University of Texas Press

Julian Carrillo and "Sonido Trece" ("Dedicated to the Memory of Nabor Carrillo")Author(s): Gerald R. BenjaminReviewed work(s):Source: Anuario, Vol. 3 (1967), pp. 33-68Published by: University of Texas PressStable URL: http://www.jstor.org/stable/779745 .Accessed: 01/11/2011 15:51

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JULIAN CARRILLO AND "SONIDO TRECE"

(DEDICATED TO THE MEMORY OF NABOR CARRILLO)

By Gerald R. Benjamin

Juliain Carrillo's life (1875-1965) falls into three distinct time periods not only in terms of compositional style but also by the type of life he led in each. From 1885-1905, Carrillo was

engrossed in musical studies - first in Mexico, and then, from 1899 until his return, in Europe. Stylistically speaking, this is his "classical" period. From 1906-1924, he occupied himself with many civic responsibilities: as conductor, director, educator, etc. The musical compositions from this period are strikingly atonal. From 1926-65, the composer was primarily concerned with working out the potentialities of a musical system (sonido trece - thirteenth sound), the roots of which went back to his

early conservatory days as a student. Stylistically, this is the most interesting of the three periods. Although most of the works within it are written in the sonido 13 medium (or media, owing to new sounds and new instruments), the technique of

composition itself is continuous, incorporating a formalistic prin- ciple which can be documented some years before 1911, when Carrillo was elected president of the International Congress on

Mlusic in Rome, at which Debussy, Puccini, R. Strauss, Paderew-

sky, and others, listened to and approved of Julian's unidad ideol6gica y variedad tonal as applied to such traditional music forms as the as the sonata, concerto, symphony, and quartet.'

In Part I of this essay, I shall give a brief biographical sketch of Carrillo's life as outlined in the preceding paragraph.

1Julidn Carrillo: su vida y su obra (Autobiografia), ed. del "Grupo 13 Metropolitano," Mexico, 1945, 251ff. Much information used in this study was made available to me through personal interviews with Carrillo's daughter, Dolores ("Lolita"), and from other sources (docu- ments, program notes, special publications, etc.).

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Holograph score of Misa en 40S de tono by Julihn Carrillo.

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Holograph score of Misa en 40s de tono by Julian Carrillo.

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Although his life must be put into proper perspective with the changing times in and around MIexico City during the first fifty years of this century, it seems irrelevant in a study of this type to dwell on the many social, political, philosophical, economic, and artistic "revolutions" except as they relate directly to Carrillo's development as a creative musician. For example, most interesting and important were his activities and associa- tions with Jos6 Vasconcelos, Secretary of Public Education and grand deus-ex-machina for all Mexican art, during oMexico's "Classical" revival in the early 1920s. The three periods of Carrillo's life will be delineated further by a brief stylistic description of characteristic works from each. Part II will deal exclusively with the notational system - the classical restitution and the new sonido trece. Part III is a tentative listing of Carrillo's compositions, theoretical writings and recordings. These have been divided into two sections: works in the classical and those in the sonido 13 systems. The compositions have been subdivided further into the categories of orchestral, dramatic, chamber, and solo works.

At present I am working on a definitive chronological and thematic catalogue of the Carillo compositions in collaboration with the maestro's daughter, Lolita. Since microfilms of all these compositions are in my possession, I am currently working on a stylistic investigation of selected compositions in the sonido 13 system - tracing relationships between them and pre- cepts stated in the theoretical writings.

PART I

BIOGRAPHICAL SKETCH

Period I (1885-1905)

JuliAn Carrillo Trujillo was born on January 28, 18I75, in the little town of Ahualulco (today, del Sonido 13) in the state of San Luis Potosi, Mexico. His parents were Don Nabor Carrillo and Dofia Antonia Trujillo de Carrillo. After some preliminary studies at the Academy of Don Flavio F. Carlos in San Luis Potosi (1885-1890), Julian was taken to Mexico City and entered the National Conservatory of Music where he studied violin with Pedro Manzano, composition with Melesio Morales,

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and acoustics with Francisco Ortega y Fonseca. It was during this period that Carrillo became interested in the relationships (and discrepancies) between music theory and practice. He coined the term sonido 13 at this time as referring to a specific sound, i.e., the first ascending 16th heard between the notes sol and la on the fourth string of the violin; since this was the first sound to break up the "classical 12," it later became the generic or symbolic name which Carrillo applied to the whole microtonal system as defined during the late 'teens and early twenties of the next century (see Part II, "Notational System -

Sonido 13" for a fuller explanation and application).

It was not, however, by a "revolutionary" theory that Carrillo first came to the attention of Mexico's principal cientifco, Porfirio Diaz, but through his violin playing during one of the Conservatory's graduation ceremonies at which Diaz was present.2 If ever fate were a determining factor in the life of Carrillo, this was certainly one instance. Julian had been sick nearly the entire school year of 1898 and was absent from the conservatory (Autobiografia, 95). Thus, when Don Jose' Rivas, then director of the National Conservatory, asked Juliatn to play for the annual graduation exercises, he agreed although realizing that he himself would not be eligible for any of the special awards. It just so happened that on the eventful day, President Porfirio Diaz was in the audience; Julian must have performed very well for Don Porfirio was led to wonder aloud why it was that a violinist who played so well received no award along with the other students. When presented with the facts concerning Carrillo's misfortune, Diaz felt that the whole situation was unfair and decided to give him a scholarship to study at the Paris Conservatory.3 Since Carrillo was already twenty-four years old, he was not accepted there. Undaunted, the young composer asked the Mexican government for permis- sion to study in Leipzig instead. In retrospect, this seems to have been a very wise choice, not only because of the good scien- tific training in mathematics, acoustics, etc., which Carrillo re-

'A cientifico was a Spanish-French positivist as interpreted by Gavino Barreda and Justo Sierra through the English positivists, John Stuart Mill and Herbert Spencer. See Leopoldo Zea, The Latin Amer- ican Mind, trans. Dunham, 1963.

3For a good study on the Frenchified atmosphere surrounding Mexico City in these days, see Samuel Ramos, "Influencia de la cultura francesa en MVxico," Cuadernos Americanos, XVII, 1944, 145ff.

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ceived in Leipzig, but also because of the stylistic complement it offered his compositional development as a composer. He already knew the French and Italian traditions in music through the compositions of Gustavo Campa and Melesio Morales, respectively; moreover, the conductor, J. Carlos Meneses, had made the works of Debussy known to the young Julian. But except for an occasional programming of a Beethoven symphony, concerto, or piano sonata by one of the many foreign touring symphonies and artists, the Germanic traditions were held in abeyance by the overwhelming dominance of Italian/French opera and salon music.4 Throughout the Porfirian era (1872- 1911), Mexican composers continued to produce works in imita- tion of the Italian style, whether full-scale operas or short zarzuelas. To this were added the many short piano pieces cast in a Europeanized Romantic vein, such as the innumerable fantasias and danzas of Julio Ituarte (1845-1905), Ernesto Elorduy (1853-1912), and Felipe Villanueva (1862-1923).

