Pythagoras and Pierrot

STERNE, COLIN C., Pythagoras and Pierrot: An approach to Schoenberg’s use of numerology in the construction of "Pierrot lunaire”, Perspectives of New Music, 2/://2 (1982:Fall/Winter—1983:Spring/Summer) Extracted from PCI Full Text, published by ProQuest Information and Learning Company. ÉL Qiu p6a2;k 4 PYTHAGORAS AND PIERROT an approach to Schoenberg’s use of numerology in the construction of ‘Pierrot lunaire’ | CoC. lSte irne n “It is not superstition, it is belief.”* Thus did Arnold Schoenberg defend the importance he attached to the power of numerology and to its influence on his life. His fear of the number thirteen is common knowledge. So, too, is the way in which that number marked his birth (September 13, 1874) and death (Friday, July 13, 1951, at age 76). Schoenberg is said to have observed the flagging of his creative energy during the compositional process at measures whose numbers were thirteen or its multiples, a circumstance that reportedly led to his numbering of measures in his manuscripts as 12, 12a, 14. We are told that even the choice of a name for his son, Lawrence Adam, was made only after Roland, the name originally intended for him (and an anagram of his father’s first name), was found to be numerologically unfavorable. Schoenberg's almost pathological fear of the number thirteen produced forebodings of his death, and, one suspects, may even have contributed to bringing it about. Nor has the number symbolism of Schoenberg’s Pierrot lunaire (ur been completely overlooked. It has been noted that for his Opus 21 Schoenberg chose 21 of Albert Giraud’s fifty poems as texts (translated from French into German by Otto Erich Hartleben), giving the work the complete title Dreimal sieben Gedichte aus ALBERT GIRAUDs Pierrot lunaire, and beginning to compose it in the third month of a year containing the symbolic digits 21 in reverse order, 1912. In spite of all this, surprisingly little attention has been focused on the part that the Copyright (c) 2001 ProQuest Information and Learning Company Copyright (c) Perspectives of New Music, Inc.

Pythagoras and Pierrot: An Approach to Schoenberg's Use of Numerology in the Construction of 'Pierrot lunaire' Author(s): Colin C. Sterne Source: Perspectives of New Music, Vol. 21, No. 1/2 (Autumn, 1982 - Summer, 1983), pp. 506534 Published by: Perspectives of New Music Stable URL: http://www.jstor.org/stable/832890 . Accessed: 05/02/2011 10:58 Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at . http://www.jstor.org/action/showPublisher?publisherCode=pnm. . Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. Perspectives of New Music is collaborating with JSTOR to digitize, preserve and extend access to Perspectives of New Music. http://www.jstor.org

PYTHAGORAS AND PIERROT an approach to Schoenberg's use of numerology in the construction of 'Pierrot lunaire' Colin C. Sterne "Itis not superstition, it is belief."1Thusdid ArnoldSchoenberg defendtheimportance he attachedto thepowerof numerology andto its influence on hislife.Hisfearofthenumberthirteen is commonknowledge. 13, So, too,is thewayinwhichthatnumbermarkedhisbirth(September 1874) anddeath(Friday, July13, 1951,atage 76). Schoenbergis saidto haveobservedtheflaggingof hiscreativenergyduringthecompositional processat measureswhose numberswere thirteenor its multiples,a circumstance thatreportedly led to his numberingof measuresin his 14. as 12, 12a, Wearetoldthateventhechoiceof a name manuscripts for his son, LawrenceAdam,was madeonlyafterRoland,the name intendedfor him(andan anagramof his father'sfirstname), originally wasfoundto be numerologically unfavorable. almostpathoSchoenberg's fear of the number thirteen producedforebodingsof his death, logical one even have to bringingitabout. contributed and, suspects,may Nor has the numbersymbolismof Schoenberg'sPierrotlunaire been completelyoverlooked.It has been notedthatfor his Opus 21 Schoenbergchose 21 of AlbertGiraud'sfiftypoemsas texts(translated fromFrenchintoGermanby OttoErichHartleben), givingtheworkthe title Dreimal sieben Gedichte aus ALBERT Pierrot GIRAUDs complete lunaire,and beginningto compose it in the thirdmonthof a year containingthe symbolicdigits21 in reverseorder,1912. Inspiteof all littleattentionhas been focusedon the partthatthe this, surprisingly

