Although the transition from medieval to Renaissance style is often placed by recent periodizations at around the epoch of the young Dufay (c. 1420-1430), the theorists of this epoch such as Prosdocimus and Ugolino might be viewed largely as late Ars Nova (or more generally late medieval). It is in the later 15th century, with such authors as Tinctoris and Ramos, that we move into a clearer realm of "early Renaissance music theory."
From this era through the Manneristic era of the late 16th and early 17th centuries, solmization theory continues to play an important role in the literature, and evidently in a typical course of training for musicians. Thus Tomás de Santa María (1565), for example, in a treatise devoted mainly to the art of composed or improvised keyboard music (or music for other polyphonic instruments such as the vihuela or harp), urges that the musician study the solmization of each voice. Likewise Fabio Colonna, in a treatise of 1618 on a keyboard instrument with 31 notes per octave, uses the familiar solmization syllables to demonstrate the unusual transpositions of the modes available on this instrument dividing each whole-tone into five parts.
At the same time, however, the medieval hexachord system was often treated in a rather cursory or cavalier way, with various "shortcuts" or abridgements being proposed to suit modern tastes.
Thus in Shakespeare's The Taming of the Shrew , Bianca's music tutor (and suitor) Hortensio informs her:
Madam, before you touch the instrument,
To learn the order of my fingering,
I must begin with rudiments of art;
To teach you the gamut in a briefer sort ...
To which Bianca replies:
Why, I am past my gamut long ago.
As it turns out, Hortensio's "pleasant, pithy, and effectual" of the gamut "in writing fairly drawn" is actually a kind of love poem of six lines, based on the first hexachord of the regular gamut:
"Gamut I am, the ground of all accord,
A re, to plead Hortensio's passion;
B mi, Bianca, take him for thy lord,
C fa ut, that loves with all affection:
D sol re, one cliff, two notes have I:
E la mi, show pity or I die."
Having read this poem aloud, Bianca responds:
Call you this gamut? tut, I like it not:
Old fashions please me best; I am not so nice
To change true rules for old inventions.
Musicians of the Renaissance and Manneristic eras, however, were often prepared to change the "old fashions" of the medieval hexachord system.
Thus Shakespeare's contemporary Thomas Morley, whose Plain and Easy Introduction to Practical Music (1597) presents the art of singing, counterpoint, and composition in the form of a lively dialogue, proposes for polyphonic music a gamut based on only two hexachords, the hard (G-E, with B-natural) and the soft (F-D, with Bb). He argues that these hexachords alone suffice to accommodate all song, where B is either Bmi (B-natural) or Bfa (Bb). The natural hexachord (C-A), which includes neither form of B, would be reserved for plainsong. Also, he describes a practice in which the syllable ut has a restricted use, explaining "that except it be in the lowest note of the part, we never use Ut." 
Modern authors such as Gaston G. Allaire  have urged that "the framework of the hexachordal system" provides a common basis for approaching medieval and Renaissance music alike, albeit with allowances for changing styles. From another viewpoint, one might recognize the common elements of the hexachord system indeed shared by musicians of these eras while placing more emphasis on the varying musical styles and fashions favored in different times and places.
In 1477, Tinctoris reported the opinion of connoisseurs that "there is no music worth hearing save that written in the last 40 years." Bartolomé Ramos or Ramis (1482) offers a theory which might fit with such a viewpoint, not only proposing bold innovations but expressing a less than complimentary view of medieval predecessors. One of his chapters is entitled: "Reproving the followers of Guido and showing accurately the truth of the matter." 
Most dramatically, Ramos proposes to replace the hexachord system and hand of Guido with his own gamut and hand based on a new set of eight syllables covering the range of an octave rather than a hexachord; on this proposal, see Section 4.1 below. Also, he takes an interest in calling attention to some liberties taken by singers with the established hexachord system, specifically the singing of semitones at locations other than mi-fa.
In a discussion of intervals found on a keyboard, he expresses some preferences regarding accidental inflections, of special interest in that they show how tastes may have varied in the choice of alterations to obtain "closest approach" progressions - a variation documented in the 16th century by intabulations showing exact semitones and inflections, and often showing alternative solutions for the same piece.
In either the older Pythagorean keyboard tunings with pure fifths and fourths, or the newer meantone tunings with slightly narrow fifths and pure or near-pure thirds which had evidently come into vogue around 1450, accidentals such as G#/Ab or Eb/D# are distinct. If we accept the argument of Mark Lindley  that Ramos is describing a meantone keyboard, then such pairs of accidentals would differ by about 1/5-tone.
Thus on a standard meantone keyboard with only 12 notes per octave, one must choose whether to tune a given accidental key as G# or Ab; or as Eb or D#, etc. In explaining his own preferences, Ramos both by his examples and by certain omissions may be giving us clues as to at least one viewpoint on cadences and accidentals in the 1480's.
While recognizing that many people tune the black key between G and A as G#, Ramos finds this to be the "less provident" choice. He argues that while this alternative indeed provides the perfect fifth C#-G#, such a fifth is useless, because it so rarely occurs. 
Indeed it is true that sonorities such as C#3-G#3-C#4 are uncommon; but from an earlier 14th-15th century perspective, G# has a very productive role as the major third or tenth above E in cadences to D involving an M3-5 or M10-12 progression, for example:
G[#]4 A4 C[#]4 D4 G[#]4 A4 C[#]4 D4 G[#]3 A3 C[#]4 D4 G[#]3 A3 E3 D3 E3 D3 E3 D3 (M6-8 + M3-5) (M10-12 + M6-8) (M10-12 + M6-8 + M3-5)
In the 14th and early 15th century, all three forms are idiomatic. By around the middle of the 15th century, however, the latter two forms are out of fashion because they involve parallel fifths and in the four-voice example (a hallmark of Machaut's Mass) also octaves between upper parts, progressions now more and more consistently avoided.
However, the first form (M6-8 + M3-5) is consistent with this restriction, and such a use of G# is widely attested, for example, in a source of mid-15th century keyboard music, the Buxheimer Organ Book. Might the silence of Ramos on this point in his keyboard tuning discussion suggest that such a cadential formula had become less fashionable by the last quarter of the century?