In Leipzig, at the Royal Conservatory (1899-1903), Carrillo studied composition with Salomon Jadassohn; violin with Hans Becker: theory with Karl Reinecke; and conducting with Artur Nikisch and Hans Sitt. He also served as concertmaster of the Gewandhaus Orchestra under Nikisch. Stylistically, this is his imitative period; the Symphony No. 1 in D major (dedicated to Porfirio Diaz) was written in 1902 and performed that same year by the Leipzig Conservatory Orchestra with Carrillo con- ducting. As understood in the Mexican aesthetic of the time, this was also a nationalistic period, i.e., a work of art by a Mexican was evaluated on the basis of its approximation to a great work of an already proven master (the First Symphony is modeled after Brahms). Thus, Carrillo was being nationalistic in so far as he accepted the normative artistic values of his own society. The cult of originality was not yet an explicit cultural value, at least not in the world of art. Carrillo displayed this rather refined sense of nationalism on the title page of the symphony: "This symphony is the first to be written by a Mexican composer and to be performed in Germany by a German orchestra under the baton of a Mexican Indian." Later in the century, Carrillo was to be criticized (along with a host of

4Robert Stevenson, "The Operatic Nineteenth Century," in Music in Mexico: a historical survey, New York, 1952.

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others) by Carlos Chavez and his entourage for not participating in the folk-Indian revival of music as a means for a nationalistic and hence cultural identification with things Mexican.5 A partial solution to this controversy of generations is offered in the sections on Carrillo's second and third periods.

The Symphony No. 1 has the four movements that are typical of Brahms, the romantic classicist: Largo-Allegro, Andante Sostenuto, Scherzo, Allegro final. Although facing the immediate past in terms of texture, tonality, rhythm, melody, orchestration, etc., Carrillo's symphony already shows signs of his unidad ideol6gica y variedad tonal in the treatment of the development sections. Thematically derived from the opening expositions, these developments take on the character of motivic variations featuring a soloistic treatment, and hence coloristic display of contrasting instrumental groups. A certain cyclic effect is achieved throughout the work by the derivation of all second themes (lyric) from the opening introduction to the first move- ment (ideol6gica); moreover, the many passing modulations provide a "tonal variety" in line with Julian's thesis on the need for a greater emphasis on simple structures as applied to the traditional music forms, so that sensations can be invoked more easily from the listener. These ideas were first stated by him in 1900 at the International Congress of Music in Paris which he attended unofficially. It was at this same meeting that Carrillo first suggested new names for the twelve "classical" tones; Saint-Sains approved.

In 1903-04, Carrillo was at the Ghent Conservatory studying violin with Albert Zimmer upon special recommendation from

Eugene Isaye and there he won the first prize in an Internation- al violin contest. Before returning to Mexico, he wrote his Cuarteto en Mi Bemol, a work completely in line with his ideas on ideol6gica y variedad tonal. Returning to Mexico City the following year (1905), Carrillo was honored by a concert in the Teatro Arbeu where he played Tschaikowsky's violin concerto with Carlos J. Meneses conducting the National Symphony Orchestra. Carrillo's Symphony No. 1 was also given its Mexi- can premiere at this time with Don Porfirio Diaz and Don Justo Sierra attending. Invited by the General to sit with him in his

5Carlos Ch6vez, "50 Afios de mdisica en Mexico," Mexico en el arte, X, 1950, 210ff.

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box during the symphony performance, Julihn received from his hands an Amati violin as a gift from the Mexican nation. At that moment, Carrillo was a veritable "darling of the gods." In 1906, he entered the National Conservatory as a professor of composition, thus embarking upon a new period in his life, marked by many successes but as many turmoils.

Period II (1906-1924)

Everything seemed to be going well for Carrillo and for the future of art in Mexico City up until 1910-11. In 1908, he was named Inspector General of Music in Mexico City; the fol- lowing year, he organized and directed the Beethoven Orchestra and String Quartet. According to Carrillo in his Autobiografia (225ff.), the Beethoven Orchestra was completely separate from the National Symphony Orchestra with regard to its players. Thus, it seems that there was an adequate supply of trained musicians in Mexico City at this time (not to mention the opera company orchestras - although it is true that these were mostly made up of Italian musicians). Carrillo was even commissioned by the Mexican government to write an opera for the gala centennial of Mexican independence in 1910. The result was his opera, Matilde or Mexico en 1910. The work, as with all his operas, was never performed. It seems that the pressures of the everlasting Italian troupes in Mexico City were too great even for a Porfirio Diaz or Justo Sierra to withstand.

With the abdication of Diaz in 1911, cultural life in Mexico City did not suddenly end by any means. The government still actively supported cultural affairs, e.g., it was in 1911 that Carrillo was sent by the government as a delegate to the Interna- tional Congress on Music in Rome where he also had a private audience with Pope Pius X, an event which was to have far- reaching effects for the composer in terms of sacred compositions written and performed, in spite of the intermittent persecutions of the Catholic Church by the Mexican government throughout the first thirty years of this century.

In 1913, Carrillo became the director of the National Con- servatory for the first time; for his own musical production and peace of mind, this was unfortunate. Because of his previous governmental affiliations, he was branded successively a Por-

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firista, Reyista, Maderista, and finally, a Huertista. As director, he had to shoulder all the grievances voiced by former conductors and teachers who felt neglected, and of students who came to regard all European culture - in short, anything foreign - as Porfirian and hence decadent. For the moment, they chose to obliterate one hundred years of their history, making believe that the year 1910 was the final liberation from Spanish Colonial domination. A spirit of indigenismo, long dormant, now made its way to the surface as the vertical stratification of society disinte- grated (Zea, 162). It was felt that the old horizontal (foreign) forms had to be rejuvenated by a superimposition of indigenous materials (content). In art music, this took the form of popu- larizing folk elements, e.g., Manuel M. Ponce introduced many arrangements of folk songs, systematically collected from varying geographical areas and arranged according to types - the can- ciones picarescas, sones, and corridos, or those of the tristeza.6 In painting, it led to the pulqueria murals on the popular level, and on the academic, to the students' leaving the indoor confines of the art academy (San Carlos) for the open-air retreats in Santa Anita, where local colorisms and subjective interpretations could be expressed.7

Even before the revolutionary forces of Carranza, Obreg6n, Villa, and Zapata descended upon Mexico City in 1915, Carrillo's position as director of the Conservatory had been undermined by intrigues too many to be covered here. With the First Chief Carranza victorious, the anti-foreign spirit reigned supreme and had as its immediate and practical result the dismissal of those musicians who had been trained abroad during the era of the Porfirian pax. Even Jose Vasconcelos, the energetic reviver of the arts during the next regime (Obreg6n, 1920-24), was dis- missed from the newly created educational Secretariat - this in spite of his early support of Carranza. Carrillo was impressed by the fact that, because of the First World War, orchestras in the United States were experiencing a shortage of conductors. With this in mind, he set out for the city of skyscrapers.

