- The most sophisticated analysis of this kind known to me is Halsey G.D. Hewitt E. Eine gruppentheoretische Methode in der Musiktheorie Jahresbericht der Deutschen Mathematiker-Vereinigung 1978 80 151 207 but when I reported its main findings in a letter of 1979 to Milton Babbitt he replied that only a minute measure of compositional theory and practice could be encompassed by such considerations.
- For discussion of this and other related numbers in the design of Chartres Cathedral, and their Biblical significance, see James J. The Contractors of Chartres Dooralong and London, , Australia 1978 I especially pp. 150–65 passim (and check the index of ii (1981)). I am grateful for discussions with the author in the late 1970s, which led me to appreciate the significance of gematria and related doctrines for the culture of the medieval period and later. For a general study of the mathematics of cathedral building, see J. L. M. Lund, Ad quadratum. A Study of the Geometric Bases of Classic and Medieval Religious Architecture, 2 vols (London, 1921–1928)
- For an example of these complications in the case of J. [H]Obrecht van Crevel M. Secret structure Opera omnia Amsterdam 1959 I xvii xxv pt 6
- On this context, see Landon H.C. Robbins Mozart, the Golden Years 1781–1791 London 1989 259 260 ch. 12 and Mozart and the Masons … (London, 1982)
- On the prehistory of the Singspiel tradition, see Batley E.M. A Preface to the Magic Flute London 1969 chs. 1–6; and on Schikaneder as the librettist, see section 2.4.
- See, for example Bornhausen K. Mozart's Zauberflöte. Eine künsterische Einkleidung seiner Menschheitsziele im Geiste der Freimaurerei Vorträge und Aufsätze aus der Comenius-Gesellschaft 1913 21 1 1 23 (with notice even given to 18 (section 2.2) on p. 9). Among other commentators, see especially E. (von) Komorzynski: his Emanuel Schikaneder … (Berlin, 1901), pp. 104–40; the revised edition (although not so called) (Vienna, 1951), pp. 170–241; Der Vater der Zauberflöte… (Vienna, 1948), pp. 123–53; and ‘Das Urbild der Zauberflöte’, Mozart Jahrbuch (1952, pb. 1953), pp. 101–10. However, he does not notice the numerology.
- Dalchow , J. , Duda , G. and Kerner , K. 1966 . W. A. Mozart. Die Dokumentation seines Todes Pähl see especially pp. 122–4, 177–84 on numerology, and 143–62 on the Viennese lodges
- Chailley , J. 1972 . The Magic Flute. Masonic opera… London translated by H. Weinstock the original French edition was published as ‘La flute enchantée’ opéra maçonnique (Paris, 1968). The situation of Freemasonry is described in ch. 8. Unfortunately, he does not cite Dalchow (footnote 7); nor does he always indicate the number of entrances (explained in section 2.3), so that correlation of his discussion with the score is sometimes tiresome. However, this book has been the most important source for the research reported in this paper, and I have not cited every detail on which I have drawn. I shall refer below to this edition of the book as ‘Chailley’. A summary of his findings was given in his ‘Die Symbolik in der “Zauberflöte”’, Mozart Jahrbuch (1967, pb. 1968), pp. 100–10. Just prior to the publication of this book, some pertinent insights were presented in R. B. Moberley, Three Mozart Operas (London, 1967): see especially pp. 262–6.
- For example Batley A Preface to the Magic Flute London 1969 W. Mann, The Operas of Mozart (London, 1977), ch. 22 (and compare footnote 33); C. Osborne, The Complete Operas of Mozart (London, 1978), pp. 325–7; and W. Kuckartz, Die Zauberflöte Märchen und Mysterium (Essen, 1985), where the general symbolism is perhaps overstressed and numerology is ignored. Many other books on Mozart, even on his operas, are too slight for our purpose to require citation here; but see also footnote 74. The study by C. Peter provides a very interesting musicological analysis of intervals, rhythms, keys, and so on of this opera; but neither Dalchow (footnote 7) nor Chailley is cited, and their concerns are little addressed (Die Sprache der Musik in Mozart's Die Zauberflöte … (Stuttgart, 1983)). Numerology is taken more towards Fibonacci numbers (see especially pp. 298–300 on Sarastro's aria ‘O Isis und Osiris’); however, as will be explained in section 2.2, this may be rather anachronistic.
