yokermusic.scot · Abstract These projects all aim to answer the same question: to what extent must an editor make decisions in order to make a piece of music performable? Through

Playing the Glass Bead GamePart II Paper 3: Notation and Source Studies Portfolio

Candidate 2574M

Department of Music

University of Cambridge

Word count: 7654 words

May 2015

Abstract

These projects all aim to answer the same question: to what extent must an editormake decisions in order to make a piece of music performable? Through this questionI aim to study the diverse duties of an editor in the transmission of musical ideato sound through notation and the way in which an editor must interpret differentnotational systems. The three contrasting examples I have chosen will provide threeradically different perspectives to this question and therefore demonstrate that aneditor’s duties blur significantly into that of the composer and performer.

Missa ad fugam reservatam (Standley, Tr88 314v-322v, mid-fifteenth century). Thetenor and contratenor are written on the same staff but in canon, the contratenoromitting all notes below B-flat. I will be studying, through transcription of the sourceto a modern performing edition, whether the original source is performable or if thepiece is intended as an academic exercise in canon which must be “worked-out” by aneditor before performance.

Musikalisches Würfelspiel (attributed to Mozart K. 294d, 1792), a dice game whichuses the roll of a die to select measures to create a waltz. By using a computer programto generate a general solution to the game, I aim to study where in the process of gamerules to generation of single-case notational output the creation of the musical idealies: do the game rules constitute music alone or are they merely a set of instructionsto create music? In answering this I will look in detail at the extent to which the diceand the editor play in this transformation and reduction of cases to singular waltzes.

Treatise (Cornelius Cardew, 1967), a score containing 193 pages of purposefullyindeterminate graphical notation. There are no rules for its realisation and as suchthe editor must be in some senses composer and/or performer. The infinite possibilitiesthat this indeterminate score offers diminishes the responsibility of the composer andplaces much of the musical impetus in the hands of the editor and performer. Todemonstrate this difficult situation, I am using a computer program to interpret thescore into a performance as literally and accurately as possible with minimal humaninput. Through the example of this performance I aim to answer questions aboutwhether any musical notation is truly performable without some kind of editorial

iv

agency to create rules to interpret the notation and the feasibility of creating anunambiguous musical score that forgoes rules.

Contents

List of Figures vii

List of Tables ix

Introduction 1

1 Missa ad fugam reservatam 51.1 Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.2 The extended editor . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2 Musikalisches Würfelspiel 112.1 The enormous possibilities . . . . . . . . . . . . . . . . . . . . . . . . . 122.2 A general solution to the game . . . . . . . . . . . . . . . . . . . . . . 16

2.2.1 A random example . . . . . . . . . . . . . . . . . . . . . . . . . 162.3 The emergence of music . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3 Treatise 213.1 Creating a rulebook . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223.2 Performing Treatise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.2.1 Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263.2.2 Rulebook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.3 Playing the game . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

Conclusion 29

References 31

Appendix A Missa ad fugam reservatam edition 33

Appendix B Musikalisches Würfelspiel Facsimile 59

vi Contents

Appendix C Musikalisches Würfelspiel–playing computer program 67

Appendix D Graphic score interpretation program 91

Appendix E Treatise CD track listing 97

List of Figures

1.1 Real–time operation of the canon . . . . . . . . . . . . . . . . . . . . . 7

2.1 Musical key to Table 2.1 . . . . . . . . . . . . . . . . . . . . . . . . . . 142.2 Random example no. 33615319799726304 . . . . . . . . . . . . . . . . . 172.3 Part II, measure F: 11 possibilities . . . . . . . . . . . . . . . . . . . . 18

3.1 Treatise p. 4 and p. 29 . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.2 Treatise, p. 183 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.3 Artikulation, 103–114s . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

List of Tables

2.1 Bassline redundancy in the source . . . . . . . . . . . . . . . . . . . . . 15

Introduction

These rules, the sign language and grammar of the Game, constitute a kindof highly developed secret language drawing upon several sciences and arts,but especially mathematics and music (and/or musicology), and capableof expressing and establishing interrelationships between the content andconclusions of nearly all scholarly disciplines. The Glass Bead Game isthus a mode of playing with the total contents and values of our culture; itplays with them as, say, in the great age of the arts a painter might haveplayed with the colours on his palette. (Hesse, 1943/2000, p. 6)

An editor is fundamentally a decision maker. Music pedagogy deals with a limitedset of skills such that most competent performers can only read music printed withinthe last few hundred years. In the transmission of musical knowledge to subsequentgenerations, only the notational essentials are taught to ensure competency in thecommon practice style of the Western art music tradition: most extended notationsare self–evident additions to simple musical notation but this means that fluency inother musical notations is an extended set of skills not usually taught. In the Westernart music tradition at least, styles of musical notation are heavily influenced by stylesof composition and vice versa, as musical notation is the language that composers useto transmit their ideas to performers. Ideally this would be a very simple interaction:a composer would write notation to be distributed to performers. But in reality musicusually goes through the process of editing before being performed. Much in thesame way that a writer expects their draft to be read through, amended for errorsand published neatly for the reader, composers expect their original score to be read,checked through for errors and copied out neatly (nowadays usually in a printed score).This is the duty of an editor, to oversee this process and ensure that the final music islegible, free from errors and—if emphasis is placed upon performance—that the scoreis performable and musicians trained in common music pedagogy are comfortablereading it.

2 Introduction

This process of editing music is well known, but when it comes to music that is farout of the common practice sphere, the duties of an editor are altered and extendedsomewhat. An editor becomes much less of a music copyist and typesetter and beginsto incorporate aspects of composition and performance in “converting” unperformablenotation into a performable edition. In this portfolio I will be taking three differentexamples of this: in early music, in common practice music and in modernist musicand assessing the purpose and extent of the editor’s role in each example.

Hermann Hesse’s 1943 novel Das Glasperlenspiel (The Glass Bead Game) revolvesaround a mysterious and somewhat elusive game that synthesises the totality of humanunderstanding with an emphasis on mathematics and music. In playing the complexgame, the game player can create art of wondrous varieties by combining and playingwith this sum of knowledge. In approaching rule–based, chance and algorithmic com-positions in this portfolio I will explore the extent to which the editor must “play thegame” set out in notation to interpret music for performance and whether, in playingthe game, the editor is merely following a process to complete a function or indeed isplaying The Glass Bead Game and creating art.

In the first example, Missa ad fugam reservatam (Castello del Buonconsiglio, MSS1375, olim Tr88, ascribed to Standley), the notational style of the source is on theborderline of what is readable by singers versed in common practice music; singersthat sing this music from manuscript sources are trained in reading fifteenth–centurynotation. However, this particular piece of music employs a complicated canon, in thatthe contratenor part, in order to extract the notes that he must sing, must transformthe notation of the tenor by a simple rule. I will argue that this rule is impossible toimplement “on the fly” and therefore to make the music performable, diligent editionmust be undertaken to expand the canon to both the verbatim tenor and transformedcontratenor part, along with the usual editorial duties of error–correcting and convert-ing to modern notation.

