Chapter 7: On Imperfection

[e2v] 51

Chapter 7: On Imperfection Within these is understood both Imperfection and Alteration, for both are only made in signs of Perfection, both of which we will define. Imperfection is the subtraction or removal of a third part of a perfect note. A note is said to be perfect that is worth three of lesser value. [e3r] [Imperfection] happens by means of either a rest or a note or [by means of] Coloration. [Imperfection] happens by means of rest or note when either before or after a perfect note there is positioned a rest or note of lesser kind and value for a similar [note or rest] does not imperfect a similar [note]. If, however, two rests are placed after, or a ligature of semibreves, between two [notes of] greater [value], [then] no imperfection is produced neither following nor preceding. 115 There is an imperfection by coloration when two or three notes in succession are so colored, then color in Perfect signs [i.e., mensurations] commonly takes away a third part, sometimes nothing only the Alteration between two perfects disturbing this. 116 It [Coloration] operates differently in imperfect [mensuration signs] except for Hemiola. 117 Hereafter the reader will recall what I advised above: notes are imperfected [but] not rests, and will observe that commonly when lesser [notes] are causing imperfection, they only subtract from their next greater [note values] as much as they themselves are worth. The indications of this species, as Franchinus [Gaffurius] relates, 118 [namely Imperfection] are of number, distinction by Punctus, Coloration of notes. The imperfectable notes are four, namely [Maxima, Long, Breve, Semibreve]. The Maxima is imperfected by the Long in the sign 3, the Long [is imperfected] by the Breve in the sign 2. Likewise the Breve is imperfected by the Semibreve in the sign, and the Semibreve by the Minim in [the signs]. 115 That is, in the circumstances he describes, no Imperfection occurs to either note of a greater value, whether preceding or following. 116 That is, the type of technical Alteration that he will discuss in the next chapter. 117 This is Listenius only discussion of the important technique of Coloration, or Denigration as it is sometimes called. 118 Practica Musice Bk.2, Ch.10. Listenius discussion is a very much abbreviated summary of Gaffurius major points. 52

[e4r] Chapter 8: On Alteration Alteration is the replication or doubling of a note for the sake of producing a perfection, just as when two similar notes are placed by each. Only these four alone are altered not altered.. Their rests are 53

Altered in the Sign of Perfect Mood Perfect Tempus Perfect Prolation When two remain beyond a triple number and always the latter is altered, never the former. The same is preserved if between two perfect figures [figura] 119 a rest is located with its note, yet, so that the former in position is a rest and the latter a note, for as was said, the note is altered, not a rest. 120 [e4v] 119 I believe this refers to an individual note or group of notes that constitute a perfection or group of perfections. 120 In the circumstance described, a rest with a note of the same value can as a unit be altered into a perfection by virtue of the fact that the note is last in the group. It is the last member that is always altered, so a rest coming first would not present a problem by its being unalterable. 54

Chapter 9: On the Quadruple Genus of Punctus A Punctus is a dot placed on notes for the sake of either Division or Augmentation or Perfection. It is of four types. I. Of Perfection, which prevents a perfect note from imperfection, [e5r] neither adding nor subtracting. Ý Ý. II. Of Addition, which when conjoined on the right side of a note adds to it a half its value. Likewise it is called [Punctus] of Augmentation and thus increases the note: III. Of Division, which is located between two notes in a perfect [mensuration] sign and divides them so that they not be calculated together, neither adding nor subtracting from them: IV. Of Alteration, which positioned on the head or top of the note warns that the same is to be sung by twice [as long], because of the representation of a triple number in a perfect [mensuration] sign: Examples appeared above in the 3 Degrees. 121 Chapter 10: On the Tactus 122 The Tactus is a rule directing mensural music (cantus) and is of three types: I. Total or Integral, which at times they call Major, is when the Breve is measured by an undiminished Tactus 123 for calculation of Mood and Tempus. II. General or Common (vulgaris) which they sometimes call Minor, is when the Semibreve or two Minims falls under a whole Tactus. III. Special, which they call Proportionate, though I know not why, is when another note than the Semibreve is preferred for the Tactus, as when a Breve in the [e5v] sign of semiditie, or a Minim in Augmentation, or a Breve or three Semibreves in the sign of Tripla proportion are comprehended within one Tactus. 124 Chapter 11: On Syncopation 121 I believe this refers to the various Punctus types in general, not solely to the alterationis, an instance of which I cannot find in the examples he alludes to. 122 This same understanding and division of the Tactus is found in Rhau Enchiridion, Part 2, Chapter 8, I7r-v, Agricola Musica figuralis deudsch, G4v-5v, and Ornithoparchus, Part 2, Chapter 6, F3v. 123 Listenius meaning of an undiminished Tactus is probably what other authors call the Major Tactus in reference to Major Tactus = Breve and Minor Tactus as Tactus = Semibreve. The next definition of the General Tactus would seem to imply this. 124 If we accept the first, the Major Tactus, as Tactus = Breve, then these three definitions correspond to Morley s understanding about 50 years later. 55

