Reindl

AAWM Journal 11/2 (2023)

Indian Rhythmic Systems as Sources of Inspiration for Western Composers

Tomáš Reindl

Indian classical music, tabla, rhythm, contemporary composition, Glass, Messiaen, Kabelac, konnakol, solkattu, kaida, tihai

Indian classical music, whether in its North Indian or South Indian form, uses a highly elaborated and sophisticated rhythmic system. Metric cycles (tāla) of different lengths and structures, intricate work with phrases and their chaining in Carnatic music, the sound and the playing technique of north Indian tabla drums, or rhythmic recitation using special syllables (bol, konnakol, solkattu) – all of that can enrich western musicians and composers not only in a way of development their rhythmic feeling but also as an immense source of inspiration for new creativity. Indian rhythmic systems have already been inspiring composers for many decades, in different ways and at different levels. For composers such as Olivier Messiaen or Philip Glass, the contact with Indian rhythm was not only of casual interest but became the crucial impulse for the development of their characteristic musical techniques. This is true as well for the great Czech composer Miloslav Kabeláč, for which encounter with Indian music (as early as 1935), was a fundamental impulse for his original approach to rhythmic work and use of percussion instruments. The article tries to map out the various principles of Indian rhythm and ways in which composers can use them either in a traditional way or as inspiration for procedures or structures not found in the Indian tradition. In addition to the above-mentioned composers, the author addresses different ways of the impact demonstrated in examples from the works of several contemporary composers from the United States and Europe, including examples from his own compositional work.

Tomáš Reindl is a composer, multi-instrumentalist, tabla player and ethnomusicologist, who teaches at the Academy of Performing Arts in Prague.

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[1] It is well established that Indian classical music in both its North Indian (Hindustani) and South Indian (Carnatic) forms uses highly elaborate and sophisticated rhythmic systems. Western musicians and composers have long benefitted from Indian rhythmic concepts, from the enriched experience of rhythmic feeling available in metric cycles (tāla) of different lengths and structures, intricate work with phrases and their combinations in Carnatic music, the sound and the playing technique of North Indian tabla drums, rhythmic recitation using special syllables (bol, konnakol), among others. Even more, these concepts have inspired and continue to inspire innovations in rhythmic creativity; in this article, I will provide an extensive sampling of these inspirations.

[2] From the beginning of the 20th century, top Indian artists began to appear in the West, from Inayat Khan & the Royal Musicians of Hindustan in 1911 to Rabindranath Tagore shortly thereafter, and later on the Uday Shankar dance troupe (Farrell 1997, 144–167). The first books presenting Indian music to Western audiences appeared nearly simultaneously, including the pioneering The Music of Hindostan by Fox Strangways (Strangways and Henry 1914). Not surprisingly, contact with this culture soon attracted the interest of Western composers, at that time still limited by romantic rhythmic clichés despite radical changes in the harmonic language.

[3] The young Olivier Messiaen was among the first composers to find vital suggestions towards new rhythmic phenomena in this contact. In 1924, in the Encyclopédie de la musique et dictionnaire du Conservatoire (Lavignac and La Laurencie 1921), he discovered a table of 120 deśi tālas (“provincial rhythms”) that were collected in the thristeenth century treatise Sangīta Ratnākara by Śārangadēva (Śarṇgadeva 1978). These are ancient Indian rhythmic patterns no longer used in musical practice (Rowell 1992, 207–214).[1]  The term tāla in North and South Indian classical music primarily represents a rhythmic cycle, i.e., a framework within which musical events take place, as we will discuss below. Messiaen, however, did not understand the deśi tālas as cycles, but treated them in his own way. He derived from this material several rhythmic techniques, including added value (either by extending a note with a dot or by adding another small note), irregular augmentation/diminution, decomposition/reassembly of rhythmic formations, the importance of prime numbers, the chromatic scale of durations and so-called non-retrograde rhythms (Van der Walt 2007, 18).[2] For him, at that time, the table of deśi tālas was the only, very limited source of information about Indian music theory. Back then, it was unthinkable for anyone in the West to study this tradition in more depth, let alone learn to play any Indian instrument. Today, by contrast, in an age of unlimited possibilities for studying non-European cultures, we witness in ever more ways how the compositional thinking of today’s composers can be influenced by encounters with the systems of Indian music.