In the second example, Musikalisches Würfelspiel (Bonn: N. Simrock, 1793, ascribedto Mozart), each bar of the notation is performable but the music is randomised inthe process of a dice game. The notation is not performable until the game is playedand I will argue, through generating a general solution to the game, that the role ofdecision–making editor is in the dice and game player and that the composer, and alsoeditor, of the original source has edited all possible solutions of the game by limitingthe possibilities of cases.

In the third and final example, Treatise (Cornelius Cardew, 1963–1967), any formof codified notational style seems to be absent or, if present, the rules for its usage

3

are unknown. An editor, when creating a performing edition, must decide all therules that they wish to apply to the notation in order to make sense of it. I willargue that because common practice notation is completely abandoned, a refreshingsolution is simple and literal. By treating the entire score as a time/pitch graph I willdemonstrate that it is feasible to perform this music within a set of rules and therebyapproach the score without rendering it arbitrary.

Chapter 1

Missa ad fugam reservatam

The wires corresponded to the lines of the musical staff, the beads to thetime–values of the notes, and so on. In this way he could represent withbeads musical quotations or invented themes, could alter, transpose, anddevelop them, change them and set them in counterpoint to one another.In technical terms this was a mere plaything, but the pupils liked it; itwas imitated and became fashionable in England too. (Hesse, 1943/2000,p. 23)

Described by Rebecca Gerber as ‘ingenious’ and ‘the most interesting Marian mass’ (Ger-ber, 1998, p. 10) of Tr88, the sine nomine mass ascribed to “Standley” was coinedas Missa ad fugam reservatam by Laurence Feininger who discovered the solution tothe canon that governs the operation of the contratenor voice. (Feininger, 1949, in-troduction) Feininger determined that this mass used an identical canonic techniqueto an unascribed motet in Trent 89, 120v–121r: Que est ista. In the motet, the ca-nonic voice omits all notes below B to create a new voice. Given the identical canonicsolutions to both pieces, Feininger attributed the motet to Standley. Although thesolution is known, various reasonings that reach this conclusion have been posited. Inhis edition of the mass, Richard Loyan relates the line in the motet “electa ut sol” tothe solmisation syllables ut and sol. By transposing the solmisation to D, Loyan omitsall notes from ut to sol. Loyan admits however that there must have been a (nowlost) textual canon to accompany the motet. (Loyan, 1967, p. xi–xii) Gerber suggestsinstead that the answer to the canon is contained in the question asked by the motettext (an Assumption antiphon):

Que est ista, que ascendit sicut aurora consurgens, pulchra ut luna, electaut sol, terribilis ut castrorum acies ordinata

6 Missa ad fugam reservatam

What is this that comes forth like the rising of the dawn, as beautiful asthe moon, as excellent as the sun, as dreadful as an array of armies aboutto charge? (Translation from Gerber, 1998, p. 104)

The answer to this question is the Virgin Mary, the “woman clothed with the sun”(Revelation 12:1–16) being assumed into heaven—Regina, the queen of heaven. Itis through solmisation of regina that Gerber argues for the omission of low E (mifrom regina) to A (la from regina). (Gerber, 1998, p. 105) In an alternate hypothesis,Gerber draws upon Boethius, in accordance with Cicero’s classification of all pitchesabove A being not of the earth, pitches above A are celestial, Mary now being withthe stars. (Gerber, 1998, p. 105)

1.1 Performance

Regardless of the reasoning, a simple rule transforms one voice into another voice. Isit possible that this canon was operated during performance by a clever contratenorsinger, was there another, “worked–out” copy for performance, or could the entire piecemerely be an academic exercise, a feat of counterpoint? Figure 1.1 shows, throughgreyed–out notes, an example of the process of transformation that the contratenorvoice must follow. In some cases, large sections of music are skipped over at a timeand at other times only a few notes are omitted. This extremely particular and seem-ingly random type of movement makes resolution of the canon difficult to accomplishwithout copying out the part. For example, in bar 94 the voice has only a semibreveto scan over eight notes and a rest before detecting the next note to sing and in bars91 and 106 there is only a minim’s duration in which to skip four notes. Furthermorewhere rests are concerned, although it is mostly the case that if the previous note wasomitted, then the rest is also omitted, there are some cases where rests are omittedbefore an omitted note and not after, and some other cases where rests must be ofdifferent durations in the tenor and contratenor voice to resolve the canon (for a smallselection of examples, see Credo, III, b. 29, b. 37 and bb. 46–47 in Appendix A). Noscholarship has yet commented upon the possibility of performance of this particularpiece as this greatly depends upon tempo and the skill of the singers involved. Gerberhypothesises however that Standley ‘might have been another of the English com-posers at Ferrara, where knowledge of Boethius’ scales was sufficient to perform thismass without a written canon’ (Gerber, 1998, p. 105) although she does not clarifywhether in “performing” the mass she means determining the answer to the riddle

1.1 Performance 7

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(whichever riddle that might be) and understanding the notation or as far as beingable to implement the rule ex tempore.

To sing this music without fault requires utmost diligence and concentration. Inaddition to this are the facts that the original manuscript is relatively small for allthe singers to be able read from at the same time (310 × 210mm, little bigger thana piece of A4 size paper) and it is full of mistakes. (“Source: I-TRbc MS 1375 [88]”,n.d.) In order for the canon to work, all singers must be in synchronisation at all times.However, in Appendix A, we can see that, amongst other errors, notes are missing,errant notes have been added to the source and some notes are wrong. Once theseerrors are corrected, the canon works perfectly. It is clear therefore that Standleywrote the original canon without error and it is in subsequent transmission of themusic that errors have crept in. Without correction, this piece is not performablewhich begs the question: Why has it not been corrected if it was to be performed? Toanswer this question we must look in greater detail at the manuscript’s origin.

It has long been acknowledged that the principal copyist of the final four Trentcodices (90, 88, 89 and 91) is Johannes Wiser, although when the first study of thecodices was published in 1900, little was known about him. (Adler & Koller, 1900)It was not until nearly thirty years later that Renato Lunelli showed that Wiser was‘employed as schoolmaster at the cathedral school in Trent during the very periodwhen he must have been assembling his great collection’. (Wright, 2003, p. 248) Modernscholarship on the codices has largely maintained that the codices were made in and forTrent and that Wiser was the main copyist. (Gerber, 1992, p. 51; Leverett, 1995, p. 208;Wright, 1995, p. 504; Gerber, 1998, p. 2; Mitchell, 2001, p. 141; Wright, 2003, p. 248)Reinhard Strohm and Peter Wright after him make a strong case for ‘music copyingas a means by which a scribe could build a career for himself’ (Wright, 2003, p. 252)

8 Missa ad fugam reservatam

and that the manuscripts were for the Kantorei or choir school of which Wiser wasrector. (Strohm, 1993, pp. 287–291) It is generally agreed that the Trent manuscriptswere Wiser’s personal collection of music, an anthology from which performance partscould be made, making the Trent manuscripts either Wiser’s library of music or Wiseran early musicologist. (Wright, 2003, p. 252) However, Margaret Bent, Adelyn PeckLeverett and Gerber place Wiser’s musical skills into some doubt, arguing that ‘hismusical literacy…was limited’ (Leverett, 1995, p. 208) and that this ‘resulted in anoverall accretion of mistakes’. (Gerber, 1992, p. 53; Bent, 1986) Gerber also notes thatthe musical scribe of Missa ad fugam reservatam is not Wiser himself but another,Wiser filling in the text later. (Gerber, 1992, p. 69) Perhaps either the combinationof a non-musical scribe and insufficient editing by Wiser resulted in the errors whencopied from a correct exemplar, or a series of errors had accumulated through multiplecopies. Bent has challenged the idea that uncorrected copies could not be correctedin rehearsal and performance (Bent, 1981, p. 304) but she leaves only the possibilitythat the musicians memorised their parts, thereby leaving the manuscript incorrectand unperformable.