Syncopation is the fitting extension of a lesser note beyond a greater one, dissonant with the other part, [but] indeed elegant at the end of music [cantus] and at formal cadences. 125 [e6r] Chapter 12: On Proportions Many are the Proportions, some Multiplex, some Multiplex Superpartiens, some Multiplex Superparticular, others are called by other names. Since the number of them is almost infinite, even if the use is quite small, 126 I am unwilling to enumerate the individual types here, lest I seem annoying to those desirous of this skill, because of so great a catalog, and [to seem to be] throwing in and raising trivialities. I will, then, be content with these, which are used by some at this time. The more useful ones are Dupla, Tripla, Quadrupla of Greater Inequality, and Sesquialtera ad Sesquitertia of Lesser 125 The intended meaning of the passage seems to imply more than our modern concept of syncopation by including harmonic suspension or dissonance. Only about 20 years before this text, Ornithoparchus, Bk.2, Ch.8, F6r had insisted that syncopation was the proper term for Dupla Diminution. The word I have translated as extension is deductio, whose basic meaning is the act of sending or leading forth, with a secondary development from which our deduct comes. I have chosen the former because of the subsequent use of ultra maiores, beyond greater ones, which, to my mind at least, better represents the musical example. It commonly appears in Gaffurius with the meaning of progression. Lastly, the surprising awkwardness of this description to the modern ear is an excellent example of how we have over the centuries benefited from the slow formation of stable terminology, which earlier authors did not enjoy. The passage in question clearly depends upon Gaffurius Practica Musice Bk.2, Ch.15. 126 Those interested can find a very full discussion of proportions in Gaffurius, Practica Musice, Bk.4, such as Listenius has, thankfully, omitted. 56

Inequality. 127 Proportion, therefore, is nothing other than the comparison of two quantities to each other, such as when 4 is referred to 2, or 6 to 3. 128 Dupla is when a larger number compared to a smaller contains the same [smaller number] twice. 129 In music when a larger number of notes is made equal to the smaller, 130 namely 131 Ý [=] [or = ] 127 Unfortunately, here again Listenius reveals his discomfort with the more difficult aspects of mensural notation. He follows Gaffurius Practica Musice Book 2, Chapter 2 in utilizing the terminology of Major Inequality and Minor Inequality, which is also likely the source for Ornithoparchus own discussion in Micrologus Book, 2, Chapter 13 (Dowland p. 59 ff.). Both make clear, and Ornithoparchus provides many charts in support, that, in other words, Major (or Greater) Inequality is a matter of Diminution, whereas Minor (Lesser) Inequality is a matter of Augmentation. This fact is made even more clear by consistent use of the Sub- prefix in the case of the Minor Inequality proportions. Listenius clearly misunderstands this, grouping the ordinary Major Inequality Proportions with their Minor Inequality Sub- pairs, e.g., Dupla with Subdupla, Tripla with Subtripla, all as examples of Major Inequality. On the other hand, he also incorrectly labels as Proportions of Minor Inequality Sesquialtera, Sesquitertia and, implicitly, Hemiola, which are all Proportions of Major Inequality. Other instances of possible errors on Listenius part have been possibly construable as difficulty with Latin or casual oversight, but I see no way to understand this confusion as anything but error. This taken cumulatively together with problems in the chapters on Augmentation and Diminution seemingly inescapably indicate that Listenius was not entirely proficient in the finer parts of mensural notation. Fortunately, despite these problems with terminology and wording, his explanations ultimately prove correct, as supported by his musical examples. 128 In order to help in this section, I use the most common but not universal practice of reading the numerical signs, which seems to be what Listenius uses, despite his other serious confusion here. In reading, always start with the top number, i.e., 2/1 is two in the place of one, 3/2 is three in the place of two, 1/2 is one in the place of two. 129 Listenius, as already seen, is given to older medieval pedagogical devices, as here with analogy to mathematics as influenced by Gaffurius in Book 4 of the Practica Musice, which analogy I do not think serves his purpose at all well. The analogy with mathematics seems to lead the reader in the wrong direction by implying that Dupla will be a process of Augmentation not Diminution. Listenius explanation of the musical significance is correct but confusing and not less so because it appears the opposite of his mathematical analogy. Apel remarks that the representations of proportions are counterintuitive (p.147). Because this awkward analogy has become important to him, he further muddies the water by introducing the term numerus into the musical explanation and continuing with the plural when the singular would have been clearer. As a result, he has rendered obscure, and continues to do so with the following proportions, the simple idea of in dupla a note is reduced by half its value and becomes equal to the next smaller one. Thus, two of the new note in Dupla are equal to one of the former identical note value in normal mensuration. 130 The understanding of this sentence requires the next to clarify it. The crucial point that two of the new notes become equal to one of the former notes of the same value as they. In modern terms two quarter-notes take the place of one quarter-note. 131 All the rest of his definition would indicate that he means by these examples that Dupla applies to Breves, Semibreves, or Minims, for example. On the contrary, I think the effect is completely to confuse his meaning, making the reader think he is saying two Semibreves in a Breve, etc. 57

