Thine head upon thee is like Carmel, and the hair of thine head like purple; the king is held in the galleries.

Thy head upon thee is like Carmel, And the hair of thy head like purple; The king is held captive in the tresses thereof .

Thy head is like Carmel: and the hairs of thy head as the purple of the king bound in the channels.

Thy head upon thee is like Carmel, And the locks of thy head like purple; The king is fettered by thy ringlets!

Thy head upon thee as Carmel, And the locks of thy head as purple, The king is bound with the flowings!

Your head is like Carmel, and the hair of your head is like purple, in whose net the king is prisoner.

Compare and contrast with Song 5:15. The rendering in the margin takes "Carmel" as the name of a color, equivalent to "carmine" (rendered "crimson" in 2-Chronicles 2:7, 2-Chronicles 2:14; 2-Chronicles 3:14). This interpretation is favored by the parallelism with "purple," but removes a beautiful image.
Purple - A deep violet black.
The king - Rather, "A king is bound in the tresses or windings of thy hair." These last words indicate the king's approach.

Shine head - like Carmel - Rising majestically upon thy neck, and above thy shoulders, as Mount Carmel does in its district. Carmel was the name of the mountain where Elijah had his contest with the prophets of Baal. See 1-Kings 18:19, etc.
The hair of thine head like purple - Ornamented with ribbons and jewellery of this tint.
The king is held in the galleries - Or is detained in the antechamber. His heart is captivated by thy person and conduct. Some understand the ringlets of the bride's hair.

Thy head upon thee [is] like Carmel, and the hair of thy head like purple; the king [is] (c) held captive by [its] locks of hair.
(c) He delights to come near you, and to be in your company.

Thine head upon thee is like Carmel,.... Set with hair, thick and long, as Carmel with plants and trees. Now Christ is the church's Head in various senses; he is her federal and representative Head in eternity and time; her political Head, as a King to his subjects; an economical Head, as the husband to the wife, as parents to their children, and a master to servants; and, as such, may be compared to Carmel; for the multitude dependent on him, whom he represents, and is connected with under various relations; for his height, being higher than the kings of the earth, and all other heads; and for fruitfulness, all the fruits of the church, and of all true believers, coming from him. Some render the word, "as crimson", or "scarlet" (b); which may set forth his royal dignity and majesty, this colour being wore by kings and great personages; or the ardent love of Christ to his body, the church, and the members of it; or his bloody sufferings for them;
and the hair of thine head like purple; purple coloured hair has been in great esteem. Of this colour was the hair of King Nysus, according to the fable (c); and so the hair of Evadne, and of the Muses (d), were of a violet colour; the hair of Ulysses is said (e) to be like to the hyacinth flower, which is of a purple or violet colour; and Milton (f) calls the first Adam's hair hyacinthine locks; and here, in a figurative sense, the second Adam's hair is said to be like purple. By which believers that grow on Christ, the Head of the church, nay be meant, who have their dependence on him, and their strength and nourishment from him; see Song 4:1; and these may be said to be like "purple", because of their royal dignity, being made kings unto God by Christ; and because of their being washed in the purple blood of Christ; and because of the sufferings they endure for his sake; and especially such may be so compared, who have spilt their blood and laid down their lives on his account;
the king is held in the galleries; the same with the Head of the church, the King of Zion, and King of saints, whose kingdom is a spiritual and everlasting one: and by the "galleries" in which he is held may be meant the ordinances of the Gospel; where Christ and his people walk and converse together; where he discloses the secrets of his heart to them, leads them into a further acquaintance with his covenant, and the blessings and promises of it; and from whence they have delightful views of his person and fulness; see the King in his beauty, and behold the good land which is afar off: the same word as here is rendered "rafters", and by some "canals", in Song 1:17; See Gill on Song 1:17. Now Christ being said to be "held in these galleries" may signify his fixed habitation in his house and ordinances; where he has promised to dwell, and delights to be; and where he is as it were fastened to them, and hatred in them.
(b) "veluti coccinum", Pagninus, Vatablus, Mercerus; "simile est coccineo", Junius & Tremellius; "est ut coccus", Piscator; so Ainsworth; "sicut carmesinum", Schindler. (c) Ovid. Metamorph. l. 8. Fab. 1. v. 301. De Arte Amandi, l. 1. & de Remed. Amor. l. 1. v. 68. Hygin. Fab. 198. Pausan. Attica, p. 33. (d) Pindar. Olymp. Ode 6. Pyth. Ode 1. v. 2. (e) Homer. Odyss. 6. v. 231. & 23. v. 155. (f) Paradise Lost, Book 4.

upon thee--the headdress "upon" her.
Carmel--signifying a well-cultivated field (Isaiah 35:2). In Song 5:15 He is compared to majestic Lebanon; she here, to fruitful Carmel. Her headdress, or crown (2-Timothy 4:8; 1-Peter 5:4). Also the souls won by her (1-Thessalonians 2:19-20), a token of her fruitfulness.
purple--royalty (Revelation 1:6). As applied to hair, it expresses the glossy splendor of black hair (literally, "pendulous hair") so much admired in the East (Song 4:1). While the King compares her hair to the flowering hair of goats (the token of her subjection), the daughters of Jerusalem compare it to royal purple.
galleries--(so Song 1:17, Margin; Revelation 21:3). But MAURER translates here, "flowing ringlets"; with these, as with "thongs" (so LEE, from the Arabic translates it) "the King is held" bound (Song 6:5; Proverbs 6:25). Her purple crowns of martyrdom especially captivated the King, appearing from His galleries (Acts 7:55-56). As Samson's strength was in his locks (Judges 16:17). Here first the daughters see the King themselves.

