Murielle Gaude-Ferragu

'The Body of the Prince': Royal and Princely Funerals in

In the fifteenth century, royal and princely funerals underwent spectacular metamorphoses which were especially marked by the appearance of the effigy, the famous mannequin with a wooden body and a wax face and hands that represented the deceased in all his or her majesty, wearing the royal costume and supplied with the regalia. In this respect, Charles VI's 1422 funeral rites constituted a turning point; the innovations were introduced in a precise context, tied as they were to the king's madness and to the succession crises which followed, yet these rites were to enjoy a brilliant future which persisted until the beginning of the seventeenthcentury.

In a ceremonial that mirrored their spouses, fifteenth-century queens, like their husbands, embodied royal dignity and received the same funerary honours, marked by the participation of the présidents of the Parlement of Paris, among others, or the presence of the dais and the effigy (Isabeau of Bavaria, Charlotte of Savoy). In the same way, the spectacle of their deaths the kingdom's princes, often the king's relatives and owners of vast territories, cast a final earthly light. Between royal imitation and chivalrous innovations, their funerals demonstrated the ceremonial effervescence of the late Middle Ages through a complex game that mixed art and power.

The Funeral of Charles VI (1422), or the Metamorphosis of the Royal Rite

The 'invention' of the effigy

Since the beginning of the thirteenth century, royal funerals were characterized by the public exposure of the corpse, with its face and hands presented 'à la découverte' ['uncovered'], adorned with the royal costume and surrounded by the regalia. In 1314, Philip IV the Fair was carried in this way through the streets of Paris on a litter, dressed in an ermine-lined coat, his head encircled with a crown, and holding the sceptre and the main de justice. 1 Such a display was not specific to France: it was a ritual of sovereignty that was also practiced at the pontifical court and in England. 2 However, upon Charles VI's death (21 October 1422, in his hôtel Saint-Pol in Paris), it was not possible to respect tradition due to the lengthy interval between 1BAUDON DE MONY 1897, p. 7. 2See Agostino Paravicini-Bagliani's article on the papal body and Joël Burden's contribution on English sovereigns in the present volume, pp. 00. the king's passing and his interment. 3 The succession was complex: Charles VI was the mad king who had reigned over France intermittently since 1380. The political void created by his illness had plunged the kingdom into civil war, which was followed by the English conquest. This was the disaster of Azincourt (1415), followed by the signing of the Treaty of Troyes (May 1420), which established a double monarchy: Charles VI and his wife, Isabeau of Bavaria, deprived the dauphin (the future Charles VII) of his rights by excluding him from the succession to the crown. Charles VI gave his daughter, Catherine, to the English king, Henry V. At Charles VI's death, the two kingdoms were to remain independent, but under the tutelage of a single monarch: Henry V and his successors.

The English king died at Vincennes on 31 August 1422, leaving his young son, Henry VI (then ten months old) as his heir, represented in France by John, the Duke of Bedford. Yet, when Charles VI died in October of the same year, the regent was settling the Norman affairs in Rouen. 4 Charles VI's interment had to wait until the duke's return, and the body was about to present the first signs of decomposition. Charles VI's physicians and surgeons embalmed the body ('and it 3He died of quartian fever, FAUQUEMBERGUE 1903, t. II, p. 59. 4Jean of Bedford was in Rouen, where he had accompanied the body of his brother, Henry V. He stayed there to attend to administrative and military affairs.

was found that that his heart and liver were healthy') 5 and filled it with herbs and spices, 6 however such procedures could not preserve the corpse more than a few days (John of Bedford did not return until 5 November, more than fifteen days after the royal death).

The organizers of the funeral ceremony, the chancellor of France, Jean Le Clerc, and several royal counsellors -acting on their own or on the orders of the Duke of Bedford -decided to place the body on a funeral bier following its brief exposition in the mortuary chamber. 7 The presentation at the hôtel Saint-Pol was public and lasted three days, 'and there anyone who wished, could see (the body), and could pray for him '. 8 This allowed various constituencies (royal counsellors, 7The measurements taken were then ratified by the regent, Accounts in GRANDEAU 1970, p. 159-161. 8Journal d'un bourgeois de Paris 1990, p. 192: "et là le voyait chacun qui voulait, pour prier pour lui" members of the Parlement and of the Chambre des comptes, the University of Paris and the collèges), the Parisian magistrates (prévôts of Paris and of the merchants, échevins and bourgeois) to gather before the corpse one last time and, most importantly, to certify the reality of the king's death. 9 The body was presented on a lit de parement, covered with a cloth-of-gold pall, and surrounded by eight continuously burning candles.

Then, Charles VI's body was deposited in a lead casket and brought down to the hôtel Saint-Pol's lower chapel. 10 The funeral vigil continued until 9 November, the date on which the defunct was transported to his final resting place. The wake was accompanied by numerous liturgical celebrations (high and low masses and vigils), which the king's chaplains celebrated first, followed by members of Paris's four mendicant orders, who took turns in performing a veritable shield of prayers around the deceased. Four large candles made of forty pounds of wax were placed at the coffin's corners, in addition to the twelve twenty-four pound-candles blazing on the altar. 11 9MONSTRELET 1857-1862, t. IV, p. 120 and Chronique de Charles VI, p. 324. 10Account in GRANDEAU 1970, p. 180. 11Ibid., p. 180. But with the body on a funerary bier, a representation was needed to respect the royal display ritual. The idea of a funerary mannequin, of English origin (the first effigy was used in 1327 for English king Edward II), was, perhaps, suggested to the chancellor and the counsellors by John of Bedford. Or perhaps they took the initiative themselves, since this solution would seem obvious to them: Henry V's Norman convoy had used an effigy less than two months earlier. 12 [its head and face cast from [the king's] own face and from life as truly as possible, and the aforementioned head [was] embellished with hair as close to that which the aforesaid seigneur had, and the hands [were] also moulded and made from life, and dressed with white embroidered gloves]. 13 12MONSTRELET 1857-1862, t. IV, p. 112-113. On English funerals, see Joël Burden's article in the present volume, pp. 00.

During this time, haberdashers, embroiderers, and smiths tackled the making of the costume de parement and of the regalia. Before departing for Notre Dame, the effigy was dressed in a gown and coat of red cloth-of-gold, both of which were lined with ermine. The slippers were azure velvet with fleurs-de-lis. 14 The Parisian goldsmith, Christophe de Harlint, fashioned the regalia: a gold-plated silver crown chiseled only 'on the side and in front' since the back was not visible, a sceptre decorated with fleurs-de-lis, a gold-plated silver main de justice, and a gold ring.

The adoption of the effigy thus permitted the defunct to be represented in all his majesty, substituting a putrefying corpse which could no longer be openly exposed.

In this way, the king appeared in the funerary train and at the liturgical celebrations at Notre Dame and Saint Denis.

The convoy and the liturgical ceremonies: between tradition and innovation

The funeral train transported Charles VI's corpse from the hôtel Saint-Pol to the cathedral of Notre Dame of Paris for the first liturgical celebration (November 9-10 th ), then from Notre Dame to the Abbey of Saint Denis, the burial place of the kings of France, for the internment itself. 14Ibid., p. 171. On the description of the effigy, cf. the "Cérémonial de l'inhumation de Charles VI, " published in GIESEY 1987, p. 299 (after a manuscript conserved at the BnF, Fr. 18764, fol. 119) and MONSTRELET 1857-1862, t. IV, p. 122. As was traditional, the Parisian clergy lead the procession: religious communities on one side (mendicant orders, the collèges; Saint-Catherine-du-Valdes-Ecoliers, the Mathurins, the Billettes, Sainte-Croix, Saint-Merri, Saint-Germain-l'Auxerrois, the parishes, the canons of Notre Dame and of the Palace's Sainte-Chapelle) and the rector and doctors of the university of Paris on the other. 15 The prelates (the bishops of Paris, Chartres, and Thérouanne, the abbots of Saint-Magloire, Saint-Germain-des-Prés, and Sainte-Geneviève) walked closer to the body. 16 A large part of the procession was composed of members of the deceased's household: 310 officers received gowns and black hoods (costing a total of 1,352 livres tournois). 17 Two-hundred échansons, panetiers, and valets of the chambre carried torches weighting six pounds of wax decorated with royal fleurs-de-lis. 18 The accounts prove that funeral trains' famous 'pleurant' were present, not poor 15Ceremony published in GIESEY 1987, p. 298.

16MONSTRELET 1857-1862, t. IV, p. 120. 17Accounts in GRANDEAU 1970, p. 172. Present were the maîtres d'hôtel, échansons, panetiers, fruitiers, valets de chambre, fourriers, 'Cérémonial,' published in GIESEY 1987, p. 300. 18Ibid., p. 300. individuals remunerated for the occasion, but, rather, servants from the king's household. 19 The effigy was at the procession's centre, and the highest-ranking members of the king's household, as well as from the royal administration, surrounded it; some walking in front of it and others following behind. With the prévôt of Paris, the household's grands officiers walked ahead of the effigy: the first chamberlain, the stable's squires and the deceased's maîtres d'hôtel. Following the effigy were the great officers of the crown, the chancellor of France, counsellors, maîtres des requêtes, officers of the Chambre des comptes, and the king's notaries and secretaries.

The effigy itself rested on a litter, carried by the king's valets de porte to Notre Dame, then, on the long route to Saint Denis, by the 'hanouars'('salt porters'), who were accustomed to transporting heavy loads (here, the heavy lead coffin with the effigy on top). The litter was covered with an immense pall of red cloth-of-gold, bordered by azure velvet covered in fleurs-de-lis. 20 The four presidents of the Parlement of Paris, who were dressed in red (with ermine-lined cloaks, the clothing of their profession) supported the pall's corners. They did not 19On the presence of the poor at the funeral services, ALADJIDI 2008, p. 355-386. 20Accounts in GRANDEAU 1970, p. 175. The effigy's head rested on pillows of vermillion velvet which were supplied with four pearl buttons.

wear mourning clothes, demonstrating that royal justice never died. 21 Additionally, the effigy was covered with a dais of the same red cloth-of-gold bordered with embroidered fleurs-de-lis and carried on eight lances by the prévôt of the merchants and the échevins of Paris. 22 Finally, as regent and representative of the (Fig. 1).

