Geometries

What the geometry of a blade is

The geometry of a blade is the set of measurements that fix its silhouette and its cross-section. There are few of them, and all have Japanese names:

• The nagasa (長さ) is the length in a straight line from the mune-machi to the tip.
• The sori (反り) is the greatest depth between the back and the chord running from the machi to the tip. As important as how much there is is where it falls: the koshizori (腰反り) in the lower half, the toriizori (鳥居反り) towards the middle and the sakizori (先反り), which grows towards the tip.
• The mihaba (身幅) is the width, from back to edge, and it is given twice: the motohaba (元幅) at the machi and the sakihaba (先幅) at the yokote. The taper runs from one to the other. The funbari (踏ん張り) is the widening of the first centimetres above the machi, found on unshortened blades.
• The kasane (重ね) is the thickness, measured at the back, and it too is given twice: the motokasane (元重ね) at the machi and the sakikasane (先重ね) at the yokote.
• The niku (肉) is the convexity of the faces; the hira-niku (平肉) is that of the whole face, from the shinogi to the edge.
• The shinogi (鎬) is the ridge that runs along the face. It can be high or low, and the shinogi-ji (鎬地), the band between the shinogi and the back, wide or narrow.
• The kissaki (切先) is the point, from the yokote to the tip, with its fukura, the curve of the edge within it.
• The hi (樋) is the groove in the face; the commonest is the bōhi (棒樋), straight along the blade.

How each measurement is taken is in «Anatomy of the katana»; what dates each feature, in «Shape (sugata)»; and the sections that are not shinogi-zukuri (鎬造), in «Blade types». Here all the blades are shinogi-zukuri, and what changes from one geometry to another is the proportions.

The named geometries

Some shapes have a name of their own because they are recognised at first glance; that of the dōtanuki school is recognised just as easily. For each one there is a line here that places it, the measured blade that represents it and where that blade departs from the summary; the full evolution, stretch by stretch, is in «Shape (sugata)».

The dōtanuki school

The dōtanuki (同田貫) is a school of Higo (肥後), today’s Kumamoto, whose blades have a recognisable shape. The Kyūshū National Museum’s entry in ColBase makes it descend from Enju Tarō Kunimura (延寿太郎国村), a smith of the Rai school whom the Kikuchi (菊池) clan brought to Higo from Yamashiro. The blades signed Kōzuke no Suke (上野介) are, according to that entry, mostly from Bunroku to Keichō (1592–1615), between the end of the 16th century and the beginning of the 17th.

The museum describes its katana as shinogi-zukuri, with an ō-kissaki that lengthens, a somewhat shallow sori, a somewhat wide mihaba and a thick kasane, without engravings, and the school as sober and made for use, known for sturdy blades that cut well. The Japanese Wikipedia gives for the blades of that time a normal width, a thick kasane, plenty of flesh next to the edge, a lengthened point and a shallow sori, and many of them long. The NBTHK warns that a Higo dōtanuki blade can be quite heavy, and that this is usual (NBTHK 723).

The sources do not agree on the width, somewhat wide for the museum and normal for the Japanese Wikipedia; they do on the thickness and on the low curve. From the museum’s example only the nagasa (70.5 cm) and the sori (1.4 cm) are published, with neither the width nor the thickness in figures. That is why the dōtanuki goes in the comparative table with those two measurements, and without silhouette or calculation.

Kamakura tachi against late Muromachi uchigatana

The Kamakura tachi (太刀) carries the curve low, in koshizori, with funbari and a full niku; the late Muromachi uchigatana (打刀) is shorter and carries the curve towards the point, in sakizori, and those of about 60 cm, made for one hand, are the katate-uchi (片手打ち). The detail is in «Shape (sugata)», and how each was worn, the tachi slung and the uchigatana at the belt, in «Blade types». The NBTHK places the heyday of the katate-uchi between Eishō and Taiei (1504–1527), at about 2 to 2.1 shaku long, with the sori in the upper half and a short tang (NBTHK 717).