[4] For composers such as Messiaen or Philip Glass, the contact with Indian rhythm was not only of casual interest but became the crucial impulse for the development of their characteristic compositional techniques. This is true as well for the great Czech composer Miloslav Kabeláč, whose work for percussion instruments became internationally known and appreciated (Nouza 2010).[3] In addition, Indian approaches to percussion was a fundamental impulse for the development of his distinctive musical language.

Basic features of traditional Indian rhythmic systems

[5] Let us now explore typical techniques of Indian rhythm, highlighting those features that have inspired and will continue to inspire composers:

1. Metrical frame (tāla)
2. Phrase “building kits”
3. Augmentation and diminution: successive and simultaneous presentations
4. Additive and subtractive processes
5. Indian percussion instruments and their playing technique
6. Recitation of rhythmical syllables or numerals

Each technique will now be considered in detail, with corresponding examples.

Metrical Frame (Tāla)

[6] The term tāla is used in both Hindustani and Carnatic music theory. It refers to metrical cycles or frames of different length (Kippen 2020, 243).

[7] On top of these cycles, often very sophisticated compositions or improvisations unfold. In the case of Indian music, in some cases we could literally speak of bimetric structures (Tichý 2014, 55), which means that on the top of one fixed meter – tāla – there is another layer with variable metrical units (Gottlieb 1993, p. 34). This top layer in certain points coincide with the main counts of the tāla, especially in the points called sam, tālī, or khālī.

[8] A typical example from North Indian classical music is a threefold cadential resolution to the first beat (sam), called tihāī, exemplified in Table 1.[4]

[9] In this structure, we can see the triple repetition of the statement Dha Dha te te Dha arranged in such a way that the last stroke of the phrase meets the first beat of the tāla.

[10] This was an example of the most elementary tihāī; in practice we often find much more elaborate variants. For instance, an extensive threefold composition in which the statement contains another smaller tihāī is called a chakradar(Kippen 2005, 196).

[11] A process inspired by chakradar is utilized in the work of British composer Jonathan Mayer.[5] His composition Dissecting Desh is basically a small concerto for sitar and tabla, emerging from the usual form of raga performance involving improvisation by soloists. The concluding section of the piece (Example 1) is made up of a tihāī formed by triple repetition of a rhythmic statement (bracketed) over the 4/4 bar so it finishes on the downbeat. The repeated material itself consists of three parts based on the threefold repetition of “tireketa,” followed by three longer strokes, cycling through “tak tak tak,” “tun tun tun” and “dha dha dha” in different lengths.

[12] In this case the traditional structure of Indian music was taken and arranged for full symphonic orchestra; the excerpt shown in Example 1 gives only the string section. Note also the shape of the melody, which follows the development of the phrases; there is also an increase of dynamics with each repetition.

Phrase “Building Kits”

[13] We can find systematic applications of the combination of rhythmic phrases of different lengths in both North and South Indian styles. In the Hindustani tabla solo repertoire, this principle is applied to create variations in kaida type of compositions; we can also find its use in constructions of some tukras, chakradars, or gintī (counting) forms, known from kathak dance, among other examples (Gottlieb 1993). However, the most sophisticated implementation of phrase sequencing appears in Carnatic music. Phrases of different length (jāti) are chained one by one on top of the fixed metrical frame tāla (Reina 2016, 35).

[14] The basic Carnatic rhythmic building blocks (jāti) are:

1: Ta
2: Ta ka
3: Ta ki ta
4: Ta ka di mi
5: Ta di gi na tom
7: Ta ka di mi ta ki ta
9: Ta ka di mi ta ka ta ki ta

[15] For example, we can combine these phrases in the sequence of 1, 2, 3, 4, 5, 7, 9 on top of a basic cycle of eight beats (ādi tālam) and it will fit exactly to one “round” of the tāla (see Example 2).