- See Archibald R.C. The Fibonacci series Dynamic Symmetry Hambridge J. New Haven 1920 154 157
- Valuable background on Freemasonry and its rapport with music is provided in Thomson K. The Masonic Thread in Mozart London 1977 On the prehistory of sacred arithmetic, see V. F. Hopper, Medieval Number Symbolism (New York, 1938, reprinted 1969); and on the role of geometry in Masonic symbolism, see N. Pennick, Sacred geometry … (Wellingborough, 1980), especially chs. 8 and 9. An excellent edition of Plutarch is his De Isisde et Osiride, translated and edited by J. G. Griffiths (Cardiff, 1970), although the scholarly notes draw of course on Egyptology. For Masonic background in the Knights Templar and their related organizations, see for example, M. Baigent, R. Leigh, and H. Lincoln, The Holy Blood and the Holy Grail (London, 1982), chs. 6–8 passim; or R. le Forestier, in La franc maçonnerie templière et occultiste aux XVIIe et XIXe siècles, second edition, edited by A. Faivre (Paris, 1987).
- For a valuable introduction to Greek roots of sacred arithmetic, attributed to Iamblichis (fl. -4C), see The Theology of Arithmetic Grand Rapids, Michigan 1988 translated by R. Waterfield Figure 1 is known as the ‘Pythagorean tetraktys’, and the 7 dots forming the sloping sides are the ‘Platonic lambda’.
- Moberley . 1972 . The Magic Flute. Masonic opera … 264 – 264 . London translated by H. Weinstock notices Mozart's liking for names of characters in his operas, and suggests that ‘Tamino’ was changed from the correct version ‘Pamino’ so that it could start with the Masonic triad Tugend, Arbeit and Menschheitsziele. Chailley, 102 notes this change (and of ‘Tamina’ to ‘Pamina’), but treats them both as slips made by Schikaneder. I prefer Moberley's position, partly because it is not clear that enough was then known of Egyptian names for the other versions of them to have been entertained.
- The glockenspiel appears in EN2/17, 23 and 29. Mozart told his wife in his penultimate letter to her (conjecturally dated 8–9 October 1791) that it was placed on the side of the stage when he used it to (literally) play a trick on Schikaneder during a performance. See Mozart Briefe und Aufzeichnungen Kassel 1962–1975 IV 159 161 7 vols English translation in The Letters of Mozart and his Family, translated and edited by E. Anderson, third edition (London, 1985), pp. 966–9. I shall refer below to these editions as ‘Briefe’ and ‘Anderson’ respectively. On the 1790 opera, see Komorzynski Schikaneder (1951) (footnote 6), 272.
- The main published sources for these details is von Komorzynski E. Emanuel Schikaneder … Berlin 1901 160 161 his see also his ‘Sänger und Orchester des Freihaustheaters’, Mozart Jahrbuch (1951, pb. 1953), pp. 138–50. He cites a manuscript on contemporary practices in Viennese opera orchestras writen by L. von Sonnleithner and held by the Gesellschaft der Musikfreunde (Vienna). These details are adopted by H. C. Robbins Landon in his 1791. Mozart's Last Year, second edition (London, 1989), pp. 123, 224; and by R. Angermüller in his Monzart's Operas (New York, 1988), p. 224. If the account books of Schikaneder's theatre could be traced, then these details could be definitively settled for this opera.
- Köhler , K.H. , ed. 1979 . Mozart. Die Zauberflöte, Faksimile der autographen Partitur , Documenta Musicologica, series 2 Vol. 7 , Kassel together with an accompanying booklet Beiheft which alone carries copyright information.
- Hildesheimer , W. 1983 . Mozart 317 – 317 . London Compare before him the view of E. J. Dent that ‘It is hard to imagine what process of thought led’ Mozart to accept Schikaneder's libretto, and that the opera was ‘created deliberately for the masses’ (E. J. Dent, Mozart's Operas. A Critical Study, second edition (London, 1947), pp. 211, 265.