numbers 3 and 7 play as structuraldeterminantswithin the worksomethingSchoenberg'stitleobviouslysuggests.2 Pierrotlunaire is indeed governed by numbers, not by the crisp, bright numbers of mathematics,but by the more shadowy, moonlit numbers of numerology. Some knowledge of basic numerological procedureis essential,then, beforeapproachingthe music.3 The numerologistis convincedthat numbersand numberrelationships governthe universeand thatthe well-beingof an individualdepends upon his being in accordwithcosmic vibrations.He traceshis beliefback to antiquity-tothe Egyptians,Hebrews,Chaldeans,Phoenicians,Chinese, and Hindus-but it is Pythagorasto whom he gives creditfor establishing the system in the West. As to the power of numberson individuals,a person's name and birthdateare the two areas where the influenceof numbersis most stronglyfelt.To determinethe severalnumbervibrations in a person'sname,the lettersof the alphabetare numberedconsecutively from 1 through26. In all aspects of numerology,however,double-digit numbersare reduced to single-digitnumbersby adding the digits.The tenthletterof the alphabet,J, for example,is not numbered10, but 1. The followingchartwilldemonstratethe procedure. 1 2 3 4 5 6 A B C D E F J (K) L M N O S T U (V) W X 7 G P Y 8 H Q Z 9 I R Note thattwo letters,K and V, are parenthesized.They are the 1 th and 22nd lettersof the alphabetrespectively,and theyretainthose values. Exceptionsto the generalrule, 11 and 22 are neverreducedin traditional numerologyand are referredto as masternumbers. The application of the chart may be demonstrated by using Schoenberg'sname: ARNOLD SCHOEN 195634 1386552597 10=) 1 +(= 51 =) 6 = 7 B E RG

The process is thatof assigningeach letterin the name its number value, arrivingat two sums, one for the firstname and one for the last, reducingthose sums by addingdigits,and arrivingat the finalsum, 7the basic numbervaluefor Schoenberg'sname. "Expressionnumber"is the numerologicalterm. But there are additionalnumbersto be derived from a person's name. Here is a list of those pertainingto Arnold Schoenberg:4 FirstName LastName Total + = 7 1 6 Basic number(expression) + = 11 Consonants(quiescentself) 3 8 + = 5 7 Vowels(soul urge) 7 = 1 Firstinitial(cornerstone) 1 + = 7 Totalnumberof letters(namecycle) 6 1 The procedurefor arrivingat the birthdate numberis not pertinent to the matterimmediatelyat hand. Nor are the numbersassociatedwith the planets,withcolors, withgems, etc. But numbersare also associated withthe notes of the scale. The traditionalprocedure,one geared to the diatonicscale, was obviouslyof littleuse to Schoenberg.His modification, to be substantiatedpresentlyfrom its applicationin Pierrot,resultsin the followingset of numbervaluesfor the chromaticscale: C C# D D# E 1 2 3 7 5 F F# G G# A A# B 6 7 8 9 1 11 3 It will be seen that Schoenberg's procedureof assigning number valuesto scale degrees is similarto thatused forthe alphabet.A, the tenth note in the chromaticscale, is reducedto become 1, and B, the twelfth note, becomes 3. A#. as expected, is not reduced, but retainsits master number,11. Totallyunexpected,however,is the assigning of 7 to D#, the fourth

note. Schoenberg'sderivationof 7 for thatnote is not difficulto discover: D# is not only the fourthnote in a chromaticscale builton C, but the sixteenthas well. And 16=6+1 =7. But thatcan Schoenberg'sreason be? The most logicalexplanationhas to do withthatfatefulnumber,13. In reduction,13=4. And Schoenbergseems determinedto avoid 13, even in its reduction.An additionalfactormay be thatD# as E b has particular significancefor the composer:as Es in German it is his signaturenote, representingthe initialof his last name. To give this importantnote a 4 value would be unthinkable.(Therewill be occasion to returnto D#-Eb and Schoenberg'smusicalsignaturelater.)Twoadditionalbonuses result from the banishmentof 4 from the canon: (1) the scale is thus made consistentwiththe alphabet,both havinga total numbervalue of 9, and (2) the scale containsa double portionof Schoenberg'sfavoritenumbers, 1, 3, and 7. In the title of PierrotSchoenberg indicatesthe importancein the work of two numbers,3 and 7. The importanceof their product,21, is also implied,and although21 does indeed assume some importancein Pierrot,it must be rememberedthat numerologically21 =3. It has been pointedout, for example,thatthe opus numberof Pierrot,21, is reversed in the lasttwodigitsof the yearof itscomposition,1912. Butthis is notthe is nota partof the numerologist'svocabulary. point.The term"retrograde" Ratherare 12 and 21 relatedbecause both are 3 values. On the other hand,the sum of 3 and 7 is importantin Pierrot.The additionof numbers is, afterall, an essentialpartof numerology:7+3=10=1. Numerologists often point out, though, that a number arrivedat by reduction never completely loses its original imprint.A 1 arrivedat through 10, for example, still retainsthe vibrationsof 10. This fact will figure to some extentin the analysisof Pierrot. There are, then, three numbersthatassume primaryimportancein Pierrot:3, 7, and 1. Numbers21 and 10 lurkin the background,making theirpresencefelt,but not being putto use except as 3 and 1. Two other numbersfigure in Pierrotthatare not singled out in the title of the work: the master numbers, 11 and 22. There are several reasons for their appearance. The first of these has to do with their numerologicalsignificance.It must be kept in mind that3, 7, and 1 are not merelynumbersto numerologists.Theyare noteven "lucky"numbers. Ratherare they powerfulforces for good or evil, exertingtheirinfluence on the universeand profoundlyaffectingthe livesof individuals.Or at least

