“Mode versus Ficta” in context

[1]“Hinc falso sunt arbitrati qui consonantiam et harmoniam idem esse posuerunt. Nam quanquam harmonia consonantia est: omnis tamen consonantia non facit harmoniam.”⁽⁵⁾

[2] My initial misgiving about Margaret Bent’s realization of a passage from Josquin’s Ave Maria⁽⁶⁾ created a wide-ranging discussion in MTO-Talk lasting for several weeks. Since the publication of Bent’s Commentary upon that article in MTO 2.6, however, this discussion seems to have become moribund. Interest has shifted away from the original focus towards intonation. This is in one sense welcome, but in another sense a disappointment. While it is interesting to see arguments concerning the possibilities of tuning one note against another (and these have produced informative and provocative results), the disappointment is that we have inadvertently moved away from the much more crucial arguments about which actual notes need to be selected prior to deciding upon the question of their relative intonations. This essay will therefore attempt to push the discussion back to the original focus.

[3] Readers will recall that, following Bent’s final words, the position arrived at by the time of publication of MTO 2.6 was roughly as follows:

1. I had, it seemed, made a serious mistake in attempting to link ficta considerations with mode, since in theoretical works “mode” and “ficta” follow separate theoretical tracks (Judd);

2. An attempt to review early theorists’ written views on the music of their time can be regarded as simplistic and futile, (at least when their view is retrospective). This is especially so in the case of Glarean who (in relation to Josquin) must be disqualified on the grounds of chronology (Bent). Also theorists like Glarean are unreliable as “witnesses” since they had their own agendas to pursue (Judd);

3. Some theorists are, however, more credible because these agendas propagated—in the case of Hothby, Tinctoris and others—counterpoint rules which it can be seen that composers of the time generally followed (Bent);

4. “Mode” was nothing more than a means of classifying melodies arrived at externally by later writers, and was not demonstrably part of the actual polyphonic composer’s modus operandi (since his concerns were with two-voice counterpoint and its correct vertical combinations) (Judd, Bent). Further, since “mode” was not part of the composer’s mind (which was more occupied with the principles of counterpoint and consonance treatment), modern editions can remain consistent with it, no matter how their horizontal and vertical euphonies are “logically” realized, (i.e. by two-voice counterpoint rules) provided they do not violate the pragmatic melodic prescriptions of later writers (vocal range, last note of tenor etc.) (Judd, Bent);

5. In evaluating textures of three or more voices, the rules of consonance that must be applied are those that theorists prescribed for two-voice counterpoint. This is explained by the assumption that larger textures are reduceable to (sometimes overlapping) pairs of “primary voices.” (Bent) There is, apparently, no set of principles that enables us to differentiate between two-voice contrapuntal considerations and (more than two-voice) harmonic concepts, other than those that arise from dyadic harmonic thinking.

[4] Although these are the main areas of concern to this essay, there are other minor ones including pitch conceptualization. While this too will emerge from some of the material considered, many other details will have to be omitted as focal points.⁽⁷⁾ I hope to avert some of the “surface” problems I ran into previously: I will avoid using words like “tonality” (which opens up the charge of anachronistic thinking); I will not push further with Glarean (for similar reasons⁽⁸⁾); I shall also extract with greater care from the writings of others.⁽⁹⁾

[5] The first pressing line of enquiry—and one which only seeks to explore a possible theoretical relationship between “mode” and “ficta”—must be the theoretical and practical status of mode within the context of the later fifteenth century. It has been rightly urged by Powers⁽¹⁰⁾ that a careful attempt must be made to delineate between later categorizations and the compositional process itself. Only by establishing prima facie evidence to show that composers worked consciously within a modal framework can “mode” as such bear upon the argument. It does not need necessarily to be established that music was generally composed “in” modes as such, but merely that the horizontal and vertical euphonies through which their music was shaped and articulated had a modal basis.⁽¹¹⁾ That some music was at this time composed “in” particular modes is undeniable, especially where the titles indicate this.⁽¹²⁾ But do these compositions stand apart from the rest, and are those without a designated modal title “freely” composed? If so, ought we to expect that the harmonic idiom of the “modal” pieces would be essentially different, more “conservative,” less “experimental”? The answer can come only partly from the music itself (as we have already seen from the differing views on the Josquin Ave Maria example). If music of this age is in its concept essentially “modal,” then how is it? Does this affect only the vocal range, or the final cadence, or does it even percolate through into the ongoing melodic and harmonic infrastructure? If it does, how will this affect (if at all) the choice of recta and ficta (both of which can have long-term as well as short-term effects upon that euphony)? So this question has to be addressed before further progress is possible.

[6] Tinctoris, through his counterpoint rules, must stand as one of the most prominent and credible authorities furthering our understanding of fifteenth century musical composition. No account of music of this time can be contemplated without regard to his comprehensive writings. He may well provide not only an important insight into modal thought of the time, but also bring these concepts and practices into close juxtaposition with the very issues of recta and ficta that lie at the heart of the present debate. Did composed music have a modal basis? If so then how were views on recta and ficta use affected?

[7] In his Liber de natura et proprietate tonorum⁽¹³⁾ (dated 1476) Tinctoris described and named, in Chapter 1, the eight modes.⁽¹⁴⁾ He concluded the chapter by explaining how these were grouped into the four categories Protus, Deuterus, Tritus and Tetrardus. In order to allay any fear that this book would be interpreted as yet another account of ecclesiastical chant and its perceived modal categories, his final sentence in Chapter 1 reads as follow:

“Hii autem sunt octo toni, quibus non tantum in cantu gregoriano qui simplex est et planus, verum et in omni alio cantu figurato et composito utimur, circa hoc in libello nostra fert intentio.”