That is, when two notes are placed against one similar to itself, 132 whose signs are 2/1, 4/2, [such as] circles crossed or semicircles with binary number in all parts of a song (cantilena) C2. Then the song (cantilena) falls under the Proportionate Tactus, as can be seen in the vernacular song (carmen) of Johannes Walther, Nun freuet euch. Otherwise, when the same [sign] is not found in all parts, [it is] the contrary species of Subdupla, whose signs are numbers 1/2, 2/4, 3/6 or inverted [reversed?] circles, 133 that we use frequently for determining proportions. 134 [e6v] Tripla [in mathematics] is when the larger number embraces the smaller by three times. In music [this is] when a larger note value comprehending three times the [next] smaller is made equal to the same [smaller note value], as when three notes are set against one similar to them. For such three in the proportion are worth no more than otherwise one [is worth] outside the proportion, namely [they are worth one] Tactus. The signs are 3, 3/1, 6/3 135 The contrary of this is subtripla. 136 132 In other words, 2 Breves in Dupla equal 1 Breve in ordinary time. 133 A reversed (or inverted) circle is obviously impossible and begs the question of how Listenius could not have noticed. It is true that an alla breve sign or a reversed C in only one part with C in the others renders the others Subdupla. 134 Subdupla is the reverse of Dupla, it is effectively Augmentation and lengthens the notes by twice, so that a Semibreve in Subdupla = Imperfect Breve in normal mensuration. 135 Either the numerical signs were misplaced or Listenius has become confused. I have placed them where they belong, referring to Tripla, not Subtripla, which would be 1/3 3/6 136 I find Listenius explanation for Tripla even more confusing that the one for Dupla, though when finally disentangled grammatically it is actually more nearly correct. Much of this is owing to Listenius rhetorical training taking precedence over pedagogical technique; he varies the style and vocabulary instead of expressing Tripla in the same words as used for Dupla and continues to do so throughout the remainder. He perhaps senses the problem because he has here for the first time introduced the most critical term that should be used in the description of all, the Tactus. What he means is that three Semibreves in Tripla Proportion are equal to one Semibreve of normal value outside the proportion, namely the Tactus. 58

Quadrupla is the [mathematical] proportion when the larger number comprehends four of the smaller. In music when four notes are set against one. Its signs are 4/1, 8/2, 12/3. Subquadrupla is when the smaller number is compared to the larger, precisely 4 are contained in it with the reverse sign 1/4. 137 137 In modern terms, a quarter-note becomes equal to a whole-note. 59

