpolated Dual Scale Fret Placement

Okay, I just made that name up. It does however describe a better way of producing a working multiscale fret placement for any range of equally-spaced strings. Referring back to the previous diagram showing why a single point in space does not work demonstrates that by subdividing the two outer string paths and "joining the dots", each intermediate string's placement is perfectly in line.

Theoretical 22-string instrument. joining the dots from an n^th root of 2 scale placed over the outer strings

This system is more or less the basis behind how FretFind2D works when plotting multiple scales, and produces fine instruments that intonate well. If like myself, you prefer to design your instruments by hand in CAD then it is sufficient to test your multiscale layout by stretching a scale template over each string path as in the diagram above. If the points between string paths and the interpolated frets coincide, the design is proven to be good.

In Closing....

Compound scales in guitars and basses have represented a significant evolution in our instruments, and one that would be ridiculous to ignore. Amongst the many fundamental compromises and imperfections baked into our perceptions as what constitutes a guitar, continuing to maintain a single scale length is one we can happily grow out of, and continue evolving.

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