[These however are the eight modes, which we use not merely in Gregorian Chant which is simple and plain, but also in all other figured and composed songs, about which is our purpose in this booklet.]

[8] I will not attempt to do more than give a brief overview of this work, highlighting significant details. (And I am fully aware of the dangers of viewing only the “surface,” having already been censured by Judd and Bent for this very shortcoming). But it must be understood that Tinctoris, throughout, is primarily concerned with modal usage in composed music.⁽¹⁵⁾ His writing is both prescriptive and descriptive, and his profuse examples (as in other works) are expressly focussed upon the specific technical points in question.

[9] His definition of mode (“tonus”) at the beginning of chapter 1 (which is reiterated at other points, and ultimately shapes the structural presentation of chapters 19 to 49) is short and sweet:

“Tonus itaque nihil aliud est quam modus per quem principium, medium et finis cuiuslibet cantus ordinatur.”

[“Mode accordingly is nothing other than the manner by which the beginning, middle and end of any song whatsoever is arranged.”

In other words, whatever the mode, its articulation (and hence the music’s) arises through its definition at the beginning of a piece, its continuity throughout that piece (determined by its vocal range and order of tones and semitones), and ultimately its final close at the end.⁽¹⁶⁾

[10] In describing each mode, Tinctoris adopts a clinical method of classifying diapente and diatesseron usage. Not only does this avoid tying too closely each class with a “white note scalar” form (hence assuming that the system is fully transposable), but it also provides a simple platform for discussing “mixed” modes.⁽¹⁷⁾

[11] Of particular interest is his comparatively lengthy discussion of the structure of modes 5 and 6 (chapters 7 and 8) where the tritone which arises from the third-species diapente (e.g. F–B) poses an issue. But having touched upon this, he goes on to state:

“Notandum autem quod non solum in hiis duobus tonis tritonus est evitandus, sed etiam in omnibus aliis.”

[Note, however, that the tritone is avoided not only in these two modes but also in all the others.]

Following written examples in all eight modes, Tinctoris extends his observation to all the irregular modes:

“Denique sciendum quod non solum in tonis regularibus et vera musica secundum exempla praemissa tritonum praedictis modis fugere ac eo uti debemus, verum etiam in irregularibus tonis et musica ficta.”

[Finally, the understanding is that we remove the tritone and its use not only from the regular modes and musica vera according to the previous examples in the aforesaid manner, (but) truly also from the irregular modes and musica ficta.]⁽¹⁸⁾

[12] Modes 5 and 6, as noted above, involve some discussion of the tritone and diminished fifth. In none of the examples he gives is ficta as such an issue because changes occur through recta means (the lowest B♭ is not involved). He does, however, state (Chapter 8):

“Praeterea uterque istorum duorum tonorum formari potest ex quarta specie diapente quod, nisi exigente necessitate, fieri minime debet.”

[Further, it is possible to form either of these two modes from the fourth species of diapente, something which should be done as little as possible and only through pressing necessity.]

This means that when the B♭ is necessarily introduced (to eliminate the tritone), it should only be done for this express purpose.⁽¹⁹⁾

[13] Ficta and Mode are sometimes regarded as very closely interlocked, the one explaining the appearance of the other. Thus, in Chapter 18, Tinctoris does not explaina ficta use of low B♭ in a protus context as having been arrived primarily by the addition of ficta, but rather by the mixing of modes. His two-voice example, where two notes in the lower voice are flattened in order to avoid “fa contra mi” combinations with the upper voice, is preceded by this caution:

“Ultra scire debemus quod toni commixtio interdum fit necessitate et interdum voluntate, necessitate quidem ne fa contra mi in concordantia perfecte fiat.”

[Additionally, we should note that a mixing of modes is made, sometimes through necessity and sometimes through choice; by necessity so that fa will not occur against mi in a perfect concordance.]

However, the explanation which follows the example states that this change of mode is the result of ficta application:

“Namque contrapunctus iste est secundi toni quarto commixti, eo quod per illud fa in ♯ mi fictum et contra fa F fa ut gravis positum concreatur secunda species diatesseron quarto tono, ut praevidimus, specificata.”

[“Now this counterpoint is of mode 1 mixed with mode 4 because, by having changed ♯ mi to ficta fa against fa of low F fa ut, the second type of diatesseron, specified for mode 4, is created as we have seen above.”]⁽²⁰⁾

[14] Tinctoris has therefore deemed there to have been a change (or at least a mixing) of mode which, because of the need to avoid the tritone, has created a modal transformation via the application of ficta.⁽²¹⁾

[15] But perhaps his next sentences are the most telling(?):

“Voluntate vero fit toni commixtio sive in simplici sive in composito cantu, quando, praefata necessitate cessanti, compositor ea uti voluerit, debetattamen accuratissime cavere quomodo eam ordinet. Nihil enim est quod cantus distonitos efficiat quam commixtio ipsa si fuerit inordinata.”

[The mixing of modes can certainly be made by choice, whether in simple or composed song, when—the aforesaid necessity having ceased—the composer might have wished to use it; he should nevertheless take extreme care over the manner in which he arranges it. For there is nothing to make songs go more out of the mode than this mixing were it to have been ill-arranged.] ⁽²²⁾

[16] I hope that the above very brief surface view of Tinctoris at least conveys the following important points: a) modal thinking and evaluation may have become part of the later fifteenth-century counterpoint theorist’s concern, b) recta and ficta usage may not only have been conceived with regard to the hand (which device enabled them to be effectively applied in practice) but also with regard to modal thought and expression, and c) by this time “ficta” and “mode” may have been brought closer together as theoretical companions.