[16] In addition, we can rearrange the order of the phrases in any way without being “out of tāla,” so several new rhythmical structures can be derived from one initial configuration. We can also carry out further operations on the jātiphrases, including replacing notes by silences, increasing the density of notes by doubling the speed, stretching or compressing (see paragraphs 18–26: “Augmentation and diminution”), etc. Moreover, the jāti can be applied to another beat subdivision, for example to triplets, quintuplets, septuplets, or nonuplets (Reina 2016, 21).[6]

[17] Many examples of the use of this technique can be found in the work of contemporary composers, including my own compositions; particularly interesting examples of such phrase sequencing are in the work of Olivier Messiaen (1908 – 1992), despite the absence of references to the Carnatic system or to modern Hindustani kaida forms in his music. In his piano piece Regard du Fils sur le Fils, the fifth movement of the cycle Vingt regards sur l’enfant Jésu (1944), we can see combinations of ancient Indian rhythmic patterns from the already mentioned table of 120 deśi tālas (Messiaen 1998, 331). For instance, on the top staff of Example 3a, Messiaen uses a combination of three deśi rhythms: rāgavardhana (rhythm No. 93 from the original list), candrakalā (No. 105) and lakṣmīśa (No. 88); the rhythmic sources are shown on Example 3b.[7] In the excerpt, the rhythms are set above two rhythmic layers in the other staves which have completely different metrical structures, within the notated meter of 2/4 (Van der Walt 2007, 28).

 

Augmentation and Diminution: Successive and Simultaneous Presentations

[18] The core of Carnatic rhythmic practice is based on an idiosyncratic and highly sophisticated method of phrase processing, involving in particular processes of stretching or compressing, in traditional terms augmentation and diminution. It can happen in both linear and non-linear versions.

[19] For example, here we apply different forms of stretching to the traditional Carnatic 5-beat Tadiginatom phrase:

1. Linear augmentation – pauses are put in between notes evenly, for example:

Ta di gi na tom (5 beats)

Ta – di – gi – na – tom – (10 beats)

Ta – – di – – gi – – na – – tom – – (15 beats)

2. Non-linear augmentation – the phrase can be warped by putting pauses irregularly, at certain points of the phrase only, for example:

Ta di – gi na tom (6 beats)

Ta – di – gi na tom (7 beats)

Ta di – gi – na – tom (8 beats)

Ta – di – gi – na – tom (9 beats)

[20] Augmentation and diminution can be presented as a successive process, where each version of the rhythm is altered to follow some pattern of growth or decay. In Indian percussion music, a successive presentation often takes this form: the percussionist starts playing in one resolution (for example, in a straight eighth note pulse) and then moves to the same material modulated into a higher density of pulses (for example a triplet or quintuplet pulse), without loss of connection with the original metrical matrix (tāla).

[21] We encounter this successive mode in Hindustani kaidas where phrases are modulated from the basic resolution (barābar) into triplets (āri), or sometimes even into quintuplets (kuāri) or septuplets (viāri) (Gottlieb 1993, 39). However, the process occurs in its most sophisticated form in Carnatic music, where this technique is called gati bhedam (Reina 2016, 45). The principle is demonstrated in the Example 4, where the original sixteenth note phrase (chaturushra gati) is modulated into quintuplets (khanda gati).

[22] Composers developing this technique have also employed a simultaneous presentation, in which different versions of the same rhythm are layered on top of each other. The next two examples, from my own composition Utero: Concerto for Cello, Tabla and Symphonic Orchestra, show the simultaneous presentation of both linear and non-linear augmentations in polyphonic and polymetric situations (Tichý 2014, 109).

[23] In Example 5 we can see linear augmentation in its polyphonic form. A kind of Morse code “S.O.S.” motif (a sequence of three short notes, then three long and again three short notes) is used at four different resolutions of stretching: in sixteenth notes in the upper staff, in both triplet and straight eighths beneath that, and finally in dotted quavers in the bottom staff. The phrases start together on the first beat, but they diverge from each other gradually.

[24] The second excerpt, in Example 6, shows an extreme form of polyphonic non-linear augmentation. The nine-note phrase from the second bar of the upper staff is stretched in several different ways non-linearly, so the gaps between the last five notes are gradually increased, while the phrase movement as a whole is slowing down. In this case, each voice starts the phrase at a different point, but the calculation was made such a way that they finish together on a downbeat.

[25] In his composition Telescopic Ladder, from the cycle Tools (2003), the Dutch composer Ned McGowan similarly uses a highly intricate multi-layered simultaneous presentation.[8] The same melodic phrase covering sixteen beats in its basic form is modulated into three different speed levels related by the ratio 4:3 (see the Example 7). This means that the relation of the second level (trumpet) to the basic speed is 16:12, so a phrase originally lasting 16 quarter note beats shrinks to a length of only 12 beats (3/4 x 16 quarters = 12 quarters). The next diminution (flute) is in the same ratio to the trumpet phrase, lasting 9 beats (from 3/4 x 12 = 9).  Finally, the last layer (sopranino recorder) is in the 4:3 ratio to the flute part, and lasts 3/4 x 9 or 6 3/4 beats (i.e., 27 sixteenth notes).