In fact, Ramos does describe an M3-5 progression E3-G#3 to D3-A3 in his discussion of basic two-voice counterpoint , where he uses this progression to illustrate the rule that the major third expands to the fifth (tertia maior ad quintam disgregat). Thus if the lower voice descends G3 E3 D3, the added voice should avoid G3 G3 A3 (which would invite a Marchettan chromatic semitone G3-G#3, see Sections 2.2 and 2.4), but rather should sing E3 G[#]3 A3 or B3 G[#]3 A3:
G3 G[#]3 A3 E3 G[#]3 A3 B3 G[#]3 A3 not G3 E3 D3 but rather G3 E3 D3 or G3 E3 D3 1 M3 5 m3 M3 5 M3 M3 5
For whatever reason, Ramos does not mention such progressions in his weighing of the merits of a G# key.
He does note that advocates of G# may say that when the tenor (for Ramos, as for earlier medieval authors, the voice providing the main foundation for a polyphonic texture) descends from B to A, this accidental provides a major sixth leading to the octave on A, e.g.
G#4 A4 B3 A3 (M6-8)
However, Ramos urges that in such a progression the tenor should instead itself be altered so that it descends from Bb to A by a semitone, likewise resulting in a major sixth expanding to an octave:
G4 A4 Bb3 A3 (M6-8)
This choice would comport with a preference for Bb (a musica recta note found within the Guidonian hand) rather than G# (musica ficta). However, it would appear that both late medieval and Renaissance cadences on A may lean toward either option - with much discretion for performers to exercise.
As an advantage of his solution, Ramos raises the problem of adding a third middle voice. With his own chosen solution, this voice can proceed from D, a major third above the tenor at Bb, to E, the fifth above A (M3-5):
G4 A4 D4 E4 Bb3 A3 (M6-8 + M3-5)
In contrast, the version with G# would require D# in the middle voice in order to achieve M3-5 between the lower pair of voices:
G#4 A4 D#4 E4 B3 A3 (M6-8 + M3-5)
However, advocates of a keyboard with G# generally favor the range of Eb-G# for accidentals, so there would be no such D# to provide a perfect fourth for G# and a major third above the tenor B. On such a meantone keyboard, the attempted substitution of Eb for D# would produce a diminished fourth between the lower two voices about 1/5-tone larger than a regular major third, and also a drastically wide "Wolf fourth" (actually an augmented third) between the upper voices :
G#4 A4 Eb4 E4 B3 A3 (M6-8 + d4-5)
While Ramos is indeed correct on this point, it is possible that by around 1480 (the era for example of the great elder Ockeghem and of the younger Josquin, Obrecht, and Isaac), another three-voice formula had already come into vogue where the traditional M6-8 progression is combined with m3-5, involving a tritone between the upper voices. For example:
C[#]4 D4 G[#]4 A4 G3 A3 D4 E4 E3 D3 B3 A3 (M6-8 + m3-5) (M6-8 + m3-5)
Ramos might have cited the first example to argue that one does not need a G# in order to have a cadence to D with an ascending semitone. Advocates of G# might cite the second example to show that a G# key can indeed provide a viable option for such cadences on A, even if one does not have a D# key available to provide an M3-5 progression.
Given that Ramos does recognize the norm of M3-5, and more generally of closest approach (m3-1, M6-8, and also m6-5 by oblique motion, the last resolution also being recognized by 16th-century theorists such as Zarlino in 1558), one suspects that he might solve the problem of a cadence to D on his keyboard as follows:
C4 D4 G3 A3 Eb3 D3 (M6-8 + M3-5)
This solution, like the one he advocates for cadences to A, features a fa-mi or descending semitonal motion in the lowest voice (involving a flat) rather than mi-fa or ascending semitonal progressions in the upper voices (involving sharps).
In any case, having argued that cadences to A are "better, sweeter, and more suave" with his option of Bb, he responds to another argument in favor of a G# key. If one makes this key Ab instead of G#, it is asserted ,
diapente e h quadro non haberet tertiam mediam, quae major ad inferiorem et minor sit ad superiorem, ut in parte diximus secunda tractatu tertio compositionis. Sed hoc non obstat, quia, cum illa phrygii sit incitativa, non refert, si tertia careat media, vel si maior ad superiorem et minor ponatur ad inferiorem.
the fifth E to B-natural [?] would not have a mediating third which is major to the lower voice and minor to the upper one, as we have said in the second part of the third tractate of the treatise. But this does not obstruct, because, since the Phrygian mode may incite, it makes no difference if a mediating third should be lacking, or if it is placed as a major third to the highest voice and a minor third to the lower one.
Here different scholars have interpreted diapente e h quadro (using the German "h" for the "square-B" sign) in two different ways. One interpretation, followed in Clement A. Miller's translation and that immediately above, reads this as meaning "the fifth E-B." Indeed the portion of the treatise which Ramos cites discusses the origins of the modes, in which it is noted that the fifth E-B (S T T T) "is called Phrygian, for it was used by the Phrygians." 
If so, then Ramos may be discussing the unavailability in his keyboard tuning of a sonority such as E3-G#3-B3, favored for example in some pieces in the Buxheimer Organ Book. By 1482, such sonorities with thirds are approaching a status of stability and even conclusiveness; by around 1500, Josquin and Isaac for example are closing pieces on combinations including thirds.
Possibly, then, Ramos is concerned with the use of G# in E Phrygian not as a directed cadential accidental taking part in some "closest approach" progression, but rather as a major third above the mode's final E occurring in a freely treated sonority, or even a sonority serving as a cadential goal. If so, Ramos' alternative of letting the mode's fifth E-B stand without a mediating third might be illustrated by such popular formulas of the late 15th and early 16th centuries as these:
A4 B4 D3 E4 E4 E4 A3 B3 C4 B3 F3 E3 A3 E3 (M6-8 + M3-5) (M6-8)
Might his other alternative of having a voice mediate at the minor third above the lower tone of the fifth and the major third below its upper tone refer to the following kind of sonority in Phrygian, used at the close of Josquin's Mille regretz?
1 2 & | 1 ... || G4 E4. F4 G4 B3 C4 B3 G3 A3 G3 E3 A2 E3
By 1525 , Pietro Aaron illustrates the use of G# to provide a major third in concluding sonorities at final or internal cadences, and by the middle of the 16th century, a preference for major rather than minor thirds above the lowest voice in such sonorities seems to be widespread. By this epoch, it would be difficult indeed to play a typical Phrygian piece on a keyboard without G#; but in the late 15th and early 16th centuries such inflections were evidently considered less essential.
