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 Post subject: Martin guitar scale
PostPosted: Wed Oct 10, 2012 12:19 am 
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Mahogany
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First name: Enrico
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I purchased the fret slotting template from stewmac. It is the 25.34 and 24-9 martin version. They say that despite it was always advertised as 25.4, it is actually 25.34. I wonder where this odd number comes from. At first I thought it was the conversion from millimeters, given the european origin of Martin, but 25.34 is 643.636 mm, which is a weird number too. So, I am curious to find out the reason why Martin decide to set on that particular scale length.


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 Post subject: Re: Martin guitar scale
PostPosted: Wed Oct 10, 2012 11:29 am 
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I don't know the origin, but the difference between 25.4 and 25.34 is a typical saddle compensation at the first string. In other words, Martin scales are specified as the actual string length of the high 'E'.
Most scales (other than Martin) are specified as double the distance between the nut and 12th frets.

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 Post subject: Re: Martin guitar scale
PostPosted: Fri Oct 12, 2012 8:42 pm 
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Brazilian Rosewood
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Hi Enrico,

I don't come by much here anymore, but since you seemed particularly interested in this topic I thought I could at least offer you some insight.

The best theory I've come up with to date is that the original spacings were made using the nice round numbers of 25" for their short scale, and 25 1/2" for the long. Up through the late 1970's however, they were calculating their fret spacing to the literal "rule of 18", rather than the divisor 17.817 (derived from the 12th root of 2) that is almost universally used today.

When using an even 18 divisor, a 25" scale will actually end up at 12.409" nut to 12th (approx 24.818" scale), and the 25.5" base number will end up at 12.657" (25.315" scale). The way they describe their scale length however is uncommon for this trade, in that they use a rather arbitrary choice of the high E string open length including a generic average amount of compensation. Combine this with some reasonable rounding to a single decimal point, and they called then 24.9" and 25.4".

When they switched to the modern 17.817 spacing in the late 70's, they simply chose a base length to deliver approximately the same string lengths that they had before, which ended up at 24.84" and 25.34", though they still call them 24.9" and 25.4".

Through as much research of old catalogs as well as discussions with some folks at Martin, I've unfortunately not been able to find any historical data written down in Martin records to confirm this theory. It is a fact that they used the rule of 18 until roughly 35 years ago (likely changed at the time of retooling during the strike in the 70's), and in all the data I've collected those numbers do average around 25" and 25.5" base scales. Small errors in tooling can add up however, as well as dimensional change in wood to some degree, so it's impossible to find data consistent enough to declare absolute certainty as to their original intentions. Actual measurements do indeed go all over the map in different eras, leaving the job of estimating the original source numbers to be a bit like chasing the wind.

I would love to find some original source data from the people who set these templates and gang saws up, but unfortunately it appears that engineering and shop notes either were not duly saved with the company's records, or perhaps are tucked away in a file box somewhere forgotten or out of reach. All the numbers used today however (24.9" / 24.84", and 25.4" / 25.34") are only derived to describe or mimic earlier measurements, but they are not the actual base numbers Martin started with when first laying out their fretboards.

In any case, it seems much more likely from what I've seen that the original source was nothing like a conversion from metric, but rather that they started from reasonably round imperial numbers. Then after years of using a different spacing system and inconsistent tooling, a standard was set and they just decided to stick with the traditional length.

I've spent a great deal of time studying historical fret spacings, and posted in many other forum discussions if you're really interested in reading more. Google David Collins Rule of 18 Frets, I'm sure you'll find a number of posts with more details.

Of course in the end it's largely an academic study with little concern in real world application. Still interesting to look at the nuances though.

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 Post subject: Re: Martin guitar scale
PostPosted: Sat Oct 13, 2012 4:17 am 
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Mahogany
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That's right, it is very interesting indeed. Not very practical in real life, but interesting nonetheless. Thanks for this nice explanation.



These users thanked the author enricopg for the post: GaryG. (Sat Sep 17, 2016 4:44 pm)
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 Post subject: Re: Martin guitar scale
PostPosted: Sat Oct 13, 2012 6:40 pm 
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Quote:
they use a rather arbitrary choice of the high E string open length including a generic average amount of compensation.

I don't think it is arbitrary in the least. I have always located the saddle by measuring at the first string. It makes perfect sense to me, because the intonation at the first string is most critical, and a defined saddle angle will automatically determine the length of the other strings.
Another possible explanation is that the compensated distance from the 12th fret to the saddle at the first string is a nice round number.....12 3/4" for the long scale, and 12 1/2" for the short scale.
Quote:
When they switched to the modern 17.817 spacing in the late 70's.....