Crowned, the effigy holds the sceptre and the main de justice, and wears a ceremonial costume entirely covered in fleurs-de-lis, allowing the viewer to identify the monarch clearly, who is further distinguished by the face: the eyes are shown open, as they would be in the king's eternal glory. The litter is covered with a pall of red cloth-of-gold and supported by the presidents of the Parlement of Paris, also dressed in red. On the other hand, the painter does not represent the dais, which would have disturbed the visibility of the effigy and the three knights who, in the background, hold the royal sword, the helm, and the shield with fleursde-lis. In reality, these elements were absent from the convoy, but here the painter represents the funerary etiquette of the court to which he belonged; that of the Dukes of Burgundy, who exhibited the 'pièces d'honneur' of the defunct. 24 The liturgical ceremonies also mixed tradition and innovation. The first funerary service took place in front of the body in the cathedral of Notre Dame, with vigils on 9 November and a celebration of requiem mass, sung by Jean de La Rochetaillée, bishop of Paris and patriarch of Constantinople, the following day. 25 24Philippe de Mazerolles was Charles Le Téméraire's valet de chambre; the manuscript which he illuminated (BnF, Ms. Fr. 2691) was intended for Louis of Bruges, Bruges, between 1470 and 1479.

25The abbot of Saint Germain (Jean Bourron) read the gospel and the abbot of Saint Magloire (Pierre Louvel) read the epistle, Chronique de Charles VI, p. 326.

Then, after the long procession to Saint Denis, the same celebrations were performed in the royal burial church. Vigils were followed by a requiem mass the next morning, once again performed by the bishop of Paris (with the abbot of Saint Denis's permission), along with 'the bishop of Chartres, who served the office of deacon, and the abbot of Saint Denis (Jean de Bourbon de la Boulaye), who served the office of subdeacon'. 26 In both churches, the décor, though ephemeral, was resplendent. There, the body shined, lit by multiple lights, an image which anticipated the Paradise promised to the chosen: candles were placed atop the mourning cloth decorated with fleurs-de-lis, and ornamenting the nave and choir (with 1,227 one-pound candles). 27 Candles also illuminated the principal altars and the chapelle ardente [mortuary chapel], the décor's principal element. The mortuary chapel was a wooden structure, 28 covered with fine black cloth embroidered with royal coats of 26'l'évêque de Chartres fit l'office de diacre, et l'abbé de Saint-Denys (Jean de Bourbon de la Boulaye) celui de sous-diacre,' Chronique de Saint-Denys, p. 495-497. 27Accounts in GRANDEAU 1970, p. 180. 28Of 14 pieds long by 8 pieds wide, ibid., p. 178. arms, and with an azure satin band with fleurs-de-lis. 29 The four gables (which intersected, each topped with a cross) were also covered in satin, and together supported a large fleur-de-lis. 30 The chapel scintillated with hundreds of candles, [START_REF] Martial D | Les vigilles de la mort du Roy Charles VII[END_REF] while four large torches (of 30 pounds of wax) were placed in the corners of the coffin-effigy ensemble. 32 The royal arms covered the space entirely. In addition to the mortuary chapel's décor, at Notre Dame as at Saint Denis, the nave, choir, and pillars of the church were hung with an azure fleurs-de-lis cloth (at Saint Denis, the chapel of Saint John the Baptist, where Charles VI was buried, was likewise decorated with such a band). Banners, pennants, and blazons also ornamented the two edifices.

Attached at the cathedral's entrance there were two banners and two pennants of remembered that, at the heart of the convoy, the Duke of Bedford had directly followed the coffin, presenting himself as the representative of the young Henry VI in France-the king's successor was not yet to be voluntarily absent from his predecessor's funeral, quite to the contrary. 35 The chief herald's cry at the Saint Denis grave insisted upon the English transmission. First, the huissiers d'armes broke their rods, throwing them into the grave, then the sergeants lowered their maces, a sign of the king's death. The chief herald then launched the following cry: 'God willing, have pity and mercy on the soul of the most excellent, most high, and most powerful Charles, king of France, sixth of this name, natural and sovereign seigneur'; 'God give a good life to Henry, by the grace of God king of France and of England, our sovereign seigneur'. 36 The sergeants lifted their maces, crying, 'Long live the king, long live the king, long live the king'. 37 Nevertheless, 35Similarly, during the requiem mass, Bedford alone had gone to the offering, 'Cérémonial,' published in GIESEY 1987, p. 302. 36'Dieu veuille avoir pitié et mercy de l'âme de très excellent, très hault et puissant Charles, roy de France, VI e de ce nom, naturel et souverain seigneur' ; 'Dieu doint bonne vie à Henri, par la grâce de Dieu roy de France et d'Angleterre, nostre souverain seigneur.' 37'Vive le roy, vive le roy, vive le roy.' Chronique de Charles VI, p. 326. There are several versions of the cry that was delievered: 'Priez pour l'ame de tres excellent prince Charles VI, roy de France'….etc, as it was usually made. And shortly after, a herald cried loudly 'Vive Henry par the ritual had no performative power, since it did little more than express-in word and in action -the succession agreement which had been negotiated two years earlier in the Treaty of Troyes. 38 The ceremony's organizers took great care to stage the king's final entry, and the funeral cost a total of approximately 9,000 livres tournois. 39 In the context of this complicated succession, the organizers nevertheless attempted to reduce expenditure by reusing precious textiles. To this end, cloth-of-gold, ermine, and fleurs-de-lis were removed from other décors, recut, and resewn. The king's ceremonial gown and coat, for example, were fashioned using cloth-of-gold which la grace de Dieu roy de France et d'Angleterre,' 'Cérémonial', published in GIESEY 1987, p. 303. 38Later accounts gave a revised version of the funerary cry, in favour of a transmission of power to the dauphin: 'Priez pour l'âme de très excellent prince Charles VI de ce nom très glorieux et victorieux et bien servy lequel debouta et expulsa à l'aide de Dieu omnipotent les Anglois', Arsenal, Ms. 4226, fol. 150 ('Ordre et cérémonie observée à l'enterrement du roy Charles VI en l'an 1422').

39In comparison, nearly 13,000 livres tournois were spent for Philip the Good in Bruges in 1467, Archives départementales du Nord, B 2064, fol. 232 v°.

had already served for the king's blanket at the hôtel Saint-Pol, and the dais originated from one of the king's chambers. 40

Epilogue: The Legacy of Charles VI's Funeral

The innovations introduced at Charles VI's death permanently marked the royal funeral ceremony. Charles VII, who died in 1461 in his château of Mehun-sur-Yèvre, received the same honours, marked by the presentation of the effigy in majesty, the exposition of décors and precious parements (cloth-of-gold pall, dais, coats of arms, a blue mourning ribbon with fleurs-de-lis…) and with specific rituals like the cry of succession. 41 The principal change concerned the ceremonial costume, which was no longer made of red cloth-of-gold, but, rather, of blue fleurs-de-lis-covered velvet lined with ermine (as used in coronations). 42 Poor individuals were also remunerated for their participation in the procession, where they replaced servants as the candle-bearers. 43 Louis XI did not travel to attend his 40Account in GRANDEAU 1970, p. 173-175. 41ESCOUCHY 1863-1864, p. 443. 42Ibid., t. II, p. 433. On the royal habit, see CHATENET, LECOQ, 2011, p. 21-31. 43ESCOUCHY 1863-1864, p. 429. The account indicates that there was also a huissier d'armes on horseback in the convoy, 'portant les armes du roy' and marching before the body was a second, 'portant la masse ', Ibid., p. 426. By 'armes du roy', should we understand his helm, his coat of father's funeral, and Louis II of Orléans led the mourning train. His mother, Marie of Clèves, Duchess of Orléans, was present at Saint Denis, which was exceptional given that women generally did not attend mens' funerals. 44 In 1498, upon Charles VIII's death, the funeral ceremony was largely similar. 45 The wax mannequin represented the monarch in majesty, a substitute for the corpse which could no longer be displayed, but also as a portrayal of the glorious body destined in the Resurrection. 46 Nevertheless, among medieval funerals, one monarch was an exception: practicing the art of differentiation, Louis XI (1483) wanted to be buried like a arms, or his sword. The author undoubtedly refers to a piece of clothing, the tabard, with the king's arms. 46Recent historiography has effectively shown that the French king had but one body; the effigy never incarnated the monarchical permanence, the political and immortal body of the sovereign.

On the debates about the effigy, GIESEY 1987. Theory contested by Alain Boureau, (BOUREAU 1988, p. 28-34), and by Elisabeth A.R. Brown, (BROWN 1999, p. 502 et BROWN 2002, p. 113-130).

the litter. 49 Numerous people rendered a final homage to the queen; men (prelates, princes including her brother, Louis II of Bourbon, and the king's officers) as well as women (the dowager queen Blanche of Navarre, the Duchess Blanche of Orléans and the ladies-in-waiting). 50 As discussed above, the fifteenth century's principal innovation was the effigy's introduction into the royal funerary rite in 1422. Beginning with Isabeau of Bavaria's death in 1435, the queen also received such a representation. Like her husband, Isabeau died in the hôtel Saint-Pol, in Paris (29 September). Her body was displayed uncovered for three days, before being lowered into a lead coffin.

The convoy set off for Notre Dame fifteen days later, on 13 October. The queen was accompanied by fourteen crieurs de corps, one-hundred torch-bearers, the Parisian clergy, prelates (the abbot of Sainte-Geneviève, who officiated, the bishop of Paris, the bishop of Thérouanne), English lords (Lords Scales and Willoughby), 49Chronique de Jean II et de Charles V, p. 279-282. On queens' funerals more generally, GAUDE-FERRAGU 2014, p. 187-192 and GAUDE-FERRAGU 2016, p. 141-149. 50Previously, in 1371 Jeanne of Evreux, widow of Charles IV the Fair, the last Capetian sovereign, enjoyed a sumptuous funeral, with a pall of cloth-of-gold, carried by the presidents of the Parlement of Paris, and a dais. Charles V accompanied the corpse, yet he was absent from the burial of his wife, Jeanne of Bourbon, Chronique de Jean II et de Charles V, p. 152. her sister-in-law, Catherine of Alençon, and several ladies-in-waiting. 51 An effigy represented the queen: Le corps…était en haut levé sur les épaules de seize hommes vêtus de noir, et était sa représentation [effigie] moult bien faite, car elle était couchée si proprement qu'il semblait qu'elle dormît, et tenait un sceptre royal en sa main dextre.

[The body (…) was raised up on the shoulders of sixteen men dressed in black, and its representation [the effigy] was very well-made, as it was laid out so properly that it looked as if she were sleeping, and held a royal sceptre in her right hand]. 52 For reasons of potential insecurity (linked to the presence of the Armagnacs), the trajectory from Notre Dame to the abbey of Saint Denis was made via the Seine.

(Fig. 3).

Isabeau was buried in the chapel of Saint John the Baptist, alongside Charles VI.

It appears that an effigy did not figure in the convoy of Marie of Anjou, Charles VII's widow, whose funeral was celebrated in Paris on 26 January 1464 51Journal d'un bourgeois de Paris, Colette Beaune (éd.), p. 343. The bourgeois of Paris allows the reader to believe that the queen was buried poorly, abandoned by all, which is far from the truth. 52Ibid., p. 343.

