Organistrum: matching three different keyboards

Organistrum: matching three different keyboards

Describing 3 different interpretations

of  “TWO MEN LYRE”

keyboard

from Gate of Glory of Santiago de Compostela cathedral

and their efficiency.

 

Agreed that the instrument has 3 strings and 11 keys 

 

 

 

  1. The “chromatic/parallel” keyboard has 12 one-way “up and down” keys with 3 tangents each one.

Tuning: V, IV or IV, V.

 

The 36 semitones obtainable from each string occur in 1 arrangement coinciding with the tuning, they are available 3 at a time in 12 single choices which cannot be combined with each other. Therefore, the virtual range of 2 octaves minus 1 semitone is reduced to its half.

Francisco Luengo, who built this kind of keyboard in the eighties writes: “The keys are eleven … twelve available sounds, surely a chromatic octave. This fact doesn’t imply that organistrum was intended to play other than modal music, but, certainly, it was an instrument for transposition, able both to change the pitch of any composition and to carry out all exachords combinations” (Francisco Luengo in: El Portico de la Gloria. Musica, Arte y pensamento. “Cuadernos de Musica en Compostela II” Santiago de Compostela, 1988 , p.111). Approximately the same words in Christian Rault, La reconstitution de l’Organistrum (available on Google).

My only observation concerns the impossibility of transposing an 8 sounds average gregorian melody entirely within a single octave.

 

  1. The “diatonic/polyphonic” type has 10 one-way “up and down” keys and 1 both “up and down” and 180° spinning key.

Tuning: I, VIII.

 

 

3 keys operate on the bass string, 4  (3+1) on the middle one, 5 on the treble. 1 key of the latter group can be spun 180 degrees and operated both on the middle and on the treble strings alternately, producing different sounds. Then  14 sounds are available and they can be combined operating the independent keys, 2 at a time, as follows:

 

(4x5)+ (4x6) + (5x6) = 20+24+30 = 74

 

But, since part of these 74 combinations generates 22 dissonant intervals either rarely or never performed (II and VII) plus 4 tritones, the total number of actual combinations amounts to  74 - 22  - 4  = 48 .

 

On this diatonic keyboard, with this tuning: A,A, a (whole scale: one octave plus one fifth) it is possible to perform music in 2 modes: Protus plagalis and  Protus autenticus. Some advantages are that the three “mother-strings”  Do, Re and Mi  lie on the bass string and the main exachords: naturalis, durus  and  mollis  are all represented, while f# (ficta)  introduces an additional “false” exachord.

In 12th century two voices polyphonic  compositions, whatever the Mode, a range of 20 to 30  combinations of sounds is requested.   

The amount of 48 is  enough to serve no more than 1 authentic mode and its plagal, considering that they have a good deal of sounds in common.

In a mathematical way:

48:2 = 24

24<30

 

3.The “chromatic/polyphonic” keyboard has 11  both “up and down”  and 360° spinning keys bearing  5 tangents on 4 different positions each one,

Tuning: IV,V or V,IV

 

 

The 12 semitones obtainable from each string can be managed separately by using 1 key at a time. To these 36 choices some others have to be added:  the 12 “organum parallelum” choices on treble and middle strings keeping the bass as a drone. Thus  36+12 = 48 choices in total.

Furthermore, by managing 2 keys at a time, 6 combinations of sounds are available for each couple. Since keys combinations are 12x12 = 144 in total, then the sum of all possible combinations of sounds amounts to 144x6 = 864,

to which  the first group of 48 sounds has to be added:  912  possible combinations of sounds in total.

 

12x12 =    144

144x6 =    864

864+48 = 912

But, since in all 12th century music compositions, no matter which modal transposition occurs, no more than 8 keys are required, performing combinations are, as follows:

 

8x8 = 64

64x6 = 384

384+48 = 432

 

Then, all combinations that give dissonant intervals rarely or never performed (II and VII) have to be subtracted from this number: 44 dissonances between the outer strings and 4 for each semitone of the adjacent strings:

44+( 4x11) + (4x11)  = 132  in sum

Adding to this amount 28 tritones and 11 fourths (or fifths, depending on middle string pitch) not to be performed by the same key on the bass and middle strings: 132+28+11 = 171  combinations to be avoided.

Finally: 432-171 = 261  useful combinations.

 

In 12th century two voices polyphonic  compositions, whatever the Mode, an average amount of 20 to 30  combinations of sounds is requested.   

Sure enough, this advanced keyboard, actually extended over 2 octaves minus a semitone, allows us to play in each of the 8 modes.

In a mathematical way:  

261 :8 = 32,625

32>30

 

 

.

