LetterModel is spacing system described by calligrapher and type designer Frank E. Blokland, resulting from his doctoral research into historic type design and manufacturing.
Part of Blokland's central thesis is that Rennaissance punches were cut in alignment with a "cadence" grid system; between any two particular typefaces, the number of units in the grid might vary, but, within a single face, stems, counters, extenders, and sidebearings were aligned to grid coordinates.
At his research blog, Blokland [describes] (http://www.lettermodel.org/wordpress/?p=316) how the grid-based approach can be applied to typefaces designed without a grid in mind (or, in practical terms, typefaces designed on the fine-scale coordinate grids inherent in TrueType or PostScript curves).
First, a grid should be superimposed on the "n" glyph, with the number of units adjusted so that both stems are aligned on veritcal grid lines.
Second, the sidebearings are set so that each bearing is half the width of the counter inside the "n." From there, the sidebearings for the other glyphs can be computed algebraically.
For his example, Blokland applies a 36-unit grid over a normally-proportioned Roman face, and provides a chart listing the left and right sidebearings for the full uppercase and lowercase basic Latin alphabet, plus the period and comma.
Below is the resulting "cadence" table. Here, x indicates that the
bearing measurement is taken from the x-axis extremum, while s
indicates that the bearing is measured from the outer edge of the glyph's
stem:
| lb | glyph | rb | lb | glyph | rb | |
|---|---|---|---|---|---|---|
| 1x | A | 1x | 2x | a | 6s | |
| 8s | B | 3x | 5s | b | 2x | |
| 3x | C | 2x | 2x | c | 1x | |
| 8s | D | 3x | 2x | d | 6s | |
| 8s | E | 2x | 2x | e | 1x | |
| 8s | F | 2x | 6s | f | 1x | |
| 3x | G | 6s | 2x | g | 1x | |
| 8s | H | 8s | 6s | h | 6s | |
| 8s | I | 8s | 6s | i | 6s | |
| 6s | J | 6s | 6s | j | 5s | |
| 8s | K | 1x | 6s | k | 1x | |
| 8s | L | 2x | 6s | l | 6s | |
| 8s | M | 8s | 6s | m | 6s | |
| 8s | N | 8s | 6s | n | 6s | |
| 3x | O | 3x | 2x | o | 2x | |
| 8s | P | 2x | 6s | p | 2x | |
| 3x | Q | 3x | 2x | q | 5s | |
| 8s | R | 1x | 6s | r | 1x | |
| 3x | S | 3x | 3x | s | 3x | |
| 1x | T | 1x | 5x | t | 1x | |
| 6s | U | 6s | 5s | u | 5s | |
| 1x | V | 1x | 1x | v | 1x | |
| 1x | W | 1x | 1x | w | 1x | |
| 1x | X | 1x | 1x | x | 1x | |
| 1x | Y | 1x | 1x | y | 1x | |
| 2x | Z | 2x | 2x | z | 2x | |
| 3x | . | 3x | 3x | , | 3x |
The original table contains an oddity for "d", saying "left and right from x-axis extreme, right from stem." Presumably the conflicting statements about the right sidebearing are a mere clerical error; the intent is surely to measure from the stem.
The footer to the table also notes "the only area which counts, is within the x-height / the capital spaces are lc + 1." The surrounding text does not go into detail on this point; the simplest explanation is that one should increment each sidebearing on the capitals by one grid unit:
| lb | glyph | rb | lb | glyph | rb | |
|---|---|---|---|---|---|---|
| 2x | A | 2x | 2x | a | 6s | |
| 9s | B | 4x | 5s | b | 2x | |
| 4x | C | 3x | 2x | c | 1x | |
| 9s | D | 4x | 2x | d | 6s | |
| 9s | E | 3x | 2x | e | 1x | |
| 9s | F | 3x | 6s | f | 1x | |
| 4x | G | 7s | 2x | g | 1x | |
| 9s | H | 9s | 6s | h | 6s | |
| 9s | I | 9s | 6s | i | 6s | |
| 7s | J | 7s | 6s | j | 5s | |
| 9s | K | 2x | 6s | k | 1x | |
| 9s | L | 3x | 6s | l | 6s | |
| 9s | M | 9s | 6s | m | 6s | |
| 9s | N | 9s | 6s | n | 6s | |
| 4x | O | 4x | 2x | o | 2x | |
| 9s | P | 3x | 6s | p | 2x | |
| 4x | Q | 4x | 2x | q | 5s | |
| 9s | R | 2x | 6s | r | 1x | |
| 4x | S | 4x | 3x | s | 3x | |
| 2x | T | 2x | 5x | t | 1x | |
| 7s | U | 7s | 5s | u | 5s | |
