By
Luis Torres Zuleta
© Canticum Novum
Bogota, Colombia 2003

The musical rhythm is the arrangement of the sounds with base in the distinction among those with impulse character, called ARSIS, and those that have character of rest, called THESIS.

This classification starts on the smallest groups of sounds and goes relating them in more and more wide contexts, through different stages of rhythmic synthesis, in a unifier process.

In Gregorian chant the synthesis is carried out by mean of three stages: elementary rhythms, groups and great rhythm.

FIRST STAGE OF THE RHYTHMIC SYNTHESIS

ELEMENTARY RHYTHMS

The first stage of the rhythmic synthesis consists on ordering the simple times, to form elementary rhythms. The simple times are, in the Gregorian metric, the smallest, indivisible measure units, and they are similar, in modern notation, to the value of the quavers when the black note has a movement of medium speed.

In Gregorian chant it is easy to perceive which of these sounds, for their impulse character, are arsis and which, because of being a support point, are thesis of the rhythm.

1. - binary elementary rhythm

2. - ternary elementary rhythm

A. - With a simple time as arsis and two simple times as thesis

B. - With two simple times as arsis and a simple time as thesis

3. - quaternary elementary rhythm.

1. - BINARY ELEMENTARY RHYTHM

The first form of elementary rhythm is the binary elementary rhythm that is composed of a simple time as arsis and a simple time as thesis.

Succession of binary elementary rhythms:

(1)

(2)

2. - TERNARY ELEMENTARY RHYTHM

The second form of elementary rhythm is the ternary elementary rhythm which can be presented in two forms:

A. - ternary elementary Rhythm with a simple time as arsis and two simple times as thesis. There are elementary rhythms whose double thesis is by its own nature, and is given in different forms:

In this case the ternary elementary rhythm maintains, in essence, the same structure of the binary elementary rhythm, but with lengthening of the thesis to twice as much, since the neumes are a development of the same syllable. (3)

	A long note for stroficus.
	A long note for stroficus.
	A long note for a dot.
	A long note for a dot.
	A long note for a pressus.

These rhythms also conserve the structure of the binary elementary rhythms but with a prolongation of the thesis to twice as much, since the long notes are a prolongation of the same syllable.

B. - ternary elementary Rhythm with two simple times as arsis and a simple time as thesis.

The ternary elementary rhythm with two simple times as arsis and a simple time as thesis is given when a simple thetic time is followed by two without vertical episemata that, due to the form of being conjugated the text and the melody, are related rhythmically with the following thesis:

Notice that the arsis notion doesn't imply that it has to be of smaller duration than the thesis neither this has to be of more duration than the arsis (4).

These signs are given in three cases:

A.- When the first sound corresponds to an accented syllable (A) and this sound is high (B)

(A) An accented syllable can be given, either because the main tonic accent of the word relapses in her, or because a counter-accent, that is to say, a secondary accent relapses in her. The counter-accents are back of the main accent with a syllable in between. (5)
(B) LOW Sound is the one that is amid two higher sounds (in absolute form).
or it is after a sound to their same height and followed by one higher (in relative form).
or it is after a higher sound and followed by sound to their same height (in relative form).
HIGH sound is the one that is amid two lower sounds (in absolute form).
or it is higher than the previous sound (in relative form)
or it is higher than the following sound (in relative form).
Indifferent sound is the one that is among sounds to its same height. In the topic that occupies us it is considered to be under. (6)

The reason is that the impulse of an arsis is more connatural with a high sound in an accented syllable (5).

	Tonic accent of a paroxytone word with high sound.
	Tonic accent of a proparoxytone word with high sound.
	Counter accent of a paroxytone word with high sound.
	Counter accent of a proparoxytone word with high sound.
	Tonic accent of a paroxytone word with high sound.
	Counter accent of a proparoxytone word with high sound. NOTICE: The sound is considered high because is higher than the following sound

b. - When the second sound coincides with the accented syllable of a paroxytone word and this sound it is low.

The reason is that the low sound in the accented syllable makes that direct arsis-thesis relationship between the accented syllable and the following one becomes weaken, and rather the syllable previous to that of the accent gains importance (8).

	Tonic accent of paroxytone word, with low sound.
	Counter accent of paroxytone word, with low sound.
	Counter accent of paroxytone word, with low sound.

c. - When the second sound coincides with the accented syllable of a word with accent in the antepenultimate syllable with an even number of syllables, and this sound is high.

The reason is that the accented syllable is absorbed by the high sound of this syllable (9).

Note: If these conditions are not given, the rhythmic form will be similar to those cases mentioned in the letter A.

That is:

	Tonic accent of the paroxytone word, with high sound.
	Tonic accent of the proparoxytone word, with high sound.
	Tonic accent of the proparoxytone word, with high sound. NOTE: The sound is considered high because is higher than the following sound.

The monosyllables, when entering in combination with other words, form with these rhythmic outlines an equivalent to simple words, with base in which can be considered as to be a part of double arsis: (12)

	Group that is equal to a tri syllabic paroxytone word (see letter b).
	Equivalent group to a tetra syllabic paroxytone word, in which the monosyllable makes of Counter accent (see letter a).
	Group that is equal to a penta syllabic paroxytone word (see letter b).
	Equivalent group to a tetra syllabic proparoxytone word (see letter c).
	Equivalent group to a penta syllabic proparoxytone word in which the monosyllable makes of Counter accent (see letter a).
	Equivalent group to an exasyllabic proparoxytone word (see letter c).