theywere thatforArnoldSchoenberg.Hereare meaningsfor 3, 7, and 1 thatare generallyagreed upon by numerologists: 3 - artist,the realmof artisticexpression 7 - priest,the realmof spirituality 1 - creator,innovator,pioneer,the realmof invention,of innovation The three numbersmay be seen as appropriateto ArnoldSchoenberg. But more important,they are particularlyappropriateto Pierrot lunaire,where the art-artistrelationshipand the spiritualaspect of that relationshipis a primarytheme. 11 and 22 havethese meanings: 11 - idealist,visionary,dreamer,the realmof artistic inspiration 22 - practicalidealist,one who uses his powerto benefit mankind the Again, appropriatenessof these numbersto the subjectmatterof Pierrotis apparent.The strongflavorof 11 and 22 throughoutthe final the firstsong in Pierrot,suggests Schoensection of "Mondestrunken," figuredescribedthere.5 berg'sviewof the Poet-Pierrot-Schoenberg Number 11 is also importantbecause it figures among Schoenberg'sown name numbers.Andfinally,it is of some interesto note thatit is associated with someone else who figures in Schoenberg's work: Pierrothimself,whose totalname numberis 11, whose initialnumberis 7, and whose name contains7 letters. The 3X7 poems of AlbertGiraudwhich Shoenberg selected for Pierrotare each thirteenlines long. However,the poeticform,thatof the rondeau,saves the composerfromever havingto come to gripswith 13, since lines one and two of each poem are repeatedas lines seven and eight,and line one is repeatedagainas line thirteen.The resultis only 10 (=1) differentlines in each poem. Schoenberg'scomposition,his Opus 21 (=3), was composed in 1912 (=3), whenthe composerwas 37 years old (= 10= 1). He commencedworkon the compositionon Tuesday(day 3 of the week), March(month3) 12 (=3), and he had completed20 of the 21 songs by May30. He delayedcompletingthe work,however,until he could completethe remainingsong on Tuesday(day3), July(month7) 9-the numbersof the twodates, 12 and 9, addingup to 21 (=3).6 Inhis otherwiseGermantitle,Schoenbergretainsthe French"Pierrotlunaire"and a reciterare called with7 lettersin each word. Five instrumentalists

for to performthe work,and they, plus a conductor,forma group of 7. Withthe threespecifiedalternateinstruments(piccolo, bass clarinet,and viola),this numberbecomes 7+3= 10= 1. A most impressivedisplayof Pierrotnumbersis presentedon the 1914 edition'stitle page, the formatof which must certainlyhave been overseenby the composer.The numberof lettersand of words in each of its lines is used to producethe significantnumbersof the composition: words per line 3 INTERPRETIN DERERSTEN ZEHME FRAUALBERTINE INHERZLICHER FREUNDSCHAFT 3 3 letters per line 20=2 18=9 24=6 17=8 =22 DREIMAL GEDICHTE SIEBEN 21=3 AUSALBERT GIRAUDS 16=7 PIERROT LUNAIRE 14=5 VONOTTOERICH (DEUTSCH HARTLEBEN)28=1 3 3 2 5 =16= - 16=73 7 6 =16= 7' FCreineSprechstimme 19=1 Flote(auchPiccolo),Klarinette Klavier, (auchBass- 41=5 undVioloncell 40=4 Klarinette), Geige(auchBratsche) 10=1 - =11 1 1 2 =4. (MELODRAMEN) von ARNOLD SCHONBERG 10=1 3 15=6

Eventhe individualpoems of Pierrotshare,for the most part,in this number play with words and letters,and one factor in the composer's choices from Hartleben'sfiftytranslationswould seem to have been whetheror nottheirnumbersfittedhis own scheme. The textof "Mondestrunken,"the firstof the songs, fitsextremelywell: words per line 7 7 41 3J Den Wein,den man mitAugentrinkt, Giesst Nachtsder Mondin Wogen nieder, Und eine Springflutuberschwemmt Den stillenHorizont. 16= 7 41 9 5 7 7 letters per line 27=9 32=5 29=1 1 18=9 34=7 Geluste,schauerlichund suss, Durchschwimmenohne Zahldie Fluten! Den Wein,den man mitAugen trinkt, Giesst Nachtsder Mondin Wogen nieder. 25=7 31 =4 27=9 32=5 25=7 6' 6 5 8. 7 7 Der Dichter,den die Andachttreibt, 29= 11 Berauschtsich an dem heilgenTranke, 31 =4 25=7 Gen Himmelwendeter verzuckt Das Hauptund taumelndsaugt und schlurfter 37= 1 27=9 Den Wein,den man mitAugen trinkt. 32=5 19=10=1 will also serve to demonstratethe musical pro"Mondestrunken" cedure of Arnold Schoenberg. The three stanzas of Giraud's poem impose on the piece its overalldesign of threemusicalsections,the close of each section being markedby a ritard.Section I is 14 (=5) measures in length.Section IIalso consists of 14 (=5) measures,and Section IIIis