Once in New York City, Carrillo had to learn about such

6Otto Mayer-Serra, Panorama de la Mfisica Mexicana desde la inde- pendencia hasta la actualidad, Mdxico, 1941.

7Guillermo Sherwell, "Modern Tendencies in Mexican Art," Pan American Union: Bulletin, IV, 1922, 333ff.

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things as musicians' unions! However, the relationship seemed to be a happy one from the start. With his European degrees, training, and experience in the many facets of musical matters he was a "natural" in his dealings with the members. Not only was he accepted into the union, but he also interested the students of the union in forming a Union Philharmonic Orchestra to play little known compositions just for the sheer pleasure of making music, without any kind of fixed salary. This loose ag- gregate of players eventually took the name, Symphony Orchestra of America; Carrillo directed it until his return to Mexico in 1918. This orchestra also got considerable notoriety through the Century Magazine of New York, which carried an article en- titled: "Julian Carrillo, the herald of a musical Monroe doctrine, which will liberate America from the bonds of Europe" (Auto- biografia, 280). Needless to say, this started a wonderful po- lemic, with the Europeans (particularly the Germans) pointing out Carrillo's Europeanized education and his programming of European works; obviously, the adjective, Monroe, referred to the recruiting of the players solely from American reserves (isolationism). In any event, the notoriety was good for attract- ing young players around the maestro, and the benefits were reaped in purely musical terms.

During Carrillo's absence from Mexico, the Carranza regime had filled the administrative artistic posts with favorite govern- mental dilettantes such as Jesuis M. Acufia and Eduardo Gariel, personifications of poor taste incarnate! Moreover, the national government was no longer sponsoring young talented musicians abroad, and with the lax educational policies at home (most of the old faculty had been dismissed from the Conservatory in 1915), there was a dearth of competent musicians - performers and composers. By 1918, the Carranza regime saw fit to re- establish Carrillo as director of the National Symphony Orches- tra. He worked tirelessly to replenish its vacant spots and succeeded to the point that Leopold Godowski considered it on a par with the New York Philharmonic.

By 1920, the Obreg6n forces had managed to produce a working government with a formula designed to please the three forces of Mexican society with which all leaders since Juarez have had to deal: the peasants (because of their large numbers); the powerful landowners and their ideological apparatus, the

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Catholic Church; and Wall Street, U.S.A. (for reasons too obvious to mention).8 This consolidation of forces had far- reaching effects for Mexico's educational system in general and music in particular, under the leadership of Jose Vasconcelos. The new director of Public Education acted quickly in centraliz- ing his forces; he immediately reinstated competent persons in the Ministry of Education - many of whom had been exiled or at least barred from positions of responsibility during the Car- ranza regime. Thus it was that Julian Carrillo became director of the National Conservatory for the second time (1920-24) and director of the Conservatory orchestra.9 In El Desastre, Vas- concelos talks about the great contributions which Julian Carrillo and Beristain, director of the Choral Society, made to Mexican cultural life by their many tours throughout the cities of the Republic;1o thus, Vasconcelos' consolidation of the educational system had in turn allowed him to decentralize culture.

In the first volume of his P1cticas Musicales, Carrillo also envisioned an educational reform for musicians whereby students would be able to work in comparative isolation from the everyday cares of life - including revolutions! He thought that this should be a responsibility of the government and considered Chapultepec Castle a suitable environment. Carrillo also found it deplorable that most musicians knew little beyond their own instrument and supported the idea of a liberal arts education through attendance at and participation in seminars outside of their own fields. From this, it is apparent that Carrillo was never really a Porfirista or cientifico in his philosophical lean- ings, since his was obviously not a static conception of society; rather, he belonged to the new spirit of mutability set down in the works of James, Bergson, and Boutroux, as championed by the Ateneo de Juventud, founded by Antonio Caso.11 The con-

cept of mutability was much emphasized by Carrillo in his aesthetic system, i.e., the principle of metamorphosis as used in many of the compoistions of the sonido 13 medium, which em-

8Eertram D. Wolfe (text) and Diego Rivera (paintings), Portrait of Mexico, New York, 1937, 119ff.

)Carrillo gave up the conductorship when Obreg6n passed a new law whereby no civil servant was allowed to hold two governmental posts simultaneously (see Autobiografia, 297).

10Jose Vasconcelos, El Desastre, Mdxico, 1958, 57ff. 11Victor Alba, Las ideas sociales contempordneas en Mexico,

MA6xico, 1960, 139ff.

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ploy conjointly the new microtonal divisions along with the "classical" semitones.12 Carrillo realized that the exclusive use of microtones would isolate him from performers-at-large. He also believed that too rapid a change would lead to disintegra- tion; in this sense, he (like Schoenberg) had a very keen sense of historical continuity. He solved both problems by employing a Baroque concertino-ripieno ensemble, the one featuring the "new," the other, the "old" sounds.

There is a considerable overlap between Carrillo's second and third periods. The year 1924 provides a fairly good demarcation point in so far as his administrative duties are for the most part at an end. Moreover, he then dedicates himself wholeheartedly to sonido 13 activities, e.g., during 1925-26 he travels throughout Mexico with the Grupo Metropolitano playing Sonido 13 compo- sitions by himself and his students. At that time, the musicians Rafael Adame, Elvira Larios, and Soledad Padilla were active participants in this organization (Autobiografia, 308ff.). How- ever, the working out of the theory, notation, development of new or adapted instruments (strings, winds, harp, octavina, guitar), and of course the first compositions in the sonido 13 system (Preludio a Colon, 1922), all took place before the end of the second "atonal" period.

In the Introduction, it was stated that the works of this second period are atonal; it is necessary to define what Carrillo meant by this term, since it involves a technique of composition rather than a medium, i.e., there are "atonal" works throughout the second and third periods of his life in both the "classical" system of semitones and in the sonido 13 system of microtones. Carrillo in his theoretical treatise, El infinito en las escalas y en los acordes, states that any "scale" of any number of tones is atonal which does not preserve the relationship of steps to half steps as represented in the traditional major and harmonic minor scales. This work presents 462 scales with seven notes each, only two of which correspond to our major and minor (nos. 300 and 337). By using a variable number of notes/scale (still without employing microtonal divisions), Carrillo arrives at 13,300 different scales. Ultimately, then, his conception of "atonal" means any new scale invented by him, whether in- volving semitones or microtones. Along these lines, all of the

12Julin COarrillo, Leyes de metam6rfosis musicales, Mdxico, 1949.

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works from the atonal quartets on (composed during the First World War) would have to be considered "atonal." But be- cause the melodic, harmonic, and contrapuntal structures are arranged in such a way that they focus upon particular degrees or segments within a scale, the net result is extremely "tonal" within the prescribed scalar pattern.