[17] Leaving aside the question of mode for the present, another issue to examine (before we look at actual musical examples) is the question of counterpoint. Margaret Bent⁽²³⁾ stated unambiguously what she meant by the term “counterpoint”: “Counterpoint, as defined in DF from Tinctoris and earlier theorists, is concerned not with lines or vague general attributes but with two-voice progressions—what we might call two-part or dyadic harmony.” It was this view, pursued with perfect logic, that shaped her proposal for the Josquin Ave Maria passage, this view being articulated again in her recent Commentary:⁽²⁴⁾ In the disputed measures, he gives us not just one text-book sequential “cliche” chain of fifths and sixths, but two superimposed contrapuntal pairs, discant and tenor, tenor and bass both of which (not just the upper pair, pace Wibberley) have claims to perfection and place constraints on the other.⁽²⁵⁾ My problem with this explanation is the assumption that an essentially three-voice structure should be comprised of “two superimposed contrapuntal pairs.” The describing of counterpoint as “dyadic harmony” is certainly appropriate for the earlier fifteenth century (and before), but I question its exclusive application to music of the Josquin period.

[18] The quotation at the head of this essay, from Gaffurius, draws a rather clearer distinction between two-voice and three-voice textures, and may be reiterated:

“Hinc falso sunt arbitrati qui consonantiam et harmoniam idem esse posuerunt. Nam quanquam harmonia consonantia est: omnis tamen consonantia non facit harmoniam. Consonantia namque ex acuto et gravi generatur sono: Harmoniam vero ex acuto et graui conficiunt atque medio”

[Hence falsly judged are those who lay down that consonance and harmony are the same. For although harmony is consonance, all consonance does not however produce harmony. The reason is that consonance produces high and low sound: but Harmony brings about high and low as well as middle.]

[19] This different perspective on “harmony” ultimately marks the dividing line between Bent’s view (and its musical realization) and mine, and we may simply have to differ. Her discussion in [22] further emphasized this difference. She prefers (for perfectly clear reasons) to explain:

F E
B C
D C

as “. . .the primary contrapuntal cadence, the sixth to octave between the lower parts, has an added part above.” My explanation (as she notes) would be that the diminished fifth between the upper parts is supported from below. Her view is primarily “contrapuntal” wherein the harmony is dyadic (the lower two voices bearing the “primary pair”); my view is that the harmony is triadic, within which three-voice counterpoint (with appropriate voice-leading) occurs. Further, in her [26] she took issue with my (in retrospect rather uninformative) discussion of acoustics which she dismissed as being “on a separate track (again!).” Her assumption that my introduction of an acoustic element “confuses the issue,” and that my suggestion that it provides a reason for admitting the fourth as a consonance within the contrapuntal texture indicates that I have “to labour to do so,” is entirely consistent with her dyadic view of counterpoint. It is (and she is perfectly correct) a routinely simple matter to view:

f♯ g
c♯ d
a G

as a two-voice progression with an added voice in the middle (which forms its own fifth). Indeed, that is how I would describe her example (above), which could have been taken from virtually any polyphonic composition from the 13th to the early 15th century. But it does not seem to me to be a very characteristic kind of cadential formula for music of the Josquin period!

[20] Gaffurius seems to me to provide a much more clinical harmonic reason for admitting the fourth as a consonance—and one that is not in any way dependent upon the rules of two-voice counterpoint:

“Sit itaque grauissima chorda Proslambanomenos ac maior numerus .9216. Acutissima Mese et minor numerus .4608. Hae inuicem dupla dimensione diapason consonantiam sonat. His hypaten meson mediam interpono .6144. numero signatam. Hi enim ita dispositi sunt termini: ut quam extremi inuivem proportionem faciunt scilicet .9216. ad .4608. eam ipsam probet differentia maioris et medii: ad differentiam medii et parvissimi. Numerorum autem .9216. et .6144. differentia est numerus .3072. sed numerorum 6144 et 4608 differentiam facit numerus .1536. Quod quum huiusmodi differentias inuivem comparaueris uidelicet .3072. ad 1536. proportionem duplam ita conspicies: quemadmodum extremi termini scilicet .9216. ad .4608. efficere compraehenduntur.”⁽²⁶⁾

A simple paraphrase-translation (substituting for classical names the notes of the gamut) is:

“A re has a value of 9216; a re la mi has a value of 4608. They sound a consonance because the higher number is double the lower, and they have a ratio of 2:1 (and are therefore an octave apart). If the note E la mi (with a value of 6144) is placed in between, the difference between the lower two notes is twice that between the upper two notes: 9216-6144=3072; 6144-4608=1536. The ratio between 3072 and 1536 is thus also 2:1 (the same as the octave).”

[21] This is only one of a whole plethora of carefully analysed “harmonic combinations” yielding consonance offered by Gaffurius, with similar explanations. In other words, fundamental to the harmonic evaluation is the mathematical relationships of the upper parts of the texture to the lower (of which the lowest-sounding note is paramount).⁽²⁷⁾

[22] None of the evaluations here offered by Gaffurius even hints at, let alone depends upon, contrapuntal processes (not even dyadic ones). (This is hardly surprising in view of the title of the work.) Counterpoint certainly does explain how sound-combinations are arrived at the way they are, but it does not (in my view) explain why, at the point of arrival, the effect is what it is. On the other hand, “the effect being what it is” does explain why counterpoint theory ended up being what it was.

