MUSIC BY THE NUMBERS

Occasionally I encounter number symbolism in music. Just because it is so prosaic, it is not always countenanced, or even recognized. Analysts are liable to overlook clever, and often eloquent and significant instances. I exclude such banalities as a clock striking the hour, as in Danse Macabre, El Amor Brujo, or Porgy and Bess. There are enough examples that are not banalities, to justify a little thought and attention.


Thomas Weelkes: As Vesta Was Descending
This madrigal was one of 25 by different composers published in 1601 with the title The Triumphs of Oriana. ("Oriana" was an appellation of Queen Elizabeth I.) Weelkes's madrigal is scored for six voices: soprano1, soprano 2, alto, tenor 1, tenor 2, and bass. The text begins as follows:

     As Vesta was from Latmos Hill descending
     S
he saw a maiden queen the same ascending,
     Attended on by all the shepherds' swain,
     To whom Diana's darlings came running down amain,
     First two by two, then three by three together,
     Leaving their goddess all alone, hasted thither;

In the first four lines, all six voices participate more or less equally. The word "hill" is always the highest note in the phrase, and the key words "descending," "ascending," and "running down" are set to appropriately ascending or descending scales. In lines 5-6, the numbers are sung by the appropriate numbers of voices:

measures    text                            voices
47-48          first two by two            soprano 2 + alto
48-49          first two by two            soprano 1 + tenor 1
49-50          then three by three       soprano 2 + tenor 1 + bass
50-51          then three by three       soprano 1 + alto + tenor 2
51-53          together                      all six voices
(53-56         leaving their goddess    all six voices)
57-58          all alone                      soprano 1


J. S. Bach: Mass in B Minor, BWV232, Sanctus
The text in Latin -- Sanctus, sanctus, sanctus, Dominus Deus Sabaoth. Pleni sunt caeli et terra gloria ejus. -- is the Biblical verse Isaiah 6:3.

     Isaiah 6:1  In the year that king Uzziah died I saw also the Lord sitting upon a throne, high   
     and lifted up, and his train filled the temple. 2  Above it stood the seraphims: each one had   
     six wings; with twain he covered his face, and with twain he covered his feet, and with twain   
     he  did fly. 3  And one cried unto another, and said, Holy, holy, holy, is the Lord of hosts: the 
     whole earth is full of his glory.

T
his movement symbolizes the number six -- the number of wings of a seraph -- in two ways:
     1. This is the only movement in this work that is scored for a six-part choir (soprano 1, soprano 2, alto1, alto 2, tenor, and bass). All the other choral movements are either for a four-part choir (soprano, alto, tenor, and bass) or a five-part choir (soprano 1, soprano 2, alto, tenor, and bass) with the exception of Osanna in excelsis [Hosanna in the highest] which is scored for two four-part choirs. The six-part texture provides plenty of room for the voices to exchange the word "sanctus" antiphonally, as the seraphim "cried one unto another."
     2. During the first half of the movement -- the setting of the first clause "Holy, holy, holy, is the Lord of Hosts" -- almost every measure contains a pair of triplets, and many contain two pairs. Thus, a salient part of the thematic material consists of groups of six notes.


Schubert, Mass No, 2 in G major, D167, Benedictus
     This movement is in 6/8 meter, with three vocal soloists accompanied by strings and organ. The melody is sung three times.
     The first time, m3ff, the melody is sung by the soprano solo. In the accompaniment to this single voice, all the instruments play one eighth-note on each of the six beats of the measure.
     The second time, m19ff, the exact same melody is sung by the tenor solo, while the soprano sings a counterpoint. In the accompaniment to these two voices, all the instruments play two sixteenth-notes on each beat.
     The third time, m35ff, the exact same melody is sung by the bass solo, while the soprano and tenor solos sing counterpoints. In the accompaniment to these three voices, the second violions and the violas play three sixteenth-notes on each beat, while the first violins and the bassws continue to play two sixteenth-notes on each beat.
     In the orchestral coda, m51-53, all the instruments play three sixteenth-notes on each beat,


Schubert Symphony no 9 in C major, D944 "Great"
In the second movement, the first appearance of the first theme ends, in m10, with the note E played twice. From then on, almost every phrase ends with such a repeated note.
     In the third movement, m2 consists of the note C played three times. From then on, almost every phrase ends with such a threefold repeated note.
     In the fourth movement, the second theme begins, at m170, with the note C played four times. From then on, almost every phrase begins with such a fourfold repeated note. The symphony ends with triumphant statements of a note played four times


Schubert: Symphony no 8 in B minor, D769, "Unfinished"
In the second movement, the first theme always ends with the same phrase: a group of sixteenth-notes that outlines a dominant-seventh chord on B and then resolves to E (B D# F# A G# F# E).  What is relevant to the present subject, is the number of times that this end-phrase is repeated in each place.
     In the first section, the first theme is presented three times, each time concluding with its end-phrase. The first time, mm15-16, the end-phrase is played once. The second time, mm29-32, it is played twice. The third time, mm51-56, it is played three times..
     In the recapitulation, the first time, mm156-157, the end-phrase is played once. The second time, mm170-173, it is played twice. The third time, mm192-197, it is played (beginning on E) three times.
     In the coda, the end-phrase is played, mm258-268, five times. Subsequently, it is played (beginning on E-flat), mm289-290, once. At the conclusion of the movement, it is again played, mm299-308, five times.