(the queen had died in December 1463 at the abbey of the Châtelliers, while returning from a pilgrimage to Saint James of Compostela). 53 A wax mannequin represented Charlotte of Savoy, however, in the funerary train which transported her body to Notre Dame of Cléry in December 1483. An exceptional account conserved at the French National Archives mentions a payment to Jean Bourdichon, the king's painter, 54 for having devised a wooden body 'appropriate to the grandeur of the aforementioned lady" and having painted the wax face "according to her likeness'. 55 To fashion the effigy, Bourdichon had taken the advice of dowager duchess Marie of Clèves, who recalled aulic ceremonial, as she had attended numerous such rites (like those celebrated upon the death of Charles VII).

Having died on 1 December 1483 in the Château of Amboise, Charlotte of Savoy's body was embalmed before being presented publicly on a lit de parement in the royal chamber for three days. Four candles surrounded her body, which clerics exposed day and night. After being placed on the funerary bier, the wake 53CHEVALIER 1999, p. 81-98. 54Bourdicon succeeded Jean Fouquet as the king's official painter in 1481. AVRIL, REYNAUD 1995, p. 293. 55GAUDE-FERRAGU 2010, p. 779-804: 'de la grandeur de ladite dame', 'selon sa semblance'. continued for ten days inside the château's chapel -the chapel of Saint Florentintransformed for the occasion into a place of mourning: the main altar was dressed with black velvet and taffeta, the fourteen secondary altars with black buckram, and a mourning ribbon enveloped the choir and nave. A chapelle ardente illuminated the casket.

It was at Cléry, for her final entry, that the queen was presented in majesty, surrounded by numerous mourners: religious, the poor (carrying torches), members of her household and her relatives (her brother, Philip of Bresse; her daughter, Jeanne of France; her niece, Anne of Savoy). Her effigy was transported across the town on a litter covered with a cloth-of-gold pall. The queen was dressed in the royal costume, composed of a bi-colored surcot of red and blue velvet ('on her arms, the bi-colors of Savoy and of France'), and of a 'coat de parement' made of blue satin covered with fleurs-de-lis and lined with ermine (an exact replica of the coat the monarch wore during the great ceremonies of his reign). The regalia were displayed: the mannequin, crowned, was designed to hold the sceptre and the main de justice. 56 A dais covered the litter, its canopy made of red cloth-of-gold and decorated with the queen's coat of arms. 57 Charlotte of Savoy was then buried in the collegiate church of Notre Dame of Cléry, where a mourning ribbon of heraldic 56AN, KK 69, fol. 116 v-120. The head reposed on a carreau d 'honneur, covered in drap d'or. 57AN, KK 69, fol. 121. Four lances supported it, AN, KK 69, fol. 122. décor hung, made of black buckram in the nave, and of velvet in the choir. The lighting was impressive: on 14 December, nearly 700 candles illuminated the mortuary chapel, the choir, and the altars. Six large, 25-pound candles encircled the body. 58 On the orders of Charles VIII -her son -and his counsellors, in particular Pierre and Anne of Beaujeu -Charlotte of Savoy enjoyed all of the elements of the royal funerary ritual. The only difference between the customary funerals of kings and queens was that distance prevented the participation of the presidents of the Parlement of Paris and the capital's magistrates. These groups were, however, present during the celebration of Anne of Brittany's funeral in 1514, where considerable innovations were added to the traditional funerary elements; the introduction of the funerary meal rediscovered from Antiquity, for example. 59

Between Royal Imitation and Ceremonial Affirmation: The Kingdom's

Princes

During the fifteenth century, the kingdom's princes affirmed their identity and their power through the celebration of sumptuous funerals which, among other 58Two of these weighed as much as 30 pounds of wax.

59Cf. Monique Chatenet's article in the present volume, pp. 00 and Girault, 2014. ceremonies, distinguished them from "common mortals." 60 Several codes characterized their funerals: the corpse was embalmed, permitting its conservation for several days longer in its entirety; a lead coffin; a funerary pall, systematically made of cloth-of-gold and emblazoned with the deceased's arms; 61 (Fig. 4) the presence of pleurants, usually poor people remunerated for the occasion who were dressed in black gowns and hoods, these ferrymen of eternity sought out for the efficacy of their prayers but whose number also signalled the deceased's eminence; the participation of the prelates, the nobles, the urban elite, and the group of household officers (who can served the personal or public person of the defunct) in the celebration; and a profusion of light, characterized, among other things, by the presence of a chapelle ardente during the liturgical celebrations.

To these customary codes, certain princes added the exposition of their insignia, allowing them to affirm their sovereignty and distinctive power. The funeral celebrated in honor of Francis II of Brittany, who died in 1488, provides an eloquent example of this. The duke was buried in the Carmelite church of Nantes, not in a lead coffin like most princes, but with his body uncovered and dressed in ceremonial costume, like the king. Furthermore, in the funeral train the ceremony's organizer, the chancellor of Brittany, Philip of Montauban, displayed two insignia 60On this section, permit me to refer the reader to my work, GAUDE-FERRAGU 2005. of power; the duke's sword -given to him during his coronation -and the duchy's seals; an equestrian seal and a seal of majesty. The placement of these objects can be explained by the difficult context of the Breton succession. It was necessary to demonstrate to everyone in the duchy the deceased's 'almost sovereign' power, so as to affirm his political power and, above all, that of his daughter and heir, Anne of Brittany.

The same issue arose in 1503 during the celebration of the funeral of Pierre II, Duke of Bourbon, a funeral which his wife, Anne of Beaujeu, organized. Anne chose to adopt the principal elements of the royal rite; the dais, effigy, and cry of succession. The use of a wax mannequin, however, was reserved solely for the monarchs, their spouses, and princes endowed with a royal title, even if this title was fictive, as with René of Anjou, King of Naples and Sicily (1480). This 62It is only under Charles VII that the torch-bearers, dressed in mourning, were poor people remunerated for the occasion.

63The standards (guidon, emblem, pennant, banner), the arms (coat of arms and sword) and the king's ceremonial horses were then exhibited in the convoy, Alain BOUREAU 1988, p. 100-1. defunct prince. Some held his banners and others -the knights -his complete armour (both his tournament and war shield, lance, sword and helmets). 64 These honorific objects were then left on the altar inside the burial place, doubling the normal liturgical offering. 65 The chivalric offering organized for the burial of Louis of Male was impressive for the number of 'arms' offered: Philip the Bold, Duke of Burgundy and Louis's successor, presented the prince's war shield, followed by numerous gentlemen who, successively, delivered all of his pieces of armour (forty in total, eight shields, eight swords, eight chargers, eight helms, and eight banners, either of war or of tournament). One must imagine that this vast military parade traversed the entire church up to the altar. The horses' entrance, with all of the difficulties and inconveniences it could cause, is one of the most surprising elements.

This military armament, and in particular the deceased's sword or shield, was occasionally used to symbolically affirm the transmission of power. This was notably the case in the principality of Foix-Béarn, as demonstrated in a commemorative ceremony organized in 1414, two years after the death of the count, Archambaud of Grailly, which took place in the Dominican church of 64FROISSART 1872, t. XXI, p. 262-3.

65For further details on the offering, GAUDE-FERRAGU 2005, p. 208-213. Cf. also in this volume, Alain Marchandisse's article on the funerals of Philip the Good in 1467 and in 1473, pp. 00.

Orthez. 66 During the offering, the officiant was handed the count's sword 'completely bare' (a sign of death); then the count's son and successor, Jean I, received his shield which he immediately straightened, presenting it to the assembly of prelates, nobles, and urban communities, and, in doing so, demonstrating that the noble house's arms were henceforth in his hands. 67 Above all, royal and princely funerals were a Christian rite which, during the fourteenth and fifteenth centuries, became a vast public ceremony which participated in the communication of power. The 'invention' of the effigy, linked to the 1422 crisis of succession and the English presence, remains one of this transformation's most remarkable elements, even if recent historiography has demonstrated that the effigy never incarnated the king's political and immortal body. 68 66TUCOO-CHALA 1977, p. 18. 67Ibid., p. 19. 68In addition to the bibliographic references provided above in note [XX], see Monique Chatenet's article in the present volume.

  5"et fut trouvé qu'il avoit le cuer et le foye net," Chronique de Charles VI, p. 324. 6Cf. the accounts of the funeral published in GRANDEAU 1970, p. 181 (a publication which was made from a seventeenth-century copy of the register conserved at Paris's Chambre des Comptes, Bibliothèque Municipale de Rouen, collection Leber 5870, manuscript Menant, t. VIII, fol. 134-172. The body had been covered with a waxen canvas and linen shroud before being placed in lead ["mis en plomb"].

  Charles VI's painter, François d'Orléans, immediately fashioned the king's mortuary mask, creating a replica of the king's face and hands: Le chief et visage d'iceluy moslé et fait sur son propre visage et après la vie le plus proprement que on a peu, et ledit chief garny de poil au plus près de la chevelure que portoit ledit seigneur et aussy les mains moslees et faictes après la vie, et vestues de gans blancs brodez.

  deceased's successor (Henri VI), the Duke of Bedford walked alone directly behind the defunct. According to the account of Saint Denis's clergy, Bedford wore a black mourning coat and a hood with a short cornet. 23 A well-known illumination by Philippe de Mazerolles illustrates Jean Chartier's text (Chroniques du règne de Charles VII) and represents the funeral train, offering one of the loveliest representations of an effigy 21In describing the funeral of Charles VII (1461), Martial d'Auvergne explains the meaning of the costume: 'En exemple et significance / Que Justice jamais ne bouge / Pour trespas du Roy, ne muance', MARTIAL D'AUVERGNE 1724, t. II, p. 170. 22Chronique de Saint-Denys, p. 491. On the literary description of the dais, Chronique de Charles VI, p. 325. According to the author, the dais was carried from the exit of the hôtel Saint-Pol by the prévôt of the merchants and the échevins of the city of Paris. 'Et ensuite fut porté par les plus notables bourgeois chacun à son tour' ["And was then carried by the most notable bourgeois, each taking a turn."] Upon arrival at Saint Denis, the abbey's monks replaced them.23Chronique de Saint-Denys, p. 491. To the people's outrage, the princes of the blood, and notably Philip, Duke of Burgundy, did not make the journey.