Lindley proposes a different reading of the Latin diapente e h-quadro to mean the fifth from B, or "B and its fifth" , and takes the passage not to continue the discussion of G# vs. Ab, but rather to address the new matter of Eb vs. D#. In Lindley's reading, Ramos is discussing a less common form of Phrygian cadence in which a sonority including the fifth B-F# is used to approach the goal of E. Thus advocates of D# would favor a form like the first following, with a "closest approach" progression of m3-1 between the two upper voices, while Ramos would be arguing that an alternative form such as the second would be equally acceptable:
F#4 E4 F#4 E4 D#4 E4 D4 E4 B3 E3 B3 E3 (m3-1)
From a musical view, this reading of a late 15th-century treatise seems less likely to me. In 1555, it is true, Vicentino  offers an example of a Phrygian cadence for four voices (with "r" showing a rest):
1 & 2 & | 1 r E5 D5 E5 G4 F#4 G3 B3 B3 B3 E3 B2 E3
In weighing the possible interpretations of Ramos, might it be relevant to see whether and how often such progressions occur in the late 15th century? At any rate, since the rest of the passage focuses on the issue of G#/Ab and does not mention the question of Eb/D#, reading the passage in question as also referring to G# as a major third above the Phrygian final of E might more smoothly fit the context.
In his discussions of solmization and counterpoint, Ramos often introduces the concept of the semitonium subintellectum: that is, a "mentally supplied semitone" not necessarily indicated by the notation or reflected in the actual solmization syllables which might be used. This concept may not be too far removed from the modern interpretation of musica ficta as "accidental inflections supplied by performers."
In a vertically-oriented context, some of the examples which Ramos offers seem quite traditional . For example, illustrating the progression of the major sixth to the octave by the example:
D4 C[#]4 D4 F3 E3 D3 M6 M6 8
he notes that the upper voice descends from the first note to the second per semitonium subintellectum, "by an understood semitone." Similarly, in a progression like:
G3 A[b]3 G3 G3 F3 G3 1 m3 1
the third before a unison, etsi maior videatur, subintellecte efficitur minor - "although it appears to be major, is mentally made minor."
While observing that inflections of this kind should be indicated in written music by accidental signs, he cautions composers in any case to take such "understood semitones" into account in order to avoid an imperfect interval such as an augmented unison or fifth with an uninflected note in another part. This caution covers some of the same ground as the traditional rule against (unintentionally) using mi contra fa in perfect consonances (Section 2.4).
However, for Ramos, the scope of these unwritten but understood semitones goes beyond the vertical rules of "closest approach" to include more generally some common melodic progressions, and without a need for proper hexachord mutations to place the semitone at mi-fa.
In the 14th century, the Quatuor principalia had disapproved of such trends while the fifth treatise of the Berkeley manuscript had accepted them (Section 2.5).  Ramos not only takes notice of such irregular solmization, but makes it part of his case against the followers of Guido and in favor of his own new system.
Citing the opinion of John of Villanova "that a rising song desires the voice to be strengthened, and descending song to become soft," Ramos gives some examples of performer's inflections . Although the melodic figure a-c-d (without returning to c) seems to call for a solmization such as re-fa-sol (hard hexachord, G-E), yet singers actually produce a-c[#]-d, which properly should be sung ut-mi-fa; or if a singer makes this inflection while solmizing re-fa-sol, the major third between the first two notes "may be said to be understood."
Similarly, the figure g-f-g (not returning to f) involves an understood semitone "although sol-fa-sol or re-ut-re may be said," i.e. g-f[#]-g. A kindred example is d-b-c[#]-d-c[#]-d-d, which might be sung in the hard hexachord as sol-mi-fa-sol-fa-sol-sol with the semitone b-c and whole-tone c-d "mentally" altered to a whole-tone and semitone respectively; "or a mutation will be made of mi into re," placing us properly in the ficta hexachord of A-F# with c[#]-mi and d-fa.
As editor Clement Miller adds, Ramos is not unique in noticing such late 15th-century practices: His rival Gaffurius (1496) likewise writes: "Very often many sing sol as a semitone below la, especially in the progression la sol la ... as in Salve Regina." 
The controversy provoked by Ramos' treatise likely stems not only from the novel musical ideas advocated but from the humor and satire directed against followers of Guido as well as the less orthodox Marchettus of Padua. One is tempted to compare the style with that of Vincenzo Galilei (1581) in his polemic against conventional polyphony, or that of his son Galileo Galilei (1632) directed against the Aristotelian academics of his day.
From a musical point of view, Ramos not only indicates that musicians could have varying preferences for cadential inflections (e.g. Bb or G# in M6-8 cadences to A), but records some liberties both practical and conceptual which were being taken with the hexachord system.
Publishing the first edition of his Toscanello in musica in 1523, only two years after the death of Josquin des Prez (c. 1440-1521), Pietro Aaron (or Aron) named this treatise in his mother tongue after his native Tuscany. The contents range from the praise of music and its role in Classical times (a favorite 16th-century theme) to the basic rules of counterpoint, including the "closest approach" principle, and some hints for composers. 
For example, Aaron suggests that although earlier musicians often composed the cantus (the highest voice) and the tenor first, then added the other parts, this approach often produced less smooth melodic lines in the added parts. (Some contratenor parts from the earlier 15th century, for example, might illustrate this point.) Therefore the up-to-date composer should preferably compose all parts at the same time so that each may be duly melodious. 
Some of his precepts relevant to accidental inflections have a continuity with late medieval tradition: "Proceed so that the closest interval possible precedes [a perfect] consonance, such as the minor third before the unison, the major third before the fifth, the major sixth before the octave..." 
In offering examples of four-voice cadences on various degrees, Aaron provides us with some evidence in his original edition of 1523 that the inflections required to obtain such progressions might be left unwritten - as practical sources also suggest.
In these typical early 16th-century formulae, an M6-8 progression between the cantus (highest voice) and tenor (next to lowest voice) is characteristically preceded by a 7-6 suspension, an idiom which carries special musical force in a style where seconds and sevenths are generally regarded as dissonances to be treated circumspectly. While the M6-8 progression occurs naturally in cadences on C and F (with an ascending semitone in the cantus), and on E (with a descending semitone in the tenor), Aaron's other examples invite accidentals left unwritten. Here, again, "r" means a rest, and a "#" placed above a note in the highest voice represents a likely musica ficta inflection :
1 & 2 & | 1 2 || 1 & 2 & | 1 2 || 1 & 2 & | 1 2 || # r C4 B3 C4 r D4 C4 D4 r E4 D4 E4 r G3 G3 G3 r A3 A3 A3 r C3 A3 A3 r C3 D3 C3 r D3 E3 D3 r E3 F3 E3 r C3 G2 C3 r D3 A3 D3 r C3 D3 A3 1 & 2 & | 1 2 || 1 & 2 & | 1 2 || 1 & 2 & | 1 2 || # # r F4 E4 F4 r G4 F4 G4 r A4 G4 A4 r A3 C4 C4 r D4 D4 D4 r C3 E3 E3 r F3 G3 F3 r G3 A3 G3 r A3 B3 A3 r D3 C3 F2 r G2 D3 G2 r A3 E3 A2
Although Aaron leaves these accidentals unwritten, his revised 1529 and later editions of the Toscanello include a supplement which he devotes to the problem of accidentals, urging composers to be more explicit for the guidance of inexperienced and experienced performers alike.  This discussion includes some invaluable "real-world" observations on how performers negotiate the dilemmas of inflection.