 

 

 

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Organistrum: diversi modelli di tastiera a confronto

Organistrum: diversi modelli di tastiera a confronto

3 DIVERSE INTERPRETAZIONI

del meccanismo della tastiera di

“VIELLA A RUOTA A 4 MANI” (vulg. Organistrum)

nel portico della Gloria della cattedrale di san  Giacomo de Compostela

e loro rendimento.

 

Date 3 corde e 11 chiavi

 

 

  1. Nel modello adottato comunemente, che potremmo chiamare “cromatico/parallelo” con chiavi a saliscendi munite di tripla tangente

Accordato per  V, IV o IV, V

 

i 12 semitoni ottenibili da ogni corda, in tutto 36, si presentano in 1 sola combinazione corrispondente all’accordatura, disponibili  3 alla volta in 12 opzioni singole non  combinabili tra di  loro. In tal modo l’estensione dello strumento, che sarebbe di due ottave cromatiche meno un semitono, viene ridotta della metà.

Chi ha scelto questa soluzione così la giustifica:

“Le chiavi sono undici … dodici i suoni possibili, certamente un’ottava cromatica. Questo non vuol dire che l’organistrum fosse destinato a eseguire altra musica che quella modale, ma che, sicuramente, si trattava di uno strumento traspositore, con il quale si poteva variare a volontà la altezza di una composizione e che permetteva di realizzare tutte le combinazioni dell’esacordo.” (Francisco Luengo in: El Portico de la Gloria. Musica, Arte y pensamento. “Cuadernos de Musica en Compostela II” Santiago de Compostela, 1988 , p.111). La stessa valutazione, quasi con le stesse parole viene espressa da Christian Rault nella sua relazione sulla ricostruzione dello strumento.

La mia sola obiezione è che la trasposizione integrale di una melodia gregoriana, che consta mediamente di almeno 8 suoni è praticamente impossibile quando si disponga di un’estensione di una sola ottava.

 

  1. Nel modello “diatonico/polifonico” con 10 chiavi a saliscendi e 1 a saliscendi anche ruotabile di 180°

 con accordatura  I, VIII

3 chiavi agiscono sul basso, 4 (3+1) sulla corda centrale e 5 sulla corda acuta. La chiave girevole  può agire alternativamente sul cantino e sulla corda centrale. Si possono dunque amministrare 14 suoni in totale attraverso diverse combinazioni di chiavi, a partire da quelle insistenti sul basso, come segue:                                                       

 

(4x5) + (4x6) + (5x6) = 20+24+30 = 74

 

Una parte di queste  74 combinazioni genera 22 intervalli dissonanti raramente o mai  praticati  (seconde e settime) più 4 tritoni, quindi il totale delle combinazioni effettivamente utili è:

74-26 = 48 .

Con l' accordatura in LA, LA, la, i modi praticabili sono il Protus plagalis e il protus autenticus. Le tre "corde madri" Do Re e Mi sono rappresentate al basso, tutti i tetracordi fondamentali: naturale, duro e molle sono praticabili e la ficta f# introduce un ulteriore esacordo, quello “falso” di Re.

Poiché mediamente le composizioni polifoniche a due voci del secolo XII presentano un numero variabile da 15 a 30 diverse combinazioni di suoni il numero di  48 possibili combinazioni riesce a servire soltanto un modo autentico e il suo plagale, poichè essi hanno buona parte dei suoni in comune. Se volessimo operare con due modi qualsiasi invece potremmo incontrare delle limitazioni, infatti:

48:2 = 24

24 < 30.

 

 

 

  1. Nel modello “cromatico/polifonico” con 11 chiavi a saliscendi e ruotabili di 360° ciascuna munita di tangenti su 4 diverse posizioni, con accordatura IV, V o V, IV

 

 

 i 12 semitoni ottenibili da ogni corda sono amministrabili in due modI:

  1. Singolarmente, usando 1 chiave alla volta, con 36 opzioni cui si devono aggiungere le 12 opzioni di organum parallelum ottenibili sulla corda più acuta e la mediana, restando il basso con funzione di bordone.  In totale quindi disponiamo di 48
  2. manipolando 2 chiavi contemporaneamente  vi sono 6 diverse combinazioni di suoni per ogni coppia di chiavi e poiché gli abbinamenti in totale sono 12x12 = 144,  consegue che le combinazioni possibili tra tutti i suoni disponibili sono 144x6 = 864, cui dobbiamo aggiungere i 48 suoni di cui sopra, raggiungendo così il  totale di 912 possibili combinazioni di suoni.

Poiché però in ogni brano musicale, trasposto in qualunque modo,  non si usano di volta in volta più di 8 chiavi, le combinazioni effettivamente praticate sono poco meno della metà di quelle possibili, vale a dire:

8x8 = 64

64x6 = 384

384+48 = 432

Da questo numero però dobbiamo sottrarre tutte le combinazioni che danno luogo a intervalli dissonanti poco o per nulla praticati (seconde e settime): 44 fra le corde esterne e 4  per ogni semitono fra le corde contigue quindi  in totale 44+ (4x22)= 132.