Not only does the music contain errors, but the source also misses out text in theGloria and Credo. In the Gloria, four lines of text are omitted and in the Credo, thir-teen lines. To re-text the Credo and Gloria to include the missing text would makethe music incredibly syllabic. The Standley Credo in itself is only 375 semibreves long:to fit the entire missing 365–syllable Credo text to this music would mean that nearlyevery semibreve’s worth of music would require another syllable. This is nigh on im-possible and, above all else, unmusical. Although Gareth Curtis asserts that theremay well be examples of Credos with genuine text omission, (Curtis, 1979, p. 206–7)Wright and Curtis have created editions with telescoped Glorias and Credos. (Curtis,2001; Wright, 2013) James Cook hypothesises that a confused continental scribe, con-fronted with a telescoped movement, may have ‘entirely retexted the Mass, omittingmore lines of text towards the end as he ran out of room’, suggesting that such move-ments ‘may perhaps originally have been telescoped’. (Cook, 2014, p. 221)1 Followingthis, I have undertaken an exercise to telescope and reconstruct the text of part ofthe Gloria and the entirety of the Credo of this mass. My aim was not only to makeit performable, but also suitable for performance in a liturgical context, by replacingthe text in order to complete the liturgy (see Appendix A).

1I am grateful to my supervisor James Cook for suggesting a telescopic solution to my transcrip-tion.

1.2 The extended editor 9

1.2 The extended editorMissa ad fugam reservatam as written in the only extant copy in Tr88 is therefore not aperformable work without edition. The esoteric and difficult to operate canon and themistakes the source contains prevents an adequate performance of this specific piece.However, the fact that the Trent manuscripts are non-performable means that wecannot know whether Missa ad fugam reservatam was ever designed for performance:any performance would have to involve some edition. This demonstrates that it is notenough for an editor merely to faithfully copy out a source into modern notation. Tocreate a performing edition, the source must be checked through for errors and all itsprocesses verified. To claim a piece of music as canonic, the canon must be verifiedto work, or the piece corrected so that the canon works as I have done. When thereis ambiguity or error in the source, then the editor must make decisions in order tofulfil the essential requirements of his notation. Scholarship has much to say aboutpossible reconstructions and historical practice, and it is up to the editor whetherto make the decision to incorporate elements of often conflicting scholarship into hisedition. The faulty copy created under the supervision of Wiser is an example of onekind of fifteenth–century editorial practice. I have attempted not only to transcribethe source but also to undo some of the work of Wiser’s edition to reach an older,now lost source. The “composer’s intention,” whatever that may have been, is nowlost. However, speculative attempts to recreate some semblance of an original havevalue in transforming ambiguous notation—where the rules or some of the notationalinformation is lost—to more readable, performable notation with an informed editorialprocess.

Chapter 2

Musikalisches Würfelspiel

And we suspect, although we cannot prove this by citations, that the ideaof the Game also dominated the minds of those learned musicians of thesixteenth, seventeenth, and eighteenth centuries who based their musicalcompositions on mathematical speculations. (Hesse, 1943/2000, p. 9)

For even two out of a thousand stringently played Games to resembleeach other more than superficially is hardly possible. Even if it shouldso happen that two players by chance were to choose precisely the samesmall assortment of themes for the content of their Game, these two Gamescould present an entirely different appearance and run an entirely differentcourse, depending on the qualities of mind, character, mood, and virtuosityof the players. (Hesse, 1943/2000, p. 7)

In 1757, Johann Philipp Kirnberger (1721–1783) composed a musical oddity titledDer allezeit fertige Polonoisen- und Menuettenkomponist (‘The ever–ready minuetand polonaise composer’). A throw of two dice determined which measures in respect-ive tables were to be used next in the construction of Polonaises and Minuets. In theintroduction to the game, Kirnberger wrote that ‘anyone who is familiar only with diceand number and can write down notes is capable of composing as many of the aforesaidlittle pieces as he desires’. (Kirnberger, quoted in Hedges, 1978, p. 181) In the nextfifty years, at least nineteen different musical games along the same lines with extens-ive titles were published to compose all kinds of musical trifles, such as C.P.E. Bach’sEinfall einen doppelten Contrapunct in der Octave von sechs Tacten zu machen ohnedie Regeln davon zu wissen (‘A method for making six bars of double counterpoint atthe octave without knowing the rules’, Berlin: Lange 1778?), P. Hoegi’s A TabularSystem Whereby the Art of Composing Minuets Is made so Easy that Any Person,

12 Musikalisches Würfelspiel

without the least knowledge of Musick, may compose ten thousand, all different, andin the most Pleasing and Correct Manner (London: Welcker 1770?) and the titularlyimpressive Gioco pitagorico musicale col quale potra ornuno, anco senza sapere diMusica, formarsi una seria quasi infinita di picciole Ariette, e Duettini per tutti liCaratteri, Rondo, Preghiere, Polacche, Cori, ec., il tutto coll-accompagnamento delPianoforte o Arpa, o altri Strumenti (‘Pythagorean musical game by which everyone,without knowledge of music, can form a seemingly infinite series of little arias, andduets for character pieces, rondos, prayers, polonaises, choruses, etc., all to the accom-paniment of a piano or harp or other instruments’, Venice: Valle 1801). (Hedges, 1978,p. 185–187) However, arguably the most famous of all these games was printed inBonn by N. Simrock and co. in four languages and was attributed to Mozart: Walzeroder Schleifer mit zwei Würfeln zu componiren, so viele man will, ohne etwas vonder Musik oder Composition zu verstehen (‘To compose without the least knowledgeof Music so much German Walzer or Schleifer as one pleases, by throwing a certainNumber with two Dice’). The attribution is dubious, but the game itself is interest-ing. Like all the games, it relies upon throwing dice and counting their score to selectmeasures. Lawrence Zbikowski has studied the formal procedures of this particulargame and numerically categorised the source, (Zbikowski, 2002, pp. 170–184) but theemphasis of this study will be upon the compositional method of the game and therole of the editor in playing the game.

2.1 The enormous possibilities1. The letters A–H, placed at the head of the 8 Columns of the Number

Tables show the 8 tunes of each part of the Walzer. Viz. A, the first,B, the second, C, the third, &c, and the numbers in the Column underthe letters, show the number of the time in the notes.

