“Ver. 3: ὁ δὲ προφητεύων He that prophesieth.] The word προφητεύειν, to prophesy, comprehends three things, ‘singing psalms,’ ‘doctrine,’ and ‘revelation:’ as ver. 26.
I. To prophesy is taken for ‘singing psalms,’ or celebrating the praises of God, I Sam. x. 5, “Thou shalt meet a company of prophets,…with a psaltery, and a tabret, a pipe, and a harp, וְהֵמָּה מִתְנַבְּאִים and they shall prophesy:” where the Chaldee, ואינון משבחין and they shall sing or praise. And chap. xix. 24, 25, ואזל מיזל ומשבח And he went forward singing. And he put off his (royal) garment ושבח and sang.
From this signification of the word prophesying, you may understand in what sense a woman is said to prophesy, chap. xi. 5; that is, to ‘sing psalms.’ For what is there said by the apostle, “A man praying or prophesying,” and “a woman praying or prophesying,” is explained in this chapter, when it is said, “I will pray,” and “I will sing.” 
“Paul is here dealing with the assembly of the saints for worship. He says, “I will sing with the spirit and I will sing with the understanding also” (vs. 15), “Each one hath a psalm” (vs. 26). From the verb that Paul uses in verse 15 we might quite properly translate as follows: “I will sing a psalm with the spirit and I will sing a psalm with the understanding also,” just as in verse 26 he says, “Each one hath a psalm.” 
“[referencing 1 Corinthians 14:26] Assuming for the moment that Paul is, in fact, speaking here of some kind of charismatic hymn singing, it ought to be clearly understood that such a situation in no way militates against exclusive psalmody. There are two very good reasons for this. In the first place, the charismatic gifts present in the Corinthian church at the time this epistle was written, passed away with the close of the New Testament canon and are not normative for today’s church. If the advocates of non-canonical hymnody wish to use this passage to support their position, they are bound to produce Spirit-given, charismatic songs. But it ought to be obvious that such songs as these could never become the foundation for the Church’s hymnody. Such songs may be interpreted by someone with the appropriate gifts, but their spontaneous origin and glossolalic character prohibit their reproduction for corporate use. The singing alluded to in this passage is, in fact, not congregational singing at all.”
1. Lightfoot, John, From the Talmud and Hebraica. Volume 4. New York: Cosimo, 2007, page 262.
2. Murray, John & William Young. “Reports of the Committee on Song in Worship (Minority Report of the Committee on Song in the Public Worship of God Submitted to the Fourteenth General Assembly of the Orthodox Presbyterian Church).” http://www.opc.org Orthodox Presbyterian Church. Web. January 9, 2016.
3. Bushell, Michael, Songs of Zion: A Contemporary Case for Exclusive Psalmody (Third edition). Pittsburgh: Crown & Covenant Publications, 1999, page 80.