I composed the Piano Concerto in two stages: the first three movements during the years 1985-86, the next two in 1987, the final autograph of the last movement was ready by January, 1988. The concerto is dedicated to the American conductor Mario di Bonaventura. .

The markings of the movements are the following: .

1. Vivace molto ritmico e preciso .
2. Lento e deserto .
3. Vivace cantabile .
4. Allegro risoluto .
5. Presto luminoso.

The first performance of the three-movement Concerto was on October 23rd, 1986 in Graz. Mario di Bonaventura conducted while his brother, Anthony di Bonaventura, was the soloist. Two days later the performance was repeated in the Vienna Konzerthaus. After hearing the work twice, I came to the conclusion that the third movement is not an adequate finale. my feeling of form demanded continuation, a supplement. That led to the composing of the next two movements. The premiere of the whole cycle took place on February 29th, 1988, in the Vienna Konzerthaus with the same conductor and the same pianist. .

The orchestra consisted of the following: flute, oboe, clarinet, bassoon, horn, trumpet, tenor trombone, percussion and strings. The flautist also plays the piccoIo, the clarinetist, the alto ocarina. The percussion is made up of diverse instruments, which one musician-virtuoso can play. It is more practical, however, if two or three musicians share the instruments. Besides traditional instruments the percussion part calls also for two simple wind instruments: the swanee whistle and the harmonica. The string instrument parts (two violins, viola, cello and doubles bass) can be performed soloistic since they do not contain divisi. For balance, however, the ensemble playing is recommended, for example 6-8 first violins, 6-8 second, 4-6 violas, 4-6 cellos, 3-4 double basses. .

In the Piano Concerto I realized new concepts of harmony and rhythm. .

The first movement is entirely written in bimetry: simultaneously 12/8 and 4/4 (8/8). This relates to the known triplet on a doule relation and in itself is nothing new. Because, however, I articulate 12 triola and 8 duola pulses, an entangled, up till now unheard kind of polymetry is created. The rhythm is additionally complicated because of asymmetric groupings inside two speed layers, which means accents are asymmetrically distributed. These groups, as in the talea technique, have a fixed, continuously repeating rhythmic structures of varying lengths in speed layers of 12/8 and 4/4. This means that the repeating pattern in the 12/8 level and the pattern in the 4/4 level do not coincide and continuously give a kaleidoscope of renewing combinations. .

In our perception we quickly resign from following particular rhythmical successions and that what is going on in time appears for us as something static, resting. This music, if it is played properly, in the right tempo and with the right accents inside particular layers, after a certain time rises, as it were, as a plane after taking off: the rhythmic action, too complex to be able to follow in detail, begins flying. This diffusion of individual structures into a different global structure is one of my basic compositional concepts: from the end of the fifties, from the orchestral works Apparitions and Atmospheres I continuously have been looking for new ways of resolving this basic question. The harmony of the first movement is based on mixtures, hence on the parallel leading of voices. This technique is used here in a rather simple form. later in the fourth movement it will be considerably developed. .

The second movement (the only slow one amongst five movements) also has a talea type of structure, it is however much simpler rhythmically, because it contains only one speed layer. The melody is consisted in the development of a rigorous interval mode in which two minor seconds and one major second alternate therefore nine notes inside an octave. This mode is transposed into different degrees and it also determines the harmony of the movement. however, in closing episode in the piano part there is a combination of diatonics (white keys) and pentatonics (black keys) led in brilliant, sparkling quasimixtures, while the orchestra continues to play in the nine tone mode. .