2. The numbers from 2 to 12 show the sum of the number that can bethrown.

(From the source. See Appendix B)

In the number tables in the source, each half of the waltz has 8 measures (A–H) and 11different possibilities for each measure (2–12). This yields the 2×8×11 = 176 possiblemeasures. For each measure, rolling two dice gives a score, which can be looked up inthe table to select a measure. Serialising these measures creates a randomly generatedwaltz. For the first measure there are 11 possibilities, again for the second and so

2.1 The enormous possibilities 13

on until the 16th measure. Therefore the total number of possible scores and uniquewaltzes is:

nr = 1116 = 45 949 729 863 572 161

It is of course unfeasible that the creator of this game (whoever he was) explored all 45quadrillion possibilities, but he could have devised a system of composition to reducethe number of cases that he must account for. The game rules with random input (16consecutive throws of two dice) do not restrict this many distinct possibilities in anyway, so it must be that most measures are redundant. By examining the possibilitiesfor each measure, we can begin to reduce the possible cases for the waltz and thereforesimplify and understand how this musical game works.

A kind of simple harmonic analysis we can perform on each measure is to analysethe function of each possible bassline and compare similarities. There are arguably aninfinite number of permutations of decorations of an harmony possible, but the numberof feasible basslines to underly this harmony is within grasp. Upon closer inspection,the bassline and harmonic function of each bar is in fact rather invariable: each barcompletes the same basic function with little deviation. We can see in Table 2.1 andFigure 2.1 that basslines in both halves are rather redundant, never straying beyondsix basic options (with a myriad of different right–hand decorations not shown). Wecan therefore plot a singular harmony for the entire piece, and although there are over45 quadrillion possibilities, they always fall within one strict harmonic basis:

⟦I | I | Vb V | I(b) | I | Vb | (iib/IV of V ) (Ic of V ) (V of V ) | (I of V )/I⟧⟦(V(7d) of V ) | (I(b) of V ) | (iib/IV of V ) | V(b) | I(b) | I(b) | iib/IV V | I⟧

This is incredibly simple; there are only three harmonic functions: I, V and a simpleapproach chord (always iib, IV or Ic). The first four bars begin as a simple I–Vstatement of the tonic, and the second four–bar phrase in the tonic, this time using anapproach chord to the dominant. The final bar of the first half is ‘perfectly redundant’,meaning that although there are eleven different possibilities, they are all exactly thesame in the score, figuration included. This is because its function is slightly morecomplex. It has a ‘first time’ and ‘second time’ bassline. The first is a descending scalequickly modulating back to the tonic and the second is an affirmation of the new key,the dominant. In the second half, the music begins in the dominant and returns tothe tonic. First a weak cadence into the dominant is established, followed by a pivotchord of iib or IV, then a cadence back into the tonic with a V–I emphasis at the end.

This demonstrates that throughout the extraordinary number of possibilities, thecomposer has actually kept the game very simple and redundant in its output. All


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Measure Option 1 Option 2 Option 3 Option 4 Option 5 Option 6

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A All redundantB All redundantC All redundantD 13, 45, 50, 61, 85, 103, 156 41, 53, 63, 167E 28, 80, 105, 153, 154 75, 135, 140, 146, 161 99F 2, 37, 46, 47, 55, 68, 86, 133 122, 129 97G All redundantH All perfectly redundant

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A 16, 25, 35, 70, 120 65, 117 90, 102 66 138B 71, 77, 88, 143, 176 121, 139, 155, 20 4 39C 15, 64, 48, 19, 31, 108 7 26 57 126 150D 125, 132, 175 9, 29 56, 92 34, 166 82 164E 73, 112, 137, 144, 174 43, 51 76, 101 12 67F 38, 49, 58, 59 18, 160, 162 115, 136 124 168G 44, 52, 72, 109, 116, 145, 149, 173 1 23 89H 8, 14, 79, 83, 93, 111, 131, 151, 170, 172 78

Table 2.1 Bassline redundancy in the source


possibilities keep strictly to the same harmonic progression and by writing multiplemeasures that complete the same simple function, the composer has used case reduc-tion to generate a much more impressive game. After all, the game is only a parlourtriviality and it would be much to expect the game to contain great logical prowess,but the game is logical and does produce significant output.

2.2 A general solution to the game

As the game is logical, it is possible to obtain a general solution to the game andtherefore an analysis of the rules of the game that gives greater understanding ofwhen the rules become music. In Appendix C, I have detailed a Python programthat is able to generate any permutation at will. By encoding the musical sourcein the lookup tables and by writing out all possible 176 measures in musical type-setting and scripting language Lilypond, I can combine these two tools to call Lily-pond to generate any waltz at will. The program game.py completes a combinatorialfunction: it takes the rolls of the dice as input and selects the correct Lilypond–encoded measures from LH.txt and RH.txt that correspond to these rolls by usingthe CSV (comma separated values) lookup tables 1st.txt and 2nd.txt for the first andsecond half respectively. By concatenating these measures and placing them withina suitable Lilypond context, the program music2png.py (copyright © Stuart Rackham2006. Source downloaded from https://github.com/neo4j/doctools/blob/master/src/bin/asciidoc/filters/music/music2png.py, 2015-02-17) can take this script and compileit into a small cropped PNG file suitable for study.

2.2.1 A random example

Figure 2.2 shows an example of one of these waltzes generated from rolling 2, 2, 2, 2, 2,2, 2, 2, 2, 2, 4, 8, 6, 12, 8, 12. On first inspection, it seems like a very simple yet self–contained waltz. However, when taking into account the sheer volume of combinationsthat can be created from these 176 measures (the first few ten thousand of which sup-plied as a CD appendix to this portfolio constitute not even 0.0000000001% thereof),the mechanical rationale behind each compositional decision becomes apparent. Thewaltzes have not been composed as an whole, but as a series of bridges. Instead of theunfeasible task of sitting down and composing each waltz by hand, the composer hasin fact composed 15× 112 = 1815 sets of two measures as each of the eleven possiblemeasures has eleven possibilities falling after it, and as there are sixteen measures in

https://github.com/neo4j/doctools/blob/master/src/bin/asciidoc/filters/music/music2png.pyhttps://github.com/neo4j/doctools/blob/master/src/bin/asciidoc/filters/music/music2png.py

2.2 A general solution to the game 17

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total, there are fifteen pairs that can be made. As long as each measure works asan unit and flows correctly from the previous measure to the next measure, then byinduction one can assume that the piece will work as an whole.

To make each waltz coherent, the composer has begun from an harmonic basis,as we saw in Section 2.1. Working from this simple structure of harmonic function,11 possibilities have been written for each measure which flow well from one to thenext and because of the number of possibilities, it is unlikely and perhaps unfeasiblethat much more has been considered. In musical terms, the composition of such facilewaltzes is not difficult and with such a simple and sturdy harmonic basis, very littlecan go wrong. This aids the composition of many possibilities and allows the composerto think in short–term two–bar goals. The most likely method of composition wouldbegin with the bassline, because as we have seen in Figure 2.1, the basslines are themost structured component of each possibility, thereby deriving the harmony. Uponthis largely invariable bassline and rigid harmonic structure, the composer can thenbegin to decorate and voice the harmony in whichever way he sees fit, taking carethat each decoration leads well into every other possibility. For each new measure,the composer has 112 = 121 possibilities to contend with, but when the harmony is sostrict, he can begin to reduce these cases even further.