Thus, although many compositions from the final two periods of Carrillo's life are separated by large intervals of time, e.g., the Cuarteto atonal a Debussy (1917) and the Misa de la Restauracidn a S.S. Juan XXIII (1962), they bear a strong stylistic resemblance in terms of their strict adherence to a pre- scribed "tonal" format, both in their vertical and horizontal dimensions. In the Mass, the emphasis is upon smaller intervals (1/4 tones) to the point that when semitonal combinations are employed at cadential points, they are no longer recognizable as such, being divorced from their contextual framework of "clas- sical" tonal functionality. Thus, Carrillo's later works seem to confirm what Schoenberg conjectured - that once semitones had lost their classical connotations of melodic and harmonic tonal definition, they could once again be appreciated as sounds

per se. By using microtones, Carrillo was able to speed up the

evolutionary process. The Mass is without a doubt the most important and successful work of Carrillo's production, coming as it does at the end of his life and at a time when he had gained a greater perspective on a new sound medium still in its infancy. Carrillo places more restrictions on himself in this, his penulti- mate work, restricting the tonal structure to combinations of quarter and semitones. Perhaps this economy of means is partly the result of an effort to express more cogently a very pious and hallowed text. Whatever the reasons, the effect on the listener who has waded through compositions (Horizontes, Balbuceos, 3 Columbian Symphonies, etc.) using the myriad tonal combina- tions of the smaller intervals (1/5 . . . 1/16 of tones) is mentally relaxing and refreshing.

Period III (1926-1965)

This was the period wherein Carrillo brought to fruition some of the potentialities of the sonido 13 system which he and his students had spent many long hours working out in relative isolation. At the same time he became known to an international

-45-

concert audience in North and South America, Europe, and the Soviet Union, as a great theorist, inventor, educator, conductor, and most important, an avant-garde composer. The achieve- ments and successes are so numerous that I can only touch on those which seem most significant to me.

In 1926, Carrillo was invited to submit a work for the League of Composers' concert of modern music on March 13, at Town Hall; Carrillo wrote his first Sonata Casi Fantasia para violin, corno, guitarra, octavina, violonchelo, arpa en cuartos, octavos y dieciseisavos de tono for that occasion. The soloists were E. Mix, B. Ocko, G. Martinez, L. Shock, and L. Nava. The success was instantaneous and brought Carrillo to the immediate attention of Leopold Stokowski, who wanted to know more about the sonido 13 system. Completely taken with the Sonata and the microtonal medium, Stokowski said: "With the 16ths of tone, you are beginning a new musical era, and I want to be of service to this cause . .. The great difficulty of this music resides in the fact that if you do not direct it, no one will be able to grasp the subtleties which the music contains . . .213 At this point, even Stokowski felt himself engulfed in the outward complexities of the new music; but Carrillo knew the importance that Stokowski's presence on the podium could lend to furthering the cause of Sonido 13 and insisted that the great conductor interpret this music himself. Stokowski was then conductor of the Philadelphia Orchestra and thus could lend considerable prestige to Carrillo's music.

Stokowski wanted to commission a work from Carrillo which would utilize the "new" sounds but which would also allow him to use the Philadelphia Orchestra. So it was that in 1927 Carrillo received the incentive to write a composition utilizing his aesthetic of metamorphosis in tonality, i.e., the free inter- change (both in juxtaposition and superimposition) of old and new sounds. The ensemble was based on the idea of the Baroque concertino and ripieno mentioned in the preceding section. The work written for this occasion was Carillo's Concertino para violin, guitarra, violonchelo en cuartos de tono; octavina en octavos; arpa de dieciseisavos con acompanamiento de grande orquesta en semitonos. The soloists were Nicolin Zedder, E. Mix, G. Martinez, L. Kirsch, L. Nava, and Beatrice Weller. On the

13Sonido 13: recorrido histdrico, ed. del Sonido 13, M6xico 1962, 14.

-46-

day of the premiere, Stokowski made some opening remarks to the audience concerning the sonido 13 revolution: "Luckily for

America, we do not have to look to European musicians for this

revolution, since everything is owed to an Indian who descends from the children of the Continent" (Recorrido hist6rico, 15).

This is an opportune moment to recall Carrillo's interpreta- tion of nationalism. In the Autobiografia, 171ff., he makes an

apology concerning his educational reform policies, but more im- portant is his understanding of nationalism: "El asunto no es dificil y lamento que mis problemas del Sonido 13, no me permi- tan dedicar el poco tiempo de que dispongo a todos los proyectos que he enunciado a usted. [The autobiografia is written in the form of a Platonic dialogue.] Pero por otra parte, con s6lo el desarrollo de la revoluci6n musical del Sonido 13, es suficiente para dar a Mexico renombre universal. '" Thus, although far removed from Silvestre Revueltas' conscious exploitation of popular and folk themes in art music, or from the resurrection of Indian antiquity in that of Carlos Chavez, still in his own highly refined and subtle conception of nationalism as something inseparable from the individual's achievements in whatever form or medium of art, Carrillo was as "patriotic" as the so-called younger generation.

In 1930, Carrillo was back in Mexico again, and it was during this year that he and his students founded the first orchestra dedicated to playing music solely in the sonido 13 medium of microtones. The instruments included: flutes, oboes, clarinets, and bassoons in fourths of tone; horns, trumpets, trombones, and tubas in sixteenths; harps in fourths and six- teenths; and strings in quarter tones. The following year, both Carrillo and Stokowski toured Mexico with this orchestra. One of the symphonic works often programmed then was the Gran fantasia para orquesta. By this time, there was a Carrillo cult in Mexico, and in recognition of his fame, several streets in the various states (Chihuahua, Tabasco, Durango, Jalapa, Tlaxcala, Colima, etc.) were renamed in his honor. In 1933, by govern- mental decree, his birth place was renamed, Ahualulco del

*It would not be difficult, and I am sorry that my experiments with the Sonido 13 system do not leave me sufficient time to enact all the projects which I have been telling you about. But, on the other hand, the development of the 13th sound revolution will in itself be sufficient to give universal renown to Mexico.

-47-

Sonido 13. Also during the 'thirties, Carrillo patented the idea for his fifteen metamorphosing pianos: no. 1 in whole tones; no. 2 in thirds of tone; . . . no. 15 in sixteenths of tone.

During the 1940s, Carrillo traveled a good deal in Mexico and in the United States, giving lectures on and performances of his new music. In 1947, he was at New York University in this capacity. Two years later, he had already had one of his pianos (thirds of tone) built in Mexico City by Federico Busch- mann, on which Lolita gave concerts at the Anfiteatro Bolivar in the National Preparatory School. In Paris, Florent Schmitt had published an article in Le Figaro, inquiring if it was not time for musicians to go in search of thirds of tone. Carrillo was im- mediately taken with the idea of going to Paris with the thirds- of-tone piano; thus it was that in 1950, Lolita played the Con- certino para piano metamorfoseador de tercios de tono con acom- paiamiento de orquesta sinf6nica en semitonos, in the Faur6 Salon. The success was so great as to make Carrillo wonder what it would be like if all of his metamorphosing pianos could be built.