5aa Thy head upon thee as Carmel.
We say that the head is "on the man" (2-Kings 6:31; Judith 14:18), for we think of a man ideally as the central unity of the members forming the external appearance of his body. Shulamith's head ruled her form, surpassing all in beauty and majesty, as Carmel with its noble and pleasing appearance ruled the land and sea at its feet. From the summit of Carmel, clothed with trees) Amos 9:3; 1-Kings 18:42), a transition is made to the hair on the head, which the Moslem poets are fond of comparing to long leaves, as vine leaves and palm branches; as, on the other hand, the thick leafy wood is called (vid., under Isaiah 7:20) comata silva (cf. Oudendorp's Apuleii Metam. p. 744). Grδtz, proceeding on the supposition of the existence of Persian words in the Song, regards כרמל as the name of a colour; but (1) crimson is designated in the Hebrews.-Pers. not כרמל, but כרמיל, instead of תולעת שׁני (vid., under Isaiah 1:18; Proverbs 31:21); (2) if the hair of the head (if ראשׁך might be directly understood of this) may indeed be compared to the glistening of purple, not, however, to the listening of carmese or scarlet, then red and not black hair must be meant. But it is not the locks of hair, but the hair in locks that is meant. From this the eulogium finally passes to the hair of the head itself.
5ab The flowing hair of thy head like purple -
A king fettered by locks.
Hitzig supposes that כרמל reminded the poet of כּרמיל (carmese), and that thus he hit upon ארגּמן (purple); but one would rather think that Carmel itself would immediately lead him to purple, for near this promontory is the principal place where purple shell-fish are found (Seetzen's Reisen, IV 277 f.). דּלּה (from דּלל, to dangle, to hang loose, Job 28:4, Arab. tadladal) is res pendula, and particularly coma pendula. Hengst. remarks that the "purple" has caused much trouble to those who understand by דלה the hair of the head. He himself, with Gussetius, understand by it the temples, tempus capitis; but the word רקּה is used (Song 4:3) for "temples," and "purple-like" hair hanging down could occasion trouble only to those who know not how to distinguish purple from carmese. Red purple, ארגּמן (Assyr. argamannu, Aram., Arab., Pers., with departure from the primary meaning of the word, ארגּון ,drow eht), which derives this name from רגם = רקם, material of variegated colour, is dark-red, and almost glistening black, as Pliny says (Hist. Nat. ix. 135): Laus ei (the Tyrian purple) summa in colore sanguinis concreti, nigricans adspectu idemque suspectu (seen from the side) refulgens, unde et Homero purpureus dicitur sanguis. The purple hair of Nisus does not play a part in myth alone, but beautiful shining dark black hair is elsewhere also called purple, e.g., πυρφύρεος πλόκαμος in Lucian, πορφυραῖ χαῖται in Anacreon. With the words "like purple," the description closes; and to this the last characteristic distinguishing Shulamith there is added the exclamation: "A king fettered by locks!" For רהטים, from רהט, to run, flow, is also a name of flowing locks, not the ear-locks (Hitz.), i.e., long ringlets flowing down in front; the same word (Song 1:17) signifies in its North Palest. form רחיט (Chethı̂b), a water-trough, canalis. The locks of one beloved are frequently called in erotic poetry "the fetters" by which the lover is held fast, for "love wove her net in alluring ringlets" (Deshmi in Joseph and Zuleika).
(Note: Compare from the same poet: "Alas! thy braided hair, a heart is in every curl, and a dilemma in every ring" (Deut. Morg. Zeit. xxiv. 581).)
Goethe in his Westst. Divan presents as a bold yet moderate example: "There are more than fifty hooks in each lock of thy hair;" and, on the other hand, one offensively extravagant, when it is said of a Sultan: "In the bonds of thy locks lies fastened the neck of the enemy." אסוּר signifies also in Arab. frequently one enslaved by love: asîruha is equivalent to her lov.
(Note: Samaschshari, Mufaṣṣal, p. 8.)
The mention of the king now leads from the imagery of a dance to the scene which follows, where we again hear the king's voice. The scene and situation are now manifestly changed. We are transferred from the garden to the palace, where the two, without the presence of any spectators, carry on the following dialogue.

Carmel - Eminent and pleasant to the eye, and fruitful as mount Carmel was. Which may denote that her mind was replenished with knowledge, and other excellent gifts of the Holy Ghost. Purple - Which colour was anciently much esteemed. Is held - In which he walks, and having once espied thee, is unable to take off his eyes from thee.