11 (=11) measures in length. The total length of the piece is 39 (=12=3) measures,but its numerologicalengthis 5+5+11 =21 =3. The influenceof the fivenumbers,1, 3, 7, 11, and 22, is felt,however,not only in the totallengthof the piece and in the lengthsof its threesections, but in the lengthof everyone of its componentphrasesas well. The time span of each phrase(and each rest) is measuredin unitsof eighthnotes, sixteenthnotes, or, less frequently,quarternotes. Schoenberg'schoice of the unitof measureseems to depend on the predominantactivitywithina phrase. At times the activityof the lines concurrentwith a phrase will determineits unitof measure. Withineach phraseeach note will have a pitch numbervalue, and the sum of these values,in appropriatereduction,willbe the pitchnumber valueof the phraseas opposed to its time span value. Two additionalsets of numbervalues are generatedby the music. The firstof these derivesfromthe measurementof distancesbetweenthe individualpitchesof a phrase.Appliedto chords,the measurementis that of the distancebetweeneach of the pitchcomponentsof the chord.These intervallicvaluesare normallymeasuredin semitones.The second set is a simple quantitativenumbering of the pitches that go to make up a particularsegment of a line. To sum up, there are four elements in the closed number-system used by Schoenbergin Pierrot: 1. Pitch values, derived from the numbers as assigned by Schoenbergto the twelvenotes of the chromaticscale 2. Time span values, derivedfrom measuringthe lengthof a musicalstatement(or rest) in eighth notes, sixteenthnotes, or quarternotes 3. Intervallicvalues, derived from measuring the distances between pitches, in either a melodic line or a chord formation,the unit of measurement normallybeing the semitone 4. Quantitative pitchvalues,derivedfromcountingthe number of pitchesthatgo to makeup a particularmusicalstatement The process will be clarifiedby actuallyapplyingit to Schoenberg's music.A score of "Mondestrunken," containinga numerologicalanalysis, formsan integralpartof the presentarticle.Inpursuitof clarity,onlyslurs and phrasemarkingshavebeen retainedwiththe notes of each part,such markingsas those of dynamicsand tempo havingbeen eliminated.The

part for the reciter has been beamed in order to make phrases more apparent,and Schoenberg's note stem cancellationsin that part have been removed. Numbervalues for the time span of each phrase have been placed below the staff,those for pitches have been placed above, with totals circledforemphasis.Inextendedphrases,particularly those of the reciter, subtotalsof smallerunitshavebeen calculatedwheretheyare appropriate. Eachsubtotalis markedwitha semicircle.Finaltotalshavebeen computed fromthemand circled.7 "Mondestrunken" beginswitha quasi-ostinatofigureplayedbyviolin and piano.The violinfigureis one of 3 notes. Each of the two pitchesin the figure,F and D#, has a pitchvalue of 7, and 3X7=21 =3. The 3 eighthnotes of the figure,withtheirinitialeighthrest (= 1), are repeated four times, therebyoccupyinga time span of 16=7 eighth notes. The rangeof the figure(D#-F#)is 3 semitones. Meanwhile,the piano is playinga figureof 7 notes (precededby a single sixteenthrest = 1). The pitchvalueof these notes is 9+5+1 +3+ 1 +2+8=39=12=3. The four repetitionsof the figureoccupya time of 16=7 notes. The rangeof the figure,c"#-g"'#, measured span eighth in semitones,is 19= 10= 1. Alternatively, the intervalC#-G# ifconsidered withinan octave, representsa distanceof 7 semitones. The unreduced sum of the pitches is 39-the same figure as the total number of And its intervallicvalue, measured in measures in "Mondestrunken." 11. Butin thisparticular semitones,is 4+4+2+4+9+6=29= instance, an interestingalternativemeasurementcan be made withthe unitof the whole tone: G# to E=2 whole tones, E to C=2 whole tones, C to D= 1 whole tone, and D to Bb=2 whole tones. Withthe sum thus far at 7, a switchis then made to the second of the two availablewhole tone scales, and the final C# to G=3 whole tones. The result is 7+3=10=1. Acceptingthisdivisionof the 7 notes into5+2 leadsto anotherrevelation. The pitchvalue of the firstfive notes is 9+5+1 +3+11 =29= 11, and thatof the finaltwo notes is 2+8= 10. 11 + 10=21. Beforethe violinand pianofiguresare concluded,the flutemakesan entry followinga rest with a time span of 10 (=1) eighths. His line occupies a time span of 10 (=1) eighths,and the pitchvalue of his five The intervallicvalue of his phrase notes is 1+11+1+7+1=21=3. (measuredin semitones)is 14=5, a subtotalwhich,when addedto the 7 value of his second phrase,resultsin 12=3.