[23] When counterpoint theory alone (particularly two-voice) is viewed as the primary controlling agent of euphony and consonance, analyses such as the above may well seem to be “on a different track.” But even if some earlier theorists had not systematically analysed the physical properties of their sounds quite in this way (presumably because their own system did not yet require it), it is evident that musicians of the later fifteenth century had begun to do so. It is the only explanation to account for a) the increasing tendency for composers like Josquin apparently to “break” so many of the previously-accepted counterpoint rules (see below), and b) a growing number of apparently insoluble difficulties in counterpoint treatment (of the kind addressed in Ave Maria) which Bent’s ficta thesis has done so much to unravel and illuminate.⁽²⁸⁾

[24] Tying arguments together, and moving towards a musical example, I would like to consider how modal constraints upon ficta, and also ficta constraints upon mode might interact.⁽²⁹⁾

MODAL CONSTRAINTS UPON FICTA

[25] Proposition (Tinctoris): “The mixing of modes can certainly be made by choice, whether in simple or composed song, when—the aforesaid necessity having ceased—the composer might have wished to use it; he should nevertheless take extreme care over the manner in which he arranges it. For there is nothing to make songs go more out of the mode than this mixing were it to have been ill-arranged.”⁽³⁰⁾

[26] Josquin’s motet written upon the death of Ockeghem (Nymphes des bois, which could for obvious reasons not have been composed prior to Gaffurius’ Practica Musicae) provides a number of points of interest relating to mode.⁽³¹⁾ The opening of section 2 (see Example 1) is the only point where the cantus firmus is absent, leaving the remaining four voices to sing alone. Interestingly, here again we find what Bent calls a “text book” version of the standard progression leading through a sequence of sixths and fifths, again involving three voices. Bent will obviously view this passage as another case where an upper primary pair is superimposed upon a lower. As if to confirm her view, this source strategically places a flat in front of the “offending” E in voice 3. An insuperable problem is, thereby, brought into being which—for reasons to be offered—could have easily been averted had the more obvious solution been chosen.

[27] This short passage has to be repeated, and it is difficult to think of cadencing upon any other degree than that indicated by the (relative) notation. The insertion of the flat certainly perfects the interval with the highest voice, but it simply cannot be followed (unlike the passage in Ave Maria) by a flat in the lowest voice: the required cadence position would otherwise be unattainable, and the phrase is simply not long enough to establish another “more suitable” cadence degree. Additionally, the cadence has to form a link back to the starting point. The only solution would seem to be for the singer of voice 2 to descend on the next beat to E♮ (a major semitone higher than the flattened note), and for the lowest voice simultaneously to ascend to A♮ (forming a perfect consonance—yes—with voice 2, but—more crucially—also a diminished-fifth relationship with the previous flattened E). A more obvious, and less cumbersome way through this would surely have been for the singer of voice 1 to descend to recta B, thereby allowing a consonance to be formed below on recta E.

[28] This may perhaps be an example of what Tinctoris might call “cantus distonitos” [out-of-mode song], by virtue of the overuse of coniuncte effecting the euphony. The immediate crisis faces two other innocent voices who would seem to be compelled to maintain their own linear euphony (within their own modal contraints) despite compelling solicitations from the E♭ to the contrary. The crucial point, however, is that the requirements of euphony must override the perceived requirements of counterpoint (just as they must for the perceived notation of the Tenor voice). Such euphony has little to do with a conceptual view of recta or ficta (which are concerned with interval-perfection), but everything to do with a practical conceptualization of mode (and its purely melodic integrity). Here, the “mixing of modes” (Tinctoris) leading to ficta adjustment, might seem to yield a poorer result than such “mixing” leading to recta use.⁽³²⁾

[29] It is also possible—although obviously not within a dyadic view of the harmony—to accept the sound of the upper diminished fifth! This is because when harmony is partially liberated from the constraints of two-voice counterpoint, textural considerations can (and often do—see below) invite composers to voice-lead with more freedom. Migration of the contrapuntal “line” between differing voices of the texture (“vocal interchange”) frequently accounts for what would initially seem to be a casual attitude to counterpoint: even though the parts may not look as they should, they still may sound acceptable within their context. In the present example, the E in voice 3 (measure 7) is taken over by voice 2, ultimately to move up to the F. The B♭ in voice 1 (measure 7) eventually falls to the A, although its initial rise to C could be explained (outside the principles of two-voice counterpoint of course) as a result of the movement upwards by the bass whose A also takes over the line. (As in Ave Maria, the thematic and sequential movement of the melodies can possibly be said to have taken priority here in both cases.)

FICTA IMPOSITION UPON MODE

[30] “Ficta imposition upon mode” was the substance of my view of the Josquin passage previously examined.⁽³³⁾ Ave Maria, however, is not perhaps the best example through which to articulate my misgivings over such realizations.⁽³⁴⁾ I will examine what I consider to be a much better instance.

[31] Josquin’s motet Absalom fili mi was introduced (by me) into the mto-talk discussion, and some of my comments on that piece were taken up by Bent.⁽³⁵⁾ I would like to consider a passage beginning at measure 16, which again presents the by-now familiar chain of 6-5 progressions (see Example 2).

[32] In the tenor voice, the last note of measure 18 produces a “mi contra fa” with voice 1. The vertical layout can be represented as follows:

A♭
D
F

which, according to Bent’s views on two-voice counterpoint and dyadic harmony is acceptable provided that the lower two voices are the “primary pair,” and the contrapuntal movement (sixth to octave) which follows would lead to the following scenario:

A♭ G
D E♭
F E♭

This, however, does not occur, and the following reality exists:

A♭ G
D D
F G

[33] Even if it were conceded that the tenor eventually does rise to the E♭, voice 4 does not fall. It seems that there are two alternative positions: a) that the “normal” two-voice principles must nonetheless be adhered to, and b) that here is evidence of a harmonic concept that is not dyadic at all, but rather triadic. Both can lead to quite different results.

