In this album I have compiled the 5 pieces that I have composed following the harmonic pattern of the Tonnetz. Using the chromatic scale, there are 4 different tonnetz, what differentiates each of them is the determined number of notes that have their chords that can be 2, 3, 4, 6 notes respectively. Each of the first four pieces (all for piano) follows the scheme of one of these Tonnetz. In the album the pieces are ordered according to this number of notes that have their chords. In the fifth piece (which is orchestral) the four Tonnetz intervenes successively in its different parts.

In the following PDFs, one for each language, it is explained in some detail what Tonnetz is and the characteristics of the different types, for those who are interested or curious about the subject. Now that I have the information recently studied, it seemed convenient to make this summary.

Explanation in English language:

https://drive.google.com/file/d/1LxHW0Ly5Rl4RZjuPjzJj92SBHl8lzMgc/view?usp=sharing

Explicación en castellano:

https://drive.google.com/file/d/1QLABP3AOhZOl1-G_-BtHvhA5otWEg9Kv/view?usp=sharing

The 4 Tonnetz of the chromatic scale.

The rhythmic aspect of this composition is based on Euclidean rhythms (a salutation to the Greek mathematician Euclid!).
In 2005 Goldfried Toussaint published the article "The Euclidean algorithm generates traditional musical rhythms" (http://cgm.cs.mcgill.ca/~godfried/publications/banff.pdf). In this article he defines and explains the concept of Euclidean rhythm . These rhythms are so called because they can be obtained using the famous Euclid algorithm that allows us to obtain the greatest common divisor of two numbers. Using this algorithm, rhythms are achieved in which the accented beats of the measure are evenly distributed among the non-accented beats and the uniformity that is achieved is the maximum possible. The interest is that many of the prominent rhythms of world traditional music have this Euclidean rhythm arrangement.
Specifically, in this piece I have used four Euclidean rhythms, corresponding to the following popular music: "Cumbia Colombiana", "Tresillo Cubano", "Cinquillo Cubano", a bell rhythm from West Africa.
With a pair of numbers, the first indicating the number of downbeats and the second the total number of beats in the measure and using the sign   x   to represent the accented beats and the sign   .   for the weak, the cited rhythms can be represented like this:
 
"Cumbia Colombiana" :   E(3,4) = [x. x x]
"Tresillo Cubano ":    E(3,8) =  [x. . x. . x.]
"Cinquillo Cubano ":    E(5,8) = [x. x x. x x.]
West African bell rhythm:   E(7,12) =  [x. x x. x. x x. x.]

The intention has been to obtain a festive music for a certain celebration.

To contrast with such joy and to give a little more variety, in the harmony I have used more ambiguous and somber elements such as the fourth chords and also the four musical modes that I have used: Dorian, Aeolian, Phrygian and Locrian.

In the symphonic instrumentation, it is worth highlighting the inclusion of four saxophones, two sopranos and two tenors and also the absence of percussion instruments with the intention of achieving strong rhythmic sensations implicitly only with melodic instruments.

Euclidean rhythms for a celebration

Walking by four-note chords.

This work can be considered a continuation (or a second track of the same album) of one of my previous works "Parsimonious Trichords".
This is the case since in the elaboration of its harmonies I have followed the same line of work but taking one more step in the current work. In the harmony of the two works I have used the Tonnetz. This comes from the German term "Tonnetzwerk" which means network of tones. The prototypical case is the one that is formed by the major and minor chords (of three notes) organized in such a way that those that are contiguous only differ by a single note (with only a semitone or tone of difference) and on this network we can go chaining the chords following different itineraries or paths thus defining the harmonic progression. In the work "Parsimonious Trichords" I used this Tonnetz with three-note chords. The present work tries to go a step further and use four-note chords to define the Tonnetz. To achieve this I have applied the ideas developed by Dmitri Tymoczko in his excellent article "The Generalized Tonnetz" (dmitri.mycpanel.princeton.edu/tonnetzes.pdf). The objective will be the same: to get a network that organizes the chords (in this case of four notes) in such a way that those that are contiguous continue to be differentiated by a single note. In this case, to achieve this, it is necessary to use 12 chords of dominant seventh, 12 chords of half-diminished seventh, 12 chords of minor seventh and 6 chords of French sixth. To achieve To achieve the harmonic progression, on this network of chords I have defined 7 itineraries (one for each part of the work) of the so-called Hamiltonians, which means that they go through all 42 Tonnetz chords once and only once. As can be assumed, the chord succession that is achieved is also very parsimonious in the sense that there is very little variation between a chord and the one that follows it.