The reciterdelaysfor a time span of 7 eighthsbeforeenteringwitha phrasewhose time span is 21 (=3) eighths.Itspitchvalue is 1 1 +4=15 the total of =6, but thatof the followingphrase is 22+6=28=10=1, the two phrasesbeing 6+1 =7. The intervallicvalueof the firstphraseis 34=7, while that of the second phrase is 49=13=4. 7+4=11. The second phrase, incidentally,since it begins with three sixteenth notes followinga sixteenthrest, must have its time span measurementmade in sixteenths.Thatvalue is 39=12=3. The quantitative are as pitchvalues in Section I of "Mondestrunken" follows; Flute =3 5+(13=)4+(14=)5+(16=)7=21 Violin (12=)3+(28=)1 + 1 + 1 1 = 16=7 Reciter (31=)4 Piano (28=)1 +(19=)1 +9+(34=)7+(12=)3+(14=)5=26=8 The partfor the reciter in Section I contains 31 pitches, a figure which at firstseems disappointing.In measure 8, however,Schoenberg takes an unusualaction: he insertsan eighth rest betweenthe syllables "Spring"and "flut."This caesura not only producesan unexpectedpitch valueof 22 at thatpoint,butalso dividesthe line into21 pitchesplus 10 values. pitches.3 and 1 are thus the two quantitative The totalquantitative valueforthe section is 22. The totalforSection IIis also 22, and thatfor Section IIIis 11. 22+22+11 =55=10=1. Both the flute and the reciter begin and end their phrases at the on the note A (= 1) and pivotaroundthat beginningof "Mondestrunken" pitch. Of more interestis the very first note of the piece-the piano's opening G# Thatnote marksthe beginningof each of the threesections of the song. Itsnumbervalue is 9, and it functionsthus. G# is, however, not only the ninthchromaticnote, but note 21 as well-a fittingkeynote, then,to the song and to the entirecomposition. The procedureto be observedin "Mondestrunken", as it continues to unfold,is the procedurefor the whole of ArnoldSchoenberg'sPierrot lunaire.1, 3, 7, 11, and22 retaintheircontrolthroughoutthe composition. Whatis fascinating,however,is the richvarietyof approachesto those key

numbers.PartII,thatjourneyintothe darknightof the soul, summonsup, as might be expected,frequentappearancesof 13. The malevolenceof that numberis felt only briefly,however,before it is swiftlytransformed intosomethingless sinister.Examplesare the openingpianonotes of No. 8 (5+8), the firsttwo notes of the reciterin No. 9 (8+5), the firsttwo stringchordsof No. 10 (8+5), the firsttwo notes of the reciterin No. 12 (5+8), and the firsttwo notes of the reciterin No. 13 (6+7). As befitsthe poetry,thereare morefelicitousappearancesof number 5 (freedom,change, accordingto numerology)in PartIII.Two of them (5+5=10=1) in the piano partare the last instrumentalsounds of the piece. They are precededby one of Schoenberg'smusicalsignatures,in this instancea multi-layeredone (A, S, AS, and A. SCHoenBErG)played by the pianoand occurringin measure28 (= 10= 1) of the finalsong. But certainlyby now the point has been made: numbersymbolism composition,a playsa crucialrole in the organizationof thisextraordinary role that Schoenberg was carefulto point out in the title,and one that cannotbe ignoredin any thoroughstudyof the work'sstructure. Finally,in spite of the factthatthe titleof Pierrotlunaireis the single instanceof itscomposerindicatinghis use of numerologyinthe structuring of a work,the procedureis not at all peculiarto thatcomposition.Used systematicallyat least as early as the Chamber Symphony,Opus 9, numerologycontinuedto be used by Schoenbergas a structuraldevice in his music untilthe veryend of his life.Throughouthe periodSchoenberg remainedloyalto the numbersused in Pierrotlunaire:1, 3, 7, 11, and this meagertroupeassumes innumer22. Butwithastonishingversatility able roles in constantlyvaried settings and with an ever changing supportingcast. Thattheircontributionto Schoenberg'smusic has gone unnoticedis mostunfortunate. Overlookingthe prevailingnumbereuphony in a work such as Erwartung,for example, has led to frustrationon the partof thosecriticswhose diligentsearchhas beenfora moreconventional systemof order. Perhaps most astonishing of all, even Schoenberg's twelve-tone music retainsthis indispensablesecond layer of numerologicalorder. The row may proposethe sequence in which pitchesare to be used in a particularcomposition, but rhythms,phrase lengths, cadence points, section lengths,note repetitions,chordformations,and rowtranspositions are all regulated,not bythe row,butbythe numbervaluesof numerology. Indeed,an examinationof Schoenberg'srowsthemselveswillrevealthem