Figure 2.3 shows the eleven different possible measures for Part II: measure F. Theyall complete the same harmonic function of remaining static on the tonic, C major. Inscalic figures and in arpeggiation, they outline the notes of the tonic chord and theyall begin and end on a note of this chord. We can then begin to reduce this to specificcases, such as measures that begin on I (that is, all of them), measures that end on Ib(only one, the rest stay in root position), measures that begin on C (5/11), E (2/11)and G (4/11), and measures that end on C (5/11), E (4/11) and G (2/11), etc. In


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composing these measures, all the composer must do is to ensure that they match upwith the previous and forthcoming measures. Part II: measure E completes the samefunction as F in staying on the tonic and the chord at the end of the bar is either Ior Ib. Furthermore, the final notes of any possibility of measure E are C, E or G and,these notes being in the chord, flow well into measure F. Measure G begins on iib orIV and so flows well from the I or Ib at the end of measure F. The melody of measureG begins either on F (6/11), D (4/11) or A (1/11). The composer has been carefulin his configuration to prevent parallel fifths between bars: the strong harmonic basisand clever use of octave displacement of melody has prevented this at any time in any“bridge”, but he has been unable to remove parallel octaves between melody and bassfrom some possibilities. But this is not so bad as some bars are in unison in this styleanyway and the waltz is not in strict counterpoint throughout.

2.3 The emergence of music

If the compositional process is inherently granular, then does the composition of in-dividual measures and “bridges” count as composing all possibilities of waltz? It isclear that the composer has composed each measure in reference to all those that itmight coincide with, but to what extent is the combination of measures importantin the creation of these pieces? In fact, calling each combination a different pieceallocates some credit to the random selection of the measures. The use of chance incomposition was the famous hallmark of John Cage (1912–1992) and in pieces such asMusic of Changes, Cage uses chance in the form of the operations of the Chinese bookof changes, the I Ching, to dictate elements of composition much more fundamentalthan this dice game, yet it is never said that the I Ching composed a piece of mu-sic. However, the agency of other largely rule or configuration–based processes such

2.3 The emergence of music 19

as improvisational jazz or strict counterpoint is never doubted to come from the hu-man composer even though the processes are sometimes almost algorithmical in theirstrictness. Combination is an artistic process in spite of the strict rules governing themusical composition, whether the music is as structured as a fugue or pure chance likeCage’s Williams Mix (1951–1953). The game and rules are not music, but structuresfor music to be created. This is true within all musical practices: for a composer ofserial music, as long as he abides within the rules of the serialist technique, whatever hecomposes will be a serialist piece. Again in diatonicism: as long as the composer keepswithin the realms of tonic–dominant relationships, then whatever the composer writeswill be diatonic. This is exactly what the composer has done in the MusikalischesWürfelspiel: constructed a system where there are 176 measures possible and “rules”as to their usage (the table of possibilities). One could go through the table like therules of harmony and counterpoint and select one’s favourite measures, or it could beleft to chance. Nevertheless, as long as one abides by the rules of the game, then youwill compose a waltz, just the same as any other. The only difference is that the rulesof this game are so simple that they can be written down on a few pages.

The artful choice of measures, just like the artful choice of notes in any traditionalpiece, makes one a composer. In most cases, the composition of music and the codific-ation of that music into notation are separate but intertwined processes and cannot beseparated into a chronology. However, in special cases such as these, the codificationmust come before any music is to be created as the notation defines the music. Thecreator of the game is the music theorist, the creator of the system in which one com-poses. For example, in this way, Music of Changes is not composed by Cage. Cageis the theorist who devised the rules for the composition. The composer would bethe editor, in this case David Tudor (1926–1996) who realised the piece and playedthe musical game that Cage had set. The composer and editor are the same person;the editor makes the decisions for the composer thus reducing the indeterminacy thatis inherent in the musical notation. One could then say, that in the playing of theMusikalisches Würfelspiel, the waltz is in fact composed and edited by the personwho is playing the game. The computer program that plays the game by chance justas an human would do is also composer as it abides by the rules of the game. Thisdemonstrates that the role of editor becomes problematic in playing this game: theeditor’s role has been subsumed into the process of playing the game and becomesinextricably bound up with the role of the combinatorial composer. In Chapter 1 wesaw that the role of editor can be extended beyond simple error–checking but in thecase of the Musikalisches Würfelspiel, an external editor has no duties: the composer


(the game player) edits the chance score into unambiguous notation without goingthrough a separate editing process.

Chapter 3

Treatise

Incidentally, the terminology of Christian theology, or at any rate that partof it which seemed to have become a part of the general cultural heritage,was naturally absorbed into the symbolic nature of the Game. Thus one ofthe principles of the Creed, a passage from the Bible, a phrase from one ofthe Church Fathers, or from the Latin text of the Mass could be expressedand taken into the Game just as easily and aptly as an axiom of geometryor a melody of Mozart. (Hesse, 1943/2000, pp. 31–32)

Treatise (1963–1967) by Cornelius Cardew (1936–1981) is one of the largest–scale piecesof graphic notation ever written. The sizeable score consists of 193 pages of neatlydrawn graphic score. However, the enigma of Treatise is the notation in which it iswritten: the indecipherable and confusing notation was published with no perform-ance instructions, rendering Treatise a complete mystery and performance of the scoreaccording to any kind of “composer’s intentions” difficult if not impossible. The scorewas originally designed as a system of meaningful symbolic elements that could in-form performance but Cardew never came to make this symbolic language public.Initially, Cardew was deeply impressed by reading Ludwig Wittgenstein’s TractatusLogico-Philosophicus which examines the limits of language and, like Wittgenstein’sTractatus, Cardew’s Treatise was an attempt at examination of the limits of notation.Cardew was inspired by the variety of interpretations of Treatise and never publishedinstructions to accompany the score. Virginia Anderson claims that in doing this,‘Cardew released Treatise from a specific symbolic interpretation, from notation asprinted instruction, even from fixed musical or pictorial meaning’. (Anderson, 2006,p. 292) The problematic notation of Treatise presents the performer with the insur-mountable difficulty of understanding “the composer’s intention”. Treatise is a strong

22 Treatise

counter-example to the idea that a composer’s singular concept of musical expressionis encapsulated in the score that he writes. The ruleless and anarchic indetermin-acy that Cardew invokes in Treatise opens out a myriad of possible interpretationalapproaches of the notation, whether symbolic or graphical.

