Sometimes the term koten-honkyoku 古典本曲 "classical honkyoku" is also used to distinguish the traditional honkyoku that were played by the Komusō, i.e. within the Fuke-sect, from the core repertoire of the modern Shakuhachi (Kinko-ryū, Tozan-ryū) which is referred to as honkyoku as well.
The word honkyoku 本曲 is composed of the two Chinese characters hon and kyoku. Hon is used in a number of meanings, but here means something like "original", "origin", "true" or "root". Kyoku simply means "musical piece" oder "song". Thus an obvious translation would be "original pieces", but it is possible to read a little bit more out of the word honkyoku. There is a Japanese saying:
Honkyoku wa hon'nin no kyoku 本曲は本人の曲
"The Original Pieces are the Music of the Original Person / of each player himself."
What is meant by that Zen-kōan-like saying is not a question I can answer here definitively, but it is obvious that some "original" dimension of our person is referred to here, and that is somehow different from our day to day identity. That might be some deeper level of existence, where the everyday-version of ourselves has its origin and its root. I don't think it's necessary to go into a deeper interpretation here, but I wanted to open a field for further investigation.
The word hon'nin can also mean "the person him or herself" and a more down-to-the-earth reading would be: "The Original pieces belong to (the player) himself." And that would imply that each and every player has to find his own way of playing the honkyoku, has to make them his own and maybe that there is no right and wrong.
Honkyoku are the only pieces that are played with the Komusō-Shakuhachi, or it might rather be the other way around: this kind of Shakuhachi is made for playing those pieces. There are many honkyoku and they can be grouped using different categories.
Honkyoku as local Komusō traditions
The modern repertoire of the Komusō-Shakuhachi was put together relatively recently, a little more than 100 years ago. The influential player Higuchi Taizan had learned eleven honkyoku from two Komusō from the temple Futai-ji 普大寺 in Hamamatsu (now in Shizuoka Prefecture). He added five of his own compositions that are similar in style to the Futai-ji honkyoku and together with some pieces from other local traditions mentioned below, his collection is known today as the Myōan-Taizan-ha 明暗対山派 (about 33 pieces). The learning of the Komusō-Shakuhachi begins with a thorough study of those pieces. But there do exist many more local traditions, connected to certain former Komusō temples or to certain famous players who have left behind their compositions. The following is a selection of the more famous local traditions.
Itchō-ken 一朝軒 was a Komusō-temple belonging to the Yoritake-ha 寄り竹派, one of the 16 branches of the Fuke-sect, whose main temple was Meian-ji temple in Kyōto (that temple is not identical with the present Myōan-ji within the precincts of Tōfuku-ji). Itchō-ken is somewhat unique by the fact that it still exists (most of the Komusō temples have vanished) and that the Shakuhachi tradition there is still closely related to the family of the abbot. There are about ten honkyoku from Itchō-ken.
Shinpō-ryū 真法流 or Kyū-Meian-ji 旧明暗寺 ("Former Meian-temple") is the name of the repertoire transmitted from the group of Komusō affiliated to the original Meian-ji temple in Kyōto. These are about 29 honkyoku.
Futai-ken 布袋軒 was a Komusō-temple in the former province of Ōshū (present Miyagi Prefecture) and there three honkyoku from this North-Eastern part of Japan.
Echigo-Meian-ji 越後明暗寺 was a temple in the former province of Echigo (present Niigata Prefecture) and two honkyoku from there are now widely played.
Fusai-ji 普斉寺 in the former province of Ise (present day Mie Prefecture) has contributed three honkyoku to the present repertoire.
Nezasa-ha (Kinpū-ryū) 根笹派（錦風流） consists of about 10 honkyoku played by a group of Komusō from the area of present Hirosaki in Aomori Prefecture (also known as Tsugaru). Those are played with a distinct breathing technique known as komi-buki 込み吹き "pressed blowing". In that playing technique the breath is not blown into the Shakuhachi continually, but is separated into breath-waves or clusters of air. It is a demanding playing style, but it is now relatively well known and practised all over Japan.
Besides those local traditions the following Komusō have each left famous honkyoku-pieces: Miyagawa Nyozan 宮川如意 (1868-1946), Jinbo Masanosuke 神保正之助 (1841-1914) and Nakamura Kikufū 中村菊風 (1889-1971).
Honkyoku for specific occasions
Honkyoku can also be classified by their traditional usage. One group of honkyoku called honte 本手 was played at the Komusō-temples on ritual occasions, where they replaced the chanting of sutras. Kyorei 虚鈴, Kokū 虚空 and San'ya 三谷 are examples for those very dignified pieces. As those ceremonies would usually take place in the morning, there was another group of less formal pieces that where played in the afternoon, the group is actually called hirukara ("after noon"). Azuma 吾妻 is one example for those. They where played Impromptu in a more relaxed and lighter mood and were also called hade 派手 "flamboyant".