| 2x | V | 2x | 1x | v | 1x | |
| 2x | W | 2x | 1x | w | 1x | |
| 2x | X | 2x | 1x | x | 1x | |
| 2x | Y | 2x | 1x | y | 1x | |
| 3x | Z | 3x | 2x | z | 2x | |
| 3x | . | 3x | 3x | , | 3x |
The example discussed on the linked page resulted in left and right sidebearings of 6 for the "n." Naturally, the relative proportions of all the remaining bearings can be computed from that. Doing so would produce the following relative (to "n") set of bearings:
| lb | glyph | rb | lb | glyph | rb | |
|---|---|---|---|---|---|---|
| 0.333x | A | 0.333x | 0.333x | a | 1.0s | |
| 1.500s | B | 0.667x | 0.833s | b | 0.333x | |
| 0.667x | C | 0.5x | 0.333x | c | 0.167x | |
| 1.500s | D | 0.667x | 0.333x | d | 1.0s | |
| 1.500s | E | 0.5x | 0.333x | e | 0.167x | |
| 1.500s | F | 0.5x | 1.0s | f | 0.167x | |
| 0.667x | G | 1.167s | 0.333x | g | 0.167x | |
| 1.500s | H | 1.500s | 1.0s | h | 1.0s | |
| 1.500s | I | 1.500s | 1.0s | i | 1.0s | |
| 1.167s | J | 1.167s | 1.0s | j | 0.833s | |
| 1.500s | K | 0.333x | 1.0s | k | 0.167x | |
| 1.500s | L | 0.5x | 1.0s | l | 1.0s | |
| 1.500s | M | 1.500s | 1.0s | m | 1.0s | |
| 1.500s | N | 1.500s | 1.0s | n | 1.0s | |
| 0.667x | O | 0.667x | 0.333x | o | 0.333x | |
| 1.500s | P | 0.5x | 1.0s | p | 0.333x | |
| 0.667x | Q | 0.667x | 0.333x | q | 0.833s | |
| 1.500s | R | 0.333x | 1.0s | r | 0.167x | |
| 0.667x | S | 0.667x | 0.5x | s | 0.5x | |
| 0.333x | T | 0.333x | 0.833x | t | 0.167x | |
| 1.167s | U | 1.167s | 0.833s | u | 0.833s | |
| 0.333x | V | 0.333x | 0.167x | v | 0.167x | |
| 0.333x | W | 0.333x | 0.167x | w | 0.167x | |
| 0.333x | X | 0.333x | 0.167x | x | 0.167x | |
| 0.333x | Y | 0.333x | 0.167x | y | 0.167x | |
| 0.5x | Z | 0.5x | 0.333x | z | 0.333x | |
| 0.5x | . | 0.5x | 0.5x | , | 0.5x |
Consequently, it is not strictly necessary to space the "n" first, if all of the glyphs conform to LetterModel's underlying stylistic assumptions (e.g., Renaissance forms).
From a practical standpoint, the LetterModel cadence system is more complete than Tracy's method (which omitted several letters), and it does not begin with an "optical fitting" step for the starting glyph ("n" for the cadence method, as opposed to "n" and "o" for the Tracy method).
Interestingly enough, the automatic bearings chosen by the cadence method are derived from half the width of the "n", which is identical to the sidebearings prescribed by Frutiger's approach. Thus, the cadence method essentially combines Tracy and Frutiger's approaches into a single method. (Strictly speaking, Tracy suggested starting with half the wdth of the counter of n, but the next step in his approach assumed some alterations would be made.)
There are some unique properties of the method in comparison with other systems. For instance, the cadence tables produce their minimal right sidebearings on A, K, R, T, W, X, and Y, but not on L. It is also interesting that the bearings of the capitals are incremented by a fixed amount, rather than scaled.
The main limitation is the method makes assumptions about the proportions and shapes of the glyphs—namely, that they adhere to typical Rennaissance forms.
This is noticeable in a few key spots:
- The right sidebearing for g is measured from the extremum, rather than from the stem. This works for the two-story g, but is inappropriate for the one-story g.
- The right sidebearing for G is measured from the stem. This assumes that G has a more-or-less straight spur.
- The bearings of the capitals are incremented by a fixed amount, which suggests that assumptions are made about the relative stroke size and widths of the capitals with respect to the lower-case glyphs.
Further afield, the LetterModel method, like Tracy and Frutiger, applies only to upright Roman forms, not to italics.