The measured examples qualify the summary. The tachi in the table, Norikuni’s from the Kyoto National Museum, has the large curve in the lower half, according to its bulletin (NBTHK 714), but it is shortened (suriage), and the bulletin says nothing of funbari. The Kanesada in the table, of 60.5 cm, with the length of the katate-uchi of its time according to its bulletin (NBTHK 715), has only 1.3 cm of sori, and the bulletin calls it shallow without saying where it falls. A katana by Osafune Sukesada of 1523, the one in the photo, measures 64.6 cm and has 2.0 cm of sori that turns into sakizori, a kissaki of 4.5 cm and a rather thin blade, according to its bulletin (NBTHK 776).

Keichō-shintō

With the Momoyama, the smiths return to the great blades of the mid Nanbokuchō, already shortened, at about 70–75 cm: this is the Keichō-shintō (慶長新刀), after the Keichō era (1596–1615), and the detail is in «Shape (sugata)». Sesko also records the name Keigen-shintō (慶元新刀), from Keichō to Genna (1615–1624). The NBTHK tells that from Keichō to Shōhō those wide blades with a large point gradually narrow and the point shortens (NBTHK 721), and places the Keichō-shintō among the thick blades, although there are thin ones too (NBTHK 748).

The example is a katana by Iga no Kami Kinmichi: wide, with little difference between the base and the yokote, thick, with a low sori and a kissaki of 6.1 cm, according to its bulletin (NBTHK 753). The bulletin does not call it Keichō-shintō, but a dynamic shape characteristic of the Momoyama; the label, with those proportions, is Sesko’s.

Kanbun-shintō

Half a century later the shape turns around: towards the Kanbun era (1661–1673) the blade stays at about 70 cm, but narrows a great deal, with a low sori and a compact chū-kissaki. This is the Kanbun-shintō (寛文新刀), and the detail is in «Shape (sugata)», which also gives the two explanations, unproven, of why the shape changed.

The NBTHK, before a signed katana by Nagasone Kotetsu of about 1674, calls it the typical Kanbun-shintō shape and a serious style, made for combat (NBTHK 785). It is the Kotetsu in the table: of Kanbun-shintō shape, although made shortly after the Kanbun era, in Enpō. Its kissaki measures 3.3 cm: a compact chū-kissaki rather than a small point.

Kiyomaro and the shinshintō that returns to the Nanbokuchō

From the Bakumatsu to the early Meiji (1844–1876), the stretch of Sesko that «Shape (sugata)» follows, part of the shinshintō (新々刀) returns once again to the shapes of the mid Nanbokuchō, with the kasane somewhat thicker than the originals; the detail is in that topic. Sesko puts at the head of that return the school of Minamoto Kiyomaro (源清麿), with Kiyomaro himself and Masao, and warns that not all smiths took it to the extreme. The NBTHK adds that these shinshintō blades are thick and weigh in the hand (NBTHK 748).

The example is a katana by Kiyomaro of 1846, Jūyō Bijutsuhin, of 80.25 cm: long, somewhat wide, with little difference between the base and the yokote, somewhat thick, with a low sori and a long kissaki, according to its bulletin (NBTHK 818). The same NBTHK describes a katana by Taikei Naotane of 1834, of 72.35 cm, as a shinshintō of normal width and thickness, with a chū-kissaki and no exaggeration (NBTHK 819): not all shinshintō is Kiyomaro.

Side by side

One real blade per geometry, with the measurements its source publishes: the NBTHK bulletin (Tōken Bijutsu, in its English translation) or the museum’s entry in ColBase. The nagasa, the sori, the widths and the kissaki are in centimetres; the kasane, in millimetres, as in the calculator. What the source does not measure goes with a dash: no source publishes the weight of these blades, and the weight in the next section comes from the model.

The table repeats, in figures, what the texts tell. The tachi, the narrowest and the thinnest, narrows from 2.65 to 1.8 cm. The Kinmichi hardly narrows, from 3.35 to 2.85 cm, and has the longest kissaki, 6.1 cm. The Kotetsu, of Kanbun-shintō shape, goes from 3.0 to 2.0 cm with a kissaki of 3.3. The Kiyomaro, the longest, narrows little. They are blades with centuries of polishes behind them, and as «Shape (sugata)» explains, polishes change the point and the thickness; the tachi, moreover, is shortened.

What changes in the hand

The measurements alone do not show how much a blade weighs or where its balance falls. To see it, each blade of the table with all its measurements (all but the dōtanuki) has been run through the model of the «Custom sword» calculator, all with the same nagasa, 71 cm, and the rest of their published measurements. To compare only the blade, all carry the same nakago, of 20.5 cm, although the entries give their own, from 14.3 to 24.1 cm, and the same mounting: a 26 cm tsuka, a 110 g tsuba and a copper habaki. No hi and a medium niku, except where indicated.