 Si devono anche sottrarre tutti i tritoni, 28 in totale, e  le quarte (o quinte, dipende dall’accordatura della corda mediana) in tutto 11, non eseguibili con le chiavi sulla corda bassa e su quella mediana:

132+28+11 = 171

 

Il totale delle combinazioni praticabili sarà dunque

432 - 171  = 261

 

Poiché per ogni composizione del periodo compreso tra seconda metà del XII e inizi del XIII secolo riscontriamo l’utilizzo di 20 - 30 combinazioni di suoni  e poiché l’estensione di questa tastiera particolarmente avanzata è di due ottave meno un semitono, si possono praticare con essa tutti i modi con tutte le loro mutazioni e permutazioni

Se infatti dividiamo 261 per il numero dei modi gregoriani:

 

261 : 8 = 32,625

 

Ove 32 > 30

 

 

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EL PORTICO DE LA GLORIA: POLICROMIA Y POLIFONIA

EL PORTICO DE LA GLORIA: POLICROMIA Y POLIFONIA

El 2 de julio ha sido reabierto el Pórtico de la Gloria a Santiago de Compostela.  Este extraordinario documento non para de nos maravillar. Fue evidenciada la POLICROMIA del portal aportando a todo el edificio una nueva luz resplandeciente.

Al mismo tiempo, NUEVOS estudios ha descubierto el concepto de POLIFONIA leÍble en las representaciones con istrumentos musicales de los venticuatro ancianos de Apocalipsis.

Los instrumentos están rapresentados en parejas de dos (dos arpas, dos laúdes) y esto puede referirse a ejecuciones musicales duplices, y el teclado cromático del así llamado Organistrum, a la cumbre del pórtico, sugiere un progreso muy avanzado de la teoría musical a Compostela al final del siglo XII.

Por otro lado, las composiciones a dos voces del Codex Calixtinus testifican el trabajo hecho para el desarrollo de  la polifonía en la misma época.

En nuestros estudios hemos demostrado que el instrumento en la cumbre del Pórtico es verdaderamente singular, DIFERENTE de cualquier otro que conocemos. Su gama cromática, inútil por la música sagrada da la época, nos sugirió la creacion de una TECLA POLIFONICA que sirve al repertorio especifico del siglo XII. Si las viejas  "Lyras a dos hombres" con su escala diatónica, podían quizás acompañar las polifonias simples describidas en "Musica enchiriadis" y "Micrologus", el instrumento de Santiago representa una mejora, un heraldo de una música nueva: Conductus y Motetus , asi come el "canto nuevo" de la Apocalypsis).  Esta prospectiva nos enseña debajo de una luz nueva todos los instrumentos del Pórtico: el hecho que sean representados en parejas no responden simplemente a necesidades de naturaleza coreográfica, indican en realidad un pensamiento polifónico nuevo.

De manera similar la nueva restauración restituyó al Pórtico los colores originales, aportando una luz nueva a la intera obra.

(Thanks to Alejandro Gangui for original pictures of the Portico)

Para ahondar estos temas miren los blogs :

http://www.liuteriaseverini.it/index.php?option=com_k2&view=item&id=24:organistrum-symphonia-caelestis-santiago-de-compostela&Itemid=1014

http://www.liuteriaseverini.it/index.php?option=com_k2&view=item&id=32:organistrum-new-polyphonic-keyboard&Itemid=1014

https://www.youtube.com/watch?v=Ul9W_dTLXGc

 

 

Salva

Salva

Salva

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polyphonic keyboard

Organistrum: new polyphonic keyboard

My reconstruction of the instrument is mainly based on my own interpretation of its possible musical function. Since I want to consider iit  as a genuine polyphonic instrument I  invented  a  special  keyboard, fit for 12th century two voices polyphonies, suggesting also a diffferent managing of the wheel.

Keyboard

By tuning the strings  either:  A – d – a   or:  A – e – a    we get an overall extension of two chromatic octaves (minus the last semitone). Before lifting each key, the performer  can choose which string he is going to touch, simply by turning the key to the proper position: the first one allows him to operate on the bass string, the second on the middle one, the third on the higher string.

Thus it is possible to play two different melodic lines simultaneously. In Santiago sculpture the hands of the musician on the right are on the third and on the fifth key. This means he is playing  -c, g -  rather than  -d, f -  bichord on bass and middle strings,  or  - g, c’  rather than  - f, d’- bichord on middle and higher strings (first tuning).

 

First string                              a..       a#      b     c’     c’#     d’

Middle string                         d..       d#      e      f      f#      g    

Bass string                            A..       A#      B     c     c#      d

Keys                                      0          1       2     3       4      5

 

 In position 4 the key is provided with two tangents so as to act on  second and  third strings (tuned either in Fifth or Fourth)  at the same time to perform  Organum parallelum, leaving the bass string as a drone. 

