Aproximación a lo indivisible

Aproximación a lo indivisible (2013)

 

for soprano, oboe, bass clarinet, trumpet in C, trombone, percussion, piano, violin, viola, cello and contrabass

 

Aproximación a lo indivisible (approximation to the indivisible), is based on the consideration about multiplicity and unity. Several texts in different languages, each associated with a different voice treatment, present different views on this idea.

 

Written for the ManiFeste 2013 / Ensemble Intercontemporain
Recording by the Ensemble Modern, Sarah Maria Sun and Clemens Heil for col legno

Assistance during the composition of the piece: Víctor de la Rosa (help with the bass clarinet part), Cassiel Antón (help with the trombone part), Feliu Ribera (help with the percussion part), Aleida Paudice (help with Latin language pronunciation), Irène Gayraud (autor of the French text and help with French pronunciation), José María Sánchez de León (assistant about Spinoza’s text), the community of “DozensOnline” (online community about non-decimal numeric systems), Íñigo Giner (english text corrections).

Texts and notes for performers

Texts by Baruch Spinoza, Irène Gayraud and an invented tetradecimal numeral system

 

Text I: “Van de Natuur van ‘t Onëindig” Epistle XII from Baruch Spinoza to Lodewijk Meyer

 

The first and main text, in Latin, is an excerpt from a 1663 letter from Baruch Spinoza to Lodewijk Meyer titled “about the nature of infinity.” Spinoza explains how thought accesses the true nature of infinity by conceiving it as indivisible and unique while imagination grasps it under the aspect of the multiple and discontinuous.

“Multiplicity” is present not only in the subject of the writing, but also in the sources used. The original has been lost, but there are two copies preserved. The piece mainly uses the edition of “Nagelate Schrifften” (considered the official version), but also took into account a second copy made by Gottfried Leibniz. Musically, the moments when the two copies differ -and these are always words or phrasing differences, never semantic or structural- are reflected in the use of whispered voice or inspirations, and also in their association with certain instrumental colors in the ensemble. In the “Nagelate Schrifften” edition there is also a small comment in Dutch: that comment is omitted in the vocal part of the piece, but reflected timbrically in the ensemble as well.

The Latin used in Holland in the seventeenth century was mainly used in scholarly contexts. Its phonetic characteristics are difficult to define: the more distant the sources are from the medieval period, the less standardized and regulated their Latin. In the modern age, Latin is strongly influenced by the different pronunciations of the regions, and thus it would be difficult to predict which is the exact pronunciation Spinoza intends for his text.

That being said, I’m not at all opposed to the idea that the singer should suit the pronunciation to her own diction, shaped by her origin and education. Choosing a language like Latin for the main text of the piece is strongly related to the idea of multiplicity -is there a language more multiple than Latin?-, and its diversity of pronunciations is not a weakness or inaccuracy but a deliberate reference. In my approach to the work I imagined the pronunciation that results from the current Spanish and Italian pronunciation.

The vocal part for Spinoza’s text is recited throughout the piece (except the key word: unica). However, the syllabic stress of the text has been adapted to match the strong beats or subdivisions of each measure. This relationship is critical: while the text has to be recited smoothly, the music has been written so that there is a non-evident, but present, rhythmic relation. I like to think that this phenomenon allows for some groove in the recitation, a thought reinforced by the interventions of the ensemble.

Latin text

Ex quibus omnibus clarè constat, nos Modorum existentiam et Durationem, ubi, ut saepissime fit, ad solam eorum essentiam; non verò ad ordinem Naturae attendimus, ad libitum, et quidem propterea nullatenus, quem eorum habemus conceptum, destruendo, determinare, majorem minoremque concipere, atque in partes dividere posse: Aeternitatem verò, et Substantiam, quandoquidem non nisi infinitae concipi possunt, nihil eorum pati posse; nisi simul eorum conceptum destruamus.

Quare ii prorsus garriunt, ne dicam insaniunt, qui Substantiam Extensam ex partibus, sive corporibus ab invicem realiter distinctis conflatam esse putant. Perinde enim est, ac si quis ex solâ additione, et coäcervatione multorum circulorum quadratum, aut triangulum, aut quid aliud, totâ essentiâ diversum, conflare studeat. Quare omnis illa farrago argumentorum, quibus Substantiam Extensam finitam esse ostendere Philosophi vulgò moliuntur, suâ sponte ruit: Omnia enim illa Substantiam corpoream ex partibus conflatam supponunt. Ad eundem etiam modum alii, qui postquam sibi persuaserunt, lineam ex punctis componi, multa invenire potuerunt argumenta, quibus ostenderent lineam non esse in infinitum divisibilem.

Si tamen quaeras, cur naturae impulsu adeò propensi simus ad dividendam substantiam extensam: ad id respondeo, quòd quantitas duobus modis à nobis concipiatur; abstractè scilicet, sive superficialiter, prout ope sensuum eam in imaginatione habemus; vel ut substantia, quod non nisi à solo intellectu fit. Itaque si ad quantitatem, prout est in imaginatione, attendimus, quod saepissime, & facilius fit, ea divisibilis, finita, ex partibus composita, & multiplex reperietur. Sin ad eandem, prout est in intellectu, attendamus, et res, ut in se est, percipiatur, quod difficillime fit, tum, ut satis antehac tibi demonstravi, infinita, indivisibilis, et unica reperietur.

