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The passamezzo moderno ("modern half step"; also quadran, quadrant, or quadro pavan), or Gregory Walker was "one of the most popular harmonic formulae in the Renaissance period, divid[ing] into two complementary strains thus:"^[1]

1)	I	IV	I	V
2)	I	IV	I–V	I

For example, in C major the progression is as follows:

C	F	C	G	C	F	C–G	C

Gregory Walker root progression

^[a]

The progression or ground bass, the major mode variation of the passamezzo antico, originated in Italian and French dance music during the first half of the 16th century, where it was often used with a contrasting progression or section known as ripresa. Though one of Thomas Morley's characters in Plaine and Easie Introduction to Practicall Musicke denigrates the Gregory Walker, comparing unskilled singing to its sound,^[2] it was popular in both pop/popular/folk and classical musics through 1700. Its popularity was revived in the mid 19th century, and the American variant (below) evolved into the twelve bar blues.^[3]

Examples

Listed in van der Merwe (1989, 198–201):

several in The Fitzwilliam Virginal Book
"Up and Ware Them A Willie"
"Jimmie Rose"
"Darling Nelly Gray"
"Wreck of the Old 97"
Woody Guthrie's "There is a House in This Old Town"
Irving Berlin's "Alexander's Ragtime Band"
The Rolling Stones' "Honky Tonk Women" (1969)
Carole King's "You've Got a Friend" (1971)

Listed in Helms, Ilmbrecht, and Dieckelmann (1954, ^{[page needed]}):

Hans Neusidler's Gassenhauer (Nuremberg, 1536)
"Oxstedter Mühle" (folk dance from Lower Saxony) (B section)
Diego Ortiz' Recercada Prima / Segunda / Tercera sobre el Passamezzo Moderno (three-part didactic composition in Tratado de Glosas sobre cláusulas y Otros Generos de Puntos en la Música de Violones, 1553). (Readers of Spanish may benefit from the Spanish-language Wikipedia's more extensive treatment of Diego Ortiz and of the Tratado de Glosas.)

Others:

Iron & Wine's "A History of Lovers"^[4] (verses; chorus and interludes follow ripresi IV–I–IV–V progression)
Ed Rush and George Cromarty’s "Plastic Jesus"

American Gregory Walker

The American Gregory Walker, popular in parlour music, is a variation in which the subdominant (IV) chords become the progression IV–I.^[5]^[1]

1)	I	IV–I	I	V
2)	I	IV–I	I–V	I

For example, in C major this variation is as follows:

C	F–C	C	G	C	F–C	C–G	C

American Gregory Walker root progression

Examples

Listed in van der Merwe (1989, 201–202):

Other variations

On original progression

Second strain's first I becomes I–I⁷ (for a stronger "lead-in" to the upcoming IV):

"Gathering Flowers From the Hillside":^[6] The Bluegrass variation frequently occurs in conjunction with the I–I⁷ "lead-in" and/or the direct IV-to-V transition listed above.
The resulting progression is ||| I | I | I | V || I(–I⁷) | IV | (I–)V | I ||| ; examples include:

"Free Little Bird" (David Holt and Doc and Merle Watson; not to be confused with Lynyrd Skynyrd's "Free Bird").^[7]^{[failed verification]}

On American variant

IV–I is reversed, becoming I–IV or I⁷–IV:

"Tennessee Waltz" (Stewart and King 1947)^{[full citation needed]} (verse and second strain of chorus)

Notes

^ Caution: Keeping all chords in root position without using a stepwise melody produces parallel fifths (see parallel harmony), which are prohibited by classical (rather than popular) voice-leading rules. The following files may or may not be more suitable for use in strict counterpoint, though they lack the ground bass.
Progression with tonic (I) chord in root position
Tonic in first inversion
Tonic in second inversion

References

^ ^a ^b Middleton 1990, 117.
^ Morley 1597, 120.
^ van der Merwe 1989, 198–201.
^ Iron e Wine 2005, ^{[page needed]}.
^ van der Merwe 1989, 201–202.
^ Carter Family 1935.
^ Holt, Watson, and Watson 2009.

Carter Family. 1935. "Gathering Flowers From The Hillside". Columbia 37636. Recorded May 7, 1935.
Helms, Anna, Otto Ilmbrecht, and Heinrich Dieckelmann (1954). Die Tanzkette, Frankfurt am Main: Hoffmeister Verlag.
Holt, David, Doc Watson, and Merle Watson. 2009. "Free Little Bird". Piney Grove Ramblers: Bluegrass for the People website (archive from 1 March 2012, accessed 21 April 2020)
Iron e Wine [2005]. A History of Lovers CifrasFX website (accessed 22 May 2010).
Middleton, Richard. 1990. Studying Popular Music. Milton Keynes and Philadelphia: Open University Press. ISBN 0-335-15276-7 (cloth); ISBN 0-335-15275-9 (pbk). Reprinted 2002.
Morley, Thomas. 1597. A Plaine and Easie Introduction to Practicall Musicke. London: Peter Short.
van der Merwe, Peter. 1989. Origins of the Popular Style: The Antecedents of Twentieth-Century Popular Music. Oxford: Clarendon Press. ISBN 0-19-316121-4.