Who are the Characters Choirmaster, and Dove in the heading of Psalm 56?

Question

I was reading this heading, and was wondering whom the choirmaster and The Dove people are: To the choirmaster: according to The Dove on Far-off Terebinths. A Miktam of David, when the Philistines seized him in Gath.

Answer 1

Ps 56:1 is an example of a Psalm title, which can mean one of several things, including the direction to the music director/choirmaster. The "Dove" is probably part of the name of a tune.

From Holman Bible Dictionary:

Part of the superscription of Psalms 56:1 (NRSV; compare REB, NIV) probably a reference to the secular tune to which the psalm was to be sung. “Hind of the Dawn” (Psalms 22:1 REB) and “Lilies” (Psalms 45:1 NIV) are possibly other hymn tunes. An alternative explanation relates to the association of doves with the ritual of atonement. In this case the title indicates an atonement psalm. See Terebinths. KJV transliterates the Hebrew, Jonath-elem-rechokim.

More technical explanation from the IVP Dictionary of the Old Testament Wisdom, Poetry, and Writings article "Psalms 4: Titles", which identifies Ps 56:1 as Postscripts: Performance Directions

...

(1) lamnaṣṣēaḥ, “for the choir master,” occurs fifty-five times in psalm titles (Pss 4–6; 8; 9; 11–14; 18–22; 31; 36; 39–42; 44–47; 49; 51–62; 64–70; 75–77; 80; 81; 84; 85; 88; 109; 139; 140 [or postscript for the psalm preceding each of those]) and once in Habakkuk 3:19. Translations tend toward “for the leader” or “choir master,” understanding this Piel participle of nāṣaḥ to refer to “supervision” (e.g., Ezra 3:8–9), in this case supervising musicians (e.g., 1 Chron 15:21). The LXX has eis to telos (“to the end”), from its Niphal or its nominal form nēṣaḥ (“duration” [e.g., Jer 8:5]). The rabbis translated it either way: “to the Eternal” (Midr. Ps. 139) or “for the leader” (Midr. Ps. 140).

...

ʿal-yônat ʾēlem rĕḥōqîm, perhaps “to [the tune] ‘Dove of the Distant Oaks’ ” (Ps 56 [or postscript for Ps 55]; cf. Ps 55:6). The term ʾlm makes for uncertainty in this title. The LXX interpreted it as ʾēlîm (“gods” or “holy ones”), rendering it tou laou apo tōn hagiōn memakrymmenou (“the people far from the saints” or “the people far from the holies”—i.e., in exile), which the Vulgate followed with populo qui a santis longe. That fit David’s “exile” in Gath, which the title mentions. Mowinckel (2.214) approves the change to ʾēlîm (“gods”), but he says that it refers to “the doves to the distant gods,” alluding to a cultic act like that of a scapegoat but using a dove instead (linking Lev 16:8 with Lev 14:2–7, esp. v. 7). The Geneva Bible of 1599 kept the ʾēlem (“silent”) in its rendering, “dumme doue in a farre countrey” (so also NKJV, HSCB). Translations that opt for “oaks” or “terebinths” (RSV, NIV, NRSV, ESV, NLT, NET) understand ʾēlem to be an alternate form of ʾēlem from ʾayîl. Gunkel’s bias toward gentilics for any vague term that ends with -t leads him to change yônat to yawānît (“Greeks”) and render it “according to the Greek manner of the distant Islands” (Gunkel, 350). The cautious approach of transliterating it as a tune name or style called “Jonath Elem Rekhoqim” may be wise (e.g., KJV, NASB, JPS, NJPS).

Source: Brueggeman, D. A. (2008). Psalms 4: Titles. In T. Longman III & P. Enns (Eds.), Dictionary of the Old Testament: Wisdom, Poetry & Writings (p. 617). Downers Grove, IL; Nottingham, England: IVP Academic; Inter-Varsity Press.

I also came across a book excerpt about how superscriptions relate to the whole of the Psalms.

Answer 2

Psalm 56:1

"Regarding the dove of distant silence" (עַל־י֬וֹנַת אֵ֣לֶם רְ֖חֹקִים)

This refers to David (דָוִד) while in Philistine captivity - like a caged bird.

"when the Philistines seized [him] in Gath" (בֶּֽאֱחֹ֨ז אוֹת֖וֹ פְלִשְׁתִּ֣ים בְּגַֽת)