It was not until 1957 that Carrillo found a German firm

capable and willing to undertake the project - Carl Sauter in

Spaichingen Wiirt. Promised for completion by 1958, they were to be exhibited at the World's Fair in Brussels. Although the Mexican government decided at the last minute not to include them in its pavilion because they had not been manufactured in Mexico, the Belgian government saved the day by offering to exhibit them in the Royal Palace. A concert of Carrillo's works was given on November 8th which Queen Elizabeth of Belgium attended. The works performed were so well received that the

Queen decided to give a gala banquet in her palace in Laeken

honoring Carrillo; the compositions programmed were: Poema

Sinf6nico "Horizontes" para violin y violonchelo en cuartos y octavos de tono y arpa de dieciseisavos (work commissioned by Stokowski in 1951 and performed in Pittsburgh, Baltimore, Min-

neapolis, and Washington - where it was recorded by the U. S.

government); Concierto para violonchelo en cuartos y octavos de

tono; and the Concierto para piano de tercios de tono. The solo- ists were Gabrielle Devries, Reine Flachot, Monique Rollin, and Lolita Carrillo.

-48 -

After the Brussels exposition, the famous piano manu- facturer, Marcel Gaveau, offered his studio on the Rue de la Boetie in Paris for another showing; since this coincided with the International Congress of Music sponsored by UNESCO, many eminent persons came to see the pianos - among others Alois Haba and Ivan Wischnegradsky. Both of these men had proposed new musical systems dealing with microtones. Since the story has been bruited about that the two men were enemies of Carrillo, I think it might be edifying to note the words of these men upon viewing and experimenting with the Carrillo pianos.

Ivan Wischnegradsky said: "The Carrillo pianos reveal a marvelous world of sound, worthy of comparison with Columbus' discovery of America. We Europeans have been searching end- lessly for a practical keyboard which would allow us to produce quarter tones; and here Julian Carrillo surprises us with a 'classical' keyboard capable of reproducing not only fourths, but

fifths, sixths, etc., of a tone - this discovery is as miraculous as Columbus' egg" (Recorrido hist6rico, 24).

Alois Haba said: "Upon my return to Prague, I shall ask

my government to officially invite Carrillo and his fifteen metamorphosing pianos so we can admire them there" (ibid.). Since Carrillo reciprocated these good feelings by dedicating compositions to both men, I find it hard to believe the rumor too long perpetuated.

The last years of Carrillo's life were as active and fruitful as in the 1950s; commissions continued to come in, e.g., the Balbuceos para piano de 16avos. de tono con acoompaiiamiento de Orquesta de Cdmara, was performed by Lolita in Houston, Texas, with Stokowski conducting. Probably the most significant event in these last years (at least for the immediate future) was the recording of some 37 works by the Philips Company in France with Julian Carrillo conducting the Lamoureux Orchestra (see Part III, under Recordings). These recordings were made under the technical direction of Jean Etienne Marie and include as soloists G. Devries, Reine Flachot, Monique Rollin, Annik Simon, Robert Bex, Bernard de Flavigny, Robert Gende, and Jean Pierre Rampal; also performing are two string quartets: the Quartet of France (R. Gendre, J. Ghestem, S. Collot, and R.

-49-

Bex) and the V illers Quartet (Francine Villers, Nicole Lapinte, Marie-Th6rese Chaillet, Reine Flachot).

To conclude this part, something should be said concerning the future of el sonido 13. Carrillo himself realized that his

compositions within the system were but a beginning, not only in terms of sound but as regards the other elements of composi- tion as well. Now, however, with the advent of electronic music, it might seem that what Carrillo did is outdated. Today Car- rillo's sonido 13 music can be viewed in a number of ways: as an

interesting historical experiment (the purist electronic composer's view); as a transitional phenomenon; or as music for its own

sake, bound, as is all art, by the times which produced it. I for one believe in the great potentialities of this system, chiefly be- cause it allows for retention of the three-fold relationship in music (creator, interpreter, percipient), while providing ample material for the expansion of our tonal horizons.

PART II

PRECURSORS OF SONIDO TRECE REVOLUTION:

Rectification of the Classical Notational System

"That humanity ought to be able to read and write music as

easily as they might write a letter or read a newspaper." Al-

though quoted from Carrillo's Sistema general de escritura

musical, this dictum reappears throughout the maestro's theoreti- cal writings. Even though Carrillo bases his reform of the classical notational system on purely theoretical grounds, there can be little doubt that the open-air school experiments which Vasconcelos developed during the 1920s for Mexican children had considerable practical influence as well.

Horizontal Writing or Successive Sounds

Previously, the 78 ways of representing a single sound were

mentioned; the following example illustrates these (Sistema general, 12; unless stated otherwise, all subsequent examples will refer to this theoretical work):

-50-

I L. I- i Po x.. I ' r.I • • ,, il ba lY

?J 4 •P4- x,•'k "•

Example 1

The numerous ledger lines inherent in the classical system for representing the 8 cycles (or octaves) of twelve tones each

(see Example 2); the many clefs and possible accidentals; in

fact, the staff itself - all of these Carrillo reduces to a combina- tion of three lines plus twelve numbers (Example 3):

-il

F .

Example 2

01234 678 1011 (12)

Example 3

For every sound of whatever pitch in the classical system, there is but one sign in the Carrillo reform (Example 4):

--51-

+24 3519 i

.................

C ~ ~2.o•

e

9.if "5

7 9 iif 0T ZT 4 5 7.+

9

Example 4

Here we are concerned only with tones and semitones; hence, all numbers are absolute. The main referential point is the long horizontal line which always represents middle Do (whether in the classical or the sonido 13 system). In horizontal writing, then, the first cycle is always represented by a number plus a short line above, separated by a space from the absolute Do

line; cycle two, with a short line through the number, separated by a space; cycle three, by a number with a line underneath but exactly below the absolute Do line; cycle four, exactly below the Do line; cycle five, entirely on the Do line; cycle six, exactly above the Do line; cycle seven, by a number just above the Do line but with a short superior dash; cycle eight, with a line

through the number, separated from the Do line; and the final Do as indicated in the example.