The work of creating the Tonnetz of four-note chords and as well as the elaboration of the itineraries I have done it by programming a series of algorithms in Python language.

Regarding the rhythmic aspect of the work, I have used an archetype: the rhythmic "motif of the walker" (half, quarter, quarter) for two reasons: one, which is quite evident, to reinforce the concept of itinerary or path and the other as a small tribute to the recently published book "Paisajes del Romanticismo musical" by the composer and theorist Benet Casablancas since it is one of the many characteristics that he analyzes about the music of the Romantic period.

For all these reasons, the exhaustive title of this work could have been "Walking through the Hamiltonian itineraries of the graph (of minimal variation) of four-note chords." which I have not dared to use for obvious reasons.

Regarding the interpretation, it should be said that it is done through NotePerformer playback engine.
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Traducción de esta introducción al castellano:

https://drive.google.com/file/d/1daCJQkXXW8_1gj9H7pzbkHWQPANP6T7L/view?usp=sharing

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Traducció d'aquesta introducció al català:

https://drive.google.com/file/d/1DByRKuTZAfrodnbwF_1muzsVB3pV62FY/view?usp=sharing
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Walking by four-note chords

Inside a forest it sang

This piece is for a small ensemble of six instruments (flute, bass clarinet, violin, cello, piano, and percussion). It is inspired by a popular Catalan song that has precisely the same title, in Catalan "A dins d'un bosc cantava". The lyrics of the song explain that "Inside a forest a cuckoo sang with great eagerness, from the top of a towering oak, calling his companion ...".  Thus, the starting musical material has been the melody of this song. Material subjected to various transformations. The most notable is in the melodic field and has been to "chromatize" the initial diatonic melody by incorporating the necessary notes to achieve the basic melodic phrase formed by all the notes of the chromatic scale. This melodic phrase has been the effective base on which the entire work has been built. However, I have not wanted to completely dispense with the initial diatonic melody, but it also appears at different times, but with careful treatment, using the complementary musical elements to achieve a sufficiently coherent result that would overcome the possible contradiction caused by the simultaneous presence of diatonic materials and dodecaphonic materials.

Randomization is another important element that appears in composition. I have tried to present a continuous evolution of the presence of a controlled randomness, obtaining three different phases in the course of the work. The beginning has a more chaotic nature and evolves towards a much more orderly and clear-cut environment to end in the last part that takes up the more uncertain and agitated aspect of the beginning but that definitively overcomes the initial disorder.

With this approach, I wanted to achieve a music that would maintain the naive, innocent and playful character that the initial song has, but trying to make a musical rereading that was more modern and with a few more doses of complexity. All this imbued with a festive and Christmas atmosphere, which would serve to congratulate the Christmas holidays this year, which is the pragmatic reason why I wanted to compose this piece.

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Traducció al català:
https://drive.google.com/file/d/1070-eXNJGZ-Kd3d4WDnGVkjw0PAMCYgi/view?usp=sharing

Traducción al castellano:
https://drive.google.com/file/d/1A9tLdBA_H0Y5-PTGQ0nGve2nm6j_LC7l/view?usp=sharing

A dins d'un bosc cantava

This work has been composed for a brass quintet (horn, 2 trumpets, trombone and tuba) but with the addition of a complementary part of electronic synthesis. 
In the following links there are the PDF files with the theoretical introduction to this piece and also its score:

Explanation in English language:
https://drive.google.com/file/d/1Hja15n07xtgLOH0xPJw4Yrq8o94KjpWj/view?usp=sharing