[26] In the composition, this section is repeated four times, so that each time another instrument with a different tempo layer is added; the example below comes from the fourth and fullest repetition. Then all the instruments finish together on the first beat of the next bar.

Additive and Subtractive Processes

[27] This principle is typical for Carnatic rhythmic development, where the additive, expanding forms are called srotovaha yati (“river mouth”) and the subtractive, narrowing forms are called gopucca yati (“cow’s tail”) (Kippen 2020, 249). These processes are also used in Hindustani kaidas or gintī types of composition in North Indian kathakdance. In the West, a similar principle was used by Olivier Messiaen in his practice of valeur ajoutée, inspired by the ancient deśi tālas, as we have discussed above (Messiaen 2001, 11).

[28] Here is an example of traditional Carnatic “pyramid form,” sometimes called “mridanga yati,” which combines the processes of srotovaha and gopucca:

[29] The core phrase “kida tom” is developed in such a way that during each repetition we append to the front another element, here a syllable followed by a pause, until we get the full phrase “ta – di – ta – ta – kida tom –”. Then we apply the mirror process, removing the appended syllables gradually. In this case, the process unfolds within an 8-beat cycle, shown in Example 8 (Lockett 2008, 105).

[30] A similar process happens in the Hindustani gintī (“counting”) forms used often in the North Indian classical dance kathak (Kippen 2005, 185).[9] In this case numbers are used instead of syllables.[10]

The typical example is gintī tihāī in 10 beat cycle Jhaptal:

/: 1 – 1 2 – 1 2 3 – 1 2 3 4 – :/ _3x

[31] We can see a very similar procedure in the work of Czech composer Miloslav Kabeláč (Reindl, 2017, 77). In the organ part of his Symphony No.8 “Antiphones” (1970), the additive principle is applied to the isorhythmic rotation of the four-note sequence (C, D, B, A#) which is one of the basic motifs of the composition. A very striking phrasing is created by expansion of the motif by adding extra thirty-second notes gradually in sequence: 1, 2, 3, 5, 6, 7 (see the Example 9). The number 4 is intentionally omitted by the composer, since if a four-note motif was used two consecutive phrases would start on the same note, disrupting the isorhythmic concept. After reaching the 7-note phrase, the process is reversed, similar to the Carnatic “pyramid form” above.

[32] Comparable additive processes can be found in the work of Philip Glass, especially in his music from the late 1960s through the mid 1970s, from Two Pages to Music in Twelve Parts and Einstein on the Beach, which we will study in paragraph 35.

Recitation of Special Rhythmic Syllables or Numerals

[33] In both branches of Indian classical music there is a common practice of solfege in both melodic and rhythmic forms. For the recitation of rhythms there are special onomatopoeic syllables developed from the sound of different strokes of Indian drums. These are used not only for educational purposes but also as effective performance techniques.In the North, the rhythmic solfege is called bol, and it is connected to tabla strokes. In the South, the solfege (solkattu) is developed from mridangam strokes; performance in a concert setting is then called konakkol (Nelson 2008, 3). We have already seen examples of Indian solfege in sections 2, 3, and 4 (e.g., Tadiginatom, etc.).

[34] Moreover, in the North, there Hindi numerals are also used in gintī forms.[11] So, the gintī tihāī (alreadymentioned above)

/: 1 – 1 2 – 1 2 3 – 1 2 3 4 – :/ _3x

would be recited in Hindi in this way:

/: Ek – Ek Do – Ek Do Tin – Ek Do Tin Char – :/ _3x

[35] In Knee Play 3 from his opera Einstein on the Beach (1976) Philip Glass has the choir sing numerals instead of lyrics over the music; an excerpt is provided as Example 10. It is the same principle as in the previously mentioned gintī tihāī, using English instead of Hindi. Moreover, in this passage the numerals are describing the development of phrases using the additive/divisive principle: phrases of four eighth notes are gradually shortened to three and two eight notes, or combinations thereof, while maintaining the overall harmonic progression. A similar way of working can be found in his other compositions from that time (Two Pages, Music in Twelve Parts, etc.)

