Abstract
Section 12.1 analyzes Harold Powers’s provocative claim that “mode is not real.” It is shown that this claim is conceivably true only under the medieval, “octenary” doctrine. Section 12.2 is a critique of Gregory Barnett’s related claim that the seventeenth-century “church keys” “are not modes.” It is shown that to the contrary, the church keys are precisely triadic semi-keys. Finally, Sect. 12.3 revisits empirical data, originally put forward by Krumhansl and Kessler which support the existence of a nucleus-core-cluster hierarchy from a receiver-related perspective, all in the context of triadic keys. Transmitter-related data, which support the existence of a distinction between first- and second-order chromatic degrees, is presented. This latter finding undermines the notion (suggested by Krumhansl and others), that listeners form an internal representation of tonality on the basis of note distribution.
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- 1.
Trans. from Strunk (1998, p. 417).
- 2.
As Powers himself notes (1992, footnote on p. 28), “Marchetto had written that it would be senseless to call a piece that had the species of mode 3 throughout and then simply tacked on a D sol re at the end, mode 1 rather than mode 3….”
- 3.
The relation of C (cleffing) to the ambitus—in comparison to the relation of Σ (signature) to the core and of Φ to the final—is rather inconsistent. For example, on p. 451 Powers (1981) states that “the fact that the registral contrast is the reverse of the norm—the plagal representative in the modal pair with the same final lies higher than the authentic, not lower—is of no consequence. Lasso’s intentions are perfectly clear from the ordering alone.” Correspondingly, the distinction between “authentic” and “plagal” modal messages can hardly be made rigorous.
- 4.
See also Sect. 11.3, footnote 9 in particular.
- 5.
Consider Lodovico Zacconi , who assigns Palestrina’s madrigal “Vestiva i colli, ” with “minimal markers” (∅, A, HI) to mode 2 (Hypodorian), even though, as Powers does not fail to point out (1974, p. 34), his “…twelve modes include the degree A as an Aeolian finalis.” Yet it is perfectly possible that, due to the madrigal’s Prima parte ending on D, as well as some local emphases on D (see, for example, the beginning of the first phrase), for Zacconi the final of this madrigal was D, not A.
- 6.
See Powers (1981), p. 440.
- 7.
Even though Glarean was not a professional musician, his musical intuition is remarkably keen, and his ability to express it verbally is impressive. See, for example, the passage from Dodecachordon, quoted in Sect. 11.1, where Glarean describes the aurally disturbing tritone of Lydian and Phrygian (Book II, Chapter 11).
- 8.
Powers (1998, footnote on p. 339) repeats the charge that “dodecachordal theorists,” for whom “…of course an F-tonality with B-flat would have to be regarded as a transposition of the corresponding ‘Ionian’ C-mode,” “… were faced with the problem of finding (or inventing) representative musical instances for their ‘true’ Lydian and Hypolydian, the F-modes with B-natural,” as if to pretend that the fourth species of fifth is the third species is no problem at all. As we have seen in Sect. 11.1, Glarean in fact offers a very convincing explanation for what he describes as “changing from the Lydian to the Ionian.” Glarean’s explanation is the basis for our own Definition 10.10 (key, semi-key). By Theorem 10.11, which follows from the definition, a semi-key is not reducible to Lydian. See also Sect. 12.2.
- 9.
“Quatuor a primis tribus …,” literally, “the four [notes] after the first three.” In Babb’s (1978, p. 38) translation: “passing over the first three notes, the next four, namely the lichanos hypaton [D], the hypate meson [E], the parhypate meson [F], and the lichanos meson [G] are used in constructing the four modes or tropes.”
- 10.
“Sed illud quoque reprehensione dignum, quod cum uulgo quatuor finaleis ponit claueis in septem diapason modulis, reiectis tribus, cum una dumtaxat
reijcienda esset.” Citing Gerbert’s Scriptores (I, p. 41), Miller
states in his Introduction to Glarean
1965 that “as early as the 9th century, … Aurelian
reports that there were some singers who thought certain antiphons could not be adopted to the existing modal formulas, and thereupon Charlemagne
ordered that four more modes should be added” (p. 19). Powers (1992, pp. 21–22) notes that Glarean’s “construction of twelve modes” was “influenced” and “in a sense justified” by “a dodecachordal construction of the monk and abbott William of Hirsau
, as well as by the references to modes beyond the Gregorian eight (toni medii) by Berno of Reichenau
. Glarean had read both these 11th-century authors in a manuscript to which he had access in the years 1530–1536, where he also was able to read Boethius and other authors.” Fuller
(1996, footnote on p. 199) notes that Johannes Gallicus [Legrense]
“… accepts a, b, and c as legitimate (not irregular) finals,” although “there is no evidence that Glarean was acquainted with Gallicus’s treatise or ideas….” - 11.