Explicació en català:
https://drive.google.com/file/d/19L0ikzhDGwtVb9LgITglNW2XQShRtWNu/view?usp=sharing

Explicación en castellano:
https://drive.google.com/file/d/16FXnr-bdmvRe1rPxRBRKp32Uz5AzY9NA/view?usp=sharing

Score / Partitura:
https://drive.google.com/file/d/1DW1ACXAtPLe2pAiOScOBAcT1zEEG9Lty/view?usp=sharing

From French Horn To Sinusoid

When I knew that in this year 2022 the centenary of the birth of the composer Iannis Xenakis is being celebrated, I got the impulse of composing a piece inspired by his music. The result has been the composition that I present here.
In the following links you will find the PDF files with the theoretical introduction:

Explanation in English language:
https://drive.google.com/file/d/1EhCnCpk1_F1pWaDJq_ukEZ3L5T_6Wcsd/view?usp=sharing

Explicació en català:
https://drive.google.com/file/d/1xQVWTE6_MzS6bGkNNfhte2Jmh0TNL9E1/view?usp=sharing

Explicación en castellano:
https://drive.google.com/file/d/1PilJZMRNLupHWXM7ktz8nLPT0AASnyJr/view?usp=sharing

Hyperbolic Paraboloid and Xenakis

For a couple of years I have had a line of work open that is the composition of piano pieces whose harmony is based on the "Tonnetz". The one I'm publishing here is the third one that I compose (the other two are "Parsimonious Trichords" and "Walking by four-note chords") and there would still be a fourth to finish this chapter and that I think I will compose soon.
  
In the following links you will find the PDF files with the theoretical presentation of the current piece:

Explanation in English language:
https://drive.google.com/file/d/1-cz65Td04fTxB_LMbT46GTB8E7dLI7dh/view?usp=sharing

Explicació en català:
https://drive.google.com/file/d/16DUwMUx9ScDbrZiATfhkXAMf7P46EjHd/view?usp=sharing

Explicación en castellano:
https://drive.google.com/file/d/1d0bnSIus1h5v7za1y_oqH8sTv5RG2Hhf/view?usp=sharing

Six-note chords

Here ends my adventure with the Tonnetz! This is the piece that closes the series of four works that I have composed based on it.


In the following links you will find the PDF files, where I explain it in detail with the theoretical presentation of the current piece.

Explanation in English language:

https://drive.google.com/file/d/1YbM9PspOSuMw0mqS46Eyzq1bCTQJEZUr/view?usp=sharing

Explicación en castellano:

https://drive.google.com/file/d/1ezUhGhdC13jp7eCEq1SnBujtXhLKryhK/view?usp=sharing

Explicació en català:

https://drive.google.com/file/d/1H1dI8ZNRwx9iVITabbns0v4bAok1bbgN/view?usp=sharing

I have also created an album where I have gathered the 5 pieces that I have composed following the pattern of the Tonnetz. Each of the first four pieces (all of them for piano) follow the scheme of a different Tonnetz, what differentiates each one of them is the certain number of notes that their chords have. The pieces are presented ordered according to this number of notes that their chords have: 2, 3, 4, 6 notes respectively. In the fifth piece (which is orchestral) the four Tonnetz intervene successively in their different parts.

https://soundcloud.com/ramon-capsada-blanch/sets/the-4-tonnetz-of-the-chromatic

Fifth chords chained with common notes

This string quartet is inspired by the twelve-tone technique, but not in a very heavy way.

It is made up of four different parts:
1. Allegro
2. Moderato
3. Scherzo
4. Rondo

The hardest part is precisely the first movement, for that to start strongly, through a dense musical texture, with a continued and quite intense presence of the four instruments, reaching two moments of maximum intensity: just at the beginning and just at the end of the movement.

The contrast manifests itself in the relaxed and calm atmosphere created by the second movement.