Indian Percussion Instruments and their Playing Techniques

[37] Indian drums, such as the tabla, mridangam, and pakhawaj, have a special construction of heads, designed to enhance the harmonic character of their sound. Highly sophisticated finger and wrist techniques allow the player to use the sound capacity of the drum to the maximum extent. These aspects of Indian drumming have no parallel in the tradition of Western classical music; of course, many Western composers have used tabla drums in their work.

[38] However, the next example demonstrates the influence of techniques of Indian percussion on more general writing for the instrumental family. It comes from the 1970‘s, from communist Czechoslovakia, where tablas were unavailable, as were opportunities to study Indian music in general. In his cycle 8 ricercari for percussion (1967), Czech composer Miloslav Kabeláč gave special instructions for the bongo part (Example 11); it is evident that this part was inspired by tabla technique, despite the limited sound possibilities of the bongos in comparison to the heterogeneous pallette of the tabla. In the score, we can see symbols for the different type of strokes applied to different parts of the drum, as well as for the amount of pressure to apply to the skin. There are detailed instructions for stroke technique (using fingertips, side of the finger, all fingers, whole palm), the place of the stroke on the drum (in the middle of the skin, one third of the way from the bottom, or along the edge) or different possibilities of pressure to the skin (light application of the hand, rising or falling pressure on the skin, etc.). At the bottom of the page there is an instruction in Czech which translates as follows: „The muffling can be increased by the movement of the lower part of the palm towards the middle part of the skin. As a result, the pitch of the sound is raised.” This is a clear reference to the technique of the bayan, the lower drum of the tabla pair.

[39] An interesting compostional specialty are the works inspired directly by the genre and form of Hindustani tabla solo (Gottlieb 1993). One of the Indian musicians who visited the North American continent from the 1960s onwards was Pandit Sharda Sahai (1935-2011), an eminent master of the North Indian solo tabla drumming and a major exponent of the Benares gharana (Shepherd 1976).[12]  His students included, among others, Bob Becker (*1947, founding member of the percussion ensemble Nexus and member of Steve Reich and Musicians) and Payton MacDonald (*1974, currently teaching at William Paterson University in New Jersey). Both have mastered the tabla at a high level and are also skilled composers. Among Becker’s works influenced by the repetoire of the Benares gharana, mention should be made of Lahara (1977), Palta (1982) and Mudra (1990). Lahara is virtually a pure transcription of traditional tabla solo forms for the snare drum, while in Mudra the material is arranged for five percussionists, and in Palta the drum kit player takes the solo part instead the tabla.[13] The works of MacDonald most notable in this connection are the four Concertos for Tabla and Percussion Quartet (2002-2013) and the composition Samsara for large wind orchestra. The materials of these pieces are also based on traditional Indian phrases and forms, but the composer creates more elaborate structures from them. In the case of Samsara, MacDonald uses a wide range of orchestral colours, building rich orchestral textures by layering material with different rhythmic subdivisions (quintuplets, septuplets, etc.).

[40] As a suitable example to conclude this survey, we turn to the excellent composition Metal Jacket (2005) for tablaand Indian harmonium by Canadian composer Nicole Lizée (b.1973), in which she makes brilliant use of the rhythmic, technical and sonic (tonal) possibilities of this instrument. The tabla are used here as both rhythmically and melodically. The player has an extended set of drums to work with, with three different sizes of dayan drums tuned to G, A and B joining the single bass bayan. In addition, the glissando technique performed with the hammer applied to the dayan is used to maximum effect.[14]  At one particularly ingenious, satisfying spot, the tabla player uses the technique to play a unison melody with the harmonium.

[41] What principles of Indian rhythm could we trace in this composition? First of all, the opening and closing sections of the piece work with varying phrase lengths. The tabla part is built on the more or less traditional phrase DhaGeNaGete, which is systematically extended, reduced or interleaved with generally shorter measures of two eigth notes; it thus shows a characteristic use of additive and subtractive processes. In addition, the composer later works with the insertion of a pause, which is also systematically extended. We also find a distinctive application of the same material juxtaposed at two different speeds, at the basic eighth pulse and then the triplet.[15] Unlike in Indian traditions, there is no stable tāla over which the phrases are chained; the metre changes continuously in the piece to match the flexible phrase lengths.

[42] Example 12 from the middle section of Metal Jacket features an interesting, rhythmically quite complex tablapattern, again applying additive principles. This phrase forms a kind of gesture that corresponds to the decrescendo progressions in the harmonium. From the original phrase (bar 324) the composer uses only a fragment (bar 327) followed by the original form again. Then, after the same 5/8 fragment (bar 331), Lizée introduces a longer fragment (this time in 3/4 measure with an added sixteenth note value), which is then repeated twice.