Focusing on the melodic problem of the tritone or diminished fifth, which he declares should generally be "tempered" by an appropriate accidental, Aaron nevertheless cites some examples from Josquin to prove that this is not always possible, such as this bass passage from the third Agnus Dei from Clama ne cesses [Missa L'homme armé super voces musicales]:
1 & 2 & | 1 & 2 ... F3. G3 A3 B3 E3. F3 G3
Aaron comments that either the bass must sing the outlined tritone F3-G3-A3-B3, or else fall into the worse "inconvenience" of a direct diminished fifth: F3-G3-A3-B[b]3 followed by E3. He concludes that the outlined tritone is preferable, although all things being equal, it would be a "lesser error" to sing a diminished fifth than a tritone. A likely distinction here is that the tritone is outlined while the diminished fifth would be direct.
Having concluded that the singer should "choose between two evils the least inconvenient," he remarks of this and similar examples from Josquin that "these passages are not easy for the singer." We find it appealing to conclude that Josquin himself was fully aware of the challenging nature of these passages, and the element of creative tension and ambiguity for the performers to resolve with due discretion.
From the viewpoint of certain 20th-century theories of Renaissance accidentalism, it may be significant that Aaron does not mention a third solution: flatting both the Bb and the following Eb, thus:
1 & 2 & | 1 & 2 ... F3. G3 A3 B[b]3 E[b]3. F3 G3
As proposed in certain hypotheses such as Edward E. Lowinsky's "Secret Chromatic Art" and Margaret Bent's "Diatonic Ficta," this consistent avoidance of the tritone or diminished fifth would result in a spiral of remote flats.  Aaron's discussion and 16th-century intabulations of Josquin's pieces demonstrate, at any rate, that other solutions were typically favored, and that the tritone was not always avoided in such situations. 
Aaron also notes how melodic and vertical factors can interact in a performer's choice of accidentals. Raising again the issue of the outlined tritone, he gives this passage as a case where it turns out that no Bb "correction" is needed (here the beat is shown as the breve, or the semibreve in editor Peter Berquist's transcription):
1 2 & | 1 & 2 & | 1 & ... C4 A4 B4. A4 G4 F4 G4
Although only this single line is shown, Aaron evidently associates such a figure with a vertical cadence: "The rules of counterpoint require that the last semibreve [i.e. the penultimate F4] should be raised because of a sixth with the tenor, as in the natural raised cadences, and sung accidentally."  In other words, this figure typically signals a cadence on G involving an M6-8 resolution between this voice and the tenor, like Aaron's example quoted above in his set of sample four-voice cadences, with an F# inflection implied.
This inflection, which might be solmized as followed mutating from the hard hexachord G-E to the ficta hexachord D-B, converts the apparent outlined tritone B-A-G-F into a perfect fourth B-A-G-F[#], making it unnecessary to alter the B to Bb:
1 2 & | 1 & 2 & | 1 & ... C4 A4 B4. A4 G4 F[#]4 G4 Hard G4-E5: fa re mi (re) Ficta D4-B4: sol fa mi fa
This example might be offered as support for the hypothesis that singers or players seeing a single part rather than a score - a situation similar to that of Aaron's example showing only a single line - would typically recognize (and inflect) cadences based mainly on melodic and rhythmic cues in their own parts.
However, Aaron's main point in his supplement to the Toscanello is not so much to document such a common practice among experienced musicians as to emphasize that it is not infallible. Thus he offers another conclusion to a very similar melodic figure - here giving all four parts - where a Bb inflection is correct :
1 2 & | 1 & 2 | 1 2 || C4. A4 B[b]4. A4 G4 F4 E4 F4 G4 F4 E4 F4 G3 A3 G3 C4 C4 C4 C3 F3 Eb3 F3 C3 F3
In this case, the performers find that "the composer has another intention about the last fa" - the F4 in the highest voice (fa in the natural hexachord C-A) is not a tone calling for inflection in a cadence to G, but rather itself the cadential goal of cadence to F involving an m3-1 resolution with the next lower voice. Thus a Bb inflection is called for both to make an outlined tritone into a perfect fourth (B[b]-A4-G4-F4) and to avoid a vertical augmented fifth (or twelfth) with the bass at Eb3.
These examples lead to Aaron's main point: Composers should not rely upon the supposed ability of singers to "recognize at once the intent and secret of a composer" when singing a song for the first time. Rather, this intent should be indicated by the appropriate accidental signs, for the benefit of novices and experienced performers alike.
Aaron himself reports that others deem such accidentals to be unnecessary, saying that all composers expect their songs "to be understood by learned and experienced, by a quick and perceptive ear, especially when imperfect fifths, octaves, twelfths, and fifteenths occur." 
However, Aaron replies that even a "learned and practiced" performer would find it impossible to sense such intervals "without first committing the error of a little dissonance." While one performer might be quicker to sense the problem than another, there is no one "who would not be caught."  To support this conclusion, Aaron offers some examples from Josquin and other composers where inflections such as Bb or Eb are expressly indicated.
Another side of the accidental question regards the showing of sharps, called diesis signs by Aaron. Here the author acknowledges and qualifies his remarks in the main body of the Toscanello holding such signs mostly unnecessary for experienced singers. In that discussion, he gives two examples of the use of a sharp for a purpose other than a "closest approach" progression: to make what would otherwise be a minor tenth E3-G4 between the outer voices into a smoother major tenth E3-G# :
1 2 || 1 2 || E4 G[#]4 A4 G[#]4 E4 E4 C4 E4 E3 E4 F3 E3
Whether or not Ramos was referring in 1482 to this kind of major third (or tenth) above E as an argument for a 12-note keyboard with G# rather than Ab (Section 3.1 above), by 1523 Aaron considers such an inflection to be routine. Indeed he comments that "this sign is little used by learned and experienced singers but given perhaps only for the inexperienced ...," although essential for a "proper performance."