The term “church keys” originates with Lester (1978), later reworked, together with Lester (1977), into Lester (1989). Lester explains (1989, pp. 78−79) that the term accords with seventeenth-century usage (in particular, Adriano Banchieri ’s tuoni ecclesiastico). Referring to Atcherson (1973), who uses the term “pitch-key mode,” Lester (1989, footnote on p. 78) notes that the church keys are not “a ‘strictly seventeenth-century phenomenon,’ for they are used from the late sixteenth century well into the eighteenth century, and are even cited in Koch ’s Musikalisches Lexikon of 1802 (article Kirchentöne, pp. 833−834).”
- 12.
Cf. Powers (1992, pp. 11−12): “… modality and tonality may be different kinds of phenomenon, and therefore not related through any of the simple evolutionary sequences to which we are today accustomed, such as: ‘the modal system was displaced by the tonal system’; or, ‘modality evolved into tonality’; or, ‘the ancestors of our Major and minor scales were the Ionian and Aeolian modes’.” Aspects of Powers’s provocative essay have been discussed at length in the previous section.
- 13.
Cf. Christensen (1993, p. 25): “I consider it a fallacy of proximity to measure the value of a given theory in direct proportion to its chronological contiguity with the musical repertory to which it is applied.” This is not to say, of course, that one should not pay close attention to such “chronologically contiguous” theories, treating them with the utmost respect.
- 14.
In Sect. 8.2 it was suggested that (categorical) 12-tone equal temperament represents an equally extreme case of theory lagging behind practice. There was a technical reason for the late arrival of ET theory, namely, the non-existence prior to the seventeenth century of essential mathematical tools, in particular, logarithmic calculation. As noted in the previous section, in the case of modal theory the sanctioning of the octenary system by the church was a powerful obstacle to exposing its empirical as well as logical flaws.
- 15.
Tribal classes are defined in 10.8. Recall that two modes reducible to the same tribal class and sharing the same final (say, two “Dorian modes” with final D) may nonetheless be distinct, since they may have different scores (Definition 10.4). Therefore, the theory proposed in this study makes it perfectly possible to distinguish an “authentic” mode from a “plagal” one (review Sect. 11.1). However, since a definition of “authentic” vs. “plagal ” that reflects actual (polyphonic) practice does not seem to exist, for present purposes it should suffice to distinguish modes reducible to the same tribal class by their finals, ignoring the existence of scores.
- 16.
All three authors are quoted and translated in Barnett (1998), pp. 250−251. As noted in the previous section, well over a century earlier Pietro Aron voiced similar sentiments.
- 17.
Barnett (1998), footnote on p. 255.
- 18.
Barnett (1998), Table 3 (p. 256).
- 19.
In other words, unlike the extinct Lydian, a Phrygian semi-key may have existed in the seventeenth century due to remnants of dyadic modal conception and perception.
- 20.
For example, “… none of the tonalities in Tables 5 and 6 are modal, transposed or otherwise. Instead, they originate in ecclesiastical psalmody.” “… This system of tonalities—often described as modes by the theorists…—consists of the church keys that originated in the accompaniment of psalms on the organ” (p. 260). “Bononcini’s set of seven finals and key signatures originates in these psalm tone tonalities, not in the modes” (p. 261). “This core set derives, not from the modes, but from tonalities originating in the eight psalm tones used in the Catholic offices” (Abstract, p. 281). See also footnote 21.
- 21.
In footnote 34 (p. 277) Barnett dismisses Peter Allsop ’s (1992) modal-based account of precisely such “G-tonality” and “E-tonality” compositional characteristics as he accounts for in psalm-tone terms. However, Barnett fails to support his dismissal with argument. Indeed, he claims to have demonstrated that “… psalm tone characteristics, not modal features, shaped these tonalities” (emphasis added), where in fact the emphasized clause is merely asserted, never demonstrated.
- 22.
One is reminded of Powers ’s (1992, p. 18) similar move by which composers of the late sixteenth century who favored the dodecachordal system (for example, Le Jeune) are marginalized. See the previous section.
- 23.
The two possible exceptions involve an apparent use of Lydian by Antonii (see Table 6 on p. 259). Barnett, however, may have neglected to mention that the signatures in question are “incomplete.”
- 24.
Barnett continues: “The D-tonality with two sharps also appears far more frequently in the sonata literature, whereas that with one flat occurs only infrequently in practice.”
- 25.
