Beyond the Standard Rule

Hello everyone:

No this is not directly about the spinet keyboard work, although it all relates, as you will see…

Just a little followup to one topic I touched on back in January at the Mount Vernon WW conference.

Why have I started with a plate from Chippendale’s Director?   I’ve lately grown interested in alternative measurement methods.  With help from Mack Headley and Jane Rees (credit is due), I’ve begun looking at the scales in Chippendale and old rules with different divisions.

My current interest lies in scales that break into 6th and 12ths, rather than the 8ths that were the common division on our 18th century English rules.  This is what I touched on briefly at the conference and would like to muse on it again here.

On several of his drawings, Chippendale frequently offers scales like this one

The moulding scale. See how the diagonal division on the left allows for fine incremental measuring!

Note the division into 12ths and the diagonal line in the first one that allows for measuring quarter increments.  Here is the scale in context, for laying out moldings for the bookcase above:

The full plate for the mouldings and the scale, in context.

Why 6ths and 12ths?  The practice goes all the way back to Vitruvius, the Roman architectural writer in the reign of Caesar Augustus.  In his third book, chapter 1 on symmetry, Vitruvius noted that the ancient designers and mathematicians looked upon the numbers 10 and 6 as perfect numbers, mainly because of their easy divisions.  The number 6 was especially regarded and broke down into 12ths, each of which was given its own name as a unit of measure.  Check this link to Project Gutenberg’s online version of Vitruvius and the symmetry chapter.

Indeed, using a rule divided into 12ths allows for measuring halves, quarters, thirds, sixths and twelfths.  Nice!

So how about direct evidence of using these divisions?  Here’s an early 18th century rule from the CW collections (thanks to Eric Goldstein for helping me track this down):

It is divided into 8ths on one side and 12ths on the other.  Rarely will you find rules divided into finer increments. Click on the image for a closer look and you will discover that it is NOT hyper-accurate.  Little irregularities which require the workman to rely on his eye and hand to make up for.  The 4-fold rule I’m using in the shop has irregularities in different places (by comparing with set dividers). But it is accurate enough to do the job.

We have had a few rules here in the shop with divisions into 8ths, 10ths, 12ths  and 16ths.  Out of habit, I never even considered the “unusual” divisions until recently when a 12th scale helped enormously in my study of the jacks in the harpsichord at Mount Vernon, Virginia.  Here’s what I mean:  below is one of the jacks made for my current spinet in the shop.

I made this jack months ago using regular 8th divisions, using old jacks from the original instrument. I was working with some pretty fine divisions.  The early makers would not have sweated such fine measuring.  But look how the width of the gap for the tongue lays out neatly at 1/6 inch!  Unexpected, but this was repeated in the other jacks, too.  The Mount Vernon jacks show a similar using of 12th scale which allow for measuring 3rds and 6ths, really helpful.  But for copyright reasons, I can’t show those here.

I also have keyboard rules here in the shop, made by Marc Hansen and me from old spinets we studied over the years.  These are essentially rules that lay out the design of the keyboards for these musical instruments, for speed and consistency.  Bear with me as I describe this.

The Western musical scale is divided into 12 notes, for example C, C#, D, D#, E, F, F#, etc. up to B natural.  This range of notes is called an octave.  A common unit of measure for keyboards is called an octave span.  Measure from the left edge of a C key to the left edge of the C key one octave higher.  That is the octave span.  Okay.  With me?  Here is a keyboard rule with dividers set to an octave span.

Note the 12th scale.  The octave span here runs 6 1/3 wide.  While it is not dead on, any other scale would produce a very fine incremental measurement.  I have another keyboard rule made from another old spinet and the 6 1/3 measurement is precise and repeated along the entire playing range of the keyboard.  See it here.

Both of these are based on instruments from the mid 18th century. The keyboard for my current spinet, based on an earlier model, has a octave span at 6 1/4., 1/12 smaller.  Not surprising given the smaller scale of everything on those earlier instruments, but it still makes for a keyboard that is comfortable to play on.

For many of you, especially those with an architectural background (I do not), this may be old news.  But I have not considered the use of alternative rule divisions until now.  Recent research by others indicates that using shop devised divisions or other alternative units and scales may have been more prevalent in the old shops. These do not relate to the systems that we are used to now, English and metric.  I, for one, would like to double back and re-visit the data I have from old spinets and see if the 12th scale fits into the practice where I would otherwise have extra fine, 32nd inch or less measurements. I hope I have time to do that, it would be interesting to see….

Something to think about.

Best to you all,

Ed

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4 Responses to Beyond the Standard Rule

  1. Jack Ervin says:

    This is a very interesting observation of linear measure and division. What you have shown of the relation of eights and twelvths of keys brings to mind the point of overblowing of wind instruments.
    This is from Wikipedia.
    Woodwinds

    In the case of the clarinet, the instrument’s single reed beats against its mouthpiece, opening and closing the instrument’s cylindrical closed tube to produce a tone. When the instrument is overblown, with or without the aid of its register key, the pitch is a twelfth higher.
    In the case of a saxophone, which has a similar mouthpiece-reed combination to the clarinet, or of an oboe, where double reeds beat against each other to the same effect, the conical-shaped bore of these instruments gives their the closed tube properties of an open tube; when overblown, the pitch jumps an octave higher.

    I worked as a toolmaker in a musical instrument factory producing wind instruments for many years and was made aware of this phenomena of rythame.

    Thanks for this observing post,

    Jack Ervin

  2. I can definitely see a use for this, even for joinery. For example, laying out a mortise and tenon, each of which should be roughly 1/3rd the width of the stock. 12th rule makes this easy, 8th less than so.

    I have a very nice 4 fold ivory and silver rule that I bought from Tom Witte earlier this year. He told me he thinks its 18th century and it certainly looks it to me.. I believe it has 12ths on it as well. If you are interested in seeing it, let me know and I’ll shoot some pics.

  3. Jim Tolpin and I have debated why our traditional rules are divided into twelve inches rather than ten. Ten divisions as seen in the metric system works well when the focus is on numerical specifications, but twelve is much handier when stepping off divisions with dividers. Like you said, twelve can be divided in halves, quarters, thirds, sixths. We also wonder if it isn’t linked to simple geometry known in antiquity. If you take a string and use knots to divide its length into 12 equal divisions, you can then fold it into a 3-4-5 triangle and form a perfect right angle. A very handy thing to know if you build a pyramid or barn.
    George Walker

    • Interesting points, thank you. I agree, tenths such as metric allow me a quick view of relative measurements and proportions if I’m studying a piece or looking at museum specs. But I will use 12ths in no time flat for practical divisions. That trick with the string is very cool, I had no idea. Thanks, truly.

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