In his supplement of 1529, Aaron cites his own statement in the main treatise that experienced performers "will easily recognize with their intellect and excellent ear definite progressions where the raised note should properly be used or not used, as the composer intends," However, the expert's viewpoint does not justify "the attitude that it does little harm when the sign is not found." 
"This attitude and practice cannot help, let alone give notice to the inexperienced and unintelligent singer, so for this reason it is necessary that the composer signify when and where the sign is necessary."
Earlier in the supplement, following his list of examples where composers have used explicit signs to correct intervals such as vertical diminished fifths, Aaron frames this metaphor :
"[I]n travelling one sees places where there are various signs, because there are several roads one might take. By means of these signs those who do not know the country may correctly choose the right road. If there were no sign, they doubtless might choose the wrong road..."
Thus composers are "obliged" to show their intentions, "so that the singer will not stumble into something the composer did not intend." He concludes that "the sign is as useful to the learned as to the untaught." 
Such a message might be linked to the increasing numbers of less expert performers in the early 16th century, an audience addressed and cultivated by the new business of music printing and also by introductory treatises in the vernacular such as Aaron's. Showing all accidentals expressly, as Aaron recommends, could be taken as one sign of a shifting role for polyphonic music: from a "mystery" or craft for the experienced, transmitted largely by oral tradition and initiation, to an "open book" for anyone able to read the basic symbols.
While theorists such as Ramos and Aaron can give us their views on accidentalism in the era of a composer such as Josquin, another kind of source offers us, as it were, a "musical time capsule" on actual 16th-century performances of such a composer's work: tablatures showing exact semitones, for example on a lute. Such intabulations, showing for example which frets on the lute are to be pressed, give an unambiguous indication of whether the player should play B or Bb, F or F#, etc.
Robert Toft, in his book Aural Images of Lost Traditions: Sharps and Flats in the Sixteenth Century, draws on this direct musical evidence as well as music treatises to explore how theoretical principles and options might be applied - or disregarded - in practice.
He concludes both that accidentals left unwritten in the vocal sources but called for by guidelines such as that of "closest approach" typically were added in performance; and that such inflections were not, however, always applied, or applied by different performers in the same way. Thus in the following cadence on D from Josquin's Pater noster, with a Bb signature in all parts, different intabulations may use either a C# or an Eb inflection to obtain an M6-8 progression - or may leave both notes unaltered for an m6-8 progression. Here I show only the four parts active at this point in the six-part texture, with the semibreve of Toft's transcription as the beat , the notes in question being the E3 and C4 at the beginning of the second measure:
1 & 2 & | 1 & 2 & | ... C4 Bb4. A4 F4 G4 F4 E4 D4 C4 D4 r G3 A4 A4 A3 G3. F3 D3 E3 D3
In a version published in 1546, Francesco da Milano chooses a C# inflection; in 1547, Pierre di Teghi favors Eb; Simon Gintzler (1547) and Sebestian Ochsenkun (1558) leave both notes unaltered. 
As Toft remarks elsewhere, varying interpretations of this kind illustrate "the freedom with which Renaissance musicians treated such cadential passages." Indeed a single artist such as Hans Gerle varies his treatment of cadences "when he intabulates the same piece twice." 
While Aaron uses the metaphor of the performer as a traveller in need of a sign to be sure of finding the right road, we might be tempted to invoke the Elizabethan adage quoted by Thomas Morley (1597) in another musical context: "There be (as the proverb sayeth) `more ways to the wood than one.'" 
In making use of the rich evidence Toft has surveyed, we would do well to heed his own caution that the intabulations do not necessarily show what Josquin himself might have preferred, since "there is no way of determining which reading(s), vocal or instrumental, Josquin might have endorsed." 
Agreeing with Toft that "many of the sharps and flats encountered in intabulations are directly relevant to their vocal models" , we might note the suggestion of Bernard Thomas that at least for certain genres and composers such as the madrigals of Philippe Verdelot in the 1530's, lute tablatures may idiomatically lean toward certain uses of sharps more than vocal ensembles might. For example, such inflections might serve to underscore cadential progressions and "compensate for the lack of sustaining tone." 
In any case, the range of variations in the intabulations themselves, as well as the generous use of accidentals in vocal music described by theorists such as Ramos and Aaron, may make such possible distinctions between vocal and solo instrumental performances less important than the freedom and discretion applying in both settings.
Also, some of Thomas' remarks on the Verdelot madrigals focus on a feature of the lute arrangements which Toft finds uncommon in the intabulations of Josquin: the use of mi-inflections to obtain a cadence with closest approach progressions of M3-5 as well as M6-8, as is the norm in late medieval usage. Here are examples from Adrian Willaert's intabulation (1540) of Verdelot's Madonna, il tuo bel viso ; and Pierre Phalèse's intabulation (1553) of Josquin's Benedicta es :
1 & 2 & | 1 ... 1 & 2 & | 1 ... D4 C4. B3 A3 B3 C4 A3 G3 G3 F#3 G3 A3 G3 F#3 G3 E3 D3. C#3 C#3 B2 D3 F3 E3 D3 C3 C3 B3 A3 G2
Toft notes that the other six known intabulations of Josquin's piece use only F#, not C# also - in other words, M6-8 but m3-5, - a usage supporting the conclusion that the late medieval formula was "for the most part unfashionable" in the 16th century. 
This finding raises the question of whether Willaert's use of this idiom in his intabulations of Verdelot might reflect a trait of Willaert, or of Italian lute music or Italian music generally in the early epoch of the 16th-century madrigal, rather than a more widespread distinction between vocal and lute music in the use of accidentals.
Toft also shows how the development of each melodic line in the intabulations as well as in the original vocal writing can lead not only to such dissonances involving mi contra fa as the tritone or the diminished fourth or augmented fifth, but also to imperfect octaves involving B-fa (Bb) in one voice and B-mi (B-natural) in another. The tablatures lend corroboration to the view of such scholars as Peter Urquhart that singers often - but not necessarily always - accepted these dissonances when performing certain passages of Josquin and his contemporaries. 
In theory as in practice, opinions on these dissonant octaves varies; while Bermudo (1555) categorically excludes them - in contrast to other mi contra fa intervals such as diminished fourths - Correa (1626) takes note of their use, citing examples from Josquin and Gombert. Toft finds Correa's discussion, although "quite late," to offer "impressive documentation" on 16th-century practice, and adds an example from the counterpoint treatise of Tinctoris (1477). 