[Translator s note: the word Quadrupla in the example is a canon, a word or phrase of direction or explanation as to how to perform the music.] [e8r] Proportions of Lesser Inequality 138 Sesquialtera is when the larger number relates to the smaller and includes at the same time the same whole of the lesser plus its [the lesser s] half part: 139 in music when three notes are set against two of the same [value]. Its signs are 3/2, 6/4. Often it is indicated also intrinsically by means of the numerousness of the notes in some one part of the song (cantilena) or in the setting of the numbers and characters, frequently [it is indicated] with a written phrase [i.e., a canon]. Yet, if it happens in all parts of the song (cantilena) at one and the same time, 140 it stands for Tripla 141 Proportion or Hemiola, 142 if you like. Subsesquialtera is made in the reverse manner. 138 As explained above, these are not Proportions of Lesser Inequality. 139 This is precisely the opposite of the music use. 140 If Listenius is correct, this seems to be a practice analogous to the use of perfect prolation in all voices, which shifts the Tactus to the Minim. This may also account for the confusion between Tripla and Sesquialtera that Morley mentions at the end of the century (see the following note 142) and for Ornithoparchus observation about the combined use of Sesquialtera and Coloration. 141 Tripla and Hemiola precisely speaking are not the same thing, but this may not be simply Listenius error. It is clear from Ornithoparchus (1517) and Morley (1597, 1608) that very considerable confusion existed, mixing up Tripla, Hemiola and Sesquialtera in practice. A possible reason is that Imperfect mensurations had become predominant in the sixteenth century so that composers were possibly simply forgetting the complexities of using Perfect ones, which required all the rules of Imperfection and Alteration. 142 Morley later deplores this confusion of Tripla with Sesquialtera and refers to the use of Sesquialtera in all voices as called Common Tripla, to which he only grudgingly acquiesces. He also denies that it is a proportion because there is no one voice in normal mensuration with which to establish a proportion in the others (Morley, 2 nd ed. (1608) section on Annotations note references to page 29, line 3 and page 31 [sic, the page is actually 32], line 9). Listenius refers to this usage, Morley s Common Tripla, as Hemiola. Looking forward to the concluding section on Hemiola, Ornithoparchus says that some say that the use of coloration with sesquialtera results in double 60

Sesquitertia is when four are set in place of three. Its signs are 4/3, 8/6, 12/9. On Hemiola Hemiola is when notes in coloration proceed equally in all parts of the song (cantilena), but even faster than Tripla Proportion on account of the coloration, for it has both color and more quickness than white notation produces that is in Tripla Proportion when its [Tripla s] sign is prefixed. Often hemiola relates to simple counterpoint, which I at least call attention to. 143 sesquialtera (Bk.2, Ch.13; Dowland p.64-65). In that Listenius refers Sesquialtea to Coloration in Hemiola, it indicates that he does understand how the proportion works but has given a confused explanation. 143 This sounds like a confirmation of Ornithoparchus remark that there are two attitudes about Sesquialtera when in white or black notation. Some, he says, consider that Sesquialtera in black notation means double sesquialtera, which would be one-third again as fast as white sesquialtera, though I am not aware that he referred to any greater speed with the simple use of coloration. By the end of the century, at least in England, Tripla and Sesquialera had become widely confused and expressed in a variety of notations, white, coloration, and mixed, as well as through a variety of signs. In Listenius example it should be noted that he uses only coloration in all voices, thus implying sesquialtera, but with no special, extrinsic sign of sesquialtera. Thus, technically, the conditions mentioned by Ornithoparchus and Morley the sign of sesquialtera plus coloration are not fulfilled. It seems fairly clear, however, that Listenius is talking about the same thing. I am inclined to think that the diversity and confusion in practice, especially regarding triple mensurations, in Listenius time is responsible for his present description. 61

The End Of Listenius Musica 62

63

Lest there remain a blank page, we add an old song not, indeed, fruitless for those wishing to study the older modes, i.e., intervalls. 64

Glossary Cantilena song Cantus music, song Clavis The letter name of a note in the gamut plus its vox, the syllables that identify it within a hexachord; a short form for the clavis signanda or clef. Clavis signanda a clef, often shortened to clavis Deductio a pattern, or a progression, such as in the progression of the six syllables Figura a note; a shape; a group of notes, especially those that constitute a metrical unit Impar refers to an odd number, specifically to the authentic modes Modus An interval Musica music in general Par refers to an even number, specifically to the authentic modes Proprietas this term is used very diversely but seems generally to me the characteristic quality of something that defines it as such. It also is used to refer to a hexachord. Sospirus probably a group of notes that constitute a full Tempus in the mensuration Tonus mode Vox the syllable(s) that identify a pitch within a hexachord; human voice; musical sound; a pitch in general. 65

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