With rhythm 3 by four, the Scherzo wants to get an animated and amusing part. With a ternary structure, the central part displays like a dialogue between violin and viola remembering distantly the trios of the classic Scherzo

The Rondo retakes the calm environment with the Moderate tempo. Formed by 5 different parts, it alternates in a contrasted way the Moderate rhythm with the Vivace rhythm of two of these parts

It is performed by the computer program itself. (Sibelius+NotePerformer ).

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Aquest quartet de corda està inspirat en la tècnica dodecafònica, però no d'una forma molt difícil.

Està format per quatre moviments diferents:
1. Allegro
2. Moderato
3. Scherzo
4. Rondo

La part més dura és precisament el primer moviment, per allò de començar amb força, mitjançant una textura musical densa, amb una presència continuada i intensa dels quatre instruments, aconseguint dos moments de màxima intensitat: just al principi i just al final del moviment.

El contrast es manifesta amb l'atmosfera més calmada que es crea amb el segon moviment.

Amb ritme 3 per quatre, el Scherzo vol aconseguir una part animada i juguenera. Amb una estructura ternària, la part central presenta com un diàleg entre violí i viola recordant remotament els trios del els Scherzo clàssics

El Rondo reprèn l'ambient tranquil amb el tempo Moderato. Format per 5 parts diferenciades, alterna de forma contrastada el ritme Moderato amb el ritme Vivace de dues d'aquestes parts.

Està interpretada pel propi programa de l'ordinador (Sibelius+NotePerformer ).

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Este cuarteto de cuerda está inspirado en la técnica dodecafónica, pero no de una forma muy difícil.

Está formado por cuatro movimientos diferentes:
1. Allegro
2. Moderato
3. Scherzo
4. Rondo

La parte más dura es precisamente el primer movimiento, por aquello de empezar con fuerza, mediante una textura musical densa, con una presencia continuada e intensa de los cuatro instrumentos, logrando dos momentos de máxima intensidad: justo al principio y justo al final del movimiento .

El contraste se manifiesta con la atmósfera más calmada que se crea con el segundo movimiento.

Con ritmo 3 por cuatro, el Scherzo pretende conseguir una parte animada y juguetona. Con una estructura ternaria, la parte central presenta como un diálogo entre violín y viola recordando remotamente los tríos del los Scherzo clásicos

El Rondo retoma el ambiente tranquilo con el tempo Moderato. Formado por 5 partes diferenciadas, alterna de forma contrastada el ritmo Moderato con el ritmo Vivace de dos de estas partes.

Está interpretada por el propio programa del ordenador (Sibelius + NotePerformer).

String Quartet. Isometries

Toccata for synthesizer.  Subtle differences.

Since I have proposed the creation of this piece through musical composition using a computer programming language for sound, I considered that it was most appropriate to work with elements that belong exclusively to this area and that cannot be obtained with the conventional tools of musical creation. Two are the most important aspects to be highlighted, first, the definition of a microtonal musical scale, dividing the octave into 120 tonal partitions and second, the definition of four instrumental timbres, all of them from the same family, using the electronic synthesis.
I have created a piece of free-form music that allows the qualities of scale and instruments to be exhibited in a similar way as the old Baroque Toccatas but with their own musical elements.

Below are more detailed explanations if you want to go deeper.

This piece is based on three foundations:

1. A musical scale that is microtonal. The starting point for defining the microtonal scale has been to  get the maximum number of tones that were consonants, that is, they share the greatest possible number of your harmonic frequencies. To achieve this goal the number that indicates the partitions of the octave of the scale must contain prime numbers. The more, the better. Examples:

 2•3 = 6 parts
2•3•5 = 30 parts
2•3•5•7 =210 parts
etc.