- Castelli , I.F. 1861 . Memoiren meines Lebens. Gefundenes und Empfundenes. Erlebtes und Estrebtes Vol. I , 14 – 14 . Vienna and Prague 4 vols 236–7, 320–1. Nevertheless, Landon still grants Gieseke co-authorship in Years (footnote 4), 235. On his later career as the mineralogist ‘Sir Charles Giesecke’, see The Royal Dublin Society, edited by J. Meenan and D. Clarke (Dublin, 1981), pp. 153–62 passim
- Castelli . 1861 . Memoiren meines Lebens. Gefundenes und Empfundenes. Erlebtes und Estrebtes Vol. I , 14 – 14 . Vienna and Prague 232 for both details. The opera was important in 1795 in stimulating Castelli's interest in the theatre, and he played an ape in EN1/15 [E156] in performances that year (pp. 47, 50). Incidentally, the ape was itself an Egyptian symbol: the sun-worshipping baboon, representing the spirit of the dawn.
- This important observation is due to Chailley, 18 (see also p. 296). The original text is at Briefe 4 160 160 the Anderson translation uses ‘passages’ here, which is not sufficiently clear
- I have consulted the editions prepared by M. von Zallinger using the photograph of the autograph (Leipzig and Dresden, 1956, reprinted 1986), and in the Neue Mozart Ausgabe (NMA) Gruber G. Orel A. 1970 19 series 2, pt. 5 See also the next two footnotes.
- This edition was cited in footnote 18. See the article by a co-editor of the NMA edition: Grüber G. Das Autograph der “Die Zauberflöte” … Mozart Jahrbuch 1967 127 149 pb. 1968 (1968, pb. 1970), pp. 99–118
- Freyhan , M. 1986 . Towards the original text of Mozart's Die Zauberflöte . Journal of the American Musicological Association , 39 : 355 – 380 . (see especially p. 380)
- The overture does not carry any number; its first page carries the marking ‘N.13’, altered to ‘N.11’, at its head; but this seems to indicate a numbering of the whole manuscript, with the items numbered in the style ‘N°:13’. Editor Köhler of the autograph lists the numbers—wrongly, in my view—as ‘Mozart's numbering’ Beiheft 26 31 so does Grüber in NMA (footnote 24), x.
- See Mozart's letters to his wife of the first week of July in Briefe IV 144 146 (Anderson, 958–60), in which rather uncomplimentary remarks are made about Süssmayer in the course of sending instructions to him. What, by the way, is Mozart doing allowing his young assistant to be far away from Vienna with his own wife when a complicated new opera needs textual preparation in (presumably) a short time?
- Briefe , IV 177 – 178 .
- Mozart , W.A. 1814 . Jl flauto magico. Die Zauberflöte Bonn n.d. Another difference from the autograph is the inclusion of a full Italian translation of the text.
- The order of staves is: Fl., Fl., 2 x Ob., 2 x Basset horn, 2 x Cor., 2 x Fag., Trbn., Trbn., Trbn., 2 x Cl. Tyson A. Mozart, Studies of the Autograph Scores Cambridge, Mass. According to and London, 1987), ch. 14, Mozart normally had used 10-stave manuscript paper when he lived in Salzburg, but his usual Vienna medium was 12-stave, as with this opera
- The poster is shown in Landon Mozart's Last Year , second edition London 1791 123 123 1989 plate 7 and translated on pp. 139–40 (without notice being taken of the omission); it is also in Years (footnote 4), 236. Mann (footnote 9), 600 points out the omission, but he does not seek any reasons. The text of the poster is transcribed in the Eulenberg edition of the opera edited by H. Abert, (n.d. London), although for some reason the 18th line is omitted. At the front of Schikaneder's libretto (Vienna, 1791), the 19-line cast-list includes the ‘Drei Genien’ just before Papageno (see NMA (footnote 24), xxvii).