	Rhythmic set like a tretra syllabic paroxytone word (see letter a).
	Rhythmic set like a tri syllabic proparoxytone word (see letter a).
	Rhythmic set like an exa syllabic proparoxytone word (see letter c).

C. - QUATERNARY ELEMENTARY RHYTHM

Thesis for distribution

Between two marked simple times with vertical episemata cannot be more than two simple times without episemata, since of having them, it is discovered immediately that there are new implicit elementary rhythms there:

When they are simple times without episemata, like in exposed cases, the distribution form becomes obligatory, since the second of the three simple times is necessarily thetic.

When they appear four or more simple times without vertical episemata, the text can help to define the distribution form, according to the character of the syllables of Latin words.

In Latin, the final syllables of any word are thesis.

This makes that in the words that are accented in the penultimate syllable (paroxytone) the tonic accent (the main of the word) and the counter accents (secondary accents that go back of the main accent with a syllable in between) are arsic syllables, and the non accented syllables are thesis: The opposite happens with the proparoxytone word, since in this plane of elementary rhythms, the syllables of tonic accent and the syllables with Counter accent are thetic syllables:

(14)

The simple thetic time is defined by the thetic syllable of the paroxytone word.

The simple thetic time is defined by the thetic syllable of the paroxytone word.

The simple thetic time is defined by the thetic syllable of the paroxytone word.

The simple thetic time is defined by the thetic syllable of the paroxytone word.

The simple thetic time is defined by the thetic syllable of the paroxytone word.

The simple thetic time is defined by the thetic syllable of the paroxytone word.

The simple thetic time is defined by the thetic syllable of the proparoxytone word.

The simple thetic time is defined by the thetic syllable of the proparoxytone word.

The simple thetic time is defined by the thetic syllable of the proparoxytone word.

The simple thetic time is defined by the thetic syllables of the proparoxytone word and of the paroxytone word.

The simple thetic time is defined by the thetic syllable of the proparoxytone word.

The simple thetic time is defined by the thetic syllable of the proparoxytone word.

The simple thetic time is defined by the thetic syllable of the proparoxytone word.

The simple thetic time is defined by the thetic syllable of the proparoxytone word: (a) final syllable; (b) Counter accent syllable; (c) syllable of tonic accent.

However in multiple cases it is not possible to adjust the distribution form to the rhythm of the words, since the circumstances in that the simple times are presented in connection with the text vary a lot. Therefore, it is equally frequent that the distribution form coincides or not with the rhythm of the words, specially in the case of words accented in the penultimate syllable.

The theses don't relapse in the final syllable of the paroxytone words.

The theses don't relapse in the tonic accent and the final syllable of the paroxytone word.

The theses don't relapse in thetic syllables of the proparoxytone word neither of the paroxytone word.

The theses don't relapse on the thetic syllables of the paroxytone words neither on the proparoxytone word.

(a) The thesis doesn't relapse in the final syllable of the paroxytone word. (b) The thesis is adjusted to the rhythm of the proparoxytone word.

Observe that, in these cases, the form of distribution of the theses has a lot to do with the moment of neume appearance after the succession of independent simple times.

Apart from this, it is the melody with their own rhythm, the one that above all should be taken in mind.

NOTE: In the editions where the examples have been taken of, vertical episemas only appear in those places that imply some difficulty or exceptionality in the determination of the theses. The other places are supposed that the musician knows them sufficiently. Here, however, we point out them all to facilitate the observation and analysis to the maximum.

____________________

(1) Riemann, Hugo. Composición musical, cap. I, par. 3, pág.21. Ed. Labor S.A., Barcelona, 1929.

(2) Riemann, H. Fraseo musical. Parte II, cap. VI, pág. 146. Ed Labor S.A., Barcelona, 1928
Jachino, Carlo. Ritmo Musical, Enciclopedia Italiana. Vol. XXIX, Pág. 460, Nos. 13 y 37.

(3) Riemann, H. Composición musical, cap. I, par. 4, pág. 32. Ed. Labor S.A., Barcelona, 1923.

Riemann, H. Fraseo musical, 2a. parte, cap. IV, págs 107-108. Ed. Labor S.A. Barcelona. 1929.

Martínez Soques, Fernando. Método de canto gregoriano,. pág. 192, Nº 176. Ed. Pedagógica, Barcelona, 1943.

(4) Martínez Soques, Fernando. Op. cit. pág. 149.

(5) Martínez Soques, F. Op. cit. Parte tercera, Cap. XIII, págs. 141 Nº 144.

(6) Martínez Soques, F. Op. cit, págs. 177-180.

(7) Martínez Soques, F. Op. cit, pág. 149.

(8) Martínez Soques, F. Op. cit, pág. 143, Nº 146. B.

(9) Riemann, H. Composición musical, Cap. I, ej. 20, pág. 36; ej. 22, pág 37; ej. 32, pág. 45.
Riemann, H. Fraseo musical, cap. I, pág. 75
Riemann, H. Teoría general de la música, cap. III, págs 129, 130. Ed. Labor S.A., Barcelona, 1945
Jachino, C. Op. cit. pág. 460, Nº 6

(10) Martínez Soques, F. Op. cit, pág. 149, Nº 148..

(11) Martínez Soques, F. Op. cit, pág. 143, Nº 146, B

(12) Martínez Soques, F. Op. cit., Tercera Parte, cap. XII, Nº 140, pág. 137.

(13) Riemann, H. Composición musical, cap I, par.3, pág. 21, Ed. Labor S.A., Barcelona, 1929.

(14) Martínez Soques, F. Op. cit. cap. XIV, pág. 145 ss.

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