Vertical Writing or Simultaneous Sounds In vertical writing, when simultaneous sounds are involved,

the uppermost number of the chord is absolute and the lower ones are relative to it (Example 5):

-- 5- 7 Q9 1 0- 7 I 4 -0I + 5 7 7

t 7 7 9 0 0 2 4

( p 2 4 5 7 9 II 0

7 7 7 4 0 0 U 7 4 2 0 0 0 9 7 4 0 U 10 9 7 5 2 0

Example 5

-52-

and its equivalent (Example 6) :

Example 6

If however, in a chord, there is a note which is not within

the prescribed lower gamut of the upper number, but is instead

separated from it by one cycle, that sound is represented by its

number offset to the right (Example 7):

I I I

Example 7

and its equivalent (Example 8):

Example 8

-53 -

If the displacement is by two cycles, the number falls to the left (Example 9):

7-t 71

Example 9

and its equivalent (Example 10):

-54

Example 10

If more than three cycles, then all sounds are notated as they would be in a horizontal context with the addition of a vertical slur (Example 11) :

01

Example 11

-54 -

and its equivalent (Example 12):

A

Example 12

Regarding rhythmic values, the following scheme is observed (Example 13):

Example 13

and its equivalent (Example 14):

Example 14

There is no change in the notation of rests. In Julian Carrillo's revised classical system, all instruments are notated as they sound, thus eliminating transpositions (Example 15): and its equivalent (Example 16):

--55-

DvorAk A .taro mxJ-s f 1 17 k

r ou

b.A..

,t .

,,_____C

_PPP

-

_

_"_

dim.

A 2pp J dim "' PPP

J.a, - fTr Z4s 1

pi:{• " dan"-

in L mt n m Aft.

1)e As. I! dim ton sordnno

f dim.

Vso].I t• "." , i. .'an sor

'n

Trq7y if di

_

__,_,_,c

an s o rd ino

VioiM•t1 o' ...I.

HvP, coan•

_" "_ _._ _' ' _

.con

o rdino

C-i _ _ _ _ _ _

_ _ Ap - -

C~ i? IMJO • i___... .... .___

__ __

ense$din O t

*

|

co ,ajo

" )

,- ' Pr

(from Dvorak,

Symphony No. 9 in E minor, op. 95, mvmt. 2)

Example 15

--56 -

Dvorak

pp. Id[i,:==--

Tlronpits V

. PPP.I

m nl .

< ( I

,11 _ _ Ir j I j 4 6 9 9-- 8 &

PPo I.,li, n.

"" -- pn't'sriA

r A

6 5 4 9 8 11W11 1 i 113 5 5

PP- - - 'dima

Troin1.Bajo a 2.

IjTuba IT I 1 9 6 1' dim

e pa-no .. -.. .

PPP

con sordino

Viola e- Con serdina 5

Consordind

,PP CentrBais

--to I

wo, erdina 1

4' I ?PPP

(I) -fit ejempod ddedcuerdocojz la ley del fozdo 15 fu di. ce: Debe oirse el sonido que se escribe V nootro"

Example 16

-57-

From the foregoing, it is evident that Carrillo had no inten- tion of changing the classical system internally; he was merely concerned with closing the gap between theory and practice. In his "Pre-Sonido 13", he shows how our equal-tempered inter- vallic system differs in practice from its theoretical counterpart.9 For example, there are no chromatic (25/24 or 24/25) or diatonic

(16/15) semitones in our actual system. These two intervals correspond to the proportions 1.0416 and 1.0666 respectively; in

reality, our tempered system divides the octave (cycle) into 12 equidistant parts, at the proportion of 12V/2 or 1.059463. There- fore Carrillo proposes an appropriate name for it: SISTEMA MUSICAL DE DOZAVOS DE DUPLO,* or else, SISTEMA MUSICAL DE DOCE GRADOS.

1/12 --------------------------------------1.059463

2/12 --------------------------------------1.122462

3/12 --------------------------------------1.189207

4/12 --------------------------------------1.259921

5/12 --------------------------------------1.334840

6/12 --------------------------------------1.414214

7/12 --------------------------------------1.498307

8/12 --------------------------------------1.587401

9/12 --------------------------------------1.681793

10/12 --------------------------------------1.781793

11/12 --------------------------------------1.887749

12/12 --------------------------------------2.000000

EL SONIDO TRECE

Sonido 13 is a generic term used by Carrillo to designate all microtones; however, as defined within his working system of

varying microtones, it refers specifically to any interval includ-

ing but no smaller than 1/16th of a tone. The reason for stop- ping with this intervallic division was not dictated by theoretical

considerations, but by a purely physical one: Carrillo felt that

9JuliAn Carrillo, Rectificaci6n bdsica al sistema musical cldsico: andlisis fisico-musico, "Pre-sonido 13", San Luis Potosi, M6xico, 1930, 27ff.

*In this case, Carrillo uses the word, duplo, as synonymous with octave.

-58-

the human ear could not distinguish clearly beyond 1/16th of a tone. The number 13 was used simply to symbolize a division of the octave into parts smaller than the classical 12.10

In spite of the greater diversity and larger number of sounds in the microtonal system as compared with those in the classical one (780 versus 12), the only appreciable difference in the notation is that the former uses a relative number notation, the latter an absolute one. Regardless of whether one is writing in 16ths, 15ths, 14ths, etc., of tones, all divisions are equal; since there are six "whole tones" per cycle, the number of divisions in each cycle is obtained by multiplying by six the number of divisions of the whole tone:

sixteenths of tone --------6 x 16 - 96 intervals per cycle fifteenths of tone --------6 x 15 - 90 intervals per cycle fourteenths of tone ----------6 x 14 - 84 intervals per cycle thirteenths of tone ----------6 x 13 - 78 intervals per cycle twelfths of tone ---------6 x 12 - 72 intervals per cycle elevenths of tone ---------6 x 11 - 66 intervals per cycle tenths of tone ...- 6 x 10 - 60 intervals per cycle ninths of tone ...- 6 x 9 - 54 intervals per cycle eighths of tone ----------6 x 8- 48 intervals per cycle sevenths of tone ---------6 x 7 - 42 intervals per cycle sixths of tone -----------6 x 6 - 36 intervals per cycle fifths of tone -----------6 x 5 - 30 intervals per cycle fourths of tone ----------6 x 4 - 24 intervals per cycle thirds of tone ----------6 x 3 - 18 intervals per cycle semitones --------------- 6 x 2 - 12 intervals per cycle

780 intervals per cycle

The following two examples serve to illustrate the number relativity according to intervallic types employed Eighths of tone system:

0 1/8 2/8 3/8 4/8 5/8 6/8 7/8 8/8 9/8 10/8 11/8 12/8 13/8 14/8 15/8 16/8 17/8 18/8 19/8 20/8 21/8 22/8 23/8 24/8 25/8 26/8 27/8 28/8 29/8 30/8 31/8 32/8 33/8 34/8 35/8 36/8 37/8 38/8 39/8 40/8 41/8 42/8 43/8 44/8 45/8 46/8 47/8 0

lOJulian Carrillo, Genesis de la revolucidn musical del "Sonido 13", San Luis Potosi, M6xico, 1940, 27ff.

-59-

Thirds of tone system:

0 1/3 2/3 3/3 4/3 5/3 6/3 7/3 8/3 9/3 10/3 11/3 12/3 13/3 14/3 15/3 16/3 17/3 0

In Example 17, every 8th number constitutes a whole tone:

0, 8/8, 16/8, etc. Thus in horizontal writing, the numbers 0 ----------12 would equal 1 1/2 whole tones; in Example 18, where whole tones occur after every 3 numbers, the same hori- zontal writing, 0 ----------12, would result in 4 whole tones.