- It would be interesting to check if any of Mozart's subscription concerts after 1784 started at 18.00. There is such a hint in Leopold's letter of 16 February 1785 to his daughter of a concert held five days previously: ‘Freytag abends fuhren wir um 6 Uhr in sein erstes subscriptions Concert’ of ‘6 Fastenconcert’ Briefe III 372 373 Later in this letter (p. 373) is his report of Haydn's famous praise of his son, offered at a chamber concert held the night following in Mozart's apartment.
- Der Anfang ist um 7 Uhr' is announced at the bottom of the poster Landon Mozart's Last Year , second edition London 1791 123 123 1989 The intended length of performance at 180 minutes could be consistent with Mozart's October letter to his wife (footnote 18), which he started writing at 22.30 ‘on my return from the opera’; however, in his letter of the previous night, which he also started at 22.30, he had mentioned that ‘As usual’ three items ‘had to be repeated’. Thus either he left early, or or he did not mean precisely the half-hour time; or we have some implicit information here about adopted tempi (compare footnote 42); or there was a short or even no interval. The Davis recording of it (Philips 411 460), which has quite a number of cuts, is timed on the compact disc issue at 162′38″: the Acts run for about 60 and 100 minutes respectively.
- Komorzynski states that Mozart conducted the first two performances on 30 7ber and 1 8ber, and handed on to Henneberg, whose own run started with 7–9 and 13 October Schikaneder 1951 (footnote 6), 226); and his ‘Johann Baptist Henneberg, Schikaneder's Kapellmeister (1768–1822)’, Mozart Jahrbuch, (1955, pb. 1956), 243–45). These data are repeated in Angermüller (footnote 17), 225; Köhler (footnote 15), 15; and Grüber in the NMA edition (footnote 24), ix. In an article on the origins of Die Zauberflöte published in a Viennese journal in 1857, it is stated that Mozart conducted the first 3 performances (with Henneberg on glockenspiel) and that it was given ‘sixteen evenings in a row’. Chailley includes a translation of this article as an appendix of his book (on this point see p. 305); but he warns on p. 25 that the article was anonymous and written long after the event, and that on several details its accuracy is to be doubted.
- See Tyson A. Two Mozart puzzles … The Musical Times 1988 129 126 127 the fragment in question occurs in WM5 at [E115].
- According to Castelli Memoiren meines Lebens. Gefundenes und Empfundenes. erlebtes und Estrebtes Vienna and Prague 1861 I 238 238 However, the 24th performance was given within five weeks of the première (Freyhan (footnote 26), 373), or within October (Angermüller (footnote 17), 224).
- The frontispiece of Schikaneder's libretto is shown in Chailley as Plate 33. It is also in Dalchow W. A. Mozart. Die Dokumentation seines Todes Pähl 1966 Plate 12; and Landon Years (footnote 4), 236. On its symbolism, see A. Rosenberg, ‘Alchemie und Zauberflöte’, Mozart Jahrbuch (1971–1972, pb. 1973), pp. 402–14.
- Landon . 1989 . “ Years ” . In Mozart, the Golden Years 1781–1791 259 – 260 . London Interesting information on the opening Vienna performances, and on the early exports, is given in Angermüller (footnote 17), 222–32, though again no references are given and some details appear to clash with other sources.
- On the French version of the opera, see Chailley, 44–5, 90 and Plates 39–40; anti-Masonic sentiments do not seem to have been involved in the changes. Protests against the distortions were uttered at once by ‘a lady of Germany’ resident in Paris and signing herself ‘D.R.S.’, against an admiring review of the first performances written by a certain ‘S …’ Moniteur universel 1800–1801 1390 1390 1483
- Mozart's wife Constanze must have been aware of at least some of the Masonic features of Die Zauberflöte (compare his letter to her discussed in footnote 23); but she said little about them in her survey of the opera. However, she commented interestingly on the excessively slow tempi that had come to be applied to Pamina's aria WM17 and the trio WM19 Anhang zu Wolfgang Amadeus Mozart's Biographie Leipzig 1828 112 129 reprinted Hildesheim, 1984 (p. 124)
- This edition was cited in Mozart Jahrbuch 1951 Pre-established harmony determined that when researching for this paper I found and bought the copy of the Eulenberg edition of the pocket full score which was once owned by the late William Mann. His annotations include a few of the features discussed here, but they are not done in any systematic way, and (so) they are not prominent in his study (footnote 9) However, finding this copy brought back pleasant memories of the late 1960s, when for a few years my wife and I placed our small tent next to his large one at the campsite at the Aldeburgh Festival.
