The Westminster Confession of Faith, chapter 21, after discussing the Regulative Principle of Worship and “the parts of the ordinary religious worship of God“, goes on to address extra-ordinary parts of religious worship, which include “solemn fastings (Est. 4:16; Joel 2:12; Mat. 9:15; 1 Cor. 7:5), and thanksgivings upon several occasions (Est. 9:22; Psa 107 throughout); which are, in their several times and seasons, to be used in an holy and religious manner (Heb. 12:28).” These are not extra-ordinary in the sense of being more remarkable or special than the ordinary elements of worship, but rather because they are not regularly part of public worship, they are occasional.
What are these solemn fastings and thanksgivings? Robert Shaw comments:
6. Solemn fastings and thanksgivings. Stated festival-days, commonly called holy-days, have no warrant in the Word of God; but a day may be set apart, by competent authority, for fasting or thanksgiving, when extraordinary dispensations of Providence administer cause for them. When judgments are threatened or inflicted, or when some special blessing is to be sought and obtained, fasting is eminently seasonable. When some remarkable mercy or deliverance has been received, there is a special call to thanksgiving. The views of the compilers of our Confession respecting these ordinances may be found in “The Directory for the Public Worship of God.”
“The Directory for the Public Worship of God,” composed by the Westminster Assembly to accompany the Confession of Faith and Catechisms, further elaborates on this clause:
Concerning Publick Solemn Fasting
When some great and notable judgments are either inflicted upon a people, or apparently imminent, or by some extraordinary provocations notoriously deserved; as also when some special blessing is to be sought and obtained, publick solemn fasting (which is to continue the whole day) is a duty that God expecteth from that nation or people.
. . .
Besides solemn and general fasts enjoined by authority, we judge that, at other times, congregations may keep days of fasting, as divine providence shall administer unto them special occasion; and also that families may do the same, so it be not on days wherein the congregation to which they do belong is to meet for fasting, or other publick duties of worship.
Concerning the Observation of Days of Publick Thanksgiving
. . .
Let him then make some pithy narration of the deliverance obtained, or mercy received, or of whatever hath occasioned that assembling of the congregation, that all may better understand it, or be minded of it, and more affected with it.
. . .
Touching Days and Places for Publick Worship
There is no day commanded in scripture to be kept holy under the gospel but the Lord’s day, which is the Christian Sabbath.
Festival days, vulgarly called Holy-days, having no warrant in the word of God, are not to be continued.
Nevertheless, it is lawful and necessary, upon special emergent occasions, to separate a day or days for publick fasting or thanksgiving, as the several eminent and extraordinary dispensations of God’s providence shall administer cause and opportunity to his people…
The Light of Nature teaches that when God’s judgment is evident, or a society is in desperate need of repentance from a particular sin, it is appropriate to proclaim a general fast and a time of crying out to God to turn away His wrath and grant them repentance. Likewise, in times of blessing, it is appropriate to separate a day for public thanksgiving. Occasional times of fasting or thanksgiving prompted by providential events may be seen repeatedly in Scripture (as in 2 Chron. 20:2-3; Ezra 10; Neh. 9; Joel 1:14, 2:15; Zeph. 2:1-3; Matt. 9:15), whereas ecclesiastical holy days set apart by men are explicitly renounced in Scripture. Part of the rebellion and idolatry of the making and worshiping of the golden calf was the creation of a holy day of worship for “Jehovah” (Ex. 32:5). Jeroboam likewise greatly angered the Lord, in part, by mimicking prescribed Mosaic festivals and instituting a holy day “which he had devised of his own heart” (1 Kings 12:33).
Occasional times of fasting or thanksgiving called by the church are circumstances of worship since “all the particular causes, occasions, and times of fasting, could not be determined in Scripture” , but annual days set apart by the church for the commemoration of biblical events (such as the birth or resurrection of Christ) would be adding spiritual significance to a time that God did not attribute spiritual significance to and treating something as holy without divine warrant. The former are responses to immediate difficulties or blessings, as recognized by the elders of the church (or another competent authority), and their call to fast or feast in response to God in that particular set of circumstances, while the latter arise out of mechanical regulation (c.f. Mark 2:18-20; Matt. 6:16-18)  and have biblical, rather than circumstantial, subject matter, putting it on par with the Lord’s Day. If the Lord Jesus Christ wanted his church to have annual ecclesiastical holy days for the events of Christ’s life, he would have instituted them himself. But rather we find in Scripture that annual ecclesiastical holy days are Old Testament ceremonies and carnal ordinances, imposed on the old covenant church until the time of reformation (Heb. 9:10). This was entirely appropriate for the period prior to Christ’s coming, but altogether inappropriate afterwards. The “weak and beggarly elements” (Gal. 4:9-10), “the elements of the world” (Col. 2:20), the “shadows of things to come” (Col. 2:16-17), are abrogated now that Christ is come.
“Are ye so foolish? having begun in the Spirit, are ye now made perfect by the flesh? Have ye suffered so many things in vain? if it be yet in vain…But now, after that ye have known God, or rather are known of God, how turn ye again to the weak and beggarly elements, whereunto ye desire again to be in bondage? Ye observe days, and months, and times, and years. I am afraid of you, lest I have bestowed upon you labour in vain…Ye did run well; who did hinder you that ye should not obey the truth? This persuasion cometh not of him that calleth you.” (Gal. 3:3-4 & 4:9-11 & 5:7-8).
If the Old Testament holy days are abrogated, how much more inappropriate would it be to attempt to create our own without an appointment from God! How audacious are we when we institute elements of worship of our own devising!
 George Gillespie, Dispute Against English Popish Ceremonies, p. 51.
 G.I. Williamson, The Westminster Confession of Faith for Study Classes, p. 169.