to be, not arbitraryarrangements of twelve notes, but the careful integration of the number values of those notes. Itfollows, then, that to emphasize the numbers of the row in this later music, as has been done, and to ignore the mystical figures of numerology is to project a seriously distorted image of the composer and his work. NOTES (1) Quoted by WalterRubsamenin "Schoenberg in America," The Musical Quarterly,vol. XXXVII,no. 4, October, 1951. (2) George Perle,for instance,(in his article"Pierrotlunaire,"publishedin The Commonwealthof Music,editedby GustaveReese and Rose Brandel,The Free Press, New York, 1965) makes the statementthat"Schoenberg'suse of magic numbershas, of course, no musicalsignificance.Since each of the poems consists of thirteenlines, an unluckynumber,perhapshe thoughtit well to organize the whole according to two lucky numbers, three and seven." (3) Much of the informationon numerologyis supplied from Your Days Are Numbered by Florence EvylinnCampbell, M.A., The Gateway,Ferndale, Pennsylvania,1931. There are many more modern, more systematic handbookson the subject,but this ratherquaintpublication,a classic in its field, reflectsnumerologyas it was practicedduringthe firstquarterof the century,the periodwhenSchoenbergmusthavefirstbecome interestedin it. (4) The composer used the originalspellingof his name, "Schonberg,"during the periodof the compositionof Pierrot.The change to "Schoenberg"was evidentlymade soon afterhis arrivalin the UnitesStatesin 1933. The name numbersfor the originalspelling are presented below for comparison. In computingthe expression number,rawvalues have been used ratherthan reduced ones in order not to conceal the importantotal, 11. ArnoldFranz WalterSchonberg,his rarelyused full name, has a consonantnumbervalue

ARNOLD Expression Quiescentself Soul urge Cornerstone Name cycle SCHONBERG 138652597 Total FirstName LastName 28 (= 10) + 46 (= 10) = 74=1 1 11 = + 8 3 + 7 =18=9 11 =1 + =15=6 9 6 (5) ThatSchoenberg identifieswiththe poet is stronglysuggested by the music. Firstof all, the cello, havingremainedmute duringthe firsttwo sections of enters with an impassionedsong at the firstmentionof "Mondestrunken," the poet. Solidlygrounded by a 3-note pedal (10=1), and with the violin soaring airilyabove it, this line is saturatedwith 11's untilit finallycomes to rest withfive pizzicatochords. The four-notechord of the final bar, played twice, consists of the notes C, B (H in German), D# (read as Eb, S in German),A-forming the signatureA. SCH.Recallingthatreducednumbers still retainsome of theiroriginalflavor,the temptationis strongto assign A -a the value of 10 here, therebyreadingthe chord as 1+3+7+10=21 In have the the numbers that controlled as it of summation, were, piece. the to the final has been on that chord, a temptation yielded analyticalscore, chord thatthen has, not only a pitchvalue of 21, but an intervallicvalue of 21 as well. (6) The dates are from Joseph Rufer, The Worksof Arnold Schoenberg:a Catalogueof His Compositions,Writings,and Paintings,D. Newlin,tr., St. Martin'sPress, New York,1962. (7) Neitherthe intervallicnor the quantitativenumbervalues have been entered in the analyticalscore. To have done so would have been to produce an indecipherablejumble of numbers.Then too, the proceduresfor counting notes and measuringintervalsare, afterall, simple enough so as to hardly call for guidance. This action is not to be interpretedas an attemptto minimizethe importanceof either intervallicor quantitativevalues. On the contrary.There are instancesin Pierrot,for example,where the intervallic valuewould seem to take precedenceover the pitchvalue.Such a situation exists in the passacagliathemeof No. 8, wherethe head motiveof the theme, Two is not a significant E-G-Eb, has a pitch value of 5+8+7=20=2. number in Pierrot.The intervallicvalue of the same motive, however,is