- The first flute does not play in the first 3 bars and the second only in the last. The Masonic use of 3 knocks may go back to the same practice effected in medieval times at the consecration of a cathedral, along with 3 sprinklings of water and the lighting of 12 candles Hopper Medieval Number Symbolism New York 1977 114 115
- It is well known that this melody is strikingly similar to the first subject of Clementi's Piano Sonata op. 24 no. 2 (in B ), which he performed in 1780 in a competition with Mozart. At the time Mozart reported to his father with disdain about his competitor Briefe III 188 188 Anderson, 789–90); and since the melody does not reappear in the same form in the opera, there may have been some ulterior purpose in the allusion. Clementi seems not to have been a Mason, but I follow Chailley, 179, in assuming that a coincidence is not involved here; see also his ch. 11 on the significance of the 5 opening chords of the overture.
- On this and related points see Freyhan Towards the original text of Mozart's Die Zauberflöte Journal of the American Musicological Association 1986 39 375 377 where the differences of word setting between the autograph and the 1814 Simrock edition are thoughtfully discussed. For an account of the revisions of libretto made in some WMs by Goethe's brother-in-law, C. A. Vulpius, for the launch of the work in Weimar in 1794, see Komorzynski Schikaneder (1951) (footnote 6), 251–60.
- The account of these two WMs given in Landon 1791 Mozart's Last Year , second edition London 1989 130 is confusing: although he refers to WM10, he then discusses WM18.
- The rhythm of Sarastro's figure for ‘Die Stunde schlägt’ is always the 5tet qurest/qu/qu/qu/cr (on the beat), very similar to the famous motif which opens Symphony no. 5 (sic) of that numerologist and great admirer of Die Zauberflöte Beethoven …. On the symbolism of midday (which is explicitly mentioned by Papageno in EN1/14) see Chailley, 115, 208.
- This extraordinary detail is indicated, but without the details, in Dalchow W. A. Mozart. Die Dokumentation seines Todes Pähl 1966 122 122
- Landon 1791 Mozart's Last Year , second edition London 1989 129 129 divides EN2/30 into three further ENs in order to interpret the final entrance as number 33, which was a very important Rosicrucean angle (perhaps for Jesus's age, among other reasons). However, there is no textual evidence on which this division is made, and otherwise 33 does not seem to be present in the opera. Thus numerological resolutions of this denouement along the lines of 33 = 30 + 3 = 3 × 11 = 17 + (4 × 4) are not required.
- See also the end of section 4.3 for a remarkable instance of 11 elsewhere in Mozart. 11 and 17 have some important Christian associations, such as Matthew 1.1–11, 12–17, where the New Testament opens with the genealogy of Jesus from Abraham via the capture of the Jews. These numbers also feature in the Knights Templars, especially 3 and 11 Baigent The Holy Blood and the Holy grail London 1982 especially ch. 8; and note that the 33 of the previous footnote is 11 × 3). Were Austrian Measons following such traditions?
- Apart from this unclarity on p. 183; Dalchow W. A. Mozart. Die Dokumentation seines Todes Pähl 1966 is invaluable (on pp. 122–4, 182–3) for elucidating the place of 18: see, for example, footnote 48. In particular, he states that the phrase is in the 18th verse of the Psalm, which is correct for the German Biblical tradition (and numerologically more faithful, incidentally), where the incipit is counted as the first verse. Chailley, 256, misstates Papagena's age as involving ten instead of two minutes, although his French original correctly states ‘deux’ ((footnote 8), 268).
- Jahn , O. The Life of Mozart , Vol. 2 , 404 – 404 . New York : Kalmus . n.d. The first edition appeared in German in 1856.