  29'Lorsqu'on entra dans l'église (l'abbaye de Saint Denis), on y trouva aussi un nouveau luminaire non seulement au-dessus d'une espèce de chapelle en bois construite au milieu du choeur et couverte de draperies noires fleurdelisées, sous laquelle reposait le corps…, mais encore tout autour du choeur et de l'église,' Chronique deSaint-Denys, p. 493. 30Accounts in GRANDEAU 1970, p. 176. 31825 candles were placed in the mortuary chapel at Notre Dame of Paris, Ibid., p. 180 32In total, 4,753 pounds of wax were used at Notre Dame and 5, 679 at Saint Denis. For all of the rituals together, the lighting cost 2,232 livres tournois.vast dimensions, while large escutcheons with the royal arms topped the pillars of Notre Dame's principal portal.33 This décor, full of fleurs-de-lis, was one of the characteristics of royal funerals: the princes of the blood (the dukes of Burgundy, of Berry, of Anjou), on the other hand, transformed their burial place into a space of mourning, covered in a vast emblazoned black cloth. In the illuminations of the Grandes Chroniques de France, Jean Fouquet had, of course, systematized the utilization of azure fleurdelisé, but his décor corresponded well with the reality of royal funerals of the fifteenth century.In addition to the effigy's appearance, Charles VI's funeral introduced a new ritual around the tomb: the cry of succession. It is true that in the troubled political context of the first quarter of the fifteenth century, royal funerals played an exceptional role as a 'ritual of inauguration'. On the one hand, it was necessary to affirm the handover of royal powers to the English (against the potential rights of the dauphin, Charles), and, on the other hand, to uphold Bedford's role as regent of France, since some people preferred the Duke of Burgundy.34 It should be 33Chroniquede Saint-Denys, p. 493. 34Le Journal d'un bourgeois de Paris is a witness to this: on the return from Saint Denis, Jean of Bedford had carried 'l'épée du roi de France devant lui, comme régent, dont le peuple murmurait fort,' Journal d'un Bourgeoisde Paris 1990, p. 196. The carrying of the épée joyeuse is here a symbol of the new regent's entrance into service, an aspect absent from all other inauguration ceremonies.

  44GAUDE-FERRAGU 2005, p. 157-164. 45BOUREAU 1988, p. 95-114 (publication of Pierre d'Urfé's ordinance organizing Charles VIII's funeral in 1498). Cf. Monique Chatenet's article in the present volume, pp.00.

  ceremonial appropriation was justified by Pierre II's regency during the minority of CharlesVIII (1483-1488) and during the king's departure forItaly (1494-1495). This appropriation further allowed the symbolic affirmation of the Bourbon princes' power and that of the duchess, Anne, and the deceased's daughter, Suzanne, in the context of a delicate succession; a succession which was proclaimed in the funerary cry that transformed the ducal funeral into an inaugural ceremony:Vive mes dame et damoyselle duchesses de Bourbonnois et d'Auvergne, contesses de Clermont, de Fourestz, de Gien, de la Marche, vicontesses de Carlat et de Murat, dames de Beaujeulois, de Nonnay et de Bourbon Lanceys [Long live my lady and damsel the duchesses of Bourbonnois and of Auvergne, countesses of Clermont, of Fourestz, of Gien, of La Marche, viscountesses of Carlat and of Murat, ladies of Beaujeulois, of Nonnay, and of Bourbon Lanceys]. 61 But princes' funerals were not simple imitations of royal rites. In ritual, interactions were continual. The presence of the poor as torch-bears is first attested amongst the princely courts. 62 In the same manner, for a long time the chivalric offering was specific to the noble realm (it was not introduced into the royal rite until 1498, with the death of Charles VIII). 63 Appearing in the mid-thirteenth century in Flanders and England, the display of the deceased's arms, banners, and horses characterized numerous princely convoys throughout the fourteenth and fifteenth centuries. In the cortege which led Louis of Male, Count of Flanders, to the collegiate church of Saint Pierre of Lille in 1384, sixteen knights preceded the 61GAUDE-FERRAGU 2005, p. 262-263.

13Accountsin GRANDEAU 1970, p. 177.

simple person of faith, with neither effigy nor funerary pomp, not at Saint Denis but, rather, at Notre Dame of Cléry, a collegiate church which conserved a miraculous statue of the Virgin, to whom the king dedicated much devotion. The king died at Plessis-Lès-Tours and his body was embalmed before being transported to Saint Martin of Tours, where the canons displayed the body for several days before transporting it, without pomp, to Cléry. 47 'A woman in majesty': The Queen's Funeral in Fifteenth-Century France Along with their husbands, queens incarnated royal dignity, a dignity which their funerals displayed. From this perspective, the services that Charles V organized for his wife, Jeanne of Bourbon (1378), constitute a turning point in the communication of royal politics; a ceremonial transformation, but also a literary and iconographic one, as the king's chancellor, Pierre d'Orgemont, related the funeral at considerable length alongside a lovely illumination in his Chroniques.

(Fig. 2). 48 The body was exposed in the convoy, equipped with regalia (crown, sceptre, rose verge). The presidents of the Parlement of Paris held the cords of the cloth-of-gold pall and the prévôt of the merchants and échevins held a red and gold dais above 47ROYE 1894-1896, p. 137 et 398. GEORGES 2006, p. 92. 48Grandes Chroniques de France (exemplaire possédé par Charles V), BnF Fr. 2813, fol. 480 v°.


Arthur Perodou
email: arthur.perodou@doctorant.ec-lyon.fr

Anton Korniienko
email: anton.korniienko@ec-lyon.fr

Gérard Scorletti
email: gerard.scorletti@ec-lyon.fr

Ian O'connor
email: ian.oconnor@ec-lyon.fr

Systematic Design Method of Passive Ladder Filters using a Generalised Variable

Keywords: Frequency Filter Design, Passive Components, Ladder Structure

This paper focuses on the design of passive filters with a ladder structure. Based on convex optimisation, we propose an approach to extend the traditional LC-ladder filter design method to lossless passive components. To achieve this, a generalised variable T (s) is introduced, leading to a new convex formulation of the design problem. The approach is applied on an academic design problem: the design of a LC-bandpass ladder filter. This provides a first and crucial step before designing filters of practical interest.

I. INTRODUCTION

Despite the rise of digital filters, analog filters are still of importance for electronics applications. In particular, they are used in high frequency circuits or low power applications, where their digital counterparts are too costly or requires too much power [START_REF] Casson | A Review and Modern Approach to LC Ladder Synthesis[END_REF]. In RadioFrequency applications, analog passive filters, based on acoustic resonators (such as SAW/BAW), are especially appreciated for their performance, low-power consumption and high-quality factor.

In order to face future challenges, new sophisticated components with better characteristics (filtering performance, power consumption, integration,...) are emerging [START_REF] Hashimoto | Tunable RF SAW/BAW Filters: Dream or Reality?[END_REF]. The resulting system consequently becomes increasingly complex and traditional design methods cannot efficiently solve the design problems. In order to improve the design flow and to solve highly complex design problems, new systematic design methods are required. Convex optimisation is a natural candidate to develop such methods. It is a powerful framework, endowed with generic solvers, able to optimally solve a large variety of engineering problems [START_REF] Ben-Tal | Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications[END_REF]. Furthermore, many analysis and design problems can be formulated as an Linear Matrix Inequality (LMI) optimisation problem, which is an important class of convex optimisation known to be solvable in a decent computational time [START_REF] Boyd | Linear Matrix Inequalities in System and Control Theory[END_REF].

A specificity of analog filters is the configuration the elements are set in, known as the structure of the filter. Some structure may demonstrate substantial benefits. For example, LC filters with a ladder structure are known to be robust to component value variability [START_REF] Baher | Synthesis of Electrical Networks[END_REF]. However, the introduction of a structure makes the resulting design problem harder to solve. In the System Design community, it is well known that optimisation algorithms for design problems of structured systems have a prohibitive computational complexity [START_REF] Blondel | NP-hardness of some Linear Control Design problems[END_REF].

The usual design method of passive filters involves two steps. First, a transfer function s 21 , whose frequency-response is under modulus constraints, is computed. When s 21 is a standard transfer function, depending on the Laplace variable s, the synthesis problem can be transformed into an LMI optimisation problem [START_REF] Rossignol | Filter Design under Magnitude Constraints is a Finite Dimensional Convex Optimization Problem[END_REF]. Second, the resulting transfer function s 21 needs to verify realisability constraints, in order to be implementable in a given structure. These constraints are complex to find, and even harder to check, for a general structure. In fact, they generally lead to a non-convex formulation of the problem and require a good initial point to prevent convergence issues [START_REF] Casson | A Review and Modern Approach to LC Ladder Synthesis[END_REF], [START_REF] Yarman | Design of Practical Matching Networks With Lumped Elements Via Modeling[END_REF]. However, for a LC-ladder filter, i.e. a ladder filter where inductances L and capacitances C are alternatively set in the serial and the parallel arms, these conditions appear to be simple and can be easily included into the LMI optimisation problem of the synthesis of s 21 [START_REF] Baher | Synthesis of Electrical Networks[END_REF].

In the Control community, a paradigm has recently emerged to formulate analysis and design problems of structured systems as LMI optimisation problems. The underlying idea is the introduction of a generalised variable which encompasses the information pertaining to the structure. In the last decade, this approach has been successful in many areas of applications as diverse as formation flying [START_REF] Massioni | Distributed Control for Identical Dynamically Coupled Systems: A Decomposition Approach[END_REF], micro-Electronics [START_REF] Zarudniev | Network Internal Signal Feedback and Injection: Interconnection Matrix Redesign[END_REF], [START_REF] Korniienko | Performance Control for Interconnection of Identical Systems: Application to PLL network design[END_REF], biological networks [START_REF] Hara | Stability Analysis of Systems With Generalized Frequency Variables[END_REF]. Our purpose is to apply this idea to the design of structured passive filters.

Recently, the synthesis problem of a transfer function s 21 (T (s)) depending on a generalised variable T (s) has been formulated as an LMI optimisation problem [START_REF] Perodou | Frequency Design of Interconnected Dissipative Systems: a Unified LMI Approach[END_REF]. The main contribution of this paper is then to provide realisability conditions that can be included in this formulation, in the case where T (jω) * = T (jω). The resulting circuit has then a ladder structure with serial elements impedance of the form Z(T (jω)) = α • T (jω) and parallel elements admittance of the form Y (T (jω)) = β • T (jω). This is applied to the direct synthesis of LC-bandpass filter with a ladder structure. This result may be viewed as an intermediary, but crucial, result before tackling design problems of practical interest.

A. Structure of the paper

This paper is organised as follows. Section II presents the design problem of LC-ladder filters. Section III introduces and solves the extended design problem of T -elements ladder filters. The approach is illustrated in Section IV on the design of a LC-bandpass ladder filter. Section V concludes the paper.

B. Notations and Definitions

The letter s stands for the Laplace variable and j R for the entire imaginary axis. z * and e{z} respectively denote the complex conjugate and the real part of the complex number z.

