The famous shinshintō master Taikei Naotane (大慶直胤, 1778–1857) needs little introduction, but I would like to briefly recap his career before I come to the actual topic of this post.
Born in An’ei seven (安永, 1778) (some sources say An’ei eight) in Yamagata (山形) in Dewa province (present-day Yamagata Prefecture) into a family of blacksmiths that produced agricultural tools, Naotane, his real name was Shōji Minobei (荘司箕兵衛・庄司美濃兵衛), felt destined for greater things. Accordingly, some time towards the end of the Kansei era (寛政, 1789–1801), he left his home town for Edo to study with the arguably most famous swordsmith at that time, Suishinshi Masahide (水心子正秀, 1750–1825). We do not know who or if someone arranged this apprenticeship, but maybe it had helped that Masahide was originally from Dewa province as well.

Portrait of Naotane he had commissioned with a certain Takada Enshū (高田円洲) at the age of 72. It had remained with the Shōji family until it was unfortunately destroyed in the 1923 Great Kantō earthquake.
Naotane learned fast as he had entered his teacher’s forge with existing skills from his upbringing as a blacksmith, and so he was able to become independent in Kansei 13 (1801) at the young age of 23. Naotane married the daughter of a charcoal wholesaler, how practical, and moved several times (one time he lost his house due to a fire that had ravaged the Kanda district).
In Bunka nine (文化, 1812), and through the agency of his former teacher Masahide, Naotane was employed by the Akimoto (秋元) family, which ruled, until 1845, the Yamagata fief in Dewa province, and then the Tatebayashi fief in Kōzuke province. For the time being, Naotane worked from Edo, receiving the honorary titles of Chikuzen Daijō (筑前大掾) around Bunsei four or five (文政, 1821~1822), and that of Mino no Suke (美濃介) in Kaei one (嘉永, 1848), when he proceeded to Kyōto to present the aristocratic Takatsukasa family (鷹司) with a tachi.
Naotane’s fame grew and his outstanding skill allowed him to produces blades in any style, although his main artistic focus were the Bizen and Sōshū traditions. Naotane not only trained almost as many students as his teacher Masahide, he travelled extensively all over Japan and instructed local smiths in many of his temporary working locations. Naotane married his daughter to his best student Jirō Tarō Naokatsu (次郎太郎直勝, 1805–1858), who had been sent to train with him by the Tatebayashi fief and who later took over the workshop as Naotane’s official successor. Naotane died in the fourth year of Ansei ( 安政, 1857) at the age of 79. He is buried at the Honnen-ji (本然寺) in the Asakusa district of Edo/Tōkyō.
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Now to the actual topic. As surely most of you know, some swordsmiths and sword fitting makers inscribed certain works with the age they were when producing it. This practice is known as gyōnen-mei (行年銘). Naotane was one of these swordsmiths, and he started to add gyōnen-mei to some works from the age of 50 onwards.
In many cases, inscribing one’s age was often linked to an auspicious occasion, for example, turning 61 being celebrated as Kanreki (還暦), turning 70 as Koki (古希), turning 80 as Sanju (傘寿), and, very auspicious, turning 88 as Beiju (米寿). There are even more special birthdays after the age of 90, but such ages were rarely reached in post-modern times. Thus, such “milestone birthdays” if you will were seen as a starting point to inscribe one’s age to a work on a regular basis, although we also know fairly many cases where artists inscribed gyōnen-mei in their late teens, twenties, thirties, etc.
Another issue that we have to take into consideration is the different way age was counted in Japan. That is, up to some time after WWII (in practice; rendered obsolete by law in 1902), the Japanese used a method referred to as kazoedoshi (数え年), which started with the age of 1 when being born and which incremented on New Year’s Day. For example, if you were born, let’s say on October 12, 1818, you were 1 year old and turned 2 “suddenly” on Jan 1, 1819 (using the Gregorian calendar here for demonstration purposes). This way of counting then continued for the rest of your life, i.e., you turned 3 in this case on Jan 1, 1820, and not on your actual birthday October 12.
Back to Naotane. As mentioned, he started to inscribe gyōnen-mei at the age of 50. When he was 74, however, something happened as all of a sudden, he upped his age by one year. That is, in Kaei five (嘉永, 1852), when he was 74 kazoedoshi years old, he inscribed certain blades with “made at the age of 75.” He continued to do so throughout Kaei six, seven, and Ansei two (安政, 1855), but in the very same year of Ansei two, when he was actually 78 kazoedoshi years old, he occasionally upped his age by two years even, inscribing certain blades with “made at the age of 80.”

Left: Wakizashi dated Ansei two and inscribed “made at the age of 79” and right a wakizashi dated Ansei two and inscribed “made at the age of 80.” Both blades are Tokubetsu-Hozon.
This oddity is referred to as kirō-heki (喜老癖). I am not 100% sure about the reading, so I chose a standard Sino-Japanese reading for the term, which may best be translated as “habit of greatfully accepting one’s old age,” or “habit of being delighted about one’s old age.” Incidentally, I was only able to find this term in connection with swords and sword fittings, not Japanese art in general, but want to do more research in the future. Also, I am not sure if this term was coined in reference to Tang dynasty Chinese poet Bái Jūyì (白居易, 772–846) as Jūyì left a poem with the title Lǎnjìng Xǐlǎo (覧鏡喜老, Japanese: Rankyō Kirō). In this poem, 64-years-old Jūyì looks into the mirror and is delighted about having avoided premature death and having become that old.
Anyway, once again back to Naotane. Now why did he do this kirō-heki thing? Well, we do not know for sure, but there are several hypotheses. One speculates that something must have happened at age 74 when he used kirō-heki for the first time. That is, maybe he got sick and worried that he won’t life to 76, the age his teacher Masahide died, whom he greatly admired, but whom he also tried to surpass. Another one puts forward that Naotane may have tried to leave a legacy through his works of living a long life, which may also explain the “double jump” to 79 when he was 77 years old. In other words, when people will come across such a work in the future, and not knowing when he was actually born, they might admire that the smith had enjoyed a particularly long life. Or it is nothing more than a playful wish of, or encouragement for the artist to reach these ages when inscribing them on certain works (Occam’s razor may favor this approach). By the way, there exists a blade which is dated “on a spring day in the year of the snake of the Ansei era (1857).” This blade is inscribed with the kirō-heki “made at the age of 80,” so only a one year jump again. Naotane died on the 27th day of the fifth month that very year, so this blade can be considered as one as his last works.

Blade dated with a spring day in the year of the snake of the Ansei era and inscribed “made at the age of 80.” The blade is Jūyō.
Wrapping up this post, I would like to point out that Naotane was not the only artist who used kirō-heki (I had mentioned sword fittings earlier). There exists a tsuba by the first generation Niwa Norisuke (丹羽則亮, 1781–1852) which is inscribed “made at the age of 72” when the artist had actually died at the age of 71. In addition, there exists a tsuba by Tsuchiya Kunichika (土屋国親, 1788–1852), which is dated Kaei three (嘉永, 1850) and which is inscribed “made at the age of 66.” In Kaei three, Kunichika was actually 63 years old, so we are facing here a considerable kirō-heki jump of three years. Kunichika seems to have used that (at least) three-year-jump several times as the Kinkō Jiten (金工事典) mentions that works inscribed “made with the age of 68” even if the artist had died at the age of 65.

Tsuba by Tsuchiya Kunichika dated Kaei three and inscribed “made at the age of 66.”