English translation:

From all this it is clear that when we attend only to the essence of Modes (as very often happens), and not to the order of Nature, we can determine as we please their existence and Duration, conceive it as greater or less, and divide it into parts — without thereby destroying in any way the concept we have of them. But since we can conceive Eternity and Substance only as infinite, they can undergo none of these without our destroying at the same time the concept we have of them.

Hence they talk utter nonsense, not to say madness, who hold that Extended Substance is put together of parts, or bodies, really distinct from one another. This is just the same as if someone should try, merely by adding and accumulating many circles, to put together a square or a triangle or something else completely different in its essence. So that whole array of arguments by which Philosophers ordinarily labor to show that Extended Substance is finite falls of its own weight. For they all suppose that corporeal Substance is composed of parts. Similarly there are others, who, after they have persuadedthemselves that a line is composed of points, have been able to find many arguments by which they would show that a line is not divisible to infinity.

But if you ask why we are so inclined, by a natural impulse, to divide extended substance, I reply that we conceive quantity in two ways: either abstractly, or superficially, as we have it in the imagination with the aid of the senses; or as substance, which is done by the intellect alone. So if we attend to quantity as it is in the imagination, which is what we do most often and most easily, we find it to be divisible, finite, composed of parts, and one of many. But if we attend to it as it is in the intellect, and perceive the thing as it is in itself, which is very difficult, then we find it to be infinite, indivisible, and unique, as [NS: if I am not mistaken] I have already demonstrated to you before now.

The vocal part for Spinoza’s text is recited throughout the piece (except the key word: unica). However, the syllabic stress of the text has been adapted to match the strong beats or subdivisions of each measure. This relationship is critical: while the text has to be recited smoothly, the music has been written so that there is a non-evident, but present, rhythmic relation. I like to think that this phenomenon allows for some groove in the recitation, a thought reinforced by the interventions of the ensemble. 

Text II: “Cycle de l’air et du sang” by Irène Gayraud

The second text used in the piece is based on the poem “Cycle de l’air et du sang”, one of a series of poems “Cycles” of the poet Irène Gayraud The text deals metaphorically with the idea of multiplicity and unity.

 

Cycle de l’air (et du sang)

 

Les lucioles acérées

s’approchent

aiguisent leurs mille points

s’approchent                          s’approchent

ta tête peut se tourner

mais tes yeux se préservent

la brûlure aveuglante

du vol en fusion s’approche

 

Tu sais que si

sous les multiplicités est une goutte de sang

sous une goutte de sang sont les multiplicités

et les deux sont semblables

 

Bâtis un mur d’air       entre toi et la goutte de sang

transparent puis lumineux

guide invisible

des voies sonores

 

Tu vois tous les blancs s’approchent

se poser au bas du mur

 

 

 

Un jour franchis le mur clair

tu enjamberas avant

après la goutte de sang

seras devant et derrière

laisse-la pousser dans tes cheveux comme sève rouge

penche le geste, la coupe creusée de tes mains pour la goutte de soif, recueille le rite de la boire

 

 

 

Mille phosphores volent dans les pierres ramifiées

 

 

Et lorsque       air parmi l’air                tu auras fondu le mur

alors                tu t’étais approchée du monde multiple

 

Text III: Numeric System

For the third text I used a tetradecimal numeral system invented by me. The system is based on 14 digits associated to 14 words. These 14 digits reflect phonetically the properties of their multiples. For example the number 2, which on my system is named ma is reflected on the number 4: ne, 8: mname, 10: vemn(o) and 12: h(a)km(o) The list is as follows:

1 – t!(u)

2 – ma

3 – k!(œ)

4 – ne

5 – ivf(æ)

6 – kamai

7 – jju

8 – mname

9 – ke

a – vemn(æ)

b – ssai

c – h(a)km(o)

d – sho

0 – ht

It would be inefficient to describe the exact pronunciation of each number. Three indications are nevertheless useful:
• When the sign “!” is used, the preceding consonant must be pronounced as explosively as possible
• When a consonant is underlined, it must be pronounced on the throat
• Vowels in (parentheses) are not meant to be pronounced; rather, the mouth position for that particular vowel serves as a coloring for the preceding consonant’s resonance.
• Letters highlighted carry the syllabic stress of the word

In relation to the numbers used in the piece, there are two types. The first group (used until measure 167) consists of the first 8 Mersenne primes, ordered from highest to lowest. The second group (used from measure 169 until the end) consists of the first four perfect numbers ordered from high to low as well. The explanation of how these numbers are calculated is beyond the purpose of this introduction. Suffice it to say that the choice of these two groups is due to the general topic of the piece, that aims to reflect on multiplicity and indivisibility, and these numbers and their definition numerically reflect this idea.