Above all, Toft focuses on "one of the most fascinating aspects of Renaissance performance practice - the flexibility which pervaded the application of unnotated sharps."  He shows that this same flexibility could also apply to the use of unnotated flats, whether to avoid a tritone or diminished fifth, or to obtain a major sixth before an octave. 
A standard approach to intabulation was to notate one part at a time, adding accidentals and then making adjustments as new parts were added. This technique, giving due weight to each melodic line, involved the same kinds of adjustments that singers might make in rehearsing the same piece. Thus Toft concludes that "instrumentalists and vocalists did work within one and the same theoretical framework," solmization being one tool in their exercise of artful discretion. 
While authors as early the 14th century report certain licenses in solmization (Section 2.5), by the late fifteenth century some shortcuts gain recognition as recommended practices from certain theorists. A notable example is the rule favored by some writers in the 16th century that a single note occurring a step above the range of a hexachord should be sung as fa, without benefit of mutation. In the case of the natural hexachord C-A, for example, this shortcut calls for a Bb inflection:
C3 D3 E3 F3 G3 A3 B[b]3 A3 G3 ... ut re mi fa sol la fa la sol
In a treatise on solmization favoring the widespread application of this rule, Gaston Allaire (1972) quotes two French theorists of the 16th century. In 1554, Maximilian Guilliaud advises :
"Whenever a note exceeds the six degree-syllables by a second, this seventh note must be called fa without making mutation into the next hexachord. This note must be sung flat even in absence of any flat sign before or above it, unless the natural sign were to affect it."
Similarly, Jean Yssandon (1582) states :
"And should the melody move beyond the la by no more than a second, we must say fa, without making any mutation."
By the epoch of Michael Praetorius, this short-cut has been distilled into a Latin adage, which he gives in his treatise of 1614-1615 :
Una nota supra la
Semper est canenda fa.
A single note above la
Should always be sung as fa.
While the adage is often quoted in discussions of solmization and accidentals, and some modern authors such as Allaire advocate its widespread application to medieval as well as Renaissance music , Robert Toft shows that even in the 16th century, a better statement of practice might be an adage like the following, which I now propose:
Una nota supra la
Saepe est canenda fa.
A single note above la
Should often be sung as fa.
Examining cadences in motets by Josquin intabulated for a solo instrument such as the lute, Toft takes note of a cadential figure in the bass line such as this :
1 & 2 & | 1 & 2 & | 1 2 & | D4, D3 F3. G3 A3 B3 A3 D3 r D3
Here the mode is D Dorian, with a cadential figure of A3-B3-A3-D3; in terms of the hexachord system, this figure and the whole phrase (starting on the second note of the example, D3) fit within the natural hexachord of C-A, except for the top tone B3 located a sixth above the final D.
As Toft remarks: "Intabulators frequently left the sixth step unaltered even though the tritone was present" ; here the melodic tritone outline F3-G3-A3-B3 illustrates this point.
Thus the rule of fa supra la might best be treated as an optional shortcut rather than an invariable law. A related license involves singing a single note located a step below a hexachord as mi :
E4 D4 C4 B3 A3 G3 F[#]3 G3 la sol fa mi re ut mi ut
This latter shortcut of singing a semitone below a hexachord without benefit of a mutation may be one case of the more general license of singing semitones rather than whole-tones at steps such as la-sol-la, sol-fa-sol, and re-ut-re. These practices, documented as early as the 14th century (Section 2.5) and accepted as standard practice by Ramos in his discussion of the semitonium subintellectum or "understood semitone" (Section 3.1), may stem in part from the frequent association of such melodic figures with cadences.
For example, let us consider again the example in Aaron (Section 3.2) of a figure suggesting a cadence on G where a singer would deduce a semitone before the final note. Here a solmization is shown in the hard hexachord (G-E) with a shortcut which might be called mi sub ut or "mi below ut"
1 2 & | 1 & 2 & | 1 & ... C4 A4 B4. A4 G4 F[#]4 G4 fa re mi re ut mi ut
While Aaron explains that such an inflection is required by the rule of counterpoint calling for the major sixth before the octave, his example (giving only this melodic line) suggests that singers would often infer such a vertical cadence from this kind of melodic figure. As Toft  states, paraphrasing Tomás de Santa María's treatise of 1565, such progressions often carry a semitone because they "look and presumably sound like cadences."
However, as Toft also shows (Section 3.3), such figures in the tablatures do not always receive a mi inflection, whether at actual cadences or elsewhere. Artful discretion with room for varying tastes seems the best statement of the rule in practice.
Another kind of shortcut  involves the singing of a melodic fourth, fifth, or octave using the same syllable for both notes. Ockeghem's Missa Mi-mi has a title relating to this practice: Each movement opens with a bass motive of E3-A2. In this composition without signature (Section 1.6), the singing of the low A2 as mi implies a hexachord not present in the usual musica recta system: F2-D3, with Bb2 as fa. In the usual gamut, A2 can be only Are in the first hexachord G3-E3, and in this first or lowest octave there is no Bb. Thus this type of shortcut can sometimes imply musica ficta hexachords "outside the hand" of Guido (Section 1.5).
It should be added that while fourths and fifths were sometimes sung in this way, with the same syllable for both notes, a more conventional solmization could also apply, as in the opening theme of a Spanish piece of around 1500 by a composer named Ponce which makes a musical play upon the first syllables of its text La mi sola :
A3 E3 G3 A3 La mi so- la
Similarly, Josquin in his motet Virgo Prudentissima sets the text electa ut sol ("as clear as the sun") with an ascending fifth G-D occurring in turn in each of the four parts to mark the syllables ut sol. 
The late 16th and early 17th centuries constitute a timespan traditionally divided into late Renaissance and early Baroque periods, with a demarcation line at around 1600; but a more recent view advanced by scholars such as Maria Rika Maniates prefers to regard the entire era of around 1540-1640 as "Manneristic."
Possibly one might speak of two musical currents in the middle to late 16th century, one seeking the full "perfection" of established Renaissance technique, and the other exploring artful distortions premised on this technique and at the same time radically transforming it. Gioseffo Zarlino (1558) and Nicola Vicentino (1555) represent these two perspectives in their treatises.
A third writer, Tomás de Santa María (1565), interestingly places great emphasis on solmization in his treatise on keyboard composition and improvisation - or, more generally, on music for keyboards, lutes or vihuelas, harps, and other instruments which can play many voices at once. While his general outlook seems closer to Zarlino than to Vicentino's radicalism, his approach to four-voice progressions in mostly note-against-note style is original and intriguing.