Mondestrunken a numerological analysis SIcioN I I it I

1 7'-= SS 10- ( 11 7 2 5 6 - 1 _[iF l 3 2 1 7 9 7 7 1 - 5 7 2 3 391 3 ? - a 3 11 UNDEINE 6 i C' - \i 3 1-=\10= 1 7= 3 2 SPRING- FLUT OBER S 8$ 23 95 623911 I i., 1t 1 3 9 3 DEN 57= S =13 = 2 t 8 2 = t~~~~ .4; Ir 7 SCHWEMMT 666666 mm

l 59 = 7 3 2 8 - = 74 -p- ~ } Jj | I $' 5 1 2 11 S= 172= 10= ? , W}l,,',FL'.() i 11 Oj11 LEN HORI- STILL- 3J 5i I < J5)=( + l= ,4~ = ? IIT II 1IL'~'jy lJJJI I ?,, ?\, j --1 @) 1 7 b 3 7 7= -%=? "- ZONT 9 t 5 =1 12 = = 8, f10 - =D $q 2 <?6~~~~t= XY r r r ,-?I 5b6 2 ,, 1 7 3 blfY 2 3 1 5 b7 3 t^]^$ ?r, 3 36

7 3 'lo -O ? 7 9 7 -- w -' 1 = (^)_-" o-o)=? 7 3 1 r : 13- 8 7 NACHTS DER 3 2i MOND IN WO- 9 7 1 9 S 7 14 . I iLzJLz2 It b..-" 1 NIE- 1 31 = 2 1 3 # DR, 11 r S $FigfS^ (r 2 CEN j j S5 I i = 12 = 10 -C 11 2 I ^Wf^^. m 2 1 -~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~4 (64 1 7 _ 7 .. LS?; r = 27 = It . 9+- z29 = @ - - - -

3 11 2 S 11 3 7 92= a '6 & P& I fo) =T ? . -I +? ~ - \lI1 ~~~ /VX (b ? \It Jr-_ i ,_ ay (NI ,9 ? ~4 ~ /~rTie: SrCTiloI = 14 ARS =5 SPAN=

SECTION r 77 7= 79 = * = (

2f1 f / 7 7 9D f = So= ( 9 I7 11 9= 4+1 = 1 S 2 UND SUS. 1 . 31 1 = Cl = (? 7 7 3 7 711 = Z = (s f | ( 10=t I, 3 1 Gf- LU - f= 9 I 7 11 15=: , l-t4 4 9 3 7 74 JL Ji],, (+ ,lJ '(ZJ 4 ^if^:w t 7 4 IH tI. 1 ra STF, SCAAUi DURCH ,, ?J 5S7 S 3 S 2 7 & f 7 S 3 2 . i ^tf. if 1 ERLICH Ami9 2 7 I 3 ^ .if ,i1 _ L I I 4 , {J^ 19 = lo = O 7 1 = 14 = 10= lI r

7 S 9323 /50 = 12z= (3 9=11 9 ^" 3 4 kJ .J)= @ S6 7 11 / IyJ -I i$ I 9 7 3 3J = ( = * .ji 4 4~.. J 1 9= S 7 1 41 = CS = ....... 1. 2 b 3 7 = 37 - 10= .- . 1 ; 7= 7 30 = C3 7 3 . bA _ ' IfAJ^ 7b 3CHWIlMEN OHNE ZAHL DIE I= 7 7 9^ 0t (g ?^ 5 L 3 1 8 2 17 1 b = 3 Dt# MAINNrT AuOCN 2 , ?t' -~"I I? ' "Loff ds 0*3 of'. i4-J ;.l 1 1 $ " JO4)= T 7914 DEN WEIN, ~* 22 ZN >f k TEN' FLUfT 1-n I "r 3 L P4bg.-- J fgo) (: '1o} f =(D 1 11- 1 2 = I. I. J1 L J 6- ', 11 8= 7 39 = 12 = I -'?" 9 9 o =- i7 Ss = 2 -

55 = k $ffi.?r d- :r (f D (D>' 7 2i= GIESST 5 7= n 'i^J 7J J 4 = =10 = ka zr; cs NACHTS 9 1 3i 9 11 7 1 7= CS- 41I T)^ (D ) 7= 3 1f 3= 3 C, = DER MOND f l .- 1 5= 232= 7 f 1 2 s= = 12 = C I llb If TRINKT, I kI +I i , 3i1= 1 =(D9 2 ;z =C3 = 1Z IN WOOCN J f C 7= HIE - l 9 DER. 11 7 1 4 = f 7= 1 9 r i Kli I- 4 '1~~~ I~~~~~ 4 LE ) Q4) 30u

7) (D at)D^ s 7= 7 7 11= 2= 30=(3 1 9 S= fs= S I 9= I= 34j=(7 k p- 6.,. -lr=~ (:= 9 t) ) 3 3 3 f 1is=(CZ 7 s2) = 10= 7 DER 21 -2r I$ 17 ,-.i fl i) = 10=T 7 5 3= 54=c = 195s i. , I Z_ 11 Z S 11 7 1 7 7 1 6 3 3 11 2 S- - = (1 L_- 1 L I< \ t 11~' t6)= z . i$ ir?- { = io=T , ~ 14 I =SAR SECTIOn ~~~~ = TMESPA

