What is (1) the meaning of the names and (2) the structure of the “poems” found in Selichos particularly the Pizmon and the Shalmonis. (3) I note that the number of phrases in the first verse of the Pizmon is less than in subsequent verses. Why is that?
All the slichot poems are called "slichot," but they can also have different names, based on their form, their subject matter, or their location in the davening.
This answer is specific to Ashkenazi slichot.
Pticha: the first piyyut in slichot, said to introduce the paragraph of ki al rachamecha harabbim. Often has one rhyme running through the whole thing, but I'm not sure why.
Shniya: each verse has two stitches.
Shlishiya: each verse has three stitches.
Shalmonit: each verse has four stitches, but not every slicha with this type of verse is a shalmonit. According to the Da`at encyclopedia (entry "Piyyut") a shalmonit has its rhymes in the style of Rabbi Shlomo HaBavli.
Akeda: the subject matter is Akedat Yitzchak. This is usually said towards the end of the series of slichot interspersed with the 13 middot.
Pizmon: literally, "refrain"; the slicha has a refrain. Pizmonim are read responsively. Nowadays the entire piyyut is said by both chazan and kahal, but I think that the chazzan used to say the body of the verse, and the kahal used to respond with the refrain.
There is always a pizmon towards the end of the series of slichot interspersed with the 13 middot. However, not all the slichot marked as pizmonim actually have refrains.
I don't know why the first verse often has fewer stitches than the subsequent verses, but perhaps the chazzan used the first verse to tell the kahal what the refrain was.
Chatanu: a piyyut said at the point of "chatanu tzureinu, slach lanu yotzreinu" which uses that line as a refrain.
Tochecha: the piyyut instructs the speaker or congregation to do tshuva.
Shma Yisrael: a piyyut with the pasuk of "Shma Yisrael" used as the refrain.
Tchina: a piyyut said as part of tachanun, at the end of slichot. Frequently invokes the angels or other intermediaries (e.g. the Torah, the Kisei HaKavod) to pray for us.
For Pizmon, the Lubavitcher Rebbe zt"l (in his notes at the end of the Chabad Selichos) summarizes the following explanations:
- Something repeated over and over. (Responsa of Ri Migash #204)
- Related to a root for crying out. (Tishbi)
- From a Greek root meaning פזרנות ונדיבות, "largess and generosity," which we are requesting from Hashem. (Pri Megadim, second letter of introduction to Orach Chaim, citing Musaf HaAruch)
- An acronym for פיוט זה מהדרין, "this poem is repeated," since the first stanza is repeated at the end of the poem and as a refrain between stanzas. (Nimukei HaGri"v in Otzar HaTefillos, vol. 2, p. 124)
- The Rebbe there also references Aruch HaShalem s.v. פזמון, although without quoting a few other explanations that he gives: that it's a Farsi word for a type of melodic arrangement, or from another Farsi root meaning "something precious" (plus two other explanations that Kohut rejects: that it is related to בוסמא, "incense," or to "psalm").
For Shalmonis, the Rebbe quotes two explanations, although without providing sources:
- It's the name of a well-known melody to which the composition was to be sung.
- It's related to שלם, complete, because it treats its subject thoroughly.
Given that the first verse (or part of it) of a pizmon is meant to be used as a refrain between stanzas, then it makes sense that it would be shorter than them, since the stanza would carry part of the melody and the refrain would carry the rest.