Conclusion

[43] As we can see, Indian rhythmic systems have already been inspiring composers for many decades, in different ways and at different levels. This article has attempted to map out, through concrete examples, the various principles of Indian rhythm that can influence and inspire the compositional thinking of music makers. Of course, it could be argued that composers could have come to certain procedures (such as the additive principle, various types of diminution and augmentation, etc.) by their own logical reasoning. However, for the purposes of this paper, those cases have been selected where the influence of Indian rhythmic music is evident, either through a distinct compositional procedure or rhythmic formation referring to a traditional form, or where we have credible information that the composer has studied Indian traditional music and acknowledged that inspiration.

[44] For many music creators, the contact with Indian culture is a rather marginal matter; its resources serve them only as an occasional diversification of the musical language. However, for some composers it represents the primary impetus for reassessment of their rhythmic approach; for these musicians, the encounter stands at the birth of a new, distinctive musical language. The inspirational process itself can take place in different levels, from quoting a traditional form, to using a traditional form in a new and unconventional way, to integrating a traditional approach into one’s own musical language. It would then be possible to talk about syncresis or synthesis, which could be an interesting subject for a more in-depth, specialized study devoted to the influence of these phenomena on the compositional style of a particular composer.

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References

Courtney, David. 2002. A Focus on the Kaidas of Tabla. Houston (Texas): Sur Sangeet Services.

Farrell, Gerry. 1997. Indian Music and the West. Oxford: Clarendon Press.

Strangways, Fox, and Arthur Henry. 1914. The Music of Hindostan. Oxford: Clarendon Press.

Gottlieb, Robert S. 1993. Solo Tabla Drumming of North India: Its Repertoire, Styles, and Performance Practices. Delhi: Motilal Banarsidass Publishers.

Kippen, James. 2020. “Rhythmic Thought and Practice in the Indian Subcontinent.” In The Cambridge Companion to Rhythm, edited by R. Hartenberger & R. McClelland, 241–260. Cambridge: Cambridge University Press.

Kippen, James. 2005. The Tabla of Lucknow: A Cultural Analysis of a Musical Tradition. New Delhi: Manohar.

Kratochvíl, Matěj. 2013. “Philip Glass.” HIS Voice 13(3):24–27.

Rath, Arun. 2015. “The World Music Education of Philip Glass.” Accessed March 3, 2022. https://www.npr.org/transcripts/401246742?t=1646132310178

Lavignac, Albert and Lionel de La Laurencie. 1921. Encyclopédie de la musique et dictionnaire du Conservatoire. Paris: Delagrave.

Lockett, Pete. 2008. Indian Rhythms for Drumset. New York: Hudson Music.

Mertens, Wim, & Michael Nyman. 1988. American Minimal Music. London: Kahn & Averill Publishers.

Messiaen, Olivier. 2001. The Technique of my Musical Language: Text with Musical Examples. Translated by John Satterfield. Paris: Alphonse Leduc.

Messiaen, Olivier. 1998. Treatise on Rhythm, Color, and Ornithology. Volume 1. Translated by Melody Baggech. Oklahoma City: University of Oklahoma.

Nouza, Zdeněk. 2010. Miloslav Kabeláč: Tvůrčí profil skladatele. Praha: Etnologický ústav Akademie věd České republiky.

Nelson, David P. 2008. Solkattu Manual: An Introduction to the Rhythmic Language of South Indian Music. Middletown: Wesleyan University Press.

Reina, Rafael. 2016. Applying Karnatic Rhythmical Techniques to Western Music. London: Taylor and Francis.

Reindl, Tomáš. 2013. Úvod do rytmického systému indické klasické hudby. Bachelor thesis. Praha: Academy of Performing Arts in Prague.

Reindl, Tomáš. 2017. Indický rytmický systém: Zdroj inspirace západních skladatelů. Praha: Academy of Performing Arts in Prague.

Rowell, Lewis. 1992. Music and Musical Thought in Early India. Chicago: University of Chicago Press.

Śarṇgadeva, Nihśanka. 1978. Sangīta-Ratnākara Of Śarngadeva. Delhi: Motilal Banarsidass.

Shepherd, Frances Ann. 1976. Tabla and the Benares Gharana. Dissertation. Middletown (Connecticut): Wesleyan University.