How they calculated the semitones progression

Known medieval texts neither describe  nor discuss about the possibility of a chromatic scale. But, reading Boethius's De institutione musica, easy to be found in monastic libraries since 9th century on, the monks could learn a lot about semitones both from pythagorean tradition and from Aristoxen's. There are only few lines, but enough, dedicated to the description of Aristoxen's practical method to divide the monochord. From this source the medieval scholar could learn a practical method in order to draw a correct chromatic scale of 12  tempered semitones. We discuss about this in another blog in this website

http://www.liuteriaseverini.it/index.php?option=com_k2&view=item&id=24:organistrum-symphonia-caelestis-santiago-de-compostela&Itemid=1014

connecting astronomical and musical  knowledges through 10th and 12th centuries. Anyway, this idea comes from very early roman sources: Plinius and Boethius. In case the author of Santiago instrument intended to describe a revolutionary full chromatic/polyphonic keyboard we can suppose he was aware of that very ancient tradition.

 

Wheel

On the other side, the musician who is in charge of turning the crank, by a smooth, even movement of his right hand,  can also lift one or even two of the strings from the edge of the wheel with his left hand in order to stop them vibrating. This way you can either avoid conflicts between the voices or stop  undesired drone effects.  

 

LISTEN TO POLYPHONIC SYMPHONIA:

https://www.youtube.com/watch?v=B6vv4IPGgRkc

                                                                                       

THE NAME

ORGANISTRUM IS A WRONG NAME ... !

SYMPHONIA (CAELESTIS) should be preferred

- Reading Ch.Page articles in GSJ 1982, 83 convinced me to reject the name Organistrum

- Guido D'Arezzo Micrologus, XVIII, 1-18  pushed me to prefer the name Symphonia:

"...symphoniae, id est aptae vocum copulationes dicuntur, cum symphonia et de omni cantu dicatur." trad.: "...symphoniae are sound combinations, but this name indicates all songs"

Then, in Regulae rhythmicae the same author writes:

"Quinque habet ipsa tonos, duo semitonia;

Habet in se diapente et diatessaron;

maxima symphoniarum et vocum est unitas"

trad.:

"(the diapason) contains 5 tones and 2 semitones/the fifth and the fourth/is the highest unity of symphoniae, or sounds"

SYMPHONIA matches with the medieval highest idea of music and sound, while ORGANISTRUM sounds like a deformation of the word ORGAN and like a ridiculous nickmame.

I believe that the name Organistrum  fits better the later "one-man Lyre", a diatonic, melodic instruments with drones, sort of early hurdygurdy used for secular music.

(Ch.Page is of the same opinion)

 

BUILDING A REPLICA OF SANTIAGO DE COMPOSTELA INSTRUMENT

I chose one big  Red Willow (Salix purpurea) planck, seasoned in nature, from which I  carved the sound box and the base of the keyboard in one piece, average thickness  8-10 mm. Flat back, flat sides as in the original. 

GENERAL MEASURES:                      

 Total length    940mm                                                                                                           

Max width      230mm                                                                                                              

 Depth              80mm                                                                                                                

 Diapason        720mm

 

In the bottom of sound box I drilled a 10mm hole for the wooden axis, made of Beech (Fagus silvestris). Axis ends into another hole of 10mm drilled directly with no axle box in a wooden bar (Spruce) 15mm thick, glued between the two lobes of sound box which has been carved out of one piece of Spruce (Picea  abies) 8mm thick with no other bars glued underneath. Keyboard  box is independent from the body of the instrument and can be easily removed to modify  general level of the bars, changing their angle with the strings or making reparations. The 11 bars of the keys, diameter 10mm, are of Pine (Pinus nigra) and the 55 pivoting tangents of Beech. The problem of the distances among the bars is discussed in the present article. To avoid noise made by the bars returning to their previous position, after being pulled up to play, a stripe of cloth has been glued at the bottom of the keyboard. The carved lid has been made of Spruce, 8mm thick and is simply interlocked with the body of the keyboard without any hinge or other device.

The wheel, 11cm  wide and 20mm thick is of Walnut (Juglans regia) and forced on  wooden axis without any screw, nail, or wedge. No axle box at the end. The Beech crank , stuck in the square end of the axis, can be easily removed. The soundboard is glued to the body of the instrument , no sound pole in it. The bridge is of Poplar (Populus nigra) reinforced with a Beech edge. The tailpiece  of Chestnut (Castanea sativa) is linked to the bottom of sound box by a leather lace. Tuning pegs are of Beech, no need for a tuning key. Two light  layers of pure almond oil have  been used as  finishing . Gut strings: 0.80, 1.10, 1.40mm.

 

 

 

 

 

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