Locus Iste: Architecture, Mathematics, and Music

From the relationships of rhythms in time to the frequencies in pitch, and the role of proportion and aesthetic, music shares many mathematical themes with architecture. Tonight’s programme travels across the centuries and the continent exploring music linked to numbers and buildings.

More information

Programme order with notes

Guillaume Dufay (1397-1474) - Nuper rosarum flores
This piece presents the strongest mathematical and architectural challenges. Written for the consecration of the Cathedral of St Mary of the Flowers in Florence, the text compares the cathedral to a new rose blooming in the city of Florence. The music is based on a cantus firmus which is performed 4 times throughout. At each repetition the proportion of the cantus firmus changes in relation to the polyphony sung by the other parts in the ratio of 6:4:2:3.

Instrumental: John Bull (1562-1628) - Fantasia on ut, re, mi, fa, sol, la

Gregorio Allegri (1582-1652) - Miserere mei Deus
This work was composed in the 1630s for the Sistine Chapel as a falsobordone for the recitation of psalms. While the music is relatively straightforward, its fame was based on the practice of ornamentation by the singers of the Sistine Chapel choir. Adding to its mystique was the juncture that transcription and performance elsewhere was punishable by excommunication. However, according to legend, Mozart (aged 14) transcribed the work from memory upon hearing it only once. The famous high C that features in the 4 voice verses of the psalm was not in Allegri’s original. A 19th century transcription contained a section incorrectly transposed a fourth higher than intended, and this mistaken version has become a piece in its own right, now cherished by choirs and audiences.

Instrumental: Girolamo Frescobaldi (1583-1643) - Cento partite sopra passacaglia

William Byrd (1543-1623) - Tribue Domine
This tripartite motet is a setting of meditations and prayers to the Trinity attributed to Saint Augustine. It is Byrd’s largest scale early work, printed in his Cantiones Sacrae of 1575. The number three, referencing the Holy Trinity, features in many elements of the music. Byrd frequently employs trios or three pairs of duets in succession. Rhythmically, although in a duple meter throughout, there are many points where hemiolas (short sections where the meter is grouped in threes) are employed.

Interval

Instrumental: Johann Caspar Ferdinand Fischer (1656-1746) – Chaconne in G

Thomas Tallis (ca. 1505-1585) (arr. Mather) - If ye love me
One of Tallis’s earlier compositions for the reformed liturgy of the Church of England, this setting is predominantly homophonic in style with some polyphonic imitation and elaboration. Tonight we present emerging British composer Luke Mather’s arrangement of the piece in which the choir divides into two, each singing Tallis’s anthem at the same time but with one choir performing at half the speed of the other. The effect of this is both recognisably Tallis - and somewhat surprising!

Anton Bruckner (1824-1896) - Locus iste
Now a firm favourite in the choral repertoire, Bruckner’s setting of the Gradual for the dedication of a church building was originally written for the Votivkapelle at the New Cathedral in Linz where Bruckner had been cathedral organist.

Instrumental: Johann Sebastian Bach (1685-1750) Präludium und Fuge in A (BWV 889) from The Well Tempered Clavier Book 2

J.S. Bach (arr. Roberts) - Kyrie. Contrapunctus 1 from The Art of Fugue
The Art of Fugue is one of Bach’s latest works exploring the variations and possibilities for musical development. Throughout the 14 fugues and 4 canons in the work the four bar theme is present. Former Brighton Consort Musical Director Deborah Roberts added her own variation to Bach by adapting the four part Contrapunctus 1 for 4 voices with the text of the Kyrie.

Instrumental: J.S. Bach – Contrapunctus 1

Sequence - Jerusalem et Sion filiae (Prose de la Dédicace)
Text: Adam de Saint Victor Tune: Abbé d’Haudimont
Sequences were poetic metrical texts centred on a theme of a feast day or church celebration. They were common throughout the church during the mediaeval period. The Council of Trent suppressed all but four sequences for liturgical use in the 16th century; however a number continued to remain popular in various French cathedrals and abbeys, among them this sequence for the dedication/consecration of a church building, set to an 18th century metrical tune.