- I take my title for this sub-section from the excellent phrase in Chailley 65 66
- Mozart belonged to two lodges in his life: the first one was merged into the second at the end of 1785, as part of Joseph II's reforms which reduced the activity to two main lodges (Chailley, 61). It seems that the Masons deployed numerology in their own organization; for example, after these reductions the two main ones had 180 members each Landon Masons London 1989 26 26 Prior to that Mozart's first lodge had 40 members (with Mozart as no. 20: the first with this number, or as a replacement?). The second had 200, composed of 89 ‘present brothers’ (with Mozart as no. 56) and 111 (section 2.2?) ‘absent’ brothers. In addition, there were 12 ‘serving’ ones (Landon Years (footnote 4), 251–4).
- A most valuable Mozart bibliography may be found in Sadie S. The new Grove Mozart London 1982 although numerology, and Masonic connections in general, receive little attention in the text (see pp. 160–1). The Masonic (though not the numerological) aspects of several works are well analysed in Thomson (footnote 11); in particular, on pp. 162–8, the Finale of Act 1 of Die Zauberflöte. A factual summary of Mozart's Masonic commissions (excluding this opera) is provided in O. E. Deutsch, Mozart und die Wiener Logen (Vienna, 1932)
- Sadie . 1982 . The new Grove Mozart London 163 shows a folio for La Clemenza di Tito containing some additions of numbers of bars (or so I interpret them). They look to be approximations to the relative lengths of items in the work; the numbers themselves are not of numerological interest. Landon Masons (footnote 4), 23, shows a page of sketches for Piano Concerto no. 21 (K. 467, 1787), but, as he says, the mass of figures there seem to relate mostly to financial arithmetic.
- See Tyson Mozart, Studies of the Autograph Scores Cambridge, Mass. ch. 4
- von Köchel L. Chronologisch-thematisches Verzeichnis sämtlicher Tonwerke Wolfgang Amadé Mozarts , sixth edition et al. Wiesbaden 1964 this work is a prime source for a general study of the numbers of folios used by Mozart in his scores. Tyson mentions the manuscript of K.623, for its paper properties ((footnote 32), 17, 252). On the authorship of the text, see Landon Masons (footnote 4), 56. The work is available in NMA (footnote 24), series 1, part 4, vol. 4 (1957), 65–92. Thomson (footnote 11), 173–6, discusses the Masonic allusions; there seem to be few numerological properties beyond being 320 bars in total, with 100 in the third of its four movements
- See Weber G. Ergebnisse der bisherigen Forschungen über die Echtheit des Mozartschen Requiems Mainz 1826 rather than R. Maunder, Mozart's Requiem. On Preparing a New Edition (Oxford, 1988)
- A. Tyson argues interestingly that it dates from 1791, and was finished posthumously by Süssmayer Mozart's horn concertos … Mozart Jahrbuch 1987–1988 121 137 pb. 1988
- No reference to Masonhood is made in Paserowitz K.M. Mozart's schnorrer Leutgeb Mitteilungen der Internationalen Stiftung Mozarteum 1970 18 3-4 21–6. Another example of 3s for Leutgeb is given in section 4.4.
- See Mozart's Last Year , second edition London 1989 on the number 33. On Masonic features of these symphonies, see Thomson (footnote 11), 125–30. None of these considerations (or ours) is to be found in N. Zaslow's impressive study of Mozart's symphonies … (Oxford, 1989).
- In his thematic catalogue for the period 1784–1791, Mozart entered symphonies nos. 40 and 41, but neither entry carries a number: see the reproduction in King A. Hyatt A Mozart Legacy London 1984 54 54 or in Mozart Thematic Catalogue. A Facsimile (London, 1991). For a full concordance of the symphonies, see Zaslaw ibidem, 547–9. The same point about numbering applies to the quintets discussed (without numbers) in section 4.4
- The ‘G’ is exhibited, for example, in the ‘banned’ frontispiece to Schikaneder's libretto of Die Zauberflöte Stuttgart 19833
- This 11-note row must have been discussed before, but, for example, S. Kunze says just about everything else about this passage in his Mozart Symphonie g moll, KV 550 Munich 1968 33 33 In his plates he shows five of the original autograph folios. The second movement of the symphony, an Andante in Eb (3bs), is curiously different: its first subject takes 25 + 21 notes (across the violins and violas) and the second takes 21 (with two uncounted trills), modified into 9 + (6 × 2) in the development section. The second subject of the last movement is also a 21 (the pyramidal number to 6, as was mentioned in section 2.2). Landon Years (footnote 4), 206, refers to another example of Mozart's use of ‘rows’, the little Gigue for piano (K. 574, 1789); but his claim of ‘eleven of the twelve notes in the first two bars' is a little optimistic, as there are only ten: D|BGGF#CD|FEG#ACB|A. Perhaps the dedicatee, a court organist called Engel, was also found of Bach (section 5.2), and this was Mozart's manner of acknowledgement?
