Coins of Japan (1904) by Neil Gordon Munro, is the only one of my reference books that discusses the Nami (wave) sen in any detail at all. According to Munro: He points out that there are many varieties, with either 21 or 11 waves. He believes that the 21-wave version began being cast in 1768, both versions were cast in 1769, and the 11-wave version continued being cast for several more years. Many of them were cast in iron, most of which have rusted away in the 2-1/2 centuries since being created. Munro also points out that the so-called 11-wave version actually depicts only 10 waves, with one being interrupted by the central hole in the coin. He describes a number of varieties with one or more characters at the top of the wave side, functioning as mint marks. Many were cast in provincial mints as well as those under control of the central government. The Japanese Numismatic Dealers Association Catalog depicts both the 21- and 11-wave coins without mint marks - attributed as 1768 and 1769 respectively - but the six marked versions listed are all attributed as 1866. All of that being said, neither the JNDA catalog, Munro nor any other author whose English language works are in my library, comment on the reason for the different wave designs, or the difference (if any) in symbolism.