In this movement I used isolated sounds and extreme registers (piccolo in a very low register, bassoon in a very high register, canons played by the swanee whistle, the alto ocarina and brass with a harmon-mute' damper, cutting sound combinations of the piccolo, clarinet and oboe in an extremely high register, also alternating of a whistle-siren and xylophone). The third movement also has one speed layer and because of this it appears as simpler than the first, but actually the rhythm is very complicated in a different way here. Above the uninterrupted, fast and regular basic pulse, thanks to the asymmetric distribution of accents, different types of hemiolas and inherent melodical patterns appear (the term was coined by Gerhard Kubik in relation to central African music). If this movement is played with the adequate speed and with very clear accentuation, illusory rhythmic-melodical figures appear. These figures are not played directly. they do not appear in the score, but exist only in our perception as a result of co-operation of different voices. .

Already earlier I had experimented with illusory rhythmics, namely in Poeme symphonique for 100 metronomes (1962), in Continuum for harpsichord (1968), in Monument for two pianos (1976), and especially in the first and sixth piano etude Desordre and Automne a Varsovie (1985). .

The third movement of the Piano Concerto is up to now the clearest example of illusory rhythmics and illusory melody. In intervallic and chordal structure this movement is based on alternation, and also inter-relation of various modal and quasi-equidistant harmony spaces. The tempered twelve-part division of the octave allows for diatonical and other modal interval successions, which are not equidistant, but are based on the alternation of major and minor seconds in different groups. The tempered system also allows for the use of the anhemitonic pentatonic scale (the black keys of the piano). From equidistant scales, therefore interval formations which are based on the division of an octave in equal distances, the twelve-tone tempered system allows only chromatics (only minor seconds) and the six-tone scale (the whole-tone: only major seconds). .

Moreover, the division of the octave into four parts only minor thirds) and three parts (three major thirds) is possible. In several music cultures different equidistant divisions of an octave are accepted, for example, in the Javanese slendro into five parts, in Melanesia into seven parts, popular also in southeastern Asia, and apart from this, in southern Africa. This does not mean an exact equidistance: there is a certain tolerance for the inaccurateness of the interval tuning. .

These exotic for us, Europeans, harmony and melody have attracted me for several years. However I did not want to re-tune the piano (microtone deviations appear in the concerto only in a few places in the horn and trombone parts led in natural tones). After the period of experimenting, I got to pseudo- or quasiequidistant intervals, which is neither whole-tone nor chromatic: in the twelve-tone system, two whole-tone scales are possible, shifted a minor second apart from each other. Therefore, I connect these two scales (or sound resources), and for example, places occur where the melodies and figurations in the piano part are created from both whole tone scales. in one band one six-tone sound resource is utilized, and in the other hand, the complementary. In this way whole-tonality and chromaticism mutually reduce themselves: a type of deformed equidistancism is formed, strangely brilliant and at the same time slanting. illusory harmony, indeed being created inside the tempered twelve-tone system, but in sound quality not belonging to it anymore. .

The appearance of such slantedequidistant harmony fields alternating with modal fields and based on chords built on fifths (mainly in the piano part), complemented with mixtures built on fifths in the orchestra, gives this movement an individual, soft-metallic colour (a metallic sound resulting from harmonics). .

The fourth movement was meant to be the central movement of the Concerto. Its melodc-rhythmic elements (embryos or fragments of motives) in themselves are simple. The movement also begins simply, with a succession of overlapping of these elements in the mixture type structures. Also here a kaleidoscope is created, due to a limited number of these elements - of these pebbles in the kaleidoscope - which continuously return in augmentations and diminutions. .

Step by step, however, so that in the beginning we cannot hear it, a compiled rhythmic organization of the talea type gradually comes into daylight, based on the simultaneity of two mutually shifted to each other speed layers (also triplet and duoles, however, with different asymmetric structures than in the first movement). While longer rests are gradually filled in with motive fragments, we slowly come to the conclusion that we have found ourselves inside a rhythmic-melodical whirl: without change in tempo, only through increasing the density of the musical events, a rotation is created in the stream of successive and compiled, augmented and diminished motive fragments, and increasing the density suggests acceleration. .