For Zarlino , the rule of "closest approach" is an axiom not only of art but of nature itself, and he urges that in principle a sixth expanding to an octave should always be major, and that likewise a third contracting to a unison should always be minor.
In contrast to the practice of the tablatures discussed above (Section 3.3), where minor sixths before octaves occur as one possible choice, Zarlino treats the traditional rule as a categorical imperative: "This is the nature of these consonances, and it must be noted that this nature and tendency is invariable." Composers are warned that "anything used in a manner against its nature is bound to have an unpleasant effect." 
To support his opinion, Zarlino draws on what might now be called ethnomusicological evidence :
"Nature, which has jurisdiction over everything, has so designed that not only those with musical training but the unschooled and even farmers - who sing after their own fashion, without reasoning about it - are accustomed to progress from major sixth to octave, as if nature had taught them."
Further, Zarlino specifically differs with the opinion of Gaffurius (1496) that "closest approach" progressions are called for specifically at final or sectional cadences; at all points of a composition, in Zarlino's view, progressions must be "natural to the consonances involved." 
This categorical approach may reflect his view of music as an "ordered science"  with consistent rules to guide composers. Whatever may have been true of the Italian farmers whose singing Zarlino heard, German musicians of the 1530's and 1540's evidently often sung or played a minor sixth before an octave at cadences as well as other places, a practice documented in some intabulations surveyed by Toft. 
In discussing this "German custom" , Toft quotes from the preface to a collection of pieces from various countries compiled by the brothers Paul and Bartholomeus Hessen and published in 1555, just three years before Zarlino's treatise. The two editors explain that cadential sharps are frequently indicated for foreign but not for German music, where they would be contrary to national custom. They cite as their editorial philosophy this adage :
Jedes land furt seinen eignen brauch und weise
"Each country has its own custom and manner."
Vicentino  takes what might be a characteristically Manneristic approach to the question of the minor sixth before the octave. Like Zarlino, he views this progression by stepwise contrary motion as uninviting in itself :
"When it moves by the ascending step of the whole-tone, the minor sixth makes a gloomy, listless, and harsh effect."
As an example, he gives the simple progression:
C4 D4 E3 D3
Such a progression would for Vicentino, as for Zarlino, be contrary to the usual tendency of the minor sixth, which often contracts by oblique motion to the fifth, for example:
C4 B3 E3 E3
Both theorists note the role of the melodic semitone in this m6-5 progression, which for Zarlino fits the more general paradigm of "closest approach." .
Vicentino, however, suggests that any progression may be acceptable if it aptly expresses the text :
"[T]he composer's sole obligation is to animate the words and, with harmony, to represent their passions - now harsh, now sweet, now cheerful, now sad - in accordance with their subject matter. This is why every bad leap and every poor consonance, depending on their effects, may be used to set the words."
This is precisely the view championed by Claudio Monteverdi and his brother Giulio Cesare Monteverdi in their manifesto of 1607 describing a Seconda prattica or "Second practice" favoring such expressive text setting, and founded by Cipriano de Rore (1516-1565), a composer of Vicentino's epoch. Vicentino also might be regarded as one of the early exponents of this approach. 
For Zarlino, who regards the rule of "closest approach" as a categorical imperative, many accidentals may be left unwritten. Thus the common cadence with a minor third contracting to a unison :
"May always be written on any pitch without the need of an accidental to change the whole tone to a semitone, because the voice that ascends to the final is intended to have the semitone, unless the other voice descends by the same interval."
In other words, with implied accidentals indicated in brackets:
1 2 & | 1 2 || 1 2 & | 1 2 || 1 2 & | 1 2 || F4 E4 D4 B3 A3 G3 G4 F4 E4 D4 C[#]4 D4 G3 F[#]3 G3 E4 D3 E4 2 m3 1 2 m3 1 but 2 m3 1
In each case, we have a suspension of the second with the lower voice resolving downward to the minor third, which then contracts to a unison. In the cadences on D and G, the final is approached by an ascending semitone in the lower voice, calling for an unwritten accidental. In the cadence on E, however, the upper voice naturally has a descending semitone F-E, so no accidental is called for.
Vicentino, however, like Aaron (Section 3.2), favors explicitly indicating the composer's intention by writing out these accidentals. While Aaron focuses on what might be called the "user-friendly" nature of such a notation for inexperienced performers, Vicentino emphasizes that a composer might wish specifically to avoid an expected inflection :
"The rule for cadences is that when a note has to be raised, it should be marked with a sign - sharp, flat, or natural - to prevent the many errors made by singers. When such mistakes occur in performance, they can even ruin the intent of the composer who wanted to represent harshness on a particular cadential note, which singers have raised, making the music sweet."
This passage might, among other things, refer to what Vicentino calls "diatonic" progressions such as m6-8 by stepwise contrary motion - progressions avoiding all accidental steps. (Near the end of this section, I present an example from Clemens non Papa where Vicentino's advice might arguably apply.)
Additionally, Vicentino's caution against another type of mistake suggests an anomaly that may have often arisen in 16th-century performance, at least on first reading :
"In dubious cadences it is a gross error to expand a major sixth, for it will probably become a minor seventh and create great discord."
A likely example of this "error" might arise in a situation like this:
1 2 & | 1 2 | #? A4 G4 A4 b? C4 B3 A3
In this 6-8 cadence to A, the normal expectation would be that either the singer of the lower part adds a Bb or fa inflection to produce an M6-8 progression with a descending semitone Bb3-A3, or that the singer of the upper part, instead, sings a G# or mi inflection, to produce an M6-8 progression with an ascending semitone G#4-A4:
1 2 & | 1 2 || 1 2 & | 1 A4 G4 A4 A4 G[#]4 A4 C4 B[b]4 C4 B4 7 M6 8 or 7 M6 8
However, Vicentino aptly describes what might happen if both performers decided to apply their possible semitonal inflections:
1 2 & | 1 2 | A4 G[#]4 A4 C4 B[b]3 A3 7 A6 8
Here, instead of the usual major sixth before the octave, we have an augmented sixth Bb3-G#4, an unexpected dissonance with an effect, as Vicentino notes, like that of the minor seventh. 
Presumably performers might note such collisions on first reading and make adjustments in subsequent performances. At least in theory, incidentally, cadences of the above kind with a 7-6 suspension followed by an M6-8 progression provide a possible aural cue to an expert singer of the upper part.
If the singer of the lower part chooses a Bb or fa inflection, then a suspension of the major seventh (here Bb3-A4) will result, possibly alerting the other singer that no sharp or mi inflection is needed. If the singer of the lower part leaves B unaltered, then a suspension of the minor seventh (here B3-A4) will result, signaling the other singer that a sharp is called for.