Herbert Howells (1892-1983) - Salve Regina
When Herbert Howells moved to London to study at the Royal College of Music in 1912, his teacher Stanford instructed him to visit Westminster Cathedral to hear ‘Palestrina for tuppence’ (the cost of the bus fare). His introduction to Richard Terry, Director of Music, led to an enduring relationship with the newly built cathedral and its choir and to his immersion in the English Tudor style of composition. This work, composed for the cathedral choir, takes into account the effect of the building on the sound as an inherent part of the composition.

Instrumental: J.S. Bach - Canon alla ottava from The Art of Fugue

Instrumental: J.S. Bach - Canon alla Duodecima in Contrapunto alla Quinta from The Art of Fugue

Guillaume de Machaut (ca. 1300-1377) – Kyrie from La Messe de Nostre Dame
The Messe de Nostre Dame is the oldest surviving example of a polyphonic mass setting attributable to a single composer. It was written for Rheims Cathedral. Tonight we are only performing the Kyrie. It is a cantus firmus-based omposition, the tenor line being based on the chant from Vatican Kyrie IV. The stylistic cohesion and unity of the Mass as a whole are unique to compositions of this period.

Texts

Nuper rosarum flores
Nuper rosarum flores
Ex dono pontificis
Hieme licet horrida
Tibi, virgo coelica
Pie et sancte deditum
Grandis templum machinae
Condecorarunt perpetim

Hodie vicarius
Jesu Christi et Petri
Successor Eugenius
Hoc idem amplissimum
Sacris templum manibus
Sanctisque liquoribus
Consecrare dignatus est

Igitur, alma parens
Nati tui et filia
Virgo decus virginum
Tuus te Florentiae
Devotus orat populus
Ut qui mente et corpore
Mundo quicquam exorarit

Oratione tua
Cruciatus et meritis
Tui secundum carnem
Nati domini sui
Grata beneficia
Veniamque reatum
Accipere mereatur

Amen

Despite a harsh winter,
Flowers of roses have recently
been given by the Pope
To you, heavenly virgin,
Holy and blessed lady,
And they are a permanent decoration
To this church, and the huge structure
[which crowns it].

Today the vicar
Of Jesus Christ,
Successor of Peter, Eugenius,
Has thought it fit to consecrate
This same vast
Church with his holy hands
And with holy libations.

Therefore, dear mother -
And also daughter - of your son,
O virgin and epitome of virgins,
Here in Florence, its
Devoted congregation and people pray
That anyone sick in mind or body,
Who should ask anything of you,

Should, in their torment,
Be seen as worthy,
By your intercession and your merits
And through the flesh
Of your Son our Lord,
To receive His gracious blessing
And the forgiveness of sins.
Amen.

Miserere mei, Deus
Miserere mei, Domine, secundum magnam misericordiam tuam.
Et secundum multitudinem miserationum tuarum, dele iniquitatem meam.
Amplius lava me ab iniquitate mea, et a peccato meo munda me.
Quoniam iniquitatem meam ego cognosco: et peccatum meum contra me est semper.
Tibi soli peccavi, et malum contra te feci, ut justificeris in sermonibus tuis, et vincas cum judicaris.
Ecce enim in iniquitatibus conceptus sum: et in peccatis concepit me mater mea.
Ecce enim veritate dilexisti: incerta et occulta sapientiae tuae manifestasti mihi.
Asperges me hyssopo, et mundabor: lavabis me et super nivem dealbabor.
Auditui meo dabis gaudium et laetitiam; et exsultabunt ossa humiliata.
Averte faciem tuam a peccatis meis: et omnes iniquitates meas dele.
Cor mundum crea in me, Deus, et spiritum rectum innova in visceribus meis.
Ne projicias me a facie tua: et spiritum sanctum tuum ne auferas a me.
Redde mihi laetitiam salutaris tui, et spiritu principali confirma me.
Docebo iniquos vias tuas: et impii ad te convertentur.
Libera me de sanguinibus, Deus salutis meae: et exsultabit lingua mea justitiam tuam.
Domine, labia mea aperies: et os meum annuntiabit laudem tuam.
Quoniam si voluisses sacrificium, dedissem utique: holocaustis non delectaberis.
Sacrificium Deo spiritus contribulatus: cor contritum et humiliatum, Deus, non despicies.
Benigne fac, Domine, in bona voluntate tua Sion: ut aedificentur muri Jerusalem.
Tunc acceptabis sacrificium justitiae, oblationes, et holocausta: tunc imponent super altare tuum vitulos.