Thanks to the periodical structure of the composition, always new but however of the same (all the motivic cells are similar to earlier ones but none of them are exactly repeated. the general structure is therefore self-similar), an impression is created of a gigantic, indissoluble network. Also, rhythmic structures at first hidden gradually begin to emerge, two independent speed layers with their various internal accentuations. .

This great, self-similar whirl in a very indirect way relates to musical associations, which came to my mind while watching the graphic projection of the mathematical sets of Julia and of Mandelbrot made with the help of a computer. I saw these wonderful pictures of fractal creations, made by scientists from Brema, Peitgen and Richter, for the first time in 1984. From that time they have played a great role in my musical concepts. This does not mean, however, that composing the fourth movement I used mathematical methods or iterative calculus. indeed, I did use constructions which, however, are not based on mathematical thinking, but are rather craftman's constructions (in this respect, my attitude towards mathematics is similar to that of the graphic artist Maurits Escher). .I am concerned rather with intuitional, poetic, synesthetic correspondence, not on the scientific, but on the poetic level of thinking. .

The fifth, very short Presto movement is harmonically very simple, but all the more complicated in its rhythmic structure: it is based on the further development of ''inherent patterns of the third movement. The quasi-equidistance system dominates harmonically and melodically in this movement, as in the third, alternating with harmonic fields, which are based on the division of the chromatic whole into diatonics and anhemitonic pentatonics. Polyrhythms and harmonic mixtures reach their greatest density, and at the same time this movement is strikingly light, enlightened with very bright colours: at first it seems chaotic, but after listening to it for a few times it is easy to grasp its content: many autonomous but self-similar figures which crossing themselves. .

I present my artistic credo in the Piano Concerto: I demonstrate my independence from criteria of the traditional avantgarde, as well as the fashionable postmodernism. Musical illusions which I consider to be also so important are not a goal in itself for me, but a foundation for my aesthetical attitude. I prefer musical forms which have a more object-like than processual character. Music as frozen time, as an object in imaginary space evoked by music in our imagination, as a creation which really develops in time, but in imagination it exists simultaneously in all its moments. The spell of time, the enduring its passing by, closing it in a moment of the present is my main intention as a composer. .
(Gyorgy Ligeti)

Fifteen Safari Duets for Tubas was composed for playing duets with my tuba students. The fifteen duets are at different levels of difficulty and various styles so that we always had duets to play no matter what ability of student. There is something in each duet for students to learn from the basics of tone production, rhythms, melodic phrasing, jazz, graphic notation, etc. Most are sight readable and some have been performed in concerts. They are all fun to play. Although for tubas, they may be played on any instrument.

In 1988 I spent a month in Kenya on safari and experiencing the African wildlife and culture, thus the inspiration for these duets that were composed soon after the trip in 1989 and 1990 and have been a regular part of my teaching ever since. Four of these duets are recorded on the compact disc ?Tuba Safari? (Troy 1173) on Albany Records.

1. Elephants at Stave

This duet presents the cantabile style studied for playing the tuba. I find that this duet helps the student much like the melodies of Borgodni etudes. There are more elephants in Tsavo than anywhere else in Kenya. It was not uncommon to see large families of thirty elephants at a time.

2. Gallop ? Thompson Gazelle at Amboseli

This duet provides an opportunity to read in a sharp key, D major, as well as basic rhythms and articulations. I find that the more advanced students can read in a faster tempo and other students can work in a slower tempo ? a common choice in all of the duets. Large herds of playful Thompson Gazelle were a usual occurrence in most of the game parks in Kenya.

3. Rhinos at Nairobi Game Park

This waltz helps the student match phrasing in a cantabile setting. There are a few instances where the teacher (playing the first part) plays a phrase then the student plays a similar phrase. The rhinoceros is a very noble animal that can grow to more that 1,000 pounds and is known for its horn. The Nairobi game park is located just outside the city, giving a sense of surrealism to the panorama.