Once Cardew had removed the rules intended for Treatise, he went as far as to ‘[call]into question its definition as a score, even as music’; (Anderson, 2006, p. 310) themusic being in the score itself and in the interpretation of the performer. The notationof Treatise also blurs the boundaries of standard musical notation: the conventionalmusical symbols that are present in the score are placed within alien contexts or trans-formed, magnified and distorted out of their original meaning. Cardew’s contemporaryand collaborator John Tilbury highlighted Cardew’s intentional symbolic distortionand the problem that this presents for an interpretation that attempts to read it as atraditional score, arguing that a ‘non-reading musician might take a much freer, morespontaneous approach’ to Treatise than a ‘conventionally trained musician’. (Tilbury,1983, p. 8)

Brian Dennis has made an attempt to extract Cardew’s original aborted instruc-tions by examining the score of Treatise in detail, but such endeavours are not onlybound to fail, but also completely miss the point of Treatise’s indeterminacy. (Dennis,1991) Dennis surveys the work, detecting standard musical notation, circles, squaresand triangles and he comes up with frequencies and measurements of these items,but cannot go further than measurement, as the meaning of these items remains amystery. Another such analysis without conclusion is published anonymously onlinebut draws extensively upon Dennis’ survey. (“Treatise: An Animated Analysis”, n.d.)Christopher Hobbs, too, detects graphical allusions to factories, faces, human figuresand French cars but finds no meaning for these items but perhaps a ‘private enter-tainment for the performers’. (Anderson, 2006, p. 307) The fact that Cardew kepthis original rules secret after removing them from the work demonstrates that per-haps his sole intention in writing the score was in order to release the performer frominstructions.

3.1 Creating a rulebook

In Figure 3.1a, we can see that Treatise melds conventional and graphical notationtogether. In this particular example, one can make out a bass clef, staff lines, twocoloured noteheads and two flats which seem to relate to the notes. Interpreting thisnotation conventionally and ignoring the circles for the time being, the positioning of

3.1 Creating a rulebook 23

(a) Page 4 extract (b) Page 29 extract

Figure 3.1 Treatise

Figure 3.2 Treatise, p. 183…now where did I put the capacitor?

24 Treatise

Figure 3.3 Artikulation, 103–114s

the clef on the fifth line of the stave could identify it as a sub-bass clef, which wouldmean that the notes are the Ds above and below middle C. Such examples can beworked around. But when we arrive at pages where any notation is brought to ab-surdity, such as Figure 3.1b, not to mention the fact that much of the piece looks morelike a circuit diagram than a piece of music (e.g. Figure 3.2), an approach from stand-ard musical notation becomes useless. To interpret this music, it is no use attemptingto convert one form of indeterminate notation to another, but a performance of thisscore requires interpretation. A radical approach would be one that recognises theillegitimacy of symbols in this context and instead approaches the score holistically orpurely graphically. Cardew himself said that:

Graphic music is a type of musical notation. But it differs from traditionalin one very important respect. Whereas a traditional score can be designedto look like anything from Magna Carta to computer print–out (giventhe services of a cunning music typographer/designer), in other words itdoesn’t matter what it looks like except from a purely practical point ofview (legibility), in graphic music the graphic form of the score is fixed bythe composer—the way it looks is crucial, hence the term ‘musical graphics’as opposed to musical notation. (Cardew, 1976/2006c, p. 263)

It is common for graphic scores to be arranged as a time–pitch graph—indeed, mostgraphic scores are arranged vaguely this way, similar to the basic time–pitch andcartesian nature of common practice notation—it is a paradigm with which we are allfamiliar, be it standard notation, graphical representations of changing variables overtime or indeed text—and this idea carries over into modern graphic scores which aimto depict musical variables over time such as Rainer Wehinger’s aural score to György

3.2 Performing Treatise 25

Ligeti’s (1923–2006) Artikulation (1958, score created 1970) (Figure 3.3). Cardew him-self said that Treatise follows this tradition and ‘is written from left to right’. (Cardew,1971/2006b, p. 100)

3.2 Performing TreatiseTo create a performance of such music without a rulebook, the editor is forced to makecertain assumptions about the score to decrease its infinite ambiguity. In creatingrules to decipher notation, the more unlike the notation is to other kinds of notationwe recognise, the increasing number of assumptions the editor and performer mustmake and therefore their conclusions become more tenuous. Many performances ofTreatise thrive on the indeterminate, trusting the artistic impetus of the score toinform improvisation. In approaching Treatise, the jazz guitarist Keith Rowe wouldcompensate for his lack of music–reading by substituting the score with images: ‘I’dget the part from Mike Westbrook, get some idea of what the music was like, finda picture that I thought was appropriate and glue that on to the opposite page ofthe chart. I would play the picture and they would play from the dots’, (Ansell,1985) such was the variety of improvisational approaches to Treatise. Before writingTreatise, Cardew had been working as Karlheinz Stockhausen’s assistant from 1959–1961, realising Stockhausen’s scores by meticulously working through his instructions,such as Stockhausen’s “101 snappy items” for the realisation of Carré. (Cardew, 1961).Cardew resented Stockhausen’s control, such that when performing Plus–Minus inRome in 1964, he and Frederic Rzewski manipulated Stockhausen’s instructions whilststill “playing the game” that Stockhausen had set. (Anderson, 2006, p. 299) It wasCardew’s rejection of the kind of control that Stockhausen impressed upon him thatled Cardew to embrace improvisation and performer freedom as a viable alternativeto increasing performer enslavement to the score evident in Stockhausen’s music.

Both Stockhausen and Cardew are extremists: Stockhausen wished to exerciseas much control as possible over the performer by enforcing rules, whereas Cardewfreed the performer by dispensing with rules altogether. The radical experimentationof the 1960s is long over and the numerous technological advances achieved in theintervening fifty years that have revolutionised the way we create, disseminate andexperience music means that today we need not enslave the performer in order toexplicate meticulous rules. Cardew abhorred rules because his extreme left politicalviews were in opposition to the control that rules must have over another person:he had been restricted by Stockhausen’s musical dictatorship. (Cardew, 1974/2006a,

26 Treatise

p. 166; Tilbury, 1983, p. 4) In his discussion of Cardew, Coriún Aharonián describesCardew most of all as a ‘deeply ethical artist’. (Aharonián, 2001, p. 13) This unwaveringethicism is in part why the group that he co-founded in 1969, the Scratch Orchestra,was so commonly rebellious in their improvisation: the strong Marxist–Leninist viewsthat the group held in common prevented any member of the group from taking control.Creating meticulous rules for Treatise for an human to follow would be anathema toCardew, made clear in the ruleless statement of Treatise: that rules only subjugateanother human to your will, the ego of the composer.

Is it possible therefore to bring the rule–based composition of 1960s Stockhausenand the resentment of rules that was espoused in the improvisations of the ScratchOrchestra together in a single solution? The ultimate subject for rules is the blunttool that will carry out a will without bending, created solely to follow rules. Thecomputer is perhaps this ultimate tool, inoperational without strict rules to operate.Programming and rules are the very elements computers require to function. A whollycomputerised performance would perhaps be an answer to the problems of the compu-tational effort required to create editions of complex, text and rule–based compositionssuch as Stockhausen’s. If the instructions for a score can be encoded in a computerlanguage, then the computer can do the “working–out” for us much more efficientlythan we humans ever could, either in edition or in performance. With computers,composers can create complex rule–based scores and realise them without pressingtheir will upon others.

In similar fashion to Chapter 1—where I edited the source in order to make aperformable edition—and Chapter 2—where I created a general solution as editor—below are the assumptions that I have made in being composer, editor and performer,and the rulebook to play the game that presents itself in Cardew’s puzzling notationand which can then be realised with computer.

3.2.1 Assumptions• As the boundaries of where the music begins and ends are not defined, the entire

score must be considered as valid notation.

• The score reads like a “normal” score: it begins at the front and proceeds left toright in time throughout.