[34] Taking first the dyadic viewpoint, this would seem to present a situation comparable with the extract from Ave Maria. The 5-6 progressions with the highest voice (these two therefore constituting the upper “primary pair”) are superimposed over another similar 5-6 chain between the lower two voices (which are the lower “primary pair”). Since (as Bent points out [22]) these “two primary and non-cadential progressions are superimposed, and the upper part therefore cannot be treated as subsidiary,” this must require the use of fictive adjustment in order to produce the required consonances (see Example 3). There would be no alternative therefore but to flatten the D. This would, however, bring into being a chain reaction, calling for G♭, then C♭, then F♭, and finally B♭♭.

[35] This version has, I believe, some very crucial shortcomings, despite its firm adherence to two-voice principles: i) in only 6 measures, the pitch will have dropped a complete semitone (original euphonies will be restored as early as measure 24, but a semitone lower in pitch);⁽³⁶⁾ ii) the entries of the upper two voices at measure 21 will have undergone a complete change of mode (within the terms of reference of Tinctoris) whereby—despite the fact that structurally they are a restatement of the opening motif—the order of tones and semitones has been changed; and iii) there will be an unavoidable melodic tritone in voice 3 in measures 22–3. These three pieces of silver mark the price that would have to be paid in order to avoid a single vertical diminished fifth (measure 19) for which there seems to be no “acceptable” explanation! The rules of two-voice counterpoint are clear and unambiguous: under no conditions can this vertical diminished fifth be left without adjustment in the counterpoint thus presented! Let us look, therefore, for other rules and explanations.

[36] An alternative view is that the diminished fifth and its bass support are acceptable as they stand.⁽³⁷⁾ If so, it will not be because of the rules of two-voice counterpoint, but despite them. In triadic terms, the movement of the three voices together with their vertical combinations is perfectly logical: the outer voices converge on to G while the Tenor continues its syncopated ascent becoming (at the end of measure 20) the upper of two primary voices (the only two sounding).

[37] Another manifestation of triadic thinking can, I believe, be found at the end of Example 2, in measures 28–9. Here the Tenor voice indulges in what is—by dyadic principles—a dubious piece of voice-leading: the A♭, which forms the lower note of a tritone, rises to B♭ on the next chord. The explanation is not that a ficta A♮ should have been applied,⁽³⁸⁾ but rather that for textural reasons the move upwards instead of downwards is more satisfactory.⁽³⁹⁾

[38] I am not proposing in this essay that two-voice counterpoint theories and practices have become outdated; they clearly apply in many instances, especially where textures are thin. But I am suggesting that there is both theoretical and practical evidence to show that musicians were becoming conscious of other methods of contrapuntal and harmonic thought which may have had a bearing upon this repertory. In this regard, to continue a rigourous and unyielding application of concepts designed originally for two voices, in which a second added voice merely satisfies the requirements of successive vertical perfection against the given and unchangeable Tenor (other voices being merely accompanimental), may create a greater distortion of the later fifteenth-century composer’s intention than is either desirable or indeed necessary. This may become further exacerbated when some (like Josquin) provide compositions of four or five vocal lines. Texture, voicing and imitation now yield further constraints upon the unfolding of the counterpoint, and upon the linear movement of the euphony.

[39] There are many rip-cords by which we can extend our understanding and awareness. As each is withdrawn, the hope is that our parachute of enquiry will offer a smooth and meaningful descent towards the firmer ground of experience and knowledge. We may not always judge with accuracy the atmospheric turbulence provided by differing views on historical documents as we plunge into the unknown, and we may also misjudge the ideal or “correct” moment to bring our free-fall to a steady halt when noting something that is perceived (perhaps even mistakenly) to be worthy of comment or enquiry. But we can only start from where we are, and proceed to where we judge our destination to lie. Within our quest for greater insight into music of the past, Margaret Bent’s contribution is of seminal importance in helping us to understand not only where we are, but also where we have to go.

Roger Wibberley
Goldsmiths University of London
Department of Music
Lewisham Way
London SE14 6NW
England
mua01rw@gold.ac.uk

