## Some Basic Definitions

 There is an excellent glossary and tutorial on rhythm and meter by Gary Wittlich and his students at the IU School of Music. What do we mean by meter and rhythm? A meter is a temporal framework. In the simplest case it is just a series of identical, equally-spaced `beats' (discussed below). But if more than one period is involved, they are usually temporally nested with their phase zeros aligned to be roughly simultaneous. In this case, one series has twice or three times the number of cycles per second as another. The term rhythm refers either to the metrical patterns themselves (as cases of simple and repetitive rhythms), or to other more complex temporal patterns. These patterns may be longer than a cycle of the meter or less than a cycle in length. But it seems that any such rhythmic pattern (in order even to BE a pattern) is defined with respect to some specific meter. So complicated, less time-symmetric, rhythms are normally definable with respect to a simple rhythm (the meter). Thus a sequence of randomly spaced clicks would not be rhythmic by this definition - because there is by definition no structure whatever. But if you take a short series of such randomly spaced clicks and repeat the same sequence over and over, then it becomes a rhythm due to the presence of a meter produced by the repetition cycle). The point is that the presence of periodicity rhythmic patterns are always definable by a time scale of `phase'. Another aspect of the definition of rhythm is the time scale: rhythm is about structure in time that is close to the scale of human movement. So the shortest temporal intervals that are relevant to this kind of rhythm are about 50 ms, a 20th of a second, and the longest are a few seconds. Of course, there are often temporal structures in our behavior with cycles longer than that, and our auditory perception can deal with cycles much shorter than that (in the auditory range of 20Hz to 20kHz). But the `cognitive time scale' is this intermediate range from about 20 cycles/second to 2 sec (or maybe 10), that we usually call the time scale of the rhythms of speech and music. It happens also to be the approximate time range of repetitive human movements -- from a rapid drum roll (eg, on bongos) or a trill by the tongue (as in Spanish `perro') on the short end, all the way out to the step cycle of a runner or the duration of a smooth swing by the arm at the long end of the range. What do we mean by a beat? A beat is some kind of `recurring identity', the unique event that defines phase 0 of a metrical cycle. It is some event that is (a) salient and (b) keeps happening again and again. For speech, it seems that the most natural (or salient) beats are located near the onsets of vowels. Thus, if you tap a pencil ``in time with'' speech, the taps will tend to locate themselves near vowel onsets. In principle, any feature of the acoustic signal for which there is an automatic extractor can supply the beat, but in practice the beat is closely aligned with vowel onsets. Thus to do research on speech production, we need an automatic method for locating beats objectively. Sometimes it is easy to locate psychologically relevant beats in the physical speech signal, but sometimes not. We use simple signal processing techniques to find syllable onsets (beats) automatically. (See beat extractor page.) Of course, we also choose our text materials so that finding beats is as easy as possible. Measuring time as phase. Measuring time in seconds is not very informative for understanding rhythms. Whenever a meter is established, time can be measured as relative position within the temporal unit defining the pattern. This notion of `relative position within the cycle' is phase. Everyone is familiar with many ways of talking about phase: minutes in an hour (on a clock), beats per measure (in music), degrees in a circle (traditional geometry), radians in a circle, (trigonometry), etc. In this archive, we shall usually talk about phase in the range (0,1) that is, zero to one, but sometimes it may even be in units of `percent'. But all are interchangeable.