II. LC-LADDER FILTER DESIGN

A. Background about Passive Filters

A passive filter is traditionally considered as a two-port network Q, composed of analog passive elements, inserted between a generator (E g , R g ) and a resistive load R l (Fig. 1). The input-output power transfer of a passive two-port Q is characterised by the scattering matrix S: where U 1 and I 1 are respectively the complex input voltage and current. For a lossless-passive network Q, the scattering parameters are linked by the relation:

    U 1 -R g I 1 2 R g U 2 -R l I 2 2 √ R l     = s 11 s 12 s 21 s 22 :=S     U 1 + R g I 1 2 R g U 2 + R l I 2 2 √ R l    
|s 21 (jω)| 2 = 1 -|s 11 (jω)| 2 (1)
Frequency-filter constraints are set on the squared magnitude of the scattering parameter |s 21 (jω)| 2 , as it represents the power gain between the generator and the source [START_REF] Youla | A Tutorial Exposition of some Key Network-Theoretic Ideas Underlying Classical Insertion-Loss Filter Design[END_REF]. These frequency-domain constraints will be referred to as the spectral mask in the sequel.

Example 1. Typical spectral mask for passive filters are bandpass constraints, illustrated in Fig. 2 and correspond to:

∀ω ∈ R, |s 21 (jω)| ≤ 1 (2) ∀ω ∈ [0; ω U1 ], |s 21 (jω)| ≤ U 1 (3) ∀ω ∈ [ω L1 ; ω L2 ], |s 21 (jω)| ≥ L (4) ∀ω ∈ [ω U2 ; ∞[, |s 21 (jω)| ≤ U 2 (5)
The behaviour of the two-port Q terminated on R l can be represented by the input impedance z in , defined by:

z in = U 1 /I 1 .
Then, simple calculation provides the relation:

z in = R g • 1 + s 11 1 -s 11 (6)

B. Ladder Structure

Passive filters are mostly designed in a ladder form. Historically the most studied in circuit theory, ladder passive filters are known to have low sensitivity to component values variations [START_REF] Baher | Synthesis of Electrical Networks[END_REF], [START_REF] Temes | First-Order Sensitivity and Worst Case Analysis of Doubly Terminated Reactance Two-Ports[END_REF]. In addition, ladder filters have the property that all the transmission zeros are included in the anti-resonant frequencies of the series arms and the resonant frequencies of the parallel arms [START_REF] Hashimoto | Moving Tunable Filters Forward: A "Heterointegration" Research Project for Tunable Filters Combining MEMS and RF SAW/BAW Technologies[END_REF], [START_REF] Menendez | Closed-Form Expressions for the Design of Ladder-Type FBAR Filters[END_REF].

A ladder topology for four elements is illustrated in Fig. 3. This results in a specific decomposition for z in :

z in = Z 1 + 1 Y 2 + 1 Z 3 + 1 Y 4 + 1 R l (7) When Z 2i-1 (s) = α 2i-1 • s and Y 2i (s) = α 2i • s, i ∈ {1, 2}
, the decomposition of ( 7) is referred to as a continued fractional expansion.

Rg Eg Z1 Z3 R l Y2 Y4
Fig. 3: Example of a Ladder Filter

C. LC-Ladder Filter Design Problem

In a LC-ladder filter, serial and parallel elements are respectively inductances L and capacitances C. As far as the authors know, this is the only filter design problem, with a prescribed structure, which has a convex formulation.

This problem is usually decoupled into two sub-problems: 1) the synthesis of the scattering parameter s 21 under frequency modulus constraints and 2) the satisfaction of the LCladder realisability conditions [START_REF] Baher | Synthesis of Electrical Networks[END_REF].

1) Synthesis Problem: The first sub-problem deals with the synthesis of the scattering parameter s 21 , which should satisfy a spectral mask SM, such as for instance bandpass requirements.

Problem 1 (Standard Synthesis Problem). Given a spectral mask SM, Compute a 0 , . . ., a n and b 0 , . . ., b m such that

s 21 (s) = b 0 + b 1 • s + . . . + b m • s m a 0 + a 1 • s + . . . + a n • s n
and |s 21 (jω)| satisfies SM.

2) LC-Ladder Realisability Conditions: The second subproblem is about finding the conditions such that the filter, resulting from Problem 1, is in a LC-ladder form. One has then to find the conditions such that z in can be decomposed as a continued-fractional expansion in s.

Problem 2 (LC-Ladder Realisability Conditions).

Given s 21 (or z in ), Find conditions such that z in admits a continued fractional expansion in s:

z in (s) = α 1 • s + 1 α 2 • s + 1 . . . α n • s + 1 R l (or R l ) (8)
with α 1 > 0, α 2 > 0, . . ., α n > 0.

D. LC-Ladder Filter Design Methods

Structural realisability conditions are in general difficult to formulate as an LMI optimisation problem. However, those for LC-ladder filters are rather simple. It appears that sufficient conditions are that s 21 (s) is T -bounded-real, with T (s) = s, and is a stable all-pole function, i.e. s 21 (s) = 1 g(s) with g a Hurwitz polynomial [START_REF] Baher | Synthesis of Electrical Networks[END_REF].

In the traditional approach, solutions of Problem 1 are calculated using the Butterworth or the Chebyshev approximations. A prototype lowpass filter is then obtained [START_REF] Parks | Digital Filter Design[END_REF]. As these approximations always satisfy the LC-ladder realisability conditions, a prototype LC-ladder filter is synthesised. Using element and frequency transformations, other standard filters may be obtained [START_REF] Baher | Synthesis of Electrical Networks[END_REF]. However, the resulting impedances of the transformed elements may not represent components of practical interest.

In [START_REF] Rossignol | Filter Design under Magnitude Constraints is a Finite Dimensional Convex Optimization Problem[END_REF], it is shown how Problem 1 can be formulated as an LMI optimisation problem. By adding the realisability conditions, one can formulate the LC-ladder filter design problem as an LMI optimisation problem. In the next section, it is shown how this approach can be extended to ladder filter with other lossless-passive elements. To achieve this, a generalised variable T (s) is introduced. The resulting design problem remains an LMI optimisation problem.

III. GENERALISED VARIABLE APPROACH

A. Introduction of a Generalised Variable

Design problems with a prescribed system structure are known to be generally complex to solve [START_REF] Blondel | NP-hardness of some Linear Control Design problems[END_REF]. An idea has recently emerged in order to take the internal structure into account, via the introduction of a generalised variable T . From a System theory perspective, these systems are viewed as the interconnection of identical subsystems [START_REF] Hara | Stability Analysis of Systems With Generalized Frequency Variables[END_REF]. The resulting design problem is then the design of the interconnection of these subsystems [START_REF] Zarudniev | Network Internal Signal Feedback and Injection: Interconnection Matrix Redesign[END_REF].

Considering ladder filters, this paradigm can be applied as follows. Serial elements should have an impedance as Z 2i-1 (T (jω)) = α 2i-1 • T (jω), while the parallel elements should have an admittance as Y 2i (T (jω)) = α 2i • T (jω).

The resulting decision variables are then the parameters α 1 , α 2 , . . . , α n . Here, the variable T represents the internal structure of the linear model of the components. The next example illustrates this idea.

Z s (jω) = L s • ω 2 0s -ω 2 jω Y p (jω) = C p • ω 2 0p -ω 2 jω
with ω 2 0s = 1/L s C s and ω 2 0p = 1/L p C p . In the particular case where ω 2 0s = ω 2 0p = ω 2 0 , the impedance Z s and the admittance Y p can be expressed as:

Z s (T (jω)) = L s • T (jω) Y p (T (jω)) = C p • T (jω)
where T will be the generalised variable and is defined as

T (s) := ω 2 0 + s 2 s (9)
Remark 1. In this example, ω 0s and ω 0p need to be equal to a fixed, chosen ω 0 . This constraint is not specific to our approach and also appears in the standard design methodology.

For typical bandpass constraints of ( 2)-( 5), ω 0 is usually set to ω 0 = √ ω L1 ω L2 [START_REF] Parks | Digital Filter Design[END_REF].

Remark 2. Standard LC-lowpass, LC-highpass and LCbandstop ladder filters may be considered by respectively defining T (s) := s, T (s) := 1/s and T (s) := s/(ω 2 0 + s 2 ).

B. Filter Synthesis with a Generalised Variable

This subsection considers the extension of the standard synthesis problem of Problem 1 to the synthesis problem of the scattering parameter s 21 as a rational function of the generalised variable T .

Problem 3 (Generalised Variable Synthesis Problem).

Given a spectral mask SM, Compute a 0 , . . ., a n and b 0 , . . ., b m such that

s 21 (T (s)) = b 0 + b 1 • T (s) + . . . + b m • T m (s) a 0 + a 1 • T (s) + . . . + a n • T n (s)
and |s 21 (T (jω))| satisfies SM.

Based on the ideas of [START_REF] Iwasaki | Generalized KYP Lemma: Unified Frequency Domain Inequalities with Design Applications[END_REF], [START_REF] Zarudniev | Synthèse de Fréquence par Couplage d'Oscillateurs Spintroniques[END_REF], the approach developed in [START_REF] Rossignol | Filter Design under Magnitude Constraints is a Finite Dimensional Convex Optimization Problem[END_REF] has recently been extended [START_REF] Perodou | Frequency Design of Interconnected Dissipative Systems: a Unified LMI Approach[END_REF] to solve Problem 3. This leads to an equivalent LMI optimisation problem, which can then be efficiently solved.

C. T -Elements Ladder Realisability 1) New Problem Formulation: Problem 4 (T -Elements Ladder Realisability Conditions).

Given s 21 (or z in ), Find conditions such that z in admits a continued fraction in T (s):

z in (T (s)) = α 1 •T (s)+ 1 α 2 • T (s) + 1 . . . α n • T (s) + 1 R l (or R l ) (10) with α 1 > 0, α 2 > 0, . . ., α n > 0.
Having a decomposition of z in as in [START_REF] Zarudniev | Network Internal Signal Feedback and Injection: Interconnection Matrix Redesign[END_REF], the serial elements are given by Z 2i-1 (T (jω)) = α 2i-1 • T (jω) and parallel elements by Y 2i (T (jω)) = α 2i • T (jω).

2) Extended Ladder Realisability condition: The next theorem directly extends the realisability conditions from LCladder filters to T -elements ladder filters. Refer to Appendix A for the proof.

Theorem 1. Assume that T (s) = -T (-s).

Let z in be a T -positive-real rational function written as

z in (T (s)) = N (T (s)) D(T (s))
Suppose that

1 2 (z in (T ) + z in (-T )) = 1 D(-T )D(T ) (11)
Then z in (T (s)) admits a continued fraction expansion such as in [START_REF] Zarudniev | Network Internal Signal Feedback and Injection: Interconnection Matrix Redesign[END_REF], with α 1 > 0, α 2 > 0, . . ., α n > 0.

Remark 3. When T (s) = s, the usual realisability conditions are found [START_REF] Baher | Synthesis of Electrical Networks[END_REF].

