The term koto (kanji: 古刀) means "old sword" in English. It is written ことう in hiragana. It may also be rendered in English as kotou or kotō. It's pronounced roughly like "koh toe".
This refers to swords made between the period of the jokoto sword (上古刀) and the shinto (新刀); that is, from about 900 AD to the start of the Keicho Era (1596-1615). The tachi is the representative sword of the Koto Period.
The kanji for old, 古, refers to things that are physically old or worn as well as to food that has gone stale. The Japanese reading (furu), with the hiragana character for i after it, is furui (古い, ふるい).
Note that the musical instrument “koto” (琴) is unrelated to this word.