• Any mark on the page is a symbol of positive sound.

• Whitespace is meaningless, it does not contribute to sound.

3.2 Performing Treatise 27

3.2.2 Rulebook

• Proceed from the very beginning of the score to the very end at a constant speed.

• Each page is a time–pitch graph from left to right: the top of the page representsthe very highest sound and the bottom the lowest possible sound.

• A black mark is a sine wave sound.

• The vertical centre of the mark is the absolute pitch of the sound.

• The vertical extent of the mark is the power of the sound, in reference to theheight of the page.

This rulebook implements the assumptions above without more assumptions than arenecessary. However, there are still some details to work out:

• What value does the constant speed take?

• What is the very highest and very lowest sound of the music?

• How does one define a “black mark”?

These details are the most minimal assumptions. Given the larger, sweeping assump-tions as to the nature of the notation already taken in Section 3.2.1, these assumptionsare quite arbitrary. However, I believe that there is some rationale to my decisions.I decided upon a timescale of 4 hours for the entire work, which yields around 70seconds per page. I believe that this is quick enough not to bore the listener but alsoslow enough to hear the individual contours of sound. As for the highest and lowestsounds, I have chosen 20kHz and 20Hz respectively. These figures are frequently citedas the highest and lowest sounds humans can possibly hear and seem like naturalchoices. In defining a “black mark”, when scanning in the entire score to image files,the subtle variations of the paper and ink yielded various shades of grey and off-whitewhereas I wished for an ungraded distinction between black and white because I hadnot accounted for variations in colour as the score is clearly designed in black andwhite only. To create this stark distinction, I took a threshold brightness cutoff ofeach page image, creating image files of solely black and white with no greys or othercolours in–between.

28 Treatise

3.3 Playing the gamePerformance of this particular score is now trivial as long as one is diligent enough toperform the notation according to this rulebook accurately. In Appendix D, I havedetailed a Python program which implements the rulebook set out above and generatesa performance of the input graphic scores. Opening the target image, the programiterates through each column of pixels from left to right and calculates the pitch andpower of each oscillator at each point. Smoothing these data points into exponentialcurves, the program then uses the pyo synthesis module to generate sound from thisdata, finally outputting an audio file of the image. On the CDs listed in Appendix E,the full, 4–hour output from this program can be heard.

This pure, computational and electronically–generated performance has removedambiguous human input to the greatest extent possible. However, it is still the casethat the rulebook and assumptions made—so that the completely ambiguous score canbe transformed into a completely unambiguous performance—are chosen arbitrarilyby human intervention. The creation of the process was human and the assumptionswere arbitrarily chosen. It is only the execution of the performance that was put in thehands of a computer. The decision–maker (i.e. the editor) was still human: a computercannot make decisions in the same manner as an human can, it can only follow rules.Thus in codifying the rules for performance so strictly, the computer has only beenused as a tool for performance, an instrument of my own, human performance throughmy own arbitrary selection of rules by which to perform this score. This computerisedperformance is in no way less human than any other interpretation of a ruleless score,merely an exceedingly precise performance using an exceedingly precise instrument.The role of editor is still definable through the decision–making process and thereforedemonstrates that the lack of rules enhances the duties of editor because the editormust make many more decisions about performance than in an unambiguous scorethat contains well–defined rules.

Conclusion

To return now to the Glass Bead Game: what it lacked in those dayswas the capacity for universality, for rising above all the disciplines. Theastronomers, the classicists, the scholastics, the music students all playedtheir Games according to their ingenious rules, but the Game had a spe-cial language and set of rules for every discipline and sub-discipline. Itrequired half a century before the first step was taken toward spanningthese gulfs. (Hesse, 1943/2000, pp. 26–27)

Any kind of written score must be interpreted symbolically or graphically, that is eitheras a set of symbols or text that are codified instructions, or graphically as a image thatis subjected to rules either known from experience and teaching, set out in anotherpart of the score or invented arbitrarily. Any score that is not completely unambiguousoperates by some kind of codified rules. There are no a priori rules to notation: eachwritten score is a symbolic or graphical system of codified rules. The first example,Missa ad fugam reservatam demonstrates that more than just understanding the rulesof fifteenth–century notation, an editor must also discern the rules to understand thecanon throughout the mass and make decisions on aspects such as text underlay byinventing rules. The second example, Musikalisches Würfelspiel demonstrates thatrules are necessary to “play the game” in the source and the composer as editorcombines the measures according to the rules of the game. The final example, Treatisedemonstrates that without any rules known from experience or teaching or set out inanother part of the score, then rules must be invented by an editor in order to interpretthe score.

As all scores require rules and without rules a score becomes ambiguous, the onlymethod through which a score can be made unambiguous is through performance.After all, a score is little more than codified instructions to inform performance—whether sight–reading or an aide mémoire—and a score (regardless whether it is pre-scriptive or descriptive) is an attempt to write down a performance. Without thetransmission of a score from text to music, the score’s function is diminished to little

30 Conclusion

more than a musical picture or an analytical system. Notational acrobatics and GlassBead Games such as we have seen are interesting studies of the limits and quirks ofmusical notation, but without the goal of performance they cannot become music. Inother words, musical literacy’s validity is wed to orality: a purely literate practice isnot a musical practice. To decode a performance we need no rules, only hearing, andin lieu of performance a faithful audio recording can maintain the unambiguous per-formance in a format that does not require symbolic or graphic decoding. Therefore,the only unambiguous human score in this definition is, for all this portfolio’s emphasison literacy, oral transmission. It is only through memory, repetition and performancethat non-textual music can be transmitted in a way that does not require decoding,and although the transmission is not faultless, in each step it remains unambiguous.However, in literate and prescriptive notation the role of the editor cannot be dis-carded either. With the goal of performance and therefore total unambiguity throughmusical sound, the editor, who must always make decisions of some kind at least, isstill an important step in decreasing that ambiguity from composer to sound throughedition and performance. However, playing Glass Bead Games, that is, attempting togenerate art through rules, bears an important significance. Arbitrary rule–based andchance operations, their vast machinations operating in the realm of unfathomablepossibilities, serve only to remind us that perhaps:

The whole world might be no more than a breath of wind playing over thesurface, a ripple of waves over unknown depths. (Hesse, 1943/2000, p. 497)

References

Adler, G. & Koller, O. (Eds.). (1900). Sechs Trienter Codices: Geistliche und WeltlicheCompositionen des XV. Jahrhunderts, erste Auswahl. Denkmäler der Tonkunstin Österreich. Wien: K. Artaria & co.

Aharonián, C. (2001). Cardew as a basis for a discussion on ethical options. LeonardoMusic Journal, 11, 13–15.

Anderson, V. (2006). ‘‘well, it’s a verterbrate…”: performer choice in Cardew’s Treatise.Journal of Musicological Research, 25(3–4), 291–317.

Ansell, K. (1985, January). AMM: the sound as music. The Wire, 11.Bent, M. (1981). Some criteria for establishing relationships between sources of late–

medieval polyphony. In I. Fenlon (Ed.), Music in medieval and early modernEurope (pp. 295–317). Cambridge University Press.