Decimal Tetradecimal
2147483647 1652ca931
524287 D90d1
131071 35aa3
8191 2db1
127 91
31 23
7 7
3 3
Decimal Tetradecimal
8128 2d68
496 276
28 20
6 6

In the numeral system language, a number is read starting from the units, then tens, hundreds and so on. For example the number 8197 is translated to the tetradecimal system as 2DB1 would be read as 1BD2 and pronounced as t(u), ssai, sho, ma

Trumpet

Harmonic noteheads indicate only-air sounds. The pitch shows the fingering (or the position on the trombone) of the instrument when the air sound is used. All the air sounds on the trumpet are not achieved with the normal embouchure but rather resting the mouthpiece on the lower lip and lowering the bell so that the trumpet is at an angle; the air stream will be directed both into the trumpet and against the edge of the mouthpiece. The letters indicate the sound that must be pronounced when using the only-air sound. No letter means simply just air. Pronouncing ‘ht’ produces an almost percussive sound quite similar to the tongue-ram on the flute.

Keep the tongue against the teeth at the end of the “ht”; release jaw subito and very explosively for the “t!”

Stop the inhaling air stream subito by lifting the tongue to the upper teeth

Inhale air through the mouthpiece [attention to the mouthposition in the video]

Very fast random fingering changes in order to modulate the air sound.

“Trill” tongue laterally very fast (small range of movement), producing fast and soft attacks; the pitch will sound higher than the indicated position/fingering

Trombone

Harmonic noteheads indicate only-air sounds. The pitch shows the fingering (or the position on the trombone) of the instrument when the air sound is used. The letters indicate the sound that must be pronounced when using the only-air sound. No letter means simply just air. Pronouncing ‘ht’ produces an almost percussive sound quite similar to the tongue-ram on the flute.

Keep the tongue against the teeth at the end of the “ht”; release jaw subito and very explosively for the “t!”

“Trill” tongue laterally very fast (small range of movement), producing fast and soft attacks; the pitch will sound higher than the indicated position

Very fast random fingering changes in order to modulate the air sound.

Bass Clarinet

The indicated upper harmonic should appear over the pedal note. Despite the instability of the technique, the player must be as precise as possible. The dynamics on the upper voice indicate that the harmonic appears progressively.

Percussion

The piece uses: 4.5 octaves marimba 1 big tom (only to be played with a superball) 1 hi-hat, built with two small 6’-8′ splash cymbals. It is very important that the two cymbals are from the same size in order for the hi-hat to close properly. The desired sound is normally soft, very concrete and “closed”. Normally the hi-hat is played closed or very closed -achieved pressing the pedal very firmly-. Except when marked with the open sign, the metallic resonance sound must be controlled and normally avoided. The choice of a hi-hat for this score has to do with the control of the cymbal sound and its resonance, and not with the particular sound obtained when closing the hi-hat. The player must always control and “tame” the sound. The percussion part is not used as a “reinforcement” or “climatic” function: specially the hi-hat phrases must be understood as thematic motives, as small very concrete and exact cells.

Some gradations between closed and very closed are sometimes requested, with the aim of achieving different colors of sound.

Piano

Using a corner of a credit card or similar] Once the key has been played, introduce the card between the two strings on the node that yields the written note, filtering the lower harmonics out. [In the video the node is not respected]

Strings

A square note indicates a “white noise” note. If there are no other indications, the note must be played with ordinario bowing and almost on the bridge, while the string is muted. The pitch indicates the string to be played. When the square note is written alone, no previous bow position sign affects the note, and in the same way, next notes are not affected by the “almost on the bridge” bow position. Notice that the square noteheads in different combinations are always used to indicate a sort of “white noise”, and always imply muting the strings. They are to be played in this way only when no other sign (for example parallel bowing) is indicated. When combined with tremolo, it is very important to play it very regularly.

Parallel bowing: bowing parallel to the strings, moving the bow towards the fingerboard/towards the bridge; the bow position on the strings is the usual: only the direction of the movement changes; this movement can be combined with crine or legno. It is normally used with stopped strings, but it can be found on normal pitches as well. The bowing (towards the fingerboard or the bridge) will be indicated as usual on the note. When executed with muted string, a square will indicate the string to be played. Usually, this bowing movement produces a “white noise” sound. In the example, a clear attack must be heard, and this assumes that the bow starts (slightly before!) a movement from the bridge toward the fingerboard.

Whip” the bow very fast in the air, in order for the bow hair to produce an air-percussive sound.

Percussive battuto: battuto almost alla punta in order to achieve a percussive sound, resulting due to the higher bow hair tension; always crine

An almost jeté technique, but with a strong emphasis on the percussive battuto part of the first notes. It’s widely used on the lower strings of the contrabass, and as in the percussive battuto, it is meant to be played almost alla punta in order to obtain the characteristic percussive sound.

The signs indicate increasing/decreasing pressure changes in the bowing. Unless indicated, this should be a timbre modulation, and not result in a hard or aggressive distortion. These changes are rather small, nuanced gradations of bowing pressure, the intensity of which should be decided by the players according to the musical context in each particular case.

chop: string technique of folk music; while stopping the string with the left hand, attack the string with the bow but at the same time applying a hard pressure enough to stop the bow; very short movement, with an almost percussive sound. Also used without stopping the string.