Metrical structure

Generally, tonal music rhythm shows isochronous pulsation. It is frequent for listeners to tap on the floor with their foot synchronizing with some isochronous beat that corresponds with some of the pulse patterns of the music. The music which is constituted by perceptible regular beats is called “pulsed music”.

Pulse

A pulse pattern is a succession of events that occur at a regular time lapse, a simple sequence of stimuli equally spaced in time.

Pulse is a generic concept that refers to the different patterns present in pulsed music. Choosing one isochronous distributed pattern arising from a musical fragment is choosing just one among other possible ones.

In western music, when metrical structure has been an organizing element of a musical composition, the structure is recognizable by the listeners. They can identify it by establishing multiplicative relations among different pulses extracted from music.

Metrical Structure and Proportional Rhythm

The distinctive characteristic of proportional rhythm is the use of isochronous pulse patterns related as integral multiples. When 3 or more patterns remain along a musical fragment, they configure a hierarchical organization, like an architectural structure: the metrical structure. Due to its nature, at least 3 different pulse levels are needed to configure it.

Tactus: basic pulse level

Listeners usually select at first those pulse patterns which are neither very close nor much separated in time. Their responses tend to gravitate to the median, being the most prominent those which period is around 100 events per minute. The most prominent pulse of a music event is called “tactus”. It is not necessary for tactus to be explicit all the time in order for it to be perceived, and the priority of one or another pulse level could be conditioned by the tempo of the musical fragment.

Tactus is the basic measure unit to establish relations with the other pulse levels. These inter-relations determine the metrical structure. It is considered basic because it makes it easy to identify the other pulse levels. In musical theory it is denominated “bar beat” o “bar unit” but, due to differences between notation and perception and the diverse meanings in which the word “beat” has been used in western tradition, the concept of “tactus” is preferred for listening.

Subtactus and metrical foot

Besides tactus, proportional music usually presents other brief period patterns. They are tactus sub-units, which several theoretical models call sub-tactus.

In divisive rhythm it is possible to group by 2 or by 3. In traditional music theory, this pattern is known as division (of a beat), or subdivision (of a bar), all of them names related with notation. For listening, the preferred concept is foot, taken from the Greek, because it is considered a concept that refers to groups of sounds in minimum units by 2 or by 3.

The foot is the relation between the tactus and the subtactus. Isolating the subtactus consists in identifying the pulse level immediately lower than the tactus level provided by a piece of music, but abstracting the foot means establishing a relation between these pulses in which one of them subdivides the other into 2 or 3 equal parts, so that the foot could be binary or ternary.

Metre

Another of the perceptible pulse levels is that one immediately above the tactus level, called metre. When it remains along a musical fragment, it is supported by musical discourse characteristics, such as melodic phrasing, melodic segmentation, theme redundancy or harmonic rhythm.

Again, abstracting the metre is not just isolating the supratactus from the information provided by a piece of music, but relating it with the tactus to determine if it is grouped by 2 or by 3 beats. Metre could be binary or ternary too.

Many music examples can provide more pulse levels, either faster or slower, which could be added to the metrical structure at an upper or lower level. For example, the next level up from the metre is called hipermetre.

Generally, pulse levels are represented in dot diagrams. For example, in “Twinkle, Twinkle Little Star” level 1 coincides with the verbal rhythm, except for the end of each verse. Level 2 is the tactus and level 3 is the metre.

References

Cooper, G. & Meyer, L. B. (1960). The rhythmic structure of music. Chicago: University of Chicago Press. (Trad. Silles, T. P. (2000). Barcelona, Idea Books)

Malbrán, S. (2004). El oído de la mente. La Plata: Fundación para la Educación Musical

Parncutt, R. (1987). The perception of pulse in musical rhythm. In: A. Gabrielsson (Ed.). Action and Perception in Rhythm and Music. Nº 55. Sweden: The Royal Swedish Academic of Music.

Parncutt, R. (1994). Pulse salience and metrical accent. Music Perception 11. Nº4, 409 – 464