My choice has been three prime numbers:   2•3•5 = 30. But I wanted to play big and get a scale with a very considerable number of partitions (to bring to a high level the advantages that this entails: great chromatism, immense combinations, many possibilities of subscales, ...). For this I have decided to double twice the 30 divisions:

2• 2•2•3•5 = 120

Thus, the octave of the defined scale has 120 divisions. These divisions are all the same and the relation between two consecutive notes is:  2 ^ (1/120) = 1.00579. This implies very subtle differences. For example, the previous note and the one after "A  440Hz" have the these frequencies:

437.46578 Hz
440 Hz
442.5488941 Hz

Undoubtedly, a tough test of distinction even for the most educated ear! In monotonous series with many notes the interesting effect of "the change without noticing it" is achieved. It is achieved that in the same octave there are up to 14 consonant notes with respect to the first note, in the sense that an important number of their harmonics coincide. A possible subscale is also the twelve-tone.

2. Musical timbres from synthesizer. Working with instruments created with computer synthesizers is the most consistent way to implant a microtonal scale with so many divisions.
I have defined four different instruments from an existing op code in the Csound programming language, called "prepiano" that allows to define instruments of the type of stringed percussion.. It can be considered a synthesizer of the type "physical model" that uses complex mathematics in its definition and contains an important number of configurable parameters, such as: the number of strings struck as a cluster by the hammer, stiffness of the strings, detuning between the strings, decay and release time, mass of the hammer, frequency of the striking hammer, rubber is present or not on each string, rattle is present or not on each string, etc.
The four instruments used in this piece are obtained from configuring "prepiano" with four different sets of values.

3. Musical composition through programming language. Csound has been the environment where the musical composition has been developed using the programming algorithms typical of this language (i-Time, k-Time, conditional and control structures, ...).

Toccata for synthesizer.  Subtle differences.

This piece is more "modern" and more "atonal" than the Extensions quartet . But as it is very short I think you can also listen quite well. The first audition may sound a little strident. But, as always, against more times you listen more you like it!

It is inspired by the prime numbers and in particular in the spiral of Ulam which is the distribution that is seen in the attached image. The intention (poetic) has been to feel how this distribution of prime numbers would sound by doing several direct and inverse sequential readings.

As always, I hope you like it and thanks for listening to it.

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Aquesta peça és més "moderna" i més "atonal" que el quartet Extensions. Però com que és molt curteta crec que també es pot escoltar força bé. La primera audició pot sonar una mica estrident. Però, com sempre passa, contra més vegades l'escoltes més t'agrada !

Està inspirada en els nombres primers i en particular en l'espiral d'Ulam que és la distribució que es veu en la imatge adjunta. L'intenció (poètica) ha estat sentir com sonaria aquesta distribució de nombres primers fent diverses lectures seqüencials directes i inverses.
Com sempre, espero que us agradi i gràcies per escoltar-la.

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Esta pieza es más "moderna" y más "atonal" que el cuarteto Extensions. Pero como es muy cortita creo que también se puede escuchar bastante bien. La primera audición puede sonar un poco estridente. Pero, como siempre ocurre, contra más veces lo escuchas más te gusta!

Está inspirada en los números primos y en particular en la espiral de Ulam que es la distribución que se ve en la imagen adjunta. La intención (poética) ha sido sentir como sonaría esta distribución de números primos haciendo varias lecturas secuenciales directas e inversas.

Como siempre, espero que os guste y gracias por escucharla.

Chords from the Ulam Spiral

I have composed this piece to congratulate Christmas.

It is a song for voice and piano, in Catalan, in the manner of the "lieds" of romantic classical music but with novel style.

To see the lyrics and the animated images I have made two videos on youtube:

1. The same soundtrack as here on SoundCloud. The voice is a MIDI contralto.  She sings very well but does not articulate the words. The lyrics are written with Catalan and English subtitles :

https://youtu.be/lK4pLMlsefQ

2. I sing the song myself. I don't sing very well but I'm saying the lyrics of the song (my family has loved hearing my voice) :

https://youtu.be/TVg6vpFJjuE

I hope you like it and have a great Christmas festivities!

Nadala 2019

I have composed this piece expressly for the contest that has been convened on the "Forum Composer" website, organized by Gav Brown, under the motto of "Dancing" (I finally ranked second.  Oops!  I almost win). 
It is written for an orchestra of seven instruments (oboé, trumpet, trombone, tuba, violin, viola and double bass).
The intention has been to create a jovial, festive and fun atmosphere using innovative musical elements of different harmonic nature, doing smooth transitions between parts with marked consonant harmony to more dissonant others.

