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Fausset's Bible Dictionary [1]

Shoshannim (plural.) Titles of Psalm 45; Psalm 69; Psalm 80. The "upon" expresses the object of the psalm. In Psalm 60 the singular Shushan occurs. Shoshannim means "lilies," i.e. beautiful virgins. The beauty of the innocent, pure, lily like "virgins" ( Psalms 45:9;  Psalms 45:14) is spiritual; for the other psalms of the authors of Psalm 45, namely, "the sons of Korah," are all spiritual. In Psalm 80 Shoshannim Eduth is the "testimony" ( Psalms 78:5;  Psalms 81:5) which points out the lovely ("lily like") salvation of the Lord. Hence, thrice is repeated "we shall be saved,"  Psalms 80:3;  Psalms 80:6;  Psalms 80:19, and  Psalms 80:2, "save us." The lily is the enigmatic expression for loveliness. David delighted in enigmatic titles. Shushan Eduth (Psalm 60) is "the lily of testimony"; God's promise (Genesis 49; Deuteronomy 33;  Numbers 24:17-19) of Canaan to Israel ( Numbers 24:6) is His lovely testimony, of which the assurance was already given in a partial deliverance ( Numbers 24:4-5).

Smith's Bible Dictionary [2]

Shoshan'nim. (Lilies). "To the chief musician upon Shoshannim" is a musical direction, to the leader of the Temple choir, which occurs in  Psalms 45:1;  Psalms 69:1, and most probably, indicates the melody "after" or "in the manner of" (Authorized Version, upon"), which the psalms were to be sung.

Shoshannim-eduth occurs, in the same way, in the title of  Psalms 80:1. As the words now stand, they signify "Lilies, A Testimony", and the two are separated, by a large distinctive accent. In themselves, they have no meaning in the present text, and must, therefore, be regarded as, probably, a fragment of the beginning, of an older psalm, with which the choir were familiar.

Morrish Bible Dictionary [3]

A word in the headings of  Psalm 45 ,  Psalm 69 , and  Psalm 80 , with the word Eduth 'a testimony,' added. The first Hebrew word signifies 'lilies.' Gesenius refers it to the form of the instruments as resembling lilies. Fürst, as the name of one of the musical choirs. The LXX has 'for alternate [strains].' In the heading of  Psalm 60 is a similar word: SHUSHAN-EDUTH,'the lily of testimony.'

Hawker's Poor Man's Concordance And Dictionary [4]

This is used as a title to several of the psalms. Some have supposed that the word hath a reference to some musical instruments. But whoever reads  Psalms 45:1-17, where it is used, and with the additional title, A song of loves, will, I conceive, be inclined to think with me that somewhat higher is intended by it. If the whole psalm be of Christ, is it not likely that the title should be? See Musician

Holman Bible Dictionary [5]

 Psalm 45:1 Psalm 60:1 Psalm 69:1 Psalm 80:1

Easton's Bible Dictionary [6]

 Psalm 45 69

Cyclopedia of Biblical, Theological and Ecclesiastical Literature [7]

(Heb. Shoshannim', שֹׁשִׁנַּי , Lilies, as often), a technical term, found as such in the phrase "To the chief musician upon Shoshannim," which is a musical direction to the leader of the temple choir that occurs in Psalms 45, 69, and most probably indicates the melody "after" or "in the manner of" ( עִל , Al, A.V. "upon") which the Psalms were to be sung. (See Shoshannim- Eduth). As "Shoshannim" literally signifies "lilies," it has been suggested that the word denotes lily shaped instruments of music (Simonis, Lex. s.v.), perhaps cymbals (rather trumpets), and this view appears to be adopted by De Wette ( Die Psalmen, p. 34). Hengstenberg gives to it an enigmatical interpretation, as indicating "the subject or subjects treated, as Lilies figuratively for biride in 45; the delightful consolations and deliverances experienced in 69, etc." (Davidson, Introd. 2, 246), which Dr. Davidson very truly characterizes as "a most improbable fancy." The Sept. and Vulg. have in both Psalms Ὑπὲρ Τῶν Ἀλλοιωθησομένων , and Pro Ius Qui Immutabuntur respectively, reading apparently עִל מְשֻׁנַּי ם . Ben Zeb ( Otsar Hashshor, s.v.) regards it as an instrument of psalmody, and Junius and Tremellius, after Kirnchi, render it "hexachorda," an instrument with six strings, referring it to the root Shesh, "six," and this is approved by Eichhorn in his edition of Simonis. (See Psalms).