Have mercy upon me, Lord, in accordance with your great mercifulness, and in accordance with the abundance of your pity, cancel out my wickedness.
Wash me thoroughly clean of my wickedness, and cleanse me from my sin, for I know my wickedness and my sin is always visible in front to me.
I have sinned against you alone, and have done evil against you, as you have rightly declared in your words; and your judgment is supreme.
For behold, I was conceived in wickedness, and my mother conceived me in sin.
For behold, you delight in truth: you have shown me the unknown and hidden aspects of your wisdom. You will rinse me in hyssop, and I will be cleansed: you will wash me and I will be made whiter than snow.
You will give me joy and happiness to hear you, and my humbled bones will rejoice.
Turn your face away from my sins and cancel out all my wicked deeds.
Create a pure heart in me, Lord, and renew a righteous spirit in my body.
Do not drive me away from your sight, and do not take your holy spirit away from me.
Give me back happiness in your protection and strengthen me by your divine spirit.
I will teach your ways to the sinful, and the sinners will be turned to you.
Free me from blood[-guilt], God of my protection: and my tongue will praise your justice.
Lord, you will open my lips, and my mouth will proclaim your praise.
For if you had wanted a sacrifice, I would have offered you one accordingly; you are not pleased by burnt offerings.
A troubled spirit is a [suitable] sacrifice to the Lord: you will not despise a repentant and humble heart, God.
Lord, look kindly on Sion, in accordance with your good will: thus the walls of Jerusalem will be built.
Then in recognition of your justice, you will receive sacrifice, prayers and burnt offerings: then people will place calves on your altar.

Tribue, Domine
Tribue, Domine, ut, donec in hoc fragili corpore positus sum,
laudet te cor meum, laudet te linguq mea, et omnia ossa mea dicant:
‘Domine, quis similis tui?’ Tu es Deus omnipotens, quem trinum in personis et unum in substantia deitatis colimus et adoramus
Patrem ingenitum, Filium de Patre unigenitum, Spiritum Sanctum de utroque procedentem et in utroque permanentem,
sanctam et individuam Trinitatem, unum Deum omnipotentem.

Te deprecor, supplico et rogo, auge fidem, auge spem, auge charitatem.
Fac nos ipsam gratiam tuam semper in fide stabiles et in opera efficaces,
ut per fidem rectam et condigna fidei opera, ad vitam -te miserante -
perveniamus aeternam.

Gloria Patri, qui creavit nos;
gloria Filio, qui redemit nos;
gloria Spiritui Sancto, qui sanctificavit nos.
Gloria summae et individuae Trinitati,
cuius opera inseparabilia sunt,
cuius imperium sine fine manet.
Te decet laus, Te decet hymnus,
Tibi debetur omnis honor, Tibi benedictio et claritas,
Tibi gratiarum actio, Tibi honor, virtus et fortitudo,
Deo nostro, in saecula saeculorum. Amen.

Grant, O Lord, that for as long as I am placed in this fragile body,
my heart shall praise you, my tongue shall praise you and all my bones shall say,
'Lord, who is like you?’ You are almighty God, whom we worship and praise as both three beings
and one divine essence -
unbegotten Father, only Son of the Father and the Holy Spirit proceeding from both and for ever dwelling in both,
the holy and undivided Trinity, one almighty God.