I cannot imagine any modern factory using the rule of 18 that late. When I first discovered the 12th root of 2 in the late-1960's, it was common knowledge. Even then, I thought the rule of 18 was only practiced by ignorant luthiers in third world countries.

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 Post subject: Re: Martin guitar scale
PostPosted: Sat Oct 13, 2012 8:07 pm 
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Brazilian Rosewood
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It may not be an arbitrary number in the context of the whole instrument layout, but I call it that because I believe the term "scale length" should directly and accurately describe the fretboard without inclusion of elements which may vary from instrument to instrument. Varying amounts of compensation between different instrument styles (electric, acoustic, classical guitars, banjos, etc), as well as which point in the compensation range (treble string, center average, bass string) is chosen to include could result in the same fretboard being described as different (and often rounded/imprecise) scale lengths. My feeling is that this only makes the term somewhat vague, less precise, and occasionally confusing.

I've posted this excerpt from a paper of mine on other forums, but I think it best describes the dilemmas I see in terminology here.

Quote:
Though it may seem a basic and fundamental point of fretted instrument design, “scale length” has become (or perhaps always been) a rather ambiguous term in the field of fretted instruments. There are in fact several distinct definitions applied to the term by different companies and technicians, as well as some common usages which I hesitate to qualify as proper definitions. The Martin Guitar Company’s use of the term is a prime example of this*.

At least for the purpose of this writing, I will clarify my own definitions of two distinct descriptions of scale length that are most commonly used.

Base Scale Length: The base number from which the fret spacing is calculated. In other words, it is the original length from which the fret scale (i.e., rule, template) is laid out.

Relative Scale Length: 2x the distance from the nut to the center of the 12th fret. This definition does not always directly determine or reflect the spacing of the frets relative to each other. Though this is probably less pure a definition of scale length than the former, it is generally considered the more useful of the two, and certainly more widely used. It's value lies both in it's ease of calculation, as well as it's ability to provide consistent comparisons between boards of different fret placement systems. Assuming all setup criteria remain constant between them, and intonation is conventionally adjusted to 0¢ offset at the 12th fret, the same relative scale length will result in the same end string length, even between boards of different fret spacing systems or nut compensation.

    *In efforts of disambiguation, at least one other common use of the term deserves to be mentioned. The Martin Guitar Company defines their “scale length” according to the open length of the high E string, including average compensation (of approximately .060”). This method of defining scale length as the total length of a string is likely carried over from non-fretted relatives such as the violin. On fretless instruments where there are no frets to govern the total string length, the string length of course will instead dictate the fingering positions. This makes defining scale length as the total string length both appropriate and necessary as a relative term for comparing these instruments.

    On fretted instruments however, I feel this usage suffers great inadequacies. Foremost is the fact that with a system of straight frets, each string will require a different amount of compensation, and end at a total open length different from others. This leaves the rather arbitrary choice of which string or point along the saddle one chooses to refer to. Martin uses the total high E string length today, but you will hear of others using the average among all strings, and still others choosing the low E. Furthermore, the end length with compensation will change relative to details such as setup or string choice, presenting us with the possibility of the same instrument being describable as several different scale lengths dependant on changes in these details.

    While it is unlikely we will see this usage of the term disappear, I feel it best reserved for use as a layman’s approximation. It carries little to no benefit in any technical discussion, and can serve simply to confuse when any need for accuracy is involved. I have personally encountered cases in which small builders have misplaced their bridge, where the fingerboard was sold as a “25.4” scale, and the saddle template labeled the same, but the two used incompatible definitions. For purpose of technical discussions therefore, I prefer to omit this usage entirely, and reserve the term “scale length” to either the “relative” or “base” definitions listed above.

.....

If a board were slotted to the modern standard of 2^(1/12) spacing and the nut located accordingly with no compensation, the Base and Relative scale lengths would be identical. When a board is spaced to an alternate system such as the true rule of 18 however, the relative scale lengths would indeed be quite different, even though they began with the same base scale length.

For example, if a spacing were to start from a 24.75” Base Scale Length, and use the true rule of 18, the 12th fret would not fall at the halfway point of 12.375” as it would using the 2^(1/12) rule. Rather, it would fall notably short at 12.285”, and in order to intonate properly at the 12th fret, the bridge position would need to be adjusted accordingly. The same 24.75” Base Scale Length is used in each scenario, yet the Relative Scale Length of the “rule of 18” board would end up at 24.57”, while a 2^(1/12) spaced board's relative scale would remain at 24.75”. This is in fact where much confusion occurs in the labeling of scale lengths on Gibson guitars, and demonstrates the need to distinguish the two definitions as independent.


