This is the second of a multi-part post. (Please see previous posts below for earlier instalments.)
Example 3a, a Miserere by John Redford (d. 1547, master of the choristers at St Paul’s Cathedral, London), is an example of Sextupla or 6 descant notes to each one of the plainsong. As in Exx. 2a-b, all the leaps in the descant are consonant, and the rest of it moves stepwise; but in addition to passing-tones and accented passing-tones Ex. 3a includes lower and upper neighbors (or auxiliaries). These are indicated below the staves; for example, at the beginning of bar 2, the second note in the bass, E, is a dissonant 11th (or 4th) below A in the plainsong; it is a lower neighbour because it is preceded and followed by the note F which is consonant against the A.
Example 3a (recorded up 4th) John Redford, Miserere (30513, fols 10v-11r), 6:1, passing-tones (pt), accented passing-tones (apt), lower neighbours (ln) and upper neighbours (un)
This Miserere by Redford can be used as a further demonstration of how beginners could practice playing ‘species-counterpoint’-style descants against a simple plainsong. Ex. 3b is a note-against-note contrapunctus of Redford’s Miserere, with just two alterations to the consonances: these are notated as black semibreves on the note G, to avoid the melodic tritone between B and F; and some notes are put up or down an 8ve. (The ‘hidden 8ve’, created by similar motion to a perfect consonance at plainsong notes 21-22, is being allowed to stand as it is not ‘forbidden’ in Tudor style.)
Example 3b Contrapunctus (1:1) of Redford’s Miserere:
Examples 3c-e are Dupla (2:1), Tripla (3:1), and Quadrupla (4:1) descants based on the contrapunctus in Ex. 3b of Redford’s Miserere. The dissonances are limited to passing-tones and neighbours.
Example 3c A 2:1 descant based on the 1:1 contrapunctus of Ex. 3b:
Example 3d A 3:1 descant based on the 1:1 contrapunctus of Ex. 3b:
Example 3e A 4:1 descant based on the 1:1 contrapunctus of Ex. 3b:
Example 3f is an anonymous Miserere with 12 notes to 1 that Thomas Mulliner copied into his book right after he had copied Redford’s Miserere. If you compare the first six consonances between the notes of the descant that sound at the same time as notes of the plainsong in Ex. 3f, you will see that they are the same as the consonances in the contrapunctus of Redford’s Miserere in Ex. 3b (and of Ex. 3c-e). Perhaps Thomas Mulliner wrote this verset himself, using Redford’s Miserere as a model. The only notated dissonances are passing-tones and neighbors, as in Ex. 3b, but in bar 9 there are double-stroke ornament signs drawn through the stems of six crotchets. As such signs are used only in this bar in the verset, Desmond Hunter’s comment (regarding Virginalist music) is apropos: “embellishment implied by the signs should feature as an integral part of the music rather than simply adding surface decoration”. I suggest therefore that the crotchets with the double-strokes may be realised as two quavers (the note above the pitch of the crotchet, and the pitch of the crotchet itself), so that the long continuous run of quavers is maintained. In this case, the use of the signs could be an acknowledgment that four of the six crotchets create additional dissonances (two appoggiaturas and an unprepared or ‘fake suspension’, which will be discussed in more detail below, Ex. 4a and Ex. 7a, respectively).
Ex. 3f (recorded up 4th) Anonymous (Thomas Mulliner?) Miserere (30513, fols 11v-12v), 12:1:
 Desmond Hunter, “Virginalist embellishment: revisiting the grace signs,” Journal of the Royal College of Organists n.s. 5 (2011): 287-329 (at p. 313).