Šimundža, Mirjana. 1988. “Messiaen’s Rhythmical Organisation and Classical Indian Theory of Rhythm.” In International Review of the Aesthetics and Sociology of Music 19(1):53–73.

Tichý, Vladimír, Tomáš Kuhn and Vlastislav Matoušek. 2014. Musical kinetics. Praha: Academy of Performing Arts in Prague.

Van der Walt, Salomé. 2007. Rhythmic Techniques in a Selection of Olivier Messiaen’s Piano Works. Dissertation. Pretoria: University of Pretoria.

Welch, Allison. 1999. “Meetings along the Edge: Svara and Tāla in American Minimal Music.” In American Music 17(2):179–199.

[1]. These are one hundred and twenty rhythmic cycles ranging from one (adi-tala—marked as No. 1 in the list of deśi-tālas) to thirty (simharanadana—No. 35) counts.

[2]. Non-retrograde rhythms (Messiaen’s term) are mirror-symmetrical rhythms. The composer sought a kind of abolition of the perception of time by “reading” non-retrograde rhythms simultaneously from the front and back towards the midpoint, which symbolizes eternity.

[3]. Miloslav Kabeláč (1908–1979) was one of the greatest Czech composers of twentieth century. The main focus of his work is in eight symphonies, but he was also the first Czech composer experimenting with electronic and electroacoustic music in 70’s. At the same time, he was the first Czech composer writing for percussion instruments too. He was also deeply interested in non-European music; his first contact with Indian music was through attending a performance of Uday Shankar’s ensemble in Prague in 1935. It was a breakthrough experience which changed completely his attitude to percussion instruments and at same time it deeply influenced his rhythmical thinking. Later, in the 1960’s, he collaborated with the French ensemble Les Percussions de Strasbourg. He dedicated to them three compositions from which the 8 Inventions for percussion became internationally known; they were later used by the great American choreographer Alvin Ailey for dance performance.

[4]. In the table, the main points of the tāla are indicated with the symbols “+” for sam, “2” and “3” for tālī and “0” for the khālī.

[5]. Jonathan Mayer (*1975) is a London-based composer and sitar player. He is a son of the India-born composer John Mayer (1930 – 2004).

[6]. These subdivisions are called gati in Carnatic music.

[7]. Rāgavardhana rhythm is used here in a modified form; the original version from the deśi tāla list is:

[8]. Ned McGowan (*1970) is an American composer, flute and contrabass flute player based in Amsterdam. In his compositional work, he is fascinated with proportionally intricate rhythms inspired largely by Carnatic techniques.

[9]. Gintī (transl. counting) rhythmic forms are used in the North especially in connection with the kathak dance. They are based on phrases made of different numbers of beats which are recited by numerals during life performance. These phrases are systematically developed and calculated so they fit to the particular tāla.

[10]. See the paragraph 34.

[11]. See paragraph 30 above.

[12]. Sahai lectured at several colleges and universities in the United States and Canada, including Wesleyan, Brown, and the Berklee School of Music; he taught courses in tabla which were attended by a number of professional percussionists, some of whom are also composers.

[13]. Becker’s titles refer directly to features of the tabla repertory. For instance, the term lahara (sometimes also lehara) in North Indian music refers to a melodic loop describing the number of beats of a given rhythmic cycle (tāla), used as an accompaniment to a tabla solo. The term palta refers to a single variation of the solo tabla form kaida, which consists of a theme and a set of variations that may be either learned or improvised.

[14]. This trick is also known to Indian players, but only as a non-traditional effect not used in Indian classical music. It consists of gently placing the tuning metal hammer (held in the left hand) against the black circle (syiahi) of the dayan while the index finger of the right hand plays the open stroke Tun. The closer the face of the mallet moves to the centre of the skin, the higher the sound becomes and inversely, towards the edge of the skin, the pitch of the tone decreases. Thus, by moving the hammer, it is possible (within certain limitations) to intonate, and in addition, the characteristic glissando is created. In this way, notes in the approximate range of a fifth can be played on each drum (depending on its fundamental pitch).

[15]. In traditional Indian music, this phenomenon has a parallel in the tabla form of tripali gat, in which the same phrase undergoes rhythmic modulation from a basic eighth note pulse through a triplet pulse to a sixteenth note pulse. In a panchapali gat composition, the process described has as many as five levels.