Remark 4. Evaluated on the jω-axis, the assumption on T of Theorem 1 becomes T (jω) + T (jω) * = 0. Thus, this theorem is available for all the lossless passive elements with impedance [resp. admittance] Z(T (jω

)) = α • T (jω) [resp. Y (T (jω)) = α • T (jω)].
In particular, this includes any components modelled as the interconnection of inductances and capacitances.

Conditions of Theorem 1 seem hard to connect to the convex optimisation problem of the synthesis problem of s 21 . The aim of Corollary 1 is to provide this connection.

Corollary 1. Assume that T (s) = -T (-s).

Let s 21 (T (s)) be a T bounded-real rational function written as

s 21 (T (s)) = N (T (s)) D(T (s))
Suppose that

s 21 (T (s))s 21 (-T (s)) = 1 D(T (s))D(-T (s))
Then the resulting z in (T (s)) admits a continued fraction expansion such as in [START_REF] Zarudniev | Network Internal Signal Feedback and Injection: Interconnection Matrix Redesign[END_REF], with α 1 > 0, α 2 > 0, . . ., α n > 0.

T -elements ladder realisability conditions of Corollary 1 are that s 21 is T -bounded-real and has a constant numerator. These conditions can be easily added to the LMI optimisation problem of the synthesis of s 21 (T ). The global design problem is then an LMI optimisation problem.

IV. APPLICATION

In this section, our approach is illustrated on an academic example: the design problem of a LC-bandpass ladder filter. The constraints are those of ( 2)-( 5) with ω U1 = 0.75 rad/s, ω L1 = 1 rad/s, ω L2 = 1.5 rad/s and ω U2 = 2.2 rad/s, and U 1 = 0.1, L = 0.96 and U 2 = 0.2. The generalised variable T is defined as in [START_REF] Massioni | Distributed Control for Identical Dynamically Coupled Systems: A Decomposition Approach[END_REF] with

ω 0 = √ ω L1 • ω L2 .
In order to get the maximum power transmitted (matching impedance), the internal resistance of the generator and the resistive load are generally considered to be equal to the same value R: R g = R l = R. The value of R can be normalised to R = 1Ω, as impedance scaling may be achieved subsequently [START_REF] Baher | Synthesis of Electrical Networks[END_REF].

First, the squared magnitude |s 21 (T (jω))| 2 is computed using the Robust Control toolbox of Matlab, by applying the LMI optimisation-based approach described in [START_REF] Perodou | Frequency Design of Interconnected Dissipative Systems: a Unified LMI Approach[END_REF]: Finally, by decomposing z in (T ) as in [START_REF] Zarudniev | Network Internal Signal Feedback and Injection: Interconnection Matrix Redesign[END_REF], the ladder circuit of Fig. 5 is obtained, with:

L 1 ≈ 1.665 H C 1 = 1 L 1 • ω 2 0 ≈ 0.4004 F C 2 ≈ 2.767 F L 2 = 1 C 2 • ω 2 0 ≈ 0.2409 H L 3 ≈ 2.204 H C 3 = 1 L 3 • ω 2 0 ≈ 0.3025 F C 4 ≈ 0.848 F L 4 = 1 C 4 • ω 2 0 ≈ 0.7862 H V. CONCLUSION
In this paper, we have focused on the design of analog filter with lossless-passive elements set in a ladder structure. To achieve this, a generalised variable T (s) has been introduced. We have extended the LC-ladder filter design method to the design of T -elements ladder filters. We finally applied this approach to the direct design of LC-bandpass ladder filter.

(jω) = α s • 1 jω • ω 2 -ω 2 rs ω 2 -ω 2 as and paral- lel Z p (jω) = α p • 1 jω • ω 2 -ω 2 rp ω 2 -ω 2 ap
. This leads to the introduction of two generalised variables T s (s) and T p (s) such that

Z s (T s (jω)) = α s • T s (jω) and Z p (T p (jω)) = α p • T p (jω).
Therefore, extending the approach to two generalised variables would be another direction of practical interest.

APPENDIX PROOFS OF THEOREM 1 AND COROLLARY 1

Let first state and demonstrate the following lemma. Lemma 1. Let z be a T -positive-real rational function. Then, if it exists, a pole at infinity must be simple and have real positive residue.

Proof of Lemma 1. Let T (s) be a complex variable such that e{T (s)} > 0. Let be a pole at infinity of order n of the rational function z. In the neighbourhood of this pole, using a Laurent expansion, we may write that the dominant part of this expansion is a n • T n (s), where a n is called a residue. Using a polar form, one can write a n = |a n |e jθ1 and T (s) = |T (s)|e jθ2(s) , where θ 2 (s) ∈ -π 2 ; π 2 , as e{T (s)} > 0. Then

e{a n • T n (s)} = |a n ||T (s)| n cos (θ 1 + nθ 2 (s))
which is strictly positive for all θ 2 (s) in -π 2 ; π 2 , by definition. This implies that θ 1 = 0 and n ∈ {0, 1}. Therefore, a pole at infinity is at most simple and a n > 0.

Let demonstrate now Theorem 1.

Proof of Theorem 1. Without loss of generality, let assumes that the degree n of the numerator N is greater than or equal to the degree d of the denominator D: n ≥ d.

By Lemma 1, as z in is T -positive-real rational, a pole at infinity, if it exists, must be simple and then n and d may differ by at most 1:

|n -d| ≤ 1

Furthermore, by [START_REF] Korniienko | Performance Control for Interconnection of Identical Systems: Application to PLL network design[END_REF], N and D cannot have same degree, leading to |n -d| = 1. Then, using the partial fractional expansion technique, this leads to: then y 2 = 1/z 2 has also a pole at infinity: y 2 (T (s)) = α 2 • T (s) + y 3 (T (s)). The process can then be iterated until the value of the resistance R l is obtained. This occurs after a number of infinity pole extractions equal to the degree of the input impedance z in .

  A T -element refers to en element described by an impedance Z [resp. an admittance Y ] of the form Z(T (jω)) = α • T (jω) [resp. Y (T (jω)) = α • T (jω)], where α is a real, positive scalar. Definition 1 (Passive Element). An element with an impedance Z is said to be passive if Z satisfies: ∀ω ∈ R, Z(jω) + Z(jω) * ≥ 0. It is said to be lossless-passive if Z(jω) + Z(jω) * = 0. Definition 2 (T -positive-real). A rational function f (T (s)) of a complex variable T (s) is said to be T -positive-real if f (T (s)) is real for T (s) real and e{f (T (s))} > 0 for e{T (s)} > 0 Definition 3 (T -bounded-real). Any real rational function h(T (s)) that satisfies the conditions: 1) h(T (s)) has no poles on the closed right-half plane. 2) ∀T (jω) ∈ j R, |h(T (jω))| ≤ 1 is said to be a T -bounded-real rational function.

Fig. 1 :Fig. 2 :

 12 Fig. 1: An Analog Filter

Example 2 .Fig. 4 :

 24 Fig. 4: Usual serial/parallel arms for LC bandpass filters

  |s 21 (T )| 2 = 0.05402 T 8 +0.08091•T 6 +0.009036•T 4 -0.00008729•T 2 +0.05402 which satisfies the condition of Corollary 1. Recalling that T (jω) = -T (-jω), by (1) it comes that |s 11 (T (jω))| 2 = 1 -|s 21 (T (jω))| 2 . Then, using the spectral factorisation technique [13], s 11 (T ) is calculated: s 11 (T ) = T 4 + 0.5784 • T 3 + 0.2079 • T 2 + 0.02954 • T T 4 + 1.78 • T 3 + 1.625 • T 2 + 0.8693 • T + 0.2324 Thus, using (6), z in (T ) is obtained: z in (T ) = 1.665•T 4 +1.963•T 3 +1.525•T 2 +0.7481•T +0.1934 T 3 +1.179•T 2 +0.699•T +0.1934

Fig. 5 :Fig. 6 :

 56 Fig. 5: Illustrative Example -a LC bandpass ladder filter

z 2 (z 2 (

 22 in (T (s)) = α 1 • T (s) + z 2 (T (s))with the residue α 1 positive α 1 > 0. Moreover, as∀T (jω) ∈ j R e{z in (T (jω))} =e{z 2 (T (jω))} using the minimum-real part theorem [5],z 2 is also a Tpositive-real rational function. Furthermore, as 1 T (s)) + z 2 (-T (s))) = 1 2 (z in (T (s)) + z in (-T (s))) = K D(T (s))D(-T (s))

Finally, let demonstrate Corollary 1 .

 1 Proof of Corollary 1. As s 21 is a T -bounded-real rational function, by (1), s 11 is also a T -bounded-real rational function.Mere calculation provides:∀T (jω) ∈ j R, e{z in (T (jω))} = R g • 1 -|s 11 (T (jω))| 2 |1 -s 11 (T (jω))| 2 ≥ 0Moreover, as s 11 has no pole on the closed right-half plane, according to the maximum modulus theorem, |s 11 (T (s))| has its maximum value for T (s) ∈ j R. So e{z in (T (s))} > 0 in e{T (s)} > 0. Thus z in is a T positive-real rational function.

This work has been supported by Région Rhône-Alpes through its Academic Research Community ARC6.


Néstor Claudine Chamoreau

Francisco Hernández Torres

Juana Carolina

Hernández Torres

Ángel Martínez

Torres Coeditores

Cuento Narrado Por

Francisco Hernández

Torres Transcripción

Cecilio Álvarez Toledano

Hernández Green

Fran- Cisco Hernández Torres

Juana Hernández Torres

Torres Traducción

Caroline Perrée

Traducción

Nicolas Ellison

Ilustraciones

Françoise Couissin

: Mapa

G Óscar

Miguel Hernández

Macías Ángel

Coordinación

Del Martín

Castillo

Manihri u'ri El conejo y el tigre The rabbit and the tiger

Atahtuk

Untañahma, pesh ñahma, aĩma chibchai krih kapashkerma apaña õki kapashkra kãhã akwa, kãhã akwa, kuh uruh chitah (kukakatas chaũwa awakña).

Kwih apaña ukwa pok kahñama, atahtu'ki takatushkuma "Awikawa atona pesh ñaha akwa, pesh ñahi, pesh ñaha aĩma chibcha uruh akatas" kapurupishtah awikawã atonna patañah bokaste toshchiskwã (eldp añah ãsã kapaskrĩ kamasa ñahayo, https://elar.soas.ac.uk/Collection/MPI1050997) pabarpi ũtahrari awikawã atona tishpii iñah achuishki pesh ñaha yeisti kipii. Akãn ñaha sukuhayo sukuhri, kakorsbri, ñahbri, ukwameyh archah tahkapashki akaya, iri kakapashki, pesh akaya uchuĩ, kato'kaĩ, aoriah yeisti kira, insi ikãn chusri pataoriah, atesh newen.