Footnotes

1. Roger Wibberley, “Josquin’s Ave Maria: Ficta versus Mode.” Music Theory Online 2.5 (1996).
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2. Margaret Bent,“Diatonic ficta revisited: Josquin’s Ave Maria in Context,” Music Theory Online 2.6 (1996). [Hereinafter referred to as DF(2).]
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3. Cristle Collins Judd, “Wibberly, MTO 2.5” mto-talk (23/7/96).
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4. Margaret Bent, “Diatonic ficta,” Early Music History 4 (1984), 1–48. [Henceforward DF]. In this essay, I shall be dropping the adjective “diatonic.” It was initially an important means of countering Lowinsky’s notion of “chromaticism.” If was purely diatonic, however, the adjective leads to tautology; if it was not, then it may lead to inaccuracy.
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5. Gaffurius, De Harmonia Musicorum, III, Chapter 10 (Milan 1518).
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6. DF.
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7. In particular, I will not be addressing most of the comments and questions posed by Bent in [23] and [24] largely because I consider them to have been rhetorical. I would, however, like to take the opportunity of answering here one of her questions in [23] concerning Glarean where she asks “Does Wibberley not distinguish between subsequent comment and classification on the one hand, and what could have been in the composer’s mind, on the other?” My initial reaction can be likened to that of a first-year undergraduate who—having imparted to his tutor the news of his discovery of an astonishing example of ficta use in Josquin’s Ave Maria (beginning at bar 48), citing Margaret Bent’s authority—is soundly rebuked for not having distinguished the composer’s mind from that of a subsequent commentator. I then realized that the correspondence cited by Bent was incomplete and out of chronology. The point I made about the Josquin motet being Hypoionian answered a different mto-talk question, and merely affirmed that Glarean—who invented the category—ought to be able to recognize a motet that fulfilled his criteria. More importantly, my point about his description being concerned with the way the composer had composed the music rather than about the way others might have performed it replied to yet another mto-talk comment (again not cited by Bent) which suggested that Glareanus might equally have been commenting upon his own view of a performance. (I feel uneasy about the citing of mto-talk comments—which are often informal exchanges—in this way as a means of constructing a formalized case against another person’s views and credibility, especially when they are quoted out of their proper contexts. This is one way, surely, to discourage people from contributing to mto-talk!)
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8. Let us not, incidentally, forget that Glarean’s first three decades overlapped with Josquin’s last three. We might also bear in mind that Glarean spent about 20 years planning his Dodecachordon, and that it was completed by 1539—eight years before publication. This should be viewed against assertions like “It is indeed a big leap to go from a subsequent theorist (especially Glarean) with his own axe to grind to make the assumption that because this was in his mind it must have been in Josquin’s more than 50 years earlier.” (Bent [23])
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9. I had no wish or reason intentionally to misrepresent the work of Bent or others, let alone to do so “discourteously” (Bent, ftn. 26). That it came over that way is something I regret, and it arose more from the complexity of the material (both old and new) than any attempt wilfully to extrapolate bits and pieces from their own context.
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10. Harold Powers, “Tonal Types and Modal Categories,” JAMS 34, no. 3 (1981), 428.
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11. In a similar manner, Schoenberg’s Fourth Quartet may not on first hearing betray the hexachordal design underlying its construction, but few would doubt that its harmonic idiom arises from serial processes.
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12. Such as Josquin’s Missa L’Homme Arme Sexti Toni, or even Ockeghem’s Missa Cuiusvis Toni. No assumption is here made that the composers saw the mode concerned as being anything other than a structural artifice (e.g. the ordering of tones and semitones, together with the range of the Tenor). I am merely concerned at this point to differentiate between what later observers deduced and what actual composers planned and executed.
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13. Corpus Scriptorum de Musica, XXII/1 (1975), 65–104. Also available, using this text, on the Internet at: “gopher://IUBVM.UCS.INDIANA.EDU:70/00/tml/15th/tinldn.text.” English translation by Albert Seay, “Johannes Tinctoris: Concerning the Nature and Property of Tones,” Colorado College Music Press,Translations: Number Two (Colorado Springs, 1976).
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14. The name theorists give to mode is “tonus.” “Modus” is used in the traditional manner for describing rhythm and note-duration. I am therefore attaching no more to this term “tonus” than I would to the terms “melody” or “tune.” My interest is only in the ways in which composers organized their “tunes” in counterpoint, and what precepts they felt should, if at all, be applied additionally to those prescribed by counterpoint rules. I must also correct a misleading aspect of my article (MTO 2.5) for which I was rightly censured both by Judd and Bent. I do not consider the use of mode in itself to be the equivalent of a tonal system. I shall henceforward use the term “euphony” (which I hope is not so stereotyped), but I need to clarify that my use of the term “tonality” was only intended to convey the harmonic result of combining modally-conceived lines. I did not mean to impute to composers a preconceived “modal(=‘tonal’)” harmonic framework as a canvass for the delivery of counterpoint.
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15. Although this is his declared main concern, he does cite examples from chant at times when he is discussing modal assignations. Also, as has been noted in the past, only five of his ninety or so examples employ more than a single voice. Nonetheless, these melodies are mostly newly-composed for the purpose and show—on a small scale befitting their theoretical utility—the way in which the principles outlined are to be applied and perceived. Harold Powers (“Tonal Types. . .”, 432) mentions this work, doubting its application to then current polyphony. I would again stress that my only motive for citing passages here is to explore possible theoretical connections between “ficta” and “mode.” It is certainly not to construct a view of mode in any other way; neither is it intended to counter the views of Powers (or anybody else) with regard to the work’s authority.
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16. Chapters 19–49 are concerned with a discussion of Beginning, Middle and End. Of these chapters, Beginning is covered simply in a single chapter (19), while End requires six chapters (44–49). By contrast, however, Middle extends from chapters 20 to 43. These develop to the maximum all the possible admixtures and permutations of modes that are possible during the actual course of a composition. This section deals not only with mixed modal categories, but also with ambitus. End, however, is treated more fully than Beginning since irregular endings are discussed in some detail, including those where moves within and without the hand (gamut) via both recta and ficta are discussed and exemplified.
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17. For example, when mode 1 is mixed with mode 7 (primo septimo commixtus), as discussed in chapter 13, it uses the fourth-species diapente with the first-species diatesseron.