Attached PDF file with the score:
https://www.dropbox.com/s/nu167rpmxg8cfui/Dancing%20to%20your%20own%20tune.pdf?dl=0

Dancing to your own tune

In April 2019 I composed the string quartet "Extensions". The intention had been to create a musical work that had a "modern way of doing" but without reaching extreme forms, with the intention that it could be feasibly decoded by the majority of potential listeners.
The initial baseline for tonality and melodic reference was the use of the octatonic scale (also called diminished symmetric scale) due to the large number of both tonal and non-tonal elements it contains. But the objective was to overcome the use of this scale, making extensions of some themes, initially octotonic, and reworking them according to the chromatic scale. This scale becomes more important as the work progresses, becoming the main one.
Another aspect of the work to highlight is the importance of the fugue procedure. Although there are passages with homophonic texture, the parts with counterpoint textures of the four voices are the ones that predominate.
In March 2020 I revised the initial string quartet, creating this current version that I present here: "Extensions, distilled". This is a more depurated, refined and lighter version with the intention of extracting the essential meaning and most important aspects of the first version.

String Quartet. Extensions, distilled

Explanations about the work: 

1.  It was written to be heard at the presentation of the book "El paraigua de Joan Brossa" edited by "Papers de Versàlia" a group formed by poets from Sabadell (Barcelona).  It is a book of poems made by about a hundred poets who write in Catalan and Spanish, as a tribute to Catalan poet Joan Brossa on the centenary of his birth on 2019.

2. It consists of two parts, designed to be heard separately. Between each part the reading of several poems is planned.

3. These two parts are musically symmetrical. The music of the second part has been written strictly following a horizontal symmetry of the different musical elements of the first part, retrograde them. This arrangement wants to emphasize  the importance that geometry and symmetry have in the visual poems that Brossa wrote.

4. Some key concepts regarding the Brossa figure are: avant-garde, transgression, heterodoxy, multiple facets of art, sharpness, magic, play, criticism of power, honesty. He carried out various "musical actions", with the collaboration of the composer Josep M. Mestres Quadreny who composed the music and also of Carlos Santos who played the piano.

5. This is why the general approach of my musical piece has been to obtain a mixture, a heterogeneous blend of diverse ingredients, through the use of different musical genres; the work has a part of tonal music and another of music of a more atonal and serial nature. A mixture that wants to refer to this capacity for interrelation and the use of different facets of art by Brossa and also wants to refer to the romantic music that Brossa liked but also to the more transgressive and experimental aspect (very evident in his musical actions, previously mentioned), which would be represented by the most atonal part of the music.

6. Since the proposal was not to perform live music, but through the computer and since the computer makes all the instruments you want available to you, I wanted to make a symphonic instrumental approach. I have used: piccolo, flute, oboe, clarinet, bassoon, contrabassoon, horn, trumpet, trombone, tuba, violin, viola, cello, double bass, piano, timpani, xylophone, and tambourine. The piano has outstanding appearances because it was the dominant instrument in Brossa's musical actions, played by Carlos Santos, as I mentioned before.

7. To reinforce the poetic character, I have also incorporated a short passage with the feminine human voice spoken, not sung (speech is genuinely poetic). It is as if she were the voice of Christa Leem, who was an actress and vedette, considered an icon of freedom in the 70s in Barcelona and muse of great artists, including Joan Brossa who created several shows for her. This passage is a short poem located at the beginning of the first part and at the end of the second, due to the symmetrical nature of the two parts. To preserve this symmetry, the poem is made up of verses that are palindromes, that is, with the same meaning whether reading backward or forward. In this way the spoken message has meaning when it is pronounced in the two directional senses of the two symmetrical musical parts (only the order of the verses changes).