It is a Kantei calculation, not a weighing: the model gives the weight of the blade with a margin of ±6 %, that of the mounted sword with ±4 % and the balance with ±10 mm. The stiffness is the flat one, the one that resists the blade bending sideways, and it is given as a percentage of an average katana from our records (70.3 cm of nagasa, 3.14 and 2.2 cm of width, 6.9 and 5 mm of thickness), which is worth 100.

What the table shows:

• Of the five geometries at 71 cm, the Kinmichi, the widest and thickest, is the heaviest and the stiffest: 858 g of blade, and 111 of stiffness at the base and 130 at the yokote. Norikuni’s tachi, the narrowest and thinnest, is the lightest and the least stiff: 464 g, and 32 and 28. In the model, flat stiffness is proportional to the width and to the cube of the thickness: that is why the tachi, somewhat narrower than the Kotetsu and with 2 mm less kasane at the base, has a third of its stiffness there.
• A wide, thick yokote brings the balance forward: the Kinmichi, with 2.85 cm and 5 mm at the yokote, has it 129 mm from the tsuba; with the Kotetsu’s yokote, 2.0 cm and 4.5 mm, it would have it at 99, 30 mm further back, and would weigh 102 g less. The length of the kissaki, at equal nagasa, does not bring it forward in the model, but the opposite: with the Kotetsu’s 3.3 cm kissaki, the Kinmichi would weigh 19 g more and would have it at 136 mm, because in the model a long kissaki trades full blade for point, which weighs less. The fukura does not enter the model, which always draws the same point.
• The bōhi lightens and takes away stiffness. One of 1 mm depth takes 54 g of blade from the Kinmichi (from 858 to 804), moves the balance back 9 mm and lowers the stiffness from 111 to 76 at the base and from 130 to 89 at the yokote, almost a third.
• The niku adds a little weight and stiffness: with a lot of niku, the tachi goes from 464 to 473 g and from 32 to 34 at the base. In cutting, a full niku holds up better against hard targets and a flat one cuts well in soft ones, with a more delicate edge, as «Shape (sugata)» explains.
• Giving the Kanesada its own nagasa and nakago, 60.5 and 14.3 cm, takes 111 g of blade from it and brings the balance 19 mm closer to the tsuba (from 91 to 72 mm), with the same stiffness. It is less than a third of what separates the two extreme geometries at the same nagasa: from the tachi to the Kinmichi there are 394 g. For the calculator, 60.5 cm is already a wakizashi, because it sets the limit of the katana at two shaku.
• The sori does not enter the model: it changes neither the weight nor the balance. Sesko attributes the shape of the Kanbun-shintō to a fencing that preferred the thrust to the cut; the two explanations, unproven, are in «Shape (sugata)».

Choosing a geometry

A geometry is not chosen by its name, but by what the sword is going to be used for.

• For iaidō, weight and balance matter. Narrow, thin geometries, like that of the tachi, give lighter blades with the balance further back than wide, thick ones, like the Keichō-shintō; the bōhi lightens even more, at the cost of stiffness. The tachikaze (太刀風) is, according to the Japanese Wikipedia, the wind the blade raises when it is brandished; that the hi makes it whistle is one of the usual explanations of the hi, with no old source to back it, as «Forging and construction» tells.
• For tameshigiri, flat stiffness matters, the kind that holds up a cut with a twisted hasuji (刃筋). Width and, above all, kasane give it; the niku adds some and the bōhi takes it away. The wide, thick geometries, like the Keichō-shintō, are the stiffest in the table, and also the heaviest.
• For a collection, fidelity rules: a new blade that follows a school or an era has to have its proportions, and for that the measurements of surviving pieces like those in the table serve, and «Shape (sugata)».

Whoever commissions decides the use, the nagasa, the reference geometry and, if it matters, a weight or a balance; also whether they want a hi. The smith decides what is only resolved in the forge and in the polish: the exact niku, the height of the shinogi, the fukura and how the thickness is spread along the blade.

To try these geometries with your height and your use, and see the weight, balance and stiffness they would give, there is the calculator of «Custom sword».