The 30-day Psalter
The Psalter of the 1979 Book of Common Prayer is divided into thirty days, each with psalms for Morning Prayer and for Evening Prayer. Reading one day’s portion on each day of the month takes you through all 150 psalms.
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What the prayer book says
The division is printed in the Psalter itself, as a heading before each portion: from “First Day: Morning Prayer” before Psalm 1 (page 585) to “Thirtieth Day: Evening Prayer” before Psalm 147 (page 804). Most days break between whole psalms. Psalm 119, the longest, is spread over five portions from the evening of day 24 to the evening of day 26, always between its eight-verse sections.
The book gives no separate rubric for the thirty-day division. Morning and Evening Prayer call for “the Psalm or Psalms Appointed” (pages 84 and 118), and the Daily Office Lectionary appoints them “in a seven-week pattern which recurs throughout the year, except for appropriate variations in Lent and Easter Season” (page 934). The thirty-day headings are the Psalter’s own way through the whole book in order, a month at a time.
Whichever pattern you follow, “Gloria Patri is always sung or said at the conclusion of the entire portion of the Psalter; and may be used … after each Psalm, and after each section of Psalm 119” (Additional Directions, page 141). Each day’s page ends its Morning and Evening psalms with the Gloria.
The 31st and February
The headings stop at the thirtieth day, and the 1979 book says nothing about longer or shorter months. This site and the Gracelight app follow one rule: read the day that matches the date, read day 30 again on the 31st, and start every month at day 1. In February the cycle ends at day 28, or day 29 in a leap year, and March 1 begins again at day 1.
In the app, the thirty-day Psalter is a choice in the psalm settings for Morning and Evening Prayer; the lectionary is the default. Holy days and their eves keep the psalms the lectionary appoints.
Each psalm on its own
Every psalm also has its own page in the Psalter, with its day in this cycle and the dates the lectionary appoints it.