Within the fifteen possible intervallic systems, some are

mutually exclusive while some include several others.

System Intervallic Types

16ths of tone inclusive 16ths, 8ths, 4ths, 1/2 15 inclusive 15ths, 5ths, 3rds 14 inclusive 14ths, 7ths, 1/2 13 exclusive 13ths 12 inclusive 12ths, 6ths, 4ths, 3rds, 1/2 11 exclusive 11ths 10 inclusive 10ths, 5ths, 1/2

9 inclusive 9ths, 3rds

8 inclusive 8ths, 4ths, 1/2 7 exclusive 7ths

6 inclusive 6ths, 3rds, 1/2 5 exclusive 5ths

4 inclusive 4ths, 1/2 3 exclusive 3rds

2 exclusive 1/2

Whole tones are, of course, common to both even and odd numbered divisions, but only in the former are semi- tones found.

The following example illustrates the metamorphosis of intervallic types depending on the system employed (Example 17):

-60

Concierto para violonchelo en 4os 8os, y 16avos, de tono

*4 0- 80 1 aO l I . .

• 'U -1 0U JIL -1U'LV " WL7-I O 'PL - U -2v 72 1-7,u L iVU 7 V of. •0 IV i0OV U71 OO 1 i

6 6

Example 17

If this composition is read in the 4th-of-tone system, the first two numbers equal a whole tone: 4/16 (1/4) x 4/1 -= 16/16 = 1.

If read in the 8ths-of-tone system, the same two numbers equal a half tone: 8/64 (1/8) x 4/1 = 32/64 = 1/2.

If read in the 16ths-of-tone system, the interval is a quarter tone: 16/256 (1/16) x 4/1

-64/256 - 1/4.

However, in actual practice, varying systems are not mixed in a single composition; nevertheless, due to the inclu-

sivity of many of the systems, a variety of intervallic types is still possible with no confusion. The important point is to distinguish between the system employed and the actual intervallic types resulting within that particular system (Ex- ample 18) :

Violin I AOR 0A'IAA. ?

. P.

]!:?

0 4

0,4 940,,',.

92 '

1'o.ne _K 00007m 16111,-I

Cello LL .. J...... 4Edetene 04 820 4T3b 40O44 6416 892 092 0920320 gM0

- 0/ 9

Example 18

--61 --

4 01drtono 8 0 020

2~456404+ 64

69L Pq2 _z 1z

o

Ia

it' V

L4,.V,7 J64

A ryo ^ A -~ * - -67. V2W Wt

Example 18

-61--

(Carrillo: Concertino for violin, cello, guitar in 4ths, horn and harp in 16ths-of-tone)

This entire composition is written in a 16ths-of-tone system, even though the strings produce only quarter tones.

The preceding example illustrates Carrillo's concept of metamorphosis so important in his aesthetic and in line with the social evolutionism of Mexico's revolutionary philosophers. Out of this synthesis would result a new order, less complex though providing for complexity; less constrained though pro- viding for constraint. As we have seen, Carrillo put all of his theories to test by building new instruments and adapting old ones for the production of the new synthetic music; moreover, he composed over 100 works in the new systems, from little etudes to large sonatas, symphonies, Masses, and concertos. It is difficult to speculate concerning the outcome of his many experiments but certainly the potentiality for completion is virtually inexhaustible.

PART III

TENTATIVE LIST OF COMPOSITIONS, RECORDINGS, AND THEORETICAL WRITINGS

Works in the Classical System

ORCHESTRAL

Canon atonal a 64 voces (no text). Marcha "Mexico," para orquesta y banda militar. Ocho de Septiembre. Gran fantasia para piano y orquesta. Sinfonia en Re Mayor, no. 1, para grande orquesta. Sinfonia en Do Mayor, no. 2, para grande orquesta. Sinfonia heroica, para grande orquesta. Suite para orquesta/1898. Suite de Bagatelas no. 1, para orquesta sinf6nica. Suite no. 2, "Los Naranjos," para grande orquesta. Suite "Impresiones de La Habana," no. 3, para grande orquesta. Suite no. 4, para grande orquesta (orchestration of the 6 Prelu-

dios para piano: Ilusidn, Nostdlgico, Plenilunio en Tepepan, Medianoche, Miercoles Santo, Scherzando).

- 62 --

Triple concierto para violin, flauta, violonchelo y grande orquesta.

Trozo sinfonia atonal: un solo papel para toda la orquesta a manera de canon.

VOCAL-ORCHESTRAL

Matilde: "Mexico en 1910," 6pera en 4 actos. Misa del Sagrado Coraz6n, para voces masculinas y orquesta. Misa del Coraz6n (versi6n 2). Misa de Santa Catalina, para voces masculinas y orquesta. Ossian, 6pera en 4 actos.

Pequefio Requiem atonal, para soprano, tenor y grande orquesta. Requiem para coros y grande orquesta. Xulitl, 6pera en 3 actos.

CHAMBER

"Adios," Romanza, para tenor y piano. Canto a la bandera, para voz y piano. "Crepuscular," preludio para violin y piano. "Crepuscular," preludio para violonchelo y piano. 4 Cuartetos atonales, para 2 violines, viola y violonchelo Cuarteto en escala diat6nica de 6 grados. Cuarteto en escala diat6nica 0 1 3 4 7 8 9 0. Cuarteto en Mi bemol, para 2 violines, viola y violonchelo. "Himno a la Paz," para coro y piano. Improvisaci6n para violonchelo y piano. Lamento de Sor Juana Ines de la Cruz, para voz y piano. "Lo que soy para ti," para voz y pequefia orquesta. Metam6rfosis del cuarteto atonal. Romanzas para canto y piano: Reviendras-tul, Aleluya, Un

cautivo beso, Mexico.

Sexteto para 2 violines, 2 violas y 2 violonchelos.

"Stella," Berceuse para corno ingles, corno de 6mbolos, violon- chelo, flauta y arpa.

Suite de Bagatelas, para pequefia orquesta. Tema con variaciones, para violin con acompafiamiento de piano.

- 63-

SOLO WORKS

(piano)

Cadencias para los conciertos para piano de Beethoven (nos. 2, 3, 4).

Doce preludios para piano en las 12 alturas de la escala 0 1 3 4 7 8 9 0.

En el bosque. Gavota para piano, de la suite de Bagatelas. Isabel (Schottish). Mazurca.

Nocturno a manera de improvisaci6n. Preludios para piano: Ilusidn, Nostalgico, Plenilunio en Tepepan,

Medianoche, Miercoles Santo y Scherzando.

Reverie. Suite para piano, facilisima: Minud, Gavota, Plegaria.

(violin) 3 Sonatas.

(viola) Capricho. Concurso.