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18. This is one of numerous instances in Tinctoris (for others, see ftn 15) implying a conceptual link between Mode and Ficta, and Tinctoris brings them into close juxtaposition on other occasions in this work.
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19. The use of the Bb temporarily transforms the mode from tritus to tetrardus, and its presumed cancellation—when the necessity has disappeared—restores the mode to its proper species. This Tinctoris considers to be important.
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20. The two concepts are brought into the same evaluation.Ficta arises through the need for contrapuntal consonance (i.e. B♭–F), but the resulting melody is now explained as being a mixing of modes (by diatessaron substitution). The word “counterpoint” refers specifically to the lower voice which, in the example, is marked “Contrapunctus.” This lower voice uses a range of A–a, and ends on D, being in mode 2. When temporarily converted through this B♭ from protus to tritus, it is regarded that the plagal form will still operate (i.e. mode 4).
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21. Earlier in Chapter 8, Tinctoris stated that modes 5 and 6 could use the fourth species of diatesseron, but that this should be done as little as possible, and only because of unavoidable necessity (“. . .nisi exigente necessitate, fieri minime debet”). While it was generally assumed that these modes admitted the Bb as a normal means of melodic adjustment, for Tinctoris this was explained as a “mixing” of modes. While, therefore, the contrapuntal need for ficta has placed contraints upon the mode (because of the incipient tritone), it is also true that the resultant mixing of modes 2 and 4 (which explains how the melody has been changed) in turn has (for Tinctoris) brought constraints to bear upon the application of ficta (since ficta here is explained as a mixing of modes). Ficta and Mode are therefore (at least to Tinctoris) bound together within his evaluation.
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22. Since Tinctoris speaks of the songs rather than their performance, I interpret this as an observation of the manner in which unusual or excessive voluntary (as opposed to normal or moderate necessary) mixing of modes can effect the (at least melodic) euphony of the music. (A similar rule was advanced by Tinctoris the following year as his fifth rule of counterpoint.) If my interpretation is correct, this might echo Margaret Bent’s point at the end of her [25] when she states “Wibberley and others think that my Josquin example takes the application of the rules too far for practical purposes, and I might even agree with them, but they (and I) have yet to define precisely at what point and why &ssquo;the accepted rules of consonance’ become unacceptable. Does Wibberley have a view on this?” She also stated in [21] “. . .that there can be an ideal solution but no perfect solution makes it very difficult to define how far is too far, now that we have removed anachronistic tonal harmony, simplistic modal restraints, and, I hope, the misapplication of modern notation as defaults.” What is possibly implied here by Tinctoris is that he may have had a view on this. We may not quite know what that view amounted to in practical terms, but since the mixing of modes outlined in his statement was concerned with consonance treatment (as a “necessity”) it may not be inappropriate to infer also that further “voluntary” uses of mixed modal types were for a similar purpose. His possible caution, however, suggests that there may have been a point beyond which the music, in his opinion, may have suffered (“cantus distonitos”). Tintoris is not discussing what could be described by Bent’s phrase “simplistic modal restraints” because the modal system being outlined is both sophisticated and complex.
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23. DF(2), [3].
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24. DF(2), [19].
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25. I was not claiming perfection for the upper pair, as evidenced by my proposal for e-natural in the middle voice. If my argument suggested otherwise, it was poorly explained.
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26. De harmonia musicorum instrumentorum, III, Chapter 11. [The complete text, together with graphics, is available on the internet at: “gopher://IUBVM.UCS.INDIANA.EDU:70/11/tml/16th”.] The classical note names, together with their numeric values, are also to be found in the hexachord table at the beginning of Gaffurius’ Practica Musicae (published in 1496, only a few months prior to Ockeghem’s death). In this latter work, Book III, Gaffurius gives a traditional survey of counterpoint with musical examples. Although the two-voice examples are explained in two-voice terms (where the harmonic result is dyadic), he moves on to examples of three- and four-voice counterpoint where his discussion is not limited to dyadic terms of reference. In particular, the four-voice examples are discussed in terms of texture and spacing. It is true that he often discusses the disposition of voices in relation to the Tenor voice (sometimes all the voices are dicussed in this way), but at other times he does not. Neither does he have a purely dyadic view of “harmony,” and he eventually went on to state, as has been demonstrated, a clear difference of view between (two-voice) “consonance,” and (more-than-two-voice) “harmony.”
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27. This was what I originally meant by the term “acoustic parameters,” though the descriptive methodology of Gaffurius is infinitely better formulated. His evaluations (and calculations) seem to me evidence of triadic harmonic thinking. Dyadic harmony, realized through two-voice counterpoint, is (as Bent clearly demonstrates) evinced in three voices by a two-voice progression to which an accompanying voice is added. When the “consonant fourth” occurs therefore, it is only accompanimental to the “primary pair” (Bent) and does not have to be evaluated as a consonance with its own diatesseron. As long as it forms a consonance (diapente) with the lowest voice it is admissible. According to Gaffurius, however, not only is it viewed in relation to the lowest voice, but also in relation to the highest. Furthermore (and moving on beyond “consonance” to what Gaffurius now calls “harmony”—which is different), a mathematical relationship is seen to exist between the upper pair itself and the lower. Each component, therefore, is an essential part of the harmony. Within each harmonic complex, the smaller units (being the higher notes) are progressively subtracted from the larger ones to identify the mathematical (and hence acoustical) relationships. Finally, the upper relationships themselves are subtracted from the lower ones to define the overall level of consonance which characterizes the particular harmony. This (surely?) must undeniably give a hierachical superiority to the lower notes, and ultimately to the lowest. Now while this is, of course, also true of two-voice counterpoint giving rise to dyadic harmony, it is not necessarily the case with three-part textures which are still dyadic in concept, but which now have an added accompanying voice.
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28. I will also point out (for what it is worth only) that Glarean’s words on Ave Maria were descriptive of the harmony, no mention being made of the counterpoint. Further, the difference between Bent’s resolution of the disputed passage, and that of others, lies in her view that the middle-voice component is required to exercise (but is unable, without the most careful assistance, to excise) a gymnastic display of musical schizophrenia in being simultaneously a partner to two other voices, each of which belongs to a different “primary pair.” Her solution, if only for that reason, is all the more ingenious!