SICTlON S 1 2 11 2 5= I5= Qji 1 (, 2 7 11 7 3 9- 3 S 2 29 7 1= b1= (9 = .1 ? . O FLUTE I T) D)L 1- ) Q 1 11 ?Pr S #= 2/w = (f DICTER, RECiTE 11 9 7 -L -rd, 9 J ff 13 2 3 71&= (7 5 7 7= 19 = lo = DACHr TEtIST, BF- RAUSCHr DEN DIE AN- X,XJ;--.: = 7 = 20 - .g 1 7 9 s9 / 1 7 ,;1 i = 3 7= C X& 95 t (aW AN DEM T ~~~7 ~~ ~ ~5 " j !: 7 2 SICH 1$ f: C' 1 7 7= Jp Cs NILCON

w 1 1x' ( GEN --"' H I 1 7f=^* ?z- = (2- 9 3 2 WENDET ER VEA- ZUCKT 1 .' S~ HIMMEL 9 11 7 7 5 & 3 7= SO = C DAS HAUPT v zs^ t - ) 7~12= ~ S 2 I- I TRANKE, -z-_ 7 7 3 2 7 b- 7 -i 7=12 - 75 - 27 - 3 2 3 1 ~9 = 21a 1 - ^~~it17 11i 29=jb S" / 'I 3 9 2 1 11= 29<8)| 9 1

1 m~T 3 7 S UND TAUrIELNO SAV?T "' 3 4 S S \ 1 3 f1M 2 0= w9 = 12 = Q i^ cR DEN WEI , 3 J DCN MAN MIT 3 9 ?1 IJ 9 J = S = 1i 8 6 2 S 11 ?r jTO:4 -- ---() S 9 '' 21" -f)-Q2 S= /I = 10 = O 9 S 1 i tf n= .f,= ('/ LUD SCALuRFT ' ? i TI A' L^T3 J 1 177 Si = f2 - ( r 37 71 12 :'r"' 1 1 "' i f 2 7 - 1^if- 759 AUrIN ~) = ? f 1 2 J s I---J--=@ V- ' I

A. sci, SICTON mI = 11 sAR Tit SPAN = Stj= 11

NOTESON THEANALYTICAL SCORE Bar Beat 7 1 7 (flute)against3 (violin) 7 1,2 Throughoutthe score, chord formationsreceivetheir pitchvalues fromthe sum of theircomponents.The pianochord on the second beat of this bar,a 10=1 chordwithan intervallicvalue of 11 (and thus the implicationof 21), will laterserve as the 22-J pedal in Section III. 10 1 "stillen"receives special emphasis by being the single word sung in "Mondestrunken." Itspitchvalueis 5+8=13, implying,perhaps, that the horizon is not only still, but, lacking the saving grace of moonlight, sterile and lifeless as well. Such an interpretationis supported by the phrase in the right hand of the piano part beginningon the lastsixteenthnote of measure7. Itspitchvalue is 13 (=4). Dovetailingwith the 13 of "stillen,"the piano 13 is transformedinto a 7, after a dramaticbreak, by the mysterious 3 X 22 chords of measure 10. 10 2 As noted in the score, the pianochord here has a pitchvalueof 22. Its intervallicvalue is also 22. And with the numbers of its component pitches,it becomes a veritablecompendiumof Pierrot numbervalues: 1 +3+7+11 =22. In addition,this series draws attentionto the process by which the originaltwo numbersof the title,3 and 7, generatethe others in the set: 3+ 7= 1; 3+ 7+ 1 = 11; 3+7+1+11=22.

The isolationof the violinG and the factthatit is the only harmonic called for in the song both give the note special prominence. Its function,too, is significant:as 8 it transformsthe phrase which precedes it from a pitchvalue of 11 to one of 10. "Power"is the numerologicalmeaning for 8. Meaningsfor 11 and 10 (1) have been suggested in the body of the text. As must be apparentfrom the several comments made on the measure 10 of the piece), its activityin this measure(appropriately, significancecould best be explained by referringto the numerological meanings of numbers and to Schoenberg's personal interpretationand use of them. A thorough examinationof this subject would be extraordinarilyrevealing, not only for Pierrot lunaire, but for the entire corpus of Schoenberg's work. Such a projectis, of course, quite beyondthe scope of the presentstudy. 26 2 The 5 value as the total for the reciter'spitches in Section II is equivocal.Adding it to the 7 total of Section I results in 12=3, whereascombiningitwiththe totalof Section IIIproduces 16=7. 29 1 The numberof notes in the firstphraseof the cello line is 11, and thatof the second phraseis 10. 11 + 10=21 =3. Withthe semitone as the unit of measure, the intervallicvalue for the first phrase is 34=7. Thatfor the second phrase is 22. 7+22=29= 11. 29 1 The time span for the righthandof the piano partfromthe second halfof this beat untilthe end of bar34 is 29'= 11. 11 (flute)against3 (piano)