4. Giraffes at Nairobi Twiga Park

This is in a ?rock? style with syncopated rhythms and cantabile melodies. The Nairobi Twiga park is just outside the city and is the only place where one can feed the giraffes. Along with their long necks they have very long tongues.

5. Warthogs at Ngulia

Legato scales and syncopated rhythms are the features of this duet. Warthogs have tails that are held upright when they run.

6. Baboons at Kiliguni

This duets alternates in rock style and swing. Baboons are sometimes a problem because they will try to steal food from the tourists? tables. They will work together where one causes a diversion while the others steal.

7. Pastoral ? Cape Buffalo at Samburu

The key of A for this duet gives variation for the students. Cape Buffalo are in large herds on the savanna. The Samburu Lodge dining area was built next to a watering hole. At the beginning of breakfast there were no animals, but in fifteen minutes more than 500 cape buffalo were at the water hole.

8. Song - Hippos at Mzima Springs

This is the easiest of rhythms and range of the duets, especially for the 2nd(student) part. Hippopotamuses can grow up to 4,000 pounds and spend most of their time sleeping in the water during the day. At night they go on land to hunt.

9. Leopards at Kimana Lodge

This duet is non-metric and uses graphic notation. This was a favorite duet of my students as many have never experienced this notation before. The leopard is a large predatory cat that usually hunts at night.

10. Colobus Monkeys at the Ark

This is an Invention in the Bach style. The Ark is a building that was built in 1969 at a watering hole for tourists to watch wildlife. The colobus monkey is black with white on its forearms and chest.

11. Zebra Migration at Masai Mara

This duet is in a ?Medium Swing? jazz style. The great migration between the Masai Mara and Serengeti involves about two million wildebeest, zebras and other animals every year. It is considered one of the most impressive natural events worldwide.

12. Ostrich at Samburu

This duet works on double time and half time. The ostrich is the largest bird in the world. In Samburu there was an ostrich that hung around the lodge, her name was Margaret. She was very friendly with everybody but she would steal your hat.

13. Cheetah at Voi

This is another duet that includes graphic notation. The cheetah can run up to 80 miles an hour when chasing after prey. When not hunting prey it often walks very slowly.

14. Gallop ? Gerenuk at Buffalo Springs

This gallop displays different types of articulation. The gerenuk is an antelope with a slightly extended neck so it can eat higher leaves from trees.

15. Lions at Mara Sopa

This duet is in the style of a fanfare. The lion is considered the king of the savanna.

Gregory Fritze is a prize-winning composer and Fulbright Scholar, as well as an active performer. He recently retired from Berklee College of Music where he was Tuba Professor and Chair of Composition, serving on the faculty from 1979 to 2016. He has written over one hundred compositions for orchestra, band, chamber ensembles and soloists. He has won over sixty composition awards both nationally and internationally including First Prize in the 1991 TUBA Etude Contest. His compositions include works published by several publishers in the United States, South America and Europe that have been performed extensively throughout the world. Many of his compositions are available on ITunes, Youtube and Soundcloud.

His compositions are recorded on Albany Records, MSR Classics, Crystal Records, Mark Records and others. He has been a guest lecturer, conductor and performer at many colleges, universities and music festivals in the United States, Canada, Japan, South America and Europe. He was born in Allentown, Pennsylvania in 1954 and has Composition degrees from the Boston Conservatory and Indiana University. He now resides in Daytona Beach Shores, Florida.

Nineteen Skeletal Duets for Trombones is a set of duets of easy to moderately difficult specifically for teachers and students in private lessons. The first 15 duets are arranged from Fifteen Safari Duets for Tubas which was composed in 1989 for playing with my tuba students at Berklee College of Music. They are at different levels of difficulty and in various styles so that we always had duets to play no matter what was the ability of the student. The additional four duets were added in 2020 for trombones for this set. The title of each duet is also a name for a bone in the human body, hence the name Skeletal Duets. There is something in each duet for students to learn: the basics of tone production, rhythms, melodic phrasing, jazz, graphic notation, etc. Most are sight readable and some have been performed in concerts. Nineteen Skeletal Duets for Euphoniums are the same duets but in treble clef. Twenty-two Skeletal Duets for Hornsuses the first 19 of the trombone set with three additional duets added. Some of the trombone and horn duets are in the same key so they can be played together.