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29. Judd and Bent, remember, reject an explicit link between the two. Further both insist that it is only the external factors (e.g. range of the vocal part) that are relevant in determining the mode, since “mode” is not an internal attribute of the musical euphony itself, but only a label which can be assigned retrospectively as a result of such external criteria.
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30. Tinctoris, Liber de Natura et Proprietate Tonorum, (1476), Chapter 18.
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31. I shall be looking only at the version preserved in the Medici Codex of 1518 (facsmile ed., Edward Lowinsky, “The Medici Codex,” Monuments of Renaissance Music, V (1968), fols 125–7), where the Tenor cantus firmus is of especial interest. The pitch of the work itself is (probably intentionally) uncertain from this notation since there are no clefs (only coniuncte). The Tenor, which begins on a coniuncta, delivers in notation the standard Mode 6 version of the melody. However, the rubric states that in performance the melody must be begun a semitone lower than written. What is not spelled out, however, is that not only must this happen, but also that the mode of the melody must be changed from tritus to deuterus. Many of the intervals required will, therefore, contradict the pragmatics of the notation (which in this sense is—to use Margaret Bent’s term—very much a “weak default”).
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32. Speaking of “mixed modes” also avoids the issue of whether or not prefatory coniuncte (i.e. signatures) do or do not transpose the hand as opposed to the mode. If they transpose the hand, and (in this case) E♭ becomes a recta step, all this will mean is that one mixing of modes may still yield a better result than another (because the composer has presumably exercised “extreme care”).
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33. This notion was rejected by Judd on the basis that ficta and mode were unconnected, and that Bent’s version did not violate her (both Judd’s and Bent’s) view of “mode” as being only an external formalization of pre-existent material. Bent also rejected this criticism on the grounds that the way I was applying my concept of mode was a “modern misprision,” and that a view of mode as white-note diatonicism had little if anything to do with fifteenth-century counterpoint. But I did not provide a view of mode as being limited to “white-note” degrees, and argued that ficta/recta adjustments could also be a means of modal articulation. This was (to answer another of Bent’s questions) why I introduced the term “modal fidelity” as against her own (and Zager’s) term “modal purity.”
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34. It is true, as Bent points out, that I did not previously cite Judd’s analysis of Ave Maria (Music Analysis 4:3 (1985), 201), but my reason for not having done so will seem unclear from Bent’s statement. This analysis is not, as Bent claims, a “modal analysis,” but is a schematic analysis which considers interrelationships between text and mode (as a melodic framework), together with pitch-organization, tonal structure and structural articulation. Further, no particular importance is attached to the measures under consideration which, in the reduction, are presented purely in their unadorned white-note form (because, as Judd has recently demonstrated, she considers ficta to be on a completely different track from considerations of mode). Judd does, however, claim that the composition is written in the hypolydian mode, and even goes on to state that some have described it (on Glarean’s authority) as being hypoionian. It is clearer to me now that her view of this attribute was limited to the external features of the piece. I am, in view of Judd’s and Bent’s criticism over chronology, happy to concede that it is indeed an example of the hypolydian mode (which at least brings me into line with Judd’s view), particularly since it is indistinguishable (except in nomenclature) from the hypoionian.
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35. Under the assumption that it was I who had argued that such pieces should be composed “without removing the harmony from its base” (although, as readers will recall, this was only an observation of Glarean which he had applied to the harmony of Ave Maria within his own terms of reference), Bent was unable to understand why I should applaud Josquin’s use of modal change (“modulation”) found in Absalom fili mi as a “powerful rhetorical device.” I take seriously her caution over reading too much into a composer’s intention regarding text-setting, and will not attempt to argue for any more extra-musical association than the blindingly obvious one which seeks to express the text “et descendam in infernum” through a sequence of falling thirds culminating in a final chord of low pitch which includes a B♭ below gamma-ut.
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36. Views on pitch stability have also led to some serious misunderstandings. Margaret Bent took great exception (ftn. 26) to my inference that she viewed “modal coherence as a close relative of pitch stability.” But my assumption was not drawn from the single sentence she quoted from DF. It was arrived at on the basis of the following statement: “Did interpretations that stray from the white-note diatonicism to which we have grown accustomed sound different or special to them? It is hard for us to answer this until we have become used to thinking of sounds in a new way, to doing without the conventional dividing lines we have applied between diatonic and chromatic, recta and ficta, not to mention abandoning our inherited faith in a pre-tuned white-note scalar modal chastity that is open to petty violation up to an ill-defined point.” (DF pages 46–7. The italics are mine.) This followed an earlier statement concerning the tonal movement in her Obrecht example where sho wrote (DT p. 35) “Lowinsky objects that the singers would have to start the Gloria on F♭, not that ‘F♭’ at the end of the Kyrie makes the movement tonally incoherent. The objection disappears if we renounce frequency stability.” Then, on the following page, she wrote “Further, contemporary singers without commitment to constant frequency, having applied their coniuncte in bars 87–8, would then be in a position to read bars 89–96 as if nothing had happened.” (The italics again are mine) She objected [8] to my imputation that she assumed that “to begin a piece on F and end on F♭ was of little consequence for the singers” but this was intended to mean no more than her “as if nothing had happened.” Pitch depression is something I believe she has conclusively proved through her Obrecht example, and I cannot see anything other than a complete validation of her views on the way ficta has to operate here. Our problem seems largely to be one of misunderstanding what we are really saying, and Bent has clarified for me now that pitch “instability” when it occurred did so with the awareness of the singer. This is what I would have assumed, especially since she has also pointed out to us [4] that they had no term to distinguish F from F♭. Such a position would more credibly prescribe a greater rather than a lesser need to be aware of the pitches actually being sung.
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37. Bent (22) proposes that a diminished 5th which contracts to a 3rd is something that she “could more readily tolerate.” But this one does not do so (at least not immediately, and it is equally possible to hear the eventual E♭ as merely decorative of the D to which it again immediately falls).
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38. In untransposed position, this note would be the equivalent of F♯.
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39. The cadence, of which this is a component, has overlapped with an entry in Voice 1 where the thematic content of the line requires this voice to rise to the G; had the Tenor also fallen to G two octaves lower, not only would the texture have been highly unsatisfactory, but also the line would have had to execute an upward leap of a tenth in measure 29.
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