Bent, M. (1986). Trent 93 and Trent 90: Johannes Wiser at work. In N. Pirrotta & D.Curti (Eds.), I codici musicali trentini a cento anni dalla loro riscoperta (pp. 84–111). Provincia Autonoma di Trento.

Cardew, C. (1961). Report on Stockhausen’s Carré. The Musical Times, 1424, 620.Cardew, C. (2006a). Stockhausen serves imperialism. In E. Prévost (Ed.), Cornelius

Cardew: a reader (pp. 149–227). Harlow, Essex: Copula. (Reprinted from Stock-hausen serves imperialism, by C. Cardew, 1974, London: Latimer)

Cardew, C. (2006b). Treatise handbook. In E. Prévost (Ed.), Cornelius Cardew: areader (pp. 95–134). Harlow, Essex: Copula. (Original work published 1971)

Cardew, C. (2006c). Wiggly lines and wobbly music. In E. Prévost (Ed.), CorneliusCardew: a reader (pp. 249–266). Harlow, Essex: Copula. (Reprinted from StudioInternational, by, 1976, November)

Cook, J. (2014). Mid–fifteenth–century English mass cycles in continental sources (Doc-toral dissertation, University of Nottingham).

Curtis, G. (1979). The English masses of Brussels, Bibliothèque Royale, MS. 5557(Doctoral dissertation, University of Manchester).

Curtis, G. (Ed.). (2001). Fifteenth–century liturgical music, IV: early masses and mass–pairs. Early English Church Music. London: Published for the British Academyby Stainer and Bell Ltd.

Dennis, B. (1991, June). Cardew’s ‘Treatise’ (mainly the visual aspects). Tempo, 177,10–16. New Series.

Feininger, L. (1949). Missa ad fugam reservatam. Documenta polyphoniae liturgicaeS. Ecclesiae Romanae. Roma: Societas universalis Sanctae Ceciliae.

Gerber, R. (1992). An assessment of Johannes Wiser’s scribal activities in the Trentcodices. Musica Disciplina, 46, 51–77.

Gerber, R. (Ed.). (1998). Sacred music from the cathedral at Trent. University ofChicago Press.

32 References

Hedges, S. (1978, April). Dice music in the eighteenth century. Music & Letters, 59(2),180–187.

Hesse, H. (2000). The glass bead game (R. Winston & C. Winston, Trans.). London:Vintage. (Original work published 1943)

Leverett, A. P. (1995). Song masses in the Trent codices: the Austrian connection.Early Music History, 14, 205–256.

Loyan, R. (1967). Canons in the Trent codices. Corpus mensurabilis musicae. Roma:American Institute of Musicology.

Mitchell, R. J. (2001, October). A forgotten mass and its composer. Plainsong andMedieval Music, 10(2), 135–154.

Source: I-TRbc MS 1375 [88]. (nodate). Accessed 2015-03-30. Retrieved from http://www.diamm.ac.uk/jsp/Descriptions?op=SOURCE&sourceKey=808

Treatise: An Animated Analysis. (nodate). Accessed 2015-03-24. Retrieved from http://www.blockmuseum.northwestern.edu/picturesofmusic/pages/anim.html

Strohm, R. (1993). The rise of European music, 1380–1500. Cambridge UniversityPress.

Tilbury, J. (1983, Spring). Cornelius Cardew. Contact, 26, 4–12.Wright, P. (1995, November). Paper evidence and the dating of Trent 91. Music &

Letters, 76(4), 487–508.Wright, P. (2003, August). Watermarks and musicology: the genesis of Johannes

Wiser’s collection. Early Music History, 22, 247–332.Wright, P. (Ed.). (2013). Fifteenth–century liturgical music, VIII: settings of the

Gloria and Credo. Early English Church Music. London: Published for the BritishAcademy by Stainer and Bell Ltd.

Zbikowski, L. M. (2002). Conceptualizing music: cognitive structure, theory, and ana-lysis. Oxford University Press.

http://www.diamm.ac.uk/jsp/Descriptions?op=SOURCE&sourceKey=808http://www.diamm.ac.uk/jsp/Descriptions?op=SOURCE&sourceKey=808http://www.blockmuseum.northwestern.edu/picturesofmusic/pages/anim.htmlhttp://www.blockmuseum.northwestern.edu/picturesofmusic/pages/anim.html

Appendix A

Missa ad fugam reservatam edition

Missa ad fugam reservatam

Standley

Trent 88:314v–322vIn this edition, each movement is prefaced with the original clefs, mensural signs

and key signatures. The compass of each voice per movement is also shown. Notevalues are the same as in the manuscript. Longs and maxima can either be perfector imperfect: their exact duration can be discerned from their synchronisation in thecontext of the score. Notes of any duration may overflow a barline and the excessduration is subtracted from the following measure. No attempt to represent signumcongruentiae is made as they are rendered functionless by the explication of the canonand the transcription to score layout. However, ligatures are denoted by continuoussquare brackets and passages in colouration by a pair of angled brackets. Ficta havebeen added at the relevant places, most notably at leading–note and double leading–note cadences, as well as flattened expressions to avoid phrases with an emphasisedtritone. Text in italics is in the source but either repeated, set to a voice which did nothave any text (voices II and III throughout), or set to a different passage to which itappeared in the source. Text in square brackets does not appear in the source but hasbeen added to complete the text setting. Some original text setting in the Gloria hasbeen ignored in order to telescope the missing lines “Domine fili unigenite iesu christe”,“Qui tollis peccata mundi suscipe deprecationem nostram Qui sedes ad dexteram patrismiserere nobis” and all original text setting in the Credo has been ignored in favourof a telescoped textual reconstruction, replacing all the missing text. Assuming thatthe other extant piece by Standley, the motet Que est ista (an Assumption antiphon)

34 Missa ad fugam reservatam edition

which operates the same canonic principle as this mass is inextricably related, I haveselected the Gloria chant incipit from Missa cum jubilo (Missa IX) which is used forFeasts of the Blessed Virgin Mary. I have also used the Credo chant incipit from thesame mass as this was the only Credo incipit in use pre-reformation.

Emendations

Scoring

Voice ‘I’: unlabelled, clef C1.Voice ‘II’: Contratenor, clef C3.Voice ‘III’: Tenor, clef C3.Voice II and III are written in canon.

Kyrie eleysonIII

Bar 12: m.s. is missing flat signature until end of Kyrie.

Gloria in excelsis deoI

Bar 19: m.s. has:� � � ��

Bar 27: m.s. has: � ��

Bar 37: m.s. has:� � � ��

(the minim G and semibreve A are superfluous).

Bar 80: m.s. has: �� (the minim G is superfluous).

Bar 147: m.s. has:��

35

III

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Bar 41: m.s. is missing flat signature until end of Gloria.Bar 61: m.s. repeats the syllable “tu”.

Bars 126–127: m.s. has:

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Bar 123: m.s. has:� ��

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II

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Bar 84: m.s. is missing flat signature until end of Credo.Bar 99: ‘3’ in m.s. is superfluous.Bar 105: ‘3’ in m.s. is superfluous.

37

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Documents

yokermusic.scot · Abstract These projects all aim to answer the same question: to what extent must an editor make decisions in order to make a piece of music performable? Through