Mozart: The Magic Flute, K620
It is not news that Mozart turned the original childish fairy tale into a Masonic allegory. The text and the music are full of Masonic allusions. The number three has significance in Masonic symbolism. There are three degrees of freemasonry, and a candidate must achieve each by undergoing a trial similar to that shown in the opera. The masons are fond of sets of three virtues. (Their mottoes "union, force, virtue" and "strength, equality, justice" were models for the motto of the French Revolution, "liberty, equality, fraternity.")

What is relevant to the present subject, is the fact that the opera is full of sets of three. The key is E-flat major, which means three flats. The Queen of the Night is attended by the Three Ladies. Tamino is guided by the Three Boys. In the original production, Sarastro was accompanied by the Three Priests, and Monostatos by the Three Slaves. Tamino tries to enter the three Temples of Wisdom, of Reason, and of Nature, but is refused entry three times.

Again, what is relevant to the present subject is the fact that the music itself is full of threes. In the following list, I do not include the many threefold repetitions of cadences, which are characteristic of all of Mozart's music, not specific to this opera. Nevertheless, if while listening one is conscious of the many other sets of three, one cannot escape the feeling that they are somehow reinforced by the repeated cadences.

set of three in the text sung to repeated notes or phrases
     4 Aria of the Queen, O zittre nicht; the second line is, Du bist unschuldig, eise, fromm = GEFGG,CC,A
     8 Finale to Act 1, begins with the Three Boys; the third line is, Sei standhaf, duldsam, und verschwiegen = DED,ED,DDED; after six measures this is repeated exactly
     8 Finale to Act 1, in the Recitative of Tamino, Die Absicht ist edel, und lauter, und rein = AAABC#,C#EE,EG
     14 Aria for the Queen, Der Hoelle Rache, second stanza begins, Verstossen sei auf ewig, verlassen sei auf ewig, vertruemmert sei'n auf ewig = three octave leaps downward F-F; after three measures, Verstossen, verlassen, und vertruemmert = three octave leaps downward G-G

three fanfares
     1 Introduzione, entrance of the Three Ladies; the second line is,Triumph! Triumph!, each time after an orchestra fanfare = BbBbEb,BbBbEb,BbBbEb and EbEbF,GGF,GGF (each three-chord fanfare three times)

chord played three times
     Overture ends = EbEbEb
     5 Quintet Hm hm hm, ends = BbBbBb

three chords outlining a chord in ascending order
     Overture begins = Eb,GG,BbBb
     Overture, exposition ends = BbBbBb,DDD,FFF (each of the three chords three times)
     3.Aria of Tamino, Dies Bildnis ist; orchestra begins = BbBbGG,EbEbBbBb,G
     8 Finale to Act 1, Larghetto for Pamina, Herr ich bin zwar; orchestra begins = F,AA,CC
     9a.Threefold Chord of the Priests, following 9.March of the Priests (actually Prelude to Act 2) = BbBbBb,DDD,FFF (exact repetition of the chords at the end of the exposition in the Overture; see above)
     18 Chorus of Priests, O Isis und Osiris, the last line is, Bald, bald, bald = A,D,F#; after three measures this is repeated exactly

three melody notes outlining a chord in ascending order
     1 Introduzione, orchestra begins = EbGC,GCEb,CEbG and FBD,BDF,DFAb
     1 Introduzione, Tamino begins, Zu Huelfe, zu Huelfe, sonst bin ich twice = GGC,EbEbc,GGEb and DDB,FFD,AbAbG
     4 Aria of the Queen, O zittre nicht; Allegro moderato begins Du, du, du = Bb,D,F
     8 Finale to Act I, in the Recitative of Tamino, first Zurueck!, orchestra = ABb,BbD,DF#
     8 Finale to Act 1, in the Andante of Tamino, Wie stark ist with flute; Wo, wo, wo? = G,B,D
     12 Quintet begins, Three Ladies, Wie, wie, wie? = B,D,G; after three measures, Nie, nie, nie = E,G,C
     14 Aria of the Queen, Der Hoelle Rache, in the second stanza, Wenn nicht, durch dich,Sarastro = AC#,C#E,EG
     14 Aria of the Queen, Der Hoelle Rache, in the second stanza, Hoert, hoert, hoert! = D,F,Bb
     21 Finale to Act 2, Allegro chorus after the trials by fire and water, begins Triumph, Triumph, Triumph! = CC,EE,GG
     21 Finale to Act 2, in the Allegro chorus after the trials by fire and water, Kommt, kommt, kommt = C,E,G; after two measures it is repeated exactly
     21 Finale to Act 2, Allegro of Papageno, orchestra begins = GGGD,BBBG,DDDB
     21 Finale to Act 2, Allegro of Papageno, Papageno begins, Papagena, Papagena, Papagena! = GGGD,BBBG,DDDB
     21 Finale to Act 2, in the Allegro of Papageno, he counts, Eins, zei, drei, with panpipes after each
     21 Finale to Act 2, Allegretto for the Three Boys begins, Halt ein! Halt ein! Halt ein! = GG,BB,DD