- According to Thomson The Masonic Thread in Mozart London 1977 151 152 Another rich source for study are Mozart's 6 quartets, ‘Opera X’, dedicated to Masonic recruit Haydn (section 5.2) in emulation of his own 6 in Opus 33 …. In addition to the music, Mozart's dedicatory text, containing 183 words written on 18½ lines and dated 1 7ber 1785, is worth a look (at, for example, NMA (footnote 24), series 8, pt 20, vol. 1, book 2 (1962), xvii).
- Landon . 1989 . Mozart, the Golden Years 1781–1791 34 – 34 . London including a folio of the manuscript. In a sleeve-note for Klemperer's recording of this work, the anonymous author says with unconscious insight that the Andante ‘seems to suggest the kind of assuagement which Mozart later found in his Masonic music’ (EMI CFP 41 4488).
- In Briefe and Anderson these passages are deciphered and placed within angled brackets ‘<>’
- Briefe , I 311 – 311 . Anderson, 111 renders this as ‘friend of the counting-house’, which seems to me to be a mistranslation.
- Briefe , IV 84 – 84 . 135; Anderson, 925 (where unfortunately the strings of digits are separated by commas in the usual way as numbers), 952 (correctly rendered).
- The source for this significant piece of information is two letters sent by Constanze Mozart to Breitkopf and Härtel on 27 November 1799 and 21 July 1800 Briefe 4 299 300 360–2), referring to a note in Mozart's hand: ‘Er hat auch eine Geselschaft unter den namen: die Grotto stiften wollen’ and ‘[…] von einem Orden oder Geselschaft die er errichten wollte: Grotta genannt’. This detail does not seem to be well known; for example, it is not mentioned in Thomson (footnote 11). On the possible use of the Aigen grotto, see Chailley, Plate 41 and pp. 316–7. Presumably Salieri's opera La grotta di Trifonio (1785) is irrelevant!
- Constanze Mozart's extreme enthusiasm for Bach's fugues may also have been a stimulus to him: see his letter of 20 April 1782 to his sister in Briefe Anderson III 202 202 800–1). Was he aware of Bach's use of gematria, especially the use of 14 = 2 + 1 = 3 + 8 = b + a + c + h? For a valuable analysis, see R. Tatlow, Bach and the Riddle of the Number Alphabet (Cambridge, 1991).
- Citing only Chailley's paper The Magic Flute. Masonic opera… London 1972 translated by H. Weinstock and not his book, S. Kunze announces that Chailley's views are ‘simply contrary to common sense’ (‘schlechthin widersinnig’: Mozarts Opern (Stuttgart, 1984), 668). However, whose ‘sense’ is it that counts: modern musicologists’ or Mozart's?
- There is no article on numerology in the New Grove. The works cited in footnote 11, especially Hopper, are excellent starting-points for serious study. A brief introduction, with bibliography, is provided in my Numerology and gematria Encyclopaedia of the History and Philosophy of the Mathematical Sciences London, Routledge in my (edited) to appear
- For a detailed summary of Dante's numerological principles, see Hopper (footnote 11), ch. 7. On Figaro see Allanbrook W.J. Rhythmic Gesture in Mozart … Chicago 1983 (vide index), a book which could well launch the numerological research proposed here. Leperello's catalogue aria (no. 4) draws on 640, 231, 100, 91 and 1003 to count up the 2065 fallen women; apart from the obvious allusion in the third number, numerology does not seem to be present here: the fact that 1003 and 2065 are multiples of 59 is presumably accidental
Annals of Science
Volume 49, 1992 - Issue 3