Barnett dismisses Suess’s ideas on purely terminological grounds, insinuating that “the mention of specific Greek-named modes” does not promote a “clear understanding of the modal practice.”
- 26.
Owens cites Reese (1954, p. 186) in this regard. “In any event, it is plain that in polyphony only five modes mattered for practical purposes. Glareanus himself emphasizes that the Lydian pair, as modified into Ionian and Hypoionian, has almost completely supplanted the unmodified pair. Moreover, the distinction between an authentic mode and its plagal is, in polyphony, an academic one…. This leaves, as the really fundamental modes of Late Renaissance polyphony, the Dorian, Phrygian, Mixolydian, Aeolian, and Ionian.”
- 27.
Lerdahl’s levels b and a are easily theorized, respectively, as the final-cofinal subset of the nucleus, and further, the final all by itself. We assume that Lerdahl’s basic space is naturally “tonic oriented.”
- 28.
Krumhansl displays the ratings, for minor as well as major, in terms of the notes C, C
/D
, D, D/E, E, F, F/G, G, G/A, A, A/B, and B. In Table 12.2 these labels are replaced with the appropriate scale degrees for major and minor, on the assumption that a chromatic degree is first or second order. Thus, for example, Krumhansl’s “E” becomes \( \widehat{3} \) in major and 
in minor. - 29.
As Krumhansl notes (ibid.), “in both studies, all pitches were reduced to a single octave and transposed to a common key; these transpositions were always determined from the written key signature, taking no account of transitions or modulations. In the second study [Knopoff and Hutchinson], explicit changes in key signature were taken into account. (The first study [Youngblood] does not specify what is done in the case of a change of key signature, if relevant.) The published tables show the total number of times that each tone of the chromatic scale was sounded in the vocal lines of the pieces; the durations of the tones are not taken into account in the analysis.” Again, Krumhansl’s labels have been replaced, as in Table 12.2 (see footnote 28).
- 30.
Note, however, that \( \widehat{5} \) is more prevalent than \( \widehat{1} \), that \( \widehat{2} \) is only slightly less prevalent than \( \widehat{3} \), and that, in minor,
is more prevalent than \( \widehat{7} \). - 31.
Even apart from chromaticism, the notion that degree distribution gives rise to the internal representation of tonality seems dubious. Note, for example, that even though \( \widehat{5} \) can be more prevalent than \( \widehat{1} \), as in the distribution data presented (see Figs. 12.4 and 12.5), the tonic remains the most privileged tonal element. Huron (2006, p. 150) has recently voiced strong support for the notion, originally advanced by Krumhansl , that “… one of the primary factors influencing tonality perception is the simple frequency of occurrences of different tones.” Citing the 2003 PhD dissertation of Bret Aarden, he notes that “… in the case of scale-degree distributions, Aarden found that listeners’ expectations are pretty well on the mark.” However, in Aarden’s major/minor analyses of the “distribution of scale tones,” impressive as they are in terms of sheer sample size, “all pitches are enharmonic.” See Huron (2006), Figs. 9.1 and 9.2 on pp. 148–149.
- 32.
Somewhat inconsistently, section repeats in Op. 24 indicated by formal repeat signs have been ignored, but not the occasional varied repeats that Brahms composes. See for example Vars. 8 and 9.
- 33.
Mm. 105−128 in Op. 98, Vars. 5, 6, and 13 in Op. 24.
- 34.
Mm. 85−88 (with upbeat) represent one of few cases in Op. 24 where Brahms writes a varied repeat (see footnote 32). However, this particular case is quite unlike any other, since it does not involve just “surface” changes as registration, part distribution, etc. In mm. 85−86 Brahms “repeats” mm. 81−82 a half-step higher. The sharp notation may be Brahms’s humorous way of referring to his rather free “repetition,” since ignoring accidentals the notes are the same. Be that as it may, taking these measures at face value has a marginal effect on the statistics. For example, the percentages for tonic, non-tonic diatonic, and chromatic degrees (cf. Fig. 12.6b) are 41.38%, 41.83%, and 16.8%, respectively. The percentages for first- and second-order chromatic degrees (cf. Fig. 12.8a) are 70.7% and 29.3%, respectively.
- 35.
Note that a “probe-tone”-type experiment is not feasible in this case, since enharmonically equivalent degrees are indistinguishable by pitch.
reijcienda esset.” Citing Gerbert’s Scriptores (I, p. 41), Miller
states in his Introduction to Glarean
/D
, D, D
in minor.
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Agmon, E. (2013). Modes, Semi-keys, and Keys: A Reality Check. In: The Languages of Western Tonality. Computational Music Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39587-1_12
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