I pray, beseech and entreat you, increase my faith, increase my hope, increase my love.
Through your very grace, grant that we are steadfast in our faith and successful in our works,
so that through true faith and works worthy of that faith we may – through your mercy –
reach eternal life.

Glory be to the Father, who created us;
glory be to the Son, who redeemed us;
glory be to the Holy Spirit, who sanctified us.
Glory be to the supreme and undivided Trinity,
whose works are inseparable
and whose reign is boundless and everlasting.
You are praise and hymns, and to You, our God, is owed
all honour, blessing and renown, honour, power and might
for ever and ever. Amen.

Locus iste
Locus iste a Deo factus est, inaestimabile sacramentum.
Irreprehensibilis est.

This place was created by God, as a priceless sacrament.
The human mind cannot grasp it.

Jerusalem et Sion filiae
Jerúsalem et Sion fíliæ,
Cœtus omnis fidélis cúriæ,
Melos pangant jugis lætítiæ.
Allelúia.

Christus enim norma justítiæ
Matrem nostram despónsat hódie,
Quam de lacu traxit misériæ
Ecclésiam.

Hanc sánguinis et aquæ múnere,
Dum pénderet in crucis árbore,
De próprio prodúxit látere
Deus homo.

Formarétur ut sic Ecclésia,
Figurátur in prima fémina,
Quæ de costis Adæ est édita
Mater Eva.

Eva fuit novérca pósteris;
Hæc est mater elécti géneris,
Vitæ portus, ásylum míseris,
Et tutéla.

Hæc est cymba qua tuti véhimur;
Hoc ovíle quo tecti cóndimur;
Hæc cólumna, qua firmi nítimur
Veritátis.

O sólemnis festum lætítiæ,
Quo únitur Christus Ecclésiæ,
In quo nostræ salútis núptiæ
Celebrántur.

Justis inde solvúntur prǽmia,
Lapsis autem donátur vénia,
Et sanctórum augéntur gáudia
Angelórum.

Ab ætérno fons sapiéntiæ,
Intúitu solíus grátiæ,
Sic prævídit in rerum série
Hæc futúra.

Christus jungens nos suis nuptiis
Recréatos veris delíciis,
Intéresse fáciat gáudiis
Electórum. Amen.

Let the daughters of Jerusalem and Sion, and the whole company of the faithful host, join together to sing songs of joy. Alleluia.

For Christ, the model of justice, has today married our mother, the church, whom he has rescued from the swamp of despair.

God, made man, did this by his gift of blood and water, which he produced from his own side as he hung from the tree of the cross.

So that his church might be created, he shaped it in the first woman who was produced from Adam’s rib – our mother Eve.

Eve was stepmother to future generations; [but] the Church is the mother of the chosen people, the door of life, the refuge and protector of the wretched.

The Church is the boat in which we are carried safely; it is the sheepfold under whose roof we are gathered; it is the pillar by which we are protected by truth.

O holy festival of joy, in which Christ is united with his church, in which the marriage which assures our salvation is celebrated.

Through this marriage the just are rewarded, mercy is granted to sinners and the joy of the holy Angels is increased.

This is the source of wisdom for all time, presided over by the grace of One alone; thus the future is seen in the order of things.

By welcoming us to his wedding and filling us with true delights, may Christ permit us to join the joyful company of the Chosen. Amen

Salve Regina
Salve Regina, mater misericordiae;
vita, dulcedo et spes nostra, salve.
Eia ergo, advocata nostra,
illos tuos misericordes oculos ad nos converte.
Et Jesum, benedictum fructum ventris tui,
Nobis post hoc exsilium ostende.
O clemens, O pia, O dulcis virgo Maria.

Hail queen, mother of mercy;
our life, sweetness and hope, hail.
Hear us, therefore, our advocate,
and turn your merciful eyes to us.
And after this exile, show us
the blessed fruit of your womb, Jesus.
O merciful, holy and sweet virgin Mary.