Ĩkitama pisawaña akasteshbarwa ĩ kaya awikawama eñatis krih ikãn kãhã chuĩ awikawa aweshkrĩ artachah ye'lerĩ pesh aparalerĩ kãhã kãhã cherĩ kuk uruh katas mãyhña cherĩ: Colón, Gracias a Dios y Olancho.

Ĩyo apurupishkra pesh aoriahi. Ĩkaya awikawama pesh ñah, peshakwa ñahayo, kamasa ñahayo, peshfrãses ñahayo korskai kreish yeisti weshkra achuiskershkuen.

"Manihri u'ri" akaya krih kãhã ikan chuĩ pesh piah kapashkri pesh ñahyo ñehera arilerwa ama eñai pataoriah iñahma.

Pesh ñaha kapashta ĩawikawã kĩrima ñelerwa: Ángel Martínez Torres, Juana Carolina Hernández Torres, Francisco Hernández Torres ekaya iakaya ĩkan ñehi.

Atawẽhri katuh patayo Claudine Chamoreau, ũheka atõwehra kaya arkatushkerpirã ĩka kakorskerpirã. Akari ãsãtah kaya arilerĩ awah katushki, Teresa Campos, Directora del Museo de Antropología e Historia en San Pedro Sula, pesh aoh ñahtari Néstor Hernández Green, Oscar López, kakorska yeisti newasri, ika ĩñakata Françoise Couissinya akarwa kii.

Krihra kakaparenkabarwa, tara asna katushtihima ĩ awikawama ĩkrina chiishtĩ.

To' manihma achihiri. "Awriha paspra, ãpra". "Akarshkwa, tarwarku, aso tokku, ũrahpra" tikii manihya.

¡Akanasri! "Paspra ãpra" tikii u'ya.

Tokkeriarin, tokkeriarin, tokkeriarin. Manihma toktihi arkasaeshkuras akarshkwa.

Peshwa u'ma aso tokyope, asopera neboni.

Chiukan, neboni akan, ¡ah takore u'! "¿Ĩripikiusa takore u'?" manihya tikii.

Manihma nei, sãmpara sukuhi, pe'ki.

Akan manih kii, u' achiukan saki. Akatishki asate'te'yã.

"Ah, ¿ĩyo takaisa? taeĩnwa" u'ma wahni.

"Uuju ayã peshwakwas pikachwa amasparishkawa" manihya tikii.

"Ama pama ayuira ta'kaya" u'ya tikii.

"Akarshki, aũnhkoti wahayã naawa, pehas napeka, pama tokku aku" manihya tikii.

"Wahayã naa pehãs napeka pikatishpara aso apastipira" manihya yẽhi.

Ama pehma pe'ti' sikira pe'ki akaporki.

"¿Ah ĩyo taporkisa?"

"¿Ah ĩyo taporkisa? Pama warkoria", tikii u'ya manihra.

"Warkwishtaria" u'ya tikii.

"Tokku akupe, tokku akupe, tokku akupe" manihya tikii.

Manih nei, teshki, tõshki, te'tihi.

Akarshkwa kapanah, manihra neartapuki.

"Ẽketa, pama ĩyã, pisukuhpa, piãpahã, piãpahã, kecha tarkasauriras, warkwas takauriras" u'ya tikii.

Manih saas chwayã nei, akankah kiaki.

"Ẽketa, tauku u'" manihya tikii "ẽketa, ĩ sa akatahka akari".

"Ke wartishkawa, ĩñara akasteshkoma, ĩkukkama wartishpihã" manih tikii "ẽhĩ patamaschepihã".

"Ĩma toshchepihã, tarwarku te'sukuhu" tikii manihya u'ra.

"Pama archa pitapũnuras".

Yari nei, sukuhi u'ya.

"Kwau ĩketarpe naa" manihya tikii.

"Tasma ke akiri tasah kiuras, akaõra akonapara, naawa" tikii manihyã.

Nei, te'tihi.

Akasteshki, arkasei, manih toshki.

Akarshkwa u'ma ãyã a'ki, a'ki.

A'kiteshki.

Postfacio Postface Afterword

Génesis de este libro

La transmisión de una lengua es principalmente un proceso oral, pero la transmisión del patrimonio literario puede ser también escrita. Hasta el año 2017, no se había escrito ningún libro de cuentos o novelas en pesh. Los relatos Wichã akaki, "La madre de los peces", y Takaskro, "El sismite", constituyeron los dos primeros libros de cuentos narrados por hablantes de la variedad del Carbón. Se distribuyeron en varios pueblos (ver las versiones electrónicas: www.cemca. org.mx/wicha-akaki y www.cemca.org.mx/takaskro). Desde 2012, el proyecto "Documentación y descripción de diferentes variedades de pesh lengua chibcha de Honduras"1 favoreció el trabajo colectivo de miembros de varios pueblos y de investigadores para publicar libros en lengua pesh. Fueron escritos para que pudieran ser leídos por la comunidad y por personas interesadas en esta lengua. Por eso se incluyen las traducciones al español, al francés y al inglés.

El presente cuento Manihri u'ri, "El conejo y el tigre", fue narrado en la variedad de Culmí por Francisco Hernández Torres, oriundo de Culmí, quien actualmente vive en Nuevo Dulcenombre. Fue seleccionado por su importancia en la tradición pesh aunque también es conocido en otras culturas de Centroamérica. Los hablantes del pesh que impulsaron esta publicación son: Francisco Hernández Torres, Juana Carolina Hernández Torres y Ángel Martínez Torres. El lingüista Néstor Hernández Green hizo la primera transcripción y la pintora Françoise Couissin ilustró el cuento.

La lengua pesh

El pesh (también conocido como pech o paya) es la única lengua de la familia chibcha hablada en Honduras, las otras se ubican en Nicaragua, Costa Rica, Panamá, Colombia y Venezuela. En Honduras, se habla también el garífuna, el miskito, el tawahka, el tol (o jicaque), el ch'orti' y el isleño. El lenca y el náhuatl también se hablaron en el pasado.

En la actualidad, el pesh se habla esencialmente en el departamento de Olancho (ver el mapa p. 5) en Santa María del Carbón (en La Laguna y Agua amarilla) y en Dulce Nombre de Culmí (en los pueblos de La Campana, Zopilote, Vallecito, Pueblo Nuevo Subirana, Pisijire, Culuco y Jocomico). También se habla en los departamentos de Colón (en Silín y Moradel) y de Gracias a Dios (en Las Marías y Nuevo Dulcenombre).

El pesh es hablado por alrededor de 500 personas, de las cuales el 80% tiene más de 60 años. Los pocos niños que lo hablan viven principalmente en los pueblos de La Laguna y de Agua Amarilla. La gran mayoría de los pesh es bilingüe pesh-español. Muy pocas personas son monolingües en pesh, todas ellas son mujeres y viven en La Laguna. Por su parte, los pesh que viven o han vivido en Las Marías y Nuevo Dulcenombre son trilingües: en miskito, español y pesh.

La gramática de la lengua pesh es poco conocida y no ha sido descrita. Todos los hablantes de pesh se entienden, aunque existen algunas diferencias que permiten distinguir tres dialectos: el de Carbón, el de Culmí y el de Las Marías (para más información, ver el documental "Salió de nosotros y regresó escrito" https://youtu.be/fmDiFW5Mrrc).

Genèse de ce livre

La transmission d'une langue est principalement un processus oral, mais la transmission d'un patrimoine littéraire peut également être écrite. Jusqu'en 2017, aucun livre de contes ni de romans n'avait été écrit en pesh. Les histoires Wichã akaki, « La mère des poissons », et Takaskro, « Le sismite », furent les deux premiers livres de contes et avaient été narrés par des locuteurs de la variété du Carbón. Ils ont été distribués dans plusieurs villages (voir les versions électroniques : www.cemca.org.mx/wicha-akaki et www.cemca.org. mx/takaskro). Depuis 2012, le projet intitulé « Documentation et description de différentes variétés de la langue de pesh, chibcha du Honduras »2 a favorisé le travail collectif de membres de divers villages et de chercheurs pour la publication des premiers livres en langue pesh. Ce livre a été écrit pour pouvoir être lu la communauté et par les personnes intéressées par cette langue. C'est pourquoi il inclut des traductions en espagnol, français et anglais.

Ce conte Manihri u'ri, « Le lapin et le tigre », a été raconté par Francisco Hernández Torres, originaire de Culmí, qui vit à Nuevo Dulcenombre (variété de Culmí). Il a été choisi pour son importance pour la tradition pesh. Il est aussi connu en Amérique centrale.

Les locuteurs du pesh qui participèrent à cette publication sont : Francisco Hernández Torres, Juana Carolina Hernández Torres et Ángel Martínez Torres. Le linguiste Néstor Hernández Green effectua la première transcription et la peintre Françoise Couissin illustra ce conte.

The birth of this book

The process of transmitting a language is mainly oral, but the transmission of the oral literature can also take place via the written word. Until 2017, no book of stories or novels had been written in Pesh. The stories Wichã Akaki, "The Mother of the Fishes", and Takaskro, "The Sismite", were the first two to be published as books. They were narrated by speakers of the variety of Carbón. These were handed out in several villages (See the digital versions: www.cemca.org. mx/wicha-akaki and www.cemca.org.mx/takaskro). Since 2012, the project entitled "Documentation and description of different varieties of Pesh, a Chibcha language of Honduras"3 has promoted the collective work of members of various villages and researchers for the publication of the first books in Pesh. This book has been written to be read by the community and by people interested in this language. This is the reason why it includes translations into Spanish, French and English.

This story Manihri u'ri, "The rabbit and the tiger", has been told by Francisco Hernández Torres from Culmí who currently is living in Nuevo Dulcenombre (variety of Culmí). It has been chosen since it occupies an important place in Pesh tradition. This story is also known in other cultures of Central America.

The Pesh speakers who participated in this publication are Francisco Hernández Torres, Juana Carolina Hernández Torres and Ángel Martínez Torres. The linguist Néstor Hernández Green did the first transcription and the painter Françoise Couissin illustrated this story.

The Pesh language

The Pesh (also known as Pech or Paya) is the only one of the Chibchan language spoken in Honduras, the others are spoken in Nicaragua, Costa Rica, Panama, Colombia and Venezuela. In Honduras, other minority languages are spoken: Garífuna, Miskito, Tawahka, Tol (or Jicaque), Ch'orti' and Isleño. Lenca and Nahuatl were also spoken there in former times.

Currently, Pesh is mainly spoken in the department of Olancho (see map p. 5) in Santa María del Carbón (La Laguna and Agua amarilla) and in Dulce Numbre de Culmí (in La Campana, Zopilote, Vallecito, Pueblo Nuevo Subirana, Pisijire, Culuco and Jocomico). It is also spoken in the departments of Colón (in Silín and Moradel) and Gracias a Dios (in Las Marías and Nuevo Dulcenombre).