1. Cranium
This duet presents the cantabile ?singing? style as studied for playing the trombone. I find that this duet helps the student much like the melodies of Borgodni (Rochet) etudes.

2. Stirrup
This duet provides an opportunity to read basic rhythms and articulations. I find that the more advanced students can read in a faster tempo while the less skilled students work best in the slower tempos ? a common choice for all of the duets.
3. Humerus
This waltz helps the student match phrasing in a cantabile setting. There are a few instances where the teacher (playing the first part) plays a phrase then the student plays a similar phrase.
4. Vertebra
This is in a ?rock? style with syncopated rhythms with cantabile melodies. Articulations are especially important in this duet.
5. Axis
Legato scales and syncopated rhythms are the features of this duet. This is a good exercise for legato playing on trombone, especially when the legato tongue is needed versus when the trombonist does not need to tongue when moving across partials.
6. Tibia
This duet alternates in rock style and swing. Articulations and manipulation of ?swing? rhythms are important.
7. Clavicle
The key of A for this duet provides variation for the students.
8. Fibula nd
This duet uses the easiest of rhythms and range, especially for the 2
9. Scapula
This duet is non-metric and uses graphic notation. This was a favorite duet of my students as many had never experienced this notation before.
10. Atlas ndThis is an Invention in the Bach style. This is probably the best duet to play when the 2 part is played by bass trombone.

(student) part.

11. Radius
This duet is in a ?Medium Swing? jazz style. Each part has a chance to play a little bit of a ?walking? bass line. Articulations and manipulation of ?swing? rhythms are important in this duet.
12. Femur
This duet works on double time and half time tempo changes.
13. Patella
This is another duet that includes graphic notation. In this duet ?Free rapid legato lines? are used.
14. Anvil
This gallop displays different types of articulation.
15. Hammer
This duet is in the style of a fanfare.
16. Rib
This duet is a melody, ?Magallon Blues?, that I originally composed when I taught at a summer music camp in Magallon, Spain. In that camp each of the students would practice playing a jazz solo. This duet also has jazz chord changes so you can add piano or guitar. The use of drums is also an added option.
17. Sacrum
This duet is a short arrangement of Mozart?s ?Eine Kleine Nachtmusic?.
18. Ulna
This duet is a short arrangement of the traditional Irish folk song ?Londonderry Air?, more commonly known as ?Danny Boy?.
19. Ilium
This duet is a short arrangement of the Beethoven?s song ?Ode to Joy? which represents the triumph of universal brotherhood against war and desperation.

Gregory Fritze is a prize-winning composer and Fulbright Scholar, as well as an active performer. He recently retired from Berklee College of Music where he was Tuba Professor and Chair of Composition, serving on the faculty from 1979 to 2016. He has written over one hundred compositions for orchestra, band, chamber ensembles and soloists. He has won over sixty composition awards both nationally and internationally including First Prize in the 1991 TUBA Etude Contest for Twenty Characteristic Etudes for Tuba, an award from The American Prize for his Petite Suite for Brass Quintet and others. His compositions include works published by several publishers in the United States, South America and Europe that have been performed extensively throughout the world. Many of his compositions are available on ITunes, Youtube and Soundcloud.
His compositions are recorded on Albany Records, MSR Classics, Crystal Records, Mark Records and others. He has been a guest lecturer, conductor and performer at many colleges, universities and music festivals in the United States, Canada, Japan, South America and Europe. He was born in Allentown, Pennsylvania in 1954 and has Composition degrees from the Boston Conservatory and Indiana University. He now resides in Daytona Beach Shores, Florida.