In practice, one might ask whether expert performers in fact relied on cues of this kind, and also whether there would be enough time to perceive and then react to such cues in a sight-reading situation. Aaron and Vicentino, in any event, inform us that expert as well as novice performers could arrive at results clearly not intended by the composer.
From the perspective of an interpretive practice like that documented by Toft (Section 3.3), however, such discussions raise another issue: Must the composer necessarily have one definite "intention" as to performer's accidentals? Here Vicentino's own approach is noteworthy: He sometimes indicates accidentals while noting that performers may optionally disregard them (making necessary adjustments to avoid unintended dissonances, etc.). 
While Vicentino and Zarlino may disagree on various points, they agree in noting and approving a characteristic Renaissance progression which could be viewed as a new manifestation of the traditional "closest approach" principle. As thirds approach more and more closely to stability during the 15th century, gaining acceptance in closing sonorities by around 1500, the progression by stepwise contrary motion from a diminished fifth to a major third can be seen and heard as a progression to the nearest concord.
While the tritone or diminished fifth occurs in various medieval and early Renaissance compositions, Vicentino may be one of the first theorists to describe the regular use of the d5-M3 resolution, of which he gives examples such as the following :
1 & 2 & | 1 2 || G4 F4 E4 G3 C4 B3 C4 A3 C3 D3 A3
Here the upper pair of voices from the end of the first measure to the beginning of the second progress from the B3-F4 to C4-E4, each voice ascending or descending by a semitone. Vicentino explains that "the redemption of the imperfect fifth is brought about by the progression of these two ... semitones," which "make a bad consonance sound good." 
Zarlino similarly approves the d5-M3 progression, noting that it is used by some "older" composers as well as "the best modern musicians." An anonymous French treatise (1602) quoted by Allaire, likely a reprint of a 1583 edition, more specifically mentions the use of this progression by "Josquin, Adrien [likely Willaert], and Mouton." 
Tomás de Santa María, in his treatise on composed or improvised music for keyboard or other solo polyphonic instruments, places considerable emphasis on solmization not only as a rudiment of vocal music but as a guide to instrumental practice also. For example, in demonstrating the transpositions of the modes available on a usual 12-note meantone keyboard (Eb-G#), he gives solmization syllables for each step of an octave-species or mode to show the whole-tones and semitones .
In a discussion of cadences, relevant to vocal or instrumental music, Santa María provides two useful terms for describing a contrast basic to late medieval as well as Renaissance and Manneristic music: sostenida and remissa, which might be roughly translated "sharp" and "flat."
In a sostenida cadence, typically, one voice ascends by a semitone while another descends by a whole-tone; in a remissa cadence, one voice ascends by a whole-tone while another descends by a semitone. Using solmization to illustrate these forms, Santa María notes that in a remissa cadence one of the voices moves mi-re-mi while the other concludes by descending a semitone; in a sostenida cadence, one of the voices moves fa-mi-fa while the other concludes by descending a whole-tone. He gives examples such as the following :
1 & 2 & | 1 2 || 1 & 2 & | 1 2 || A3 G3 F3 E3 E4 D4 C#4 E4 F3 E3 D3 E3 G3 F3 E3 D3 Remissa Sostenida
Like Zarlino, Santa María considers progressions such as m6-8 by stepwise contrary motion, where both voices move by a whole-tone, to be anomalous, a "defect" of style. Applying this norm in an original way to cadences for four voices, he states the rule that cadences involving "the dissonance of the eleventh" - that is, an 11-10 (or 4-3) suspension, may not be remissa: The upper voice must ascend by semitone fa-mi-fa, not a whole-tone mi-re-mi.  Such a "defect" would occur in a passage such as this:
1 & 2 & | 1 2 Bb4 A4 G4 A4 F4 E3 E3 D4 B3 A3 D3 E3 A4 11 - m10
Here the upper voice invites the solmization fa-mi-re-mi in the soft hexachord F4-D5; using this remissa formula, we find that the suspension of the eleventh between the outer voices resolves to a minor tenth, followed by a concluding motion in which the upper voice and second lowest voice progress m6-8, both moving by a whole-tone. 
Interestingly, a passage much like the above occurs in at least one version of a motet by Clemens non Papa, Vox in Rama at the word ululatus, "wailing."  One solution, in keeping with the rule of closest approach, would be to apply a mi inflection, G#4, thus obtaining an M6-8 progression but producing a melodic progression with two successive semitones, Bb4-A4-G[#]4-A4. It could be argued that this unusual progression dramatizes the text.
However, one could also argue that the solution of leaving the cadence as is, and letting the m6-8 progression stand, would have an effect which Vicentino describes as "gloomy, listless, and harsh" - precisely the kind of effect to fit the text. Possibly this solution, almost a kind of artful understatement, might be as compelling as any. If so, it could serve as an example of Vicentino's caution that performers should not add routine inflections where these would interfere with a composer's expression of the words.
The evidence of the tablatures, as amassed by Toft, at least invites the conclusion that different performers may have reached different solutions. In Germany, for example, where cadences with m6-8 are common around 1550, this reading of the Clemens cadence might be unremarkable. In Italy, it might be heard as an unusual cadence which performers might either "correct" (with a G# inflection), or leave unaltered as a striking expression of the text.
As we move into the era around 1600, writings on vocal and instrumental music continue to present solmization as a basic technique. Thus in 1597, Thomas Morley suggests that singers would have difficulty with the proper "solfa" for a piece written with a signature of two flats, and urges that such transpositions are more appropriate for use by organists seeking to accommodate the preferred pitch of an ensemble of singers. . In 1606, Giovanni Paolo Cima uses the usual solmization names for the notes on a keyboard in guiding a player through the retunings necessary to play a sample piece in the Dorian mode concluding on each of the steps of a 12-note chromatic scale.  In 1618, Fabio Colonna uses the familiar solmization syllables to demonstrate various remote transpositions of the modes on his keyboard with 31 notes per octave dividing each whole-tone into five roughly equal steps. 
During the Renaissance and Manneristic eras, then, solmization remained a standard rudiment of music and also a musical map having various applications. At the same time, authors described shortcuts and simplifications giving the system a different character than during its "classic" medieval era. The tendency during the late 16th and early 17th centuries to specify more accidentals explicitly may reflect a similar trend.
To Section 4 - Alternative solmizations: Ramos, Lippius, and beyond.
To Table of Contents.Margo Schulter