There are about 500 speakers of Pesh, of whom 80 percent are over 60. The small number of children who speak it live mainly in the villages of La Laguna and Agua Amarilla. The vast majority of Pesh is bilingual in Pesh and Spanish. Very few are monolingual in Pesh, except for a few women in La Laguna. By contrast, the Pesh who live or have lived in Las Marías and Nuevo Dulcenombre are trilingual in Pesh, Spanish and Miskito.

The grammar of the Pesh language is relatively little known and has not been described. All Pesh speakers understand each other, although some differences lead us to distinguish three dialects: from Carbón, from Culmí and from Las Marías (for more information, see the documentary "What went out from us has come back written" https://youtu.be/BBNvI_DuDK8).

Ortografía

Con el propósito de que la escritura pesh pueda ser fácilmente leída se emplea un alfabeto práctico que se basa en el alfabeto español. La lengua pesh tiene tonos, pero no se transcriben en este cuento.

Orthographe

Dans le but de faciliter la lecture de l'écriture pesh, nous avons adapté un alphabet pratique basé sur l'alphabet espagnol. La langue pesh comporte des tons, qui ne sont pas transcrits dans ce conte.

Spelling

In an attempt to simplify the reading of Pesh texts, we have adapted a practical alphabet based on the Spanish alphabet. Pesh uses tones, which are not transcribed in this tale. The symbol ˜ indicates a nasalization (air is directed through the nose), in the vowels ã and ẽ and the consonant ñ.

"¿Ah ĩyo taporkisa? Pama warkoria" tikii u'ya manihra. "Warkwishtaria" u'ya tikii. "Tawarku, warpe nawa" manihya tikii. "Tokku akupe, tokku akupe, tokku akupe" manihya tikii. Manih nei, teshki, tõshki, te'tihi. Akarshkwa kapanah, manihra neartapuki. "Ẽketa, pama ĩyã, pisukuhpa, piãpahã, piãpahã, kecha tarkasauriras, warkwas takauriras" u'ya tikii. Manih saas chwayã nei, akankah kiaki. "Ẽketa, tauku u' " manihya tikii "ẽketa, ĩ sa akatahka akari". "Ke wartishkawa, ĩñara akasteshkoma, ĩkukkama wartishpihã" manih tikii "ẽhĩ patamaschepihã". "Ĩma toshchepihã, tarwarku te'sukuhu" tikii manihya u'ra. "Pama archa pitapũnuras". Yari nei, sukuhi u'ya. "Kwau ĩketarpe naa" manihya tikii. "Tasma ke akiri tasah kiuras, akaõra akonapara, naawa" tikii manihyã. Nei, te'tihi. Akasteshki, arkasei, manih toshki. Akarshkwa u'ma ãyã a'ki, a'ki. A'kiteshki. The rabbit went, he walked here and there, he got lost and did not come back. So the next day the tiger went to see the rabbit. "Today, you here, I will catch you, I will eat you, I will eat you because yesterday you lied to me, because you hurt me" said the tiger. The rabbit pretended to hold the stone that was laid there. "Now, uncle tiger" said the rabbit, "now this stone, I'm holding it. I'm tired, if I drop this stone, this earth will be destroyed" says the rabbit, "it will fall and kill us all. All will get lost, help me, come and hold it" said the rabbit to the tiger "because you have more strength". He convinced him, the tiger went and grabbed the stone. "Hold it up well, now I'm coming back" said the rabbit. "As I've been here for a long time, I'm going to pee, I'm leaving" said the rabbit. He left and did not come back. He left him, lied to him, the rabbit got lost. Then the tiger stayed there, he stayed. He remained there forever.

Manihri u'ri es una publicación del Centro de Estudios Mexicanos y Centroamericanos (cemca), organismo financiado por el Ministère de l'Europe et des Affaires Étrangères y por el Centre National de la Recherche Scientifique (cnrs), París, Francia. Se terminó de imprimir en Ediciones del Lirio, Azucenas 10, col. San Juan Xalpa, Iztapalapa. C.P. 09850, Ciudad de México, en mayo de 2019. La edición consta de 500 ejemplares. Se utilizó papel couché mate de 150gr. para los interiores y cartulina sulfatada con laminado mate de 16pts en los forros. Para su formación se utilizaron las fuentes OpenSans y LibreBaskerville.

  Las grafías particulares son: ch -'ch' en español su transcripción fonética es [tʃ]. sh -'ch' en francés su transcripción fonética es [ʃ]. ' -es una glotal su transcripción fonética es [Ɂ]. El símbolo ˜ indica una nasal (el aire pasa por la nariz), ya sea sobre una vocal ã, ẽ o una consonante ñ.

  Les graphies particulières sont : ch -'ch' en espagnol sa transcription phonétique est [tʃ]. sh -'ch' en français sa transcription phonétique est [ʃ]. ' -est une glottale sa transcription phonétique est [Ɂ]. Le symbole ˜ indique une nasale (l'air passe par le nez), qu'il s'agisse d'une voyelle ã, ẽ ou d'une consonne ñ.

  Some spellings to note: ch -'ch' in Spanish the phonetic transcription is [tʃ]. sh -'ch' in French the phonetic transcription is [ʃ]. ' -glottal stop the phonetic transcription is [Ɂ].

"

  Ah, with what are you sinking it? Ah, with what are you sinking it? You're nasty" said the tiger. "You are a wrongdoer" said the tiger. "Don't move, I'm leaving again" said the rabbit. "Just keep drinking, just keep drinking, just keep drinking" the rabbit repeated to him.

El proyecto es apoyado por el Programa de Documentación de la Lenguas en Peligro (eldp), el Centro de Estudios Mexicanos y Centroamericanos (cemca), y el Laboratorio de Excelencia francés "Fundamentos Empíricos de la Lingüística" (LabEx-efl).

Le projet a reçu des appuis du Programme de Documentation des Langues en Danger (eldp), du Centre d'Etudes Mexicaines et Centraméricaines (cemca), y du Laboratoire d'Excellence « Fondements Empiriques de la Linguistique » (LabEx-efl).La langue peshLe pesh (également connu comme pech ou paya) est la seule langue de la famille chibcha parlée au Honduras, les autres sont localisées au Nicaragua, au Costa Rica, au Panama, en Colombie et au Venezuela. Au Honduras, on parle aussi le Garífuna, le Miskito, le Tawahka, le Tol (ou Jicaque), le Ch'orti', l'Isleño. On y parlait autrefois le lenca et le nahuatl.Actuellement, le pesh est essentiellement parlé dans le département d'Olancho (voir carte p. 5) à Santa María del Carbón (La Laguna et Agua Amarilla) et à Dulce Nombre de Culmí (à La Campana, Zopilote, Vallecito, Pueblo Nuevo Subirana, Pisijire, Culuco et Jocomico). Il est également parlé dans les départements de Colón (à Silín et Moradel) et de Gracias a Dios (à Las Marías et à Nuevo Dulcenombre).Le pesh est parlé par environ 500 personnes, dont 80% ont plus de 60 ans. Les quelques enfants qui le parlent vivent principalement dans les villages de La Laguna et de Agua Amarilla. La grande majorité des Pesh est bilingue pesh-espagnol. Très peu de personnes sont monolingues en pesh, toutes sont des femmes et vivent à La Laguna. De leur côté, les Pesh qui vivent ou ont habité à Las Marías et à Nuevo Dulcenombre sont trilingues et parlent le miskito, l'espagnol et le pesh.La grammaire du pesh est peu connue et n'est pas décrite. Tous les locuteurs de pesh se comprennent, bien que certaines différences permettent de distinguer trois dialectes: celui du Carbón, de Culmí et de Las Marías (pour plus d'informations, voir le documentaire « Ce qui est sorti de nous est revenu écrit » https://youtu.be/z3flvMwx0yo).

The Project has been supported by the Endangered Languages Documentation Programme (eldp), the Centre for Mexican and Central-American Studies (cemca), and the French Laboratoire d'Excellence for the Empirical Foundations of Linguistics (LabEx-efl).

El chichicaste (familia de los Loasaceae) es una planta espinosa que se usa mucho con fines medicinales. Las hojas y los tallos tienen pelos espinosos que se adhieren en la piel al menor contacto. Estos pelos liberan sustancias químicas que causan una sensación de ardor.

Le chichicaste (famille des Loasaceae) est une plante très épineuse largement utilisée à des fins médicinales. Les feuilles et les tiges de chichicaste ont des poils épineux qui adhèrent sur la peau au moindre contact. Ces poils libèrent des produits chimiques qui provoquent une sensation de brûlure.

Chichicaste (Loasaceae family) is a very prickly plant, heavily used for medicinal purposes. Chichicaste leaves and stems have prickly, brittle hairs that will attach in the skin at the slightest of contacts. These hairs release chemicals that will cause a burning sensation right away.

(anr) a través del programa intitulado "Investissements d'Avenir" (inversiones con futuro) que porta la referencia anr-10-Esta investigación forma parte del programa "Investissements d'Avenir" (inversiones con futuro) administrado por la Agencia Nacional de Investigación

"Tawarku, warpe nawa" manihya tikii.

The rabbit and the tiger

They told a story about a rabbit and a tiger. One day, the tiger said to the rabbit, "I'll eat you no matter where I find you". This rabbit was sitting. The uncle tiger met the rabbit on the way. "Rabbit, now I'll catch you and I'll eat you" said the tiger. "No, no, no, don't eat me". He said, "Don't eat me" he told him "Don't eat me, now here I found a big roll of cheese." "It's like a big round cheese" the added. "I'll take it, as you are big, come help me" said the rabbit. "Let's get the water out, we'll catch it and we'll eat it" the rabbit told him. "Where is it?" asked the tiger. The rabbit took him away, and what he saw was that the moon was shining. The rabbit took the tiger away to the river. But it was the image of the moon he had seen instead of a round cheese. "Let's grab the cheese and we eat it." "Then, help me, drink the water, dry up the river" said the rabbit. Yes, it is so! "We take it out of the water and we eat it" the tiger told him. They drank, they drank, they drank. The rabbit did not drink because he was lying to him at that time. Mr. Tiger, as he drank so much water, emptied all this water. By his buttocks, everything came out so. Ah my uncle tiger! "What's the matter, uncle tiger?" said the rabbit. The rabbit left and took a chichicaste 6 leaf, and he brought it back. That's what the rabbit did, he put it on the buttocks of the tiger, and he covered them. He covered the anus. "Ah, with what do you do it? It stings me!" cried the tiger. "No, there's an animal, I want to kill him" the rabbit told him. "You, you're deceiving me" said the tiger. "So, don't be worried, I'm going to the mountain to get a piece of wood. You, carry on drinking, carry on drinking" said the rabbit. "I'm going to the mountain to get a piece of wood to plug you and the water does not come out" the rabbit told him. He did not bring back the piece of wood, what he brought back is a thorn and he sank it.