8. I have also wanted to incorporate a small detail of "Musique concrète" (Mestres Quadreny collaborated with John Cage; Carlos Santos said that Joan Brossa was the Catalan "John Cage"). It is a short passage that is located just when the first part ends (and at the beginning of the second). It is a sound that is perhaps a little difficult to identify, so I wish to explain that it is the noise that a rocking chair makes when swinging. The rocking chair is an object that appears frequently in the world of Brossa and in his poetry. When reading the poems in the middle of the two parts of the musical piece, this reading will be sandwiched between the two sounds of the rocker. This fact can make us pretend that the poet's presence exists while the reading of the different poems inspired by his work lasts.

Brossa

This is a piece for piano based on Neo-Riemannian theory. It is a MIDI version performed by a VST piano from the Vienna Symphonic Library. You can also hear a real version played by Edward Cohen, a pianist from Scotland: 
https://www.youtube.com/watch?v=pn0t5N1mXdA

In the following links there are the PDF files with the explanation of what the fundamentals of this piece are:

Explanation in English language:
https://drive.google.com/file/d/1Le66JNBocRH9bBr3d-mRrqqa-uS4nYz4/view?usp=sharing

Explanation in Spanish language:
https://drive.google.com/file/d/1t1-xbA49NjBk-WL9LEtPrqxhYZs67-Ko/view?usp=sharing

Explanation in Catalan language:
https://drive.google.com/file/d/1GR9_w7Lw_8CjItXDzzLjpKw_Stx7xaoj/view?usp=sharing

Parsimonious Trichords

With respect to form, this piece follows the line of work started in my previous work "Parsimonious Chords", which was based on the "Tonnetz" graph formed by the notes of the major and minor triads. The current work is based on the "generalized Tonnetz" that includes the previous Tonnetz but also other similar graphs defined in spaces formed by chords of any number of notes. This concept is precisely defined by Dmitri Tymoczko in his excellent article "The Generalized Tonnetz" (https://dmitri.mycpanel.princeton.edu/tonnetzes.pdf). In my specific case I have worked with four Tonnetz: those formed by chords of two, three, four and six notes. In each of them I have used Hamiltonian paths (those that visit all the chords of the graph only once) to define the harmony and the conduction of voices.

With respect to the expressive character, this work is influenced by the harshness of the health crisis that the world is experiencing and also by the atmosphere of the Christmas dates in which it was written.

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Perdidos por caminos de espacios de acordes

En cuanto a la forma, esta pieza sigue la línea de trabajo iniciada en mi anterior obra "Parsomonious Chords", que estaba basada en el grafo "Tonnetz" formado por las notas de las tríadas mayores y menores. La obra actual está basada en el "Tonnetz generalizado" que incluye al anterior Tonnetz pero también otros grafos similares  definidos en espacios formados por acordes de un número cualquiera de notas. Este concepto lo define con precisión Dmitri Tymoczko en su excelente artículo "The Generalized Tonnetz" (https://dmitri.mycpanel.princeton.edu/tonnetzes.pdf). En mi caso concreto he trabajado con cuatro Tonnetz: los formados por acordes de dos, tres, cuatro y seis notas. En cada uno de ellos he utilizado caminos hamiltonianos (aquellos que visita todos los acordes del grafo una sola vez) para definir la harmonía y la conducción de voces. 

En cuanto al carácter expresivo, esta obra está influenciada por la dureza de la crisis sanitaria que el mundo está viviendo i también por el ambiente de las fechas navideñas en la que ha sido escrita.

Lost on paths of chord spaces

A piece of music is a mentally constructed entity, of which scores and performances are partial representations by which the piece is transmitted.
(Fred Lerdahl & Ray Jackendoff)

Any tone can succeed any other tone, any tone can sound simultaneously with any other tone or tones, and any group of tones can be followed by any other group of tones, just as any degree of tension  or nuance can occur in any medium under any kind of stress or duration. Successful projection will depend upon the contextual and formal conditions that prevail, and upon the skill and soul of the composer.
(Vincent Persichetti)

Ramon Capsada Blanch

Pinned to spotlight

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