('cello) Sonatina.

(flute) Concurso.

WORKS IN THE SONIDO TRECE SYSTEM

ORCHESTRAL

Capricho para corno de 16avos. de tono y orquesta. Concertino para piano metamorfoseador de tercios de tono con

acompafiamiento de orquesta sinf6nica en semitonos. Concierto para piano de tercios de tono y orquesta de cimara. Concertino para violin, guitarra, chelo, 4os.; octavina, 8os.; corno

y arpa 16avos. de tono, con acompafiamiento de orquesta sinf6nica en tonos y semitonos.

Concertino para violonchelo en 4os. y 8os. de tono, con acompafia- miento de orquesta sinf6nica en semitonos.

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2 Conciertos en 4os. de tono para violin y orquesta. 2 Fantasias "Sonido Trece."

"Horizontes," para violin 4os. y 8os. de tono; violonchelo en 4os. 8os. de tono, arpa de 16avos. de tono con acompafiamiento de orquesta sinf6nica.

Nocturno al Rio Hudson, para grande orquesta a base de 16avos. de tono.

3 Sinfonias "Colombianas."

CHORAL

Misa de la Restauraci6n a S.S. Juan XXIII en cuartos de tono, para voces masculinas "a cappella."

2a Misa "a cappella" en 4os. de tono, para voces masculinas. "La Virgen Novena" para coro doble, arpas, violin, 'chelo,

guitarra y campana en 4os. y 16avos. de tono.

CHAMBER

"Ave Maria," para voces solos en 4os. de tono y varios instru- mentos en 4os., 8os. y 16avos. de tono.

"Balbuceos" para piano de 16os. de tono, con acompafiamiento de orquesta de camara.

2 Bosquejos en 4os. de tono para cuarteto de arcos. Coro en cuartos de tono, especialmente escrito para el Grupo

"13" de Laredo, Texas. 2 Cuartetos para voces a boca cerrada en 4os. de tono. 6 Cuartetos en 4os., 8os. y 16avos. de tono, para varios instru-

mentos. "I think of you" for soprano and small orchestra in quarter and

sixteenth tones.

Impromptu para dos sopranos y trompeta en 8os. de tono y arpa citara en 6os. de tono.

"Murmullos," para cuarteto de cuerdas en 4os. de tono y arpa de 16avos.

Preludio a Coldn, para soprano en 5os. de tono; flauta, guitarra y violin en 4os. de tono; octavina en 8os. de tono; y arpa en 16avos. de tono.

6 "Preludios Europa," para flauta, soprano, arpa, violin, guit- array octavina en 4os. y 16avos. de tono.

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Preludio para mandolina, mandola y guitarra en 4os. de tono. Preludio para violonchelo en 4os. de tono, acompafiado por varios

instrumentos en 4os., 8os. y 16avos. de tono.

Sonata casi fantasia en 4os., 8os. y 16avos. de tono para pequefia orquesta.

"Tepepan," para coro a boca cerrada en 4os. de tono con soprano solista y arpa de 16avos. de tono.

SOLO WORKS

(piano) 2 Balbuceos en 4os. de tono.

Capricho para piano metamorfoseador en 4os. de tono.

Preludio: 29 de Septiembre en tercios de tono.

Preludios para piano metamorfoseador en 5os. de tono.

(violin) 6 Casi sonatas en 4os. de tono.

3 Estudios a base de 4os. de tono en forma de "Sonatina," para violin de tres cuerdas.

Sesenta estudios en 4os. de tono.

(viola)

Capricho en 4os., 8os. y 16avos. de tono.

4 Casi sonatas en 4os. de tono.

Sesenta estudios para viola en 4os. de tono.

('cello) 6 Casi sonatas en 4os. de tono.

Sesenta estudios para violonchelo en 4os. de tono.

(contrabass) Sesenta estudios para contrabajo en 4os. de tono.

(guitar) Estudio en 3os. de tono.

Sonata en 4os. de tono.

"Suite impromptu," en 4os. de tono.

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RECORDINGS

(A) IN THE CLASSICAL SYSTEM OF 12 TONES.

Cuarteto atonal a Debussy.

Cuarteto atonal a Beethoven.

Cuarteto en Mi bemol.

"Los Naranjos," suite sinf6nica.

Sexteto para instrumentos de arco.

Sinfonia en Re Mayor, no. 1.

Sinfonia en Do Mayor, no.2.

Sinfonia atonal, no. 3.

6 Sonatas para violin solo.

Triple concierto para flauta, violin y violonchelo.

(B) IN THE SONIDO 13 SYSTEM. "Balbuceos" para piano de 16avos. de tono y orquesta de

chmara.

3 Casi sonatas en cuartos de tono para violonchelo.

Concertino para piano metamorfoseador de tercios de tono con acompafiamiento de orquesta sinf6nica en semitono.

Concierto en cuartos de tono para violin y orquesta.

Concierto para piano de tercios de tono y orquesta de camara.

Concierto para violonchelo en cuartos y octavos de tono con acompafiamiento de orquesta de chmara.

3 Cuartetos para instrumentos de arco.

"Horizontes."

"Meditaci6n" y "En secreto" en cuartos de tono para cuarteto de arco.

Misa a S. S. Juan XXIII en cuartos de tono.

Preludio a Colhn.

Sonata casi fantasia ... para pequefia orquesta. 2 Sonatas para violin en cuartos de tono.

Sonata para viola en cuartos de tono. 4 Sonatas para violonchelo en cuartos de tono.

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THEORETICAL WRITINGS

(A) SONIDO TRECE

Dos leyes de fisica musical. Ed. del Sonido 13, Mexico, 1956.

Genesis de la revoluci6n musical del sonido 13: explicacidn fundamental de los problemas del sonido 13. San Luis

Potosi, 1940.

Leyes de metamorfosis musicales. New York, 1927.

Pre-Sonido 13: Andlisis fisico-musical. New York, 1926.

Sistema general de escritura musical. Mexico, 1957.

Sonido 13: el infinito en las escalas y en los acordes. Mexico, 1957.

Sonido 13: fundamento cientifico e hist6rico. Mexico, 1948.

Teoria l6gica de la misica: razones de orden cientifico, grifico y pedag6gico para el nuevo sistema de escritura. Mexico, 1954.

NOTE: All of the above works are still available from Ediciones Sonido 13, Santisimo, 25, San Angel, Mexico, Z.P. 20.

(B) CLASSICAL

Metodo racional de solfeo. Mexico, 1941 (available, Ed. Sonido

13).

Pldticas musicales, 2 vols. Mexico, n.d. (out-of-print).

Tratado sintitico de armonia. G. Schirmer, New York, 1917.

Tratado sint6tico de canon y fuga (out-of-print).

Tratado sintitico de contrapunto. Mexico, 1948 (available).

Tratado sint6tico de instrumentaci6n para orquesta sinf6nica y banda militar. Mexico, 1948 (available).

Indiana University

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