I realize I do not have authority to unilaterally impose my preferred definitions on the whole trade, but that won't stop me from trying. :D General use of the term "scale length" has always been rather vague and arbitrary, which is fine for sales literature and layman discussions. For technical discussion within the trade however, I do feel there is a good argument for more precise definitions as those I've proposed above.

If one decides to order a Fender style board cut to 25.5" scale length, or cut one themselves, it would be highly unlikely (and entirely incorrect) that they would calculate the fret spacing based on 25.44". Is it reasonable or intuitive then to expect one to use 25.34" for the base number when using a Martin style 25.4" scale? You can see how this could (and has) easily lead to confusion due to inconsistent use of terminology within the trade.


As to usage of the rule of 18 that late, believe it or not, Gibson still uses it on their electric guitars to this very day. When I first discovered this I couldn't believe it either, but they are still cutting boards to a very precise 24_3/4" base scale spaced to the rule of 18, which results in a relative scale of 24.57" (their Montana acoustics are 24_5/8" with modern 17.817 spacing). As to Martin, their boards measure consistently to rule of 18 spacing up through some time around mid to late 1977. Seems strange, but it's true.

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 Post subject: Re: Martin guitar scale
PostPosted: Sat Oct 13, 2012 11:11 pm 
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Its hundreths. Not mm. Like thickness of tops. .080. etc. a tenth of an inch is .100. 1/4 inch is .250 Gibson has a 23.375 they used with the Byrdland. They called it the 23.5. Maybe calling them longer helps with intonation. It dont help with guitar builders though.

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 Post subject: Re: Martin guitar scale
PostPosted: Sun Oct 14, 2012 8:10 am 
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David Collins wrote:
As to usage of the rule of 18 that late, believe it or not, Gibson still uses it on their electric guitars to this very day. When I first discovered this I couldn't believe it either, but they are still cutting boards to a very precise 24_3/4" base scale spaced to the rule of 18, which results in a relative scale of 24.57" (their Montana acoustics are 24_5/8" with modern 17.817 spacing). As to Martin, their boards measure consistently to rule of 18 spacing up through some time around mid to late 1977. Seems strange, but it's true.


I have a 1998/1999, ES-335 Dot reissue and from face of the nut to the face of the bridge on the high E, 24-21/32, low E, 24-53/64, my 2012, Les Paul high E, 24-21-32, low E, 24-26/32, 13/16's Are we using the high E? or splitting the difference?


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 Post subject: Re: Martin guitar scale
PostPosted: Sun Oct 14, 2012 10:25 am 
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Brazilian Rosewood
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Clinchriver wrote:
I have a 1998/1999, ES-335 Dot reissue and from face of the nut to the face of the bridge on the high E, 24-21/32, low E, 24-53/64, my 2012, Les Paul high E, 24-21-32, low E, 24-26/32, 13/16's Are we using the high E? or splitting the difference?


None of the above. To accurately evaluate how the frets are mathematically spaced you have to look at fret positions in isolation, with the nut and saddles entirely factored out. Read this thread for a for a brief glimpse of how I go about accurately evaluating boards- http://www.mylespaul.com/forums/luthiers-corner/171960-24-625-scale-24-562-scale.html#post3300766

It gets a bit more complicated than this, like Gibson's pre-1947 geometrical (by my best hypothesis anyway) spacing. If you want to read even more on how these different spacing systems may affect intonation when combined with things like nut compensation and so on here are a few other discussions, but it's not something easily taught to any depth in a single forum thread.

http://www.mandolincafe.com/forum/showthread.php?68793-Intonation-correction-at-the-nut

http://www.mylespaul.com/forums/luthiers-corner/123950-earvana-nuts.html

If you have an appreciation for recreational mathematics, a keen interest in evolution of instrument technology, or a fetish with tuning/intonation/temperament, then this can be a fascinating area to study. Short of that however, there's not really much here that the average tech/luthier/builder will need to be terribly concerned with for day to day operations. I only chimed in originally because Enrico's curiosity over the origins of such seemingly odd numbers for scale length struck a well-intoned chord with me.

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 Post subject: Re: Martin guitar scale
PostPosted: Sun Oct 14, 2012 10:58 am 
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Good reading. Thanks for all that David!


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 Post subject: Re: Martin guitar scale
PostPosted: Sun Oct 14, 2012 1:23 pm 
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You're quite welcome Danny.

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