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     We have all along been employing the chief principle of musical
     analysis, which is simply to make observations about constituent
     elements of a piece of music. Of course, this may not always be
     such a simple matter, since prior assumptions, misleading appear-
     ances, overlooking some detail, or a whole host of other subtle
     factors may impede the accuracy of our observations.

     Nonetheless, analysis, at its most straightforward level, is a matter
     of making observations, attempting to be as accurate as possible in
     simply and clearly stating what is presented to the senses. At this
     level, one is collecting data. At the same time, we begin to compare
     one datum with another, and in this process analysis-as-observation
     attains a new level. Observation is not only made of constituent parts
     within a whole. We then attempt to comprehend how those parts are
     organized into patterns which constitute the whole.

     Musical analysis is fundamentally an act of pattern recognition. And
     this is seemingly a natural activity of the human brain. The primary
     goal of such activity is to achieve a higher degree of understanding
     of the subject under analysis.

     The chief means by which this greater understanding is achieved
     is through the paying of attention to details. The more detail
     we can take in, while not losing sight of the whole, the closer
     we can be to the inner workings of music. Then as we "map" out
     the patterns which make up the whole, we may arrive at insights
     about how a given piece of music works.  While the map is never
     the territory, the process of mapping, of laying down a template,
     does provide a means for better making our way around the terrain.


     The initial step in analysis is to experience an entire entity. This
     may mean a whole work, as in a multi-movement symphony, a one-movement
     piece, as in a folk or pop song, or even a segment of a larger work
     which has the sense of being more or less complete. Listen to the
     "Ode to Joy" segment of Beethoven's Ninth Symphony, which can be
     extracted from that larger work as an entity onto itself.

     I recommend a simple procedure of diagramming music which begins
     first of all with presenting an image of the whole structure under

     The next step is to "map" the major subdivisions of the whole struc-
     ture. This involves perceiving where the primary inception points are
     in relation to the primary goal areas. The goal areas may be easist to
     perceive in that that are cadences (literally, "to fall"), instants of
     relative repose. There is a sense here of arrival. Quite obviously, the
     strongest cadence is almost inevitably going to be the final notes, the
     goal of the whole piece. In tonal music, this is most certainly going to
     be an arrival on the tonic (I) note or chord. Interior cadences will be
     less strong, though themselves having a distinct sense of arrival. Any
     material following a cadence (and definitely the very first notes), will
     sound like some form of beginning, an inception. Depending on the length
     of the music under investigation, observation of the next level "down"
     from the whole will reveal either sectional division or phrase division.
     In the Beethoven there are 4 distinct cadences (including the final)
     which constitute the largest divisional segments of the whole. <RET>

     Once the areas from inception to goal have been mapped, comparison
     of one section to another will reveal relatedness of material. The
     Beethoven is clearly divided into 4 segments, with the 1st, 2nd, and
     4th segments containing nearly identical material and the 3rd section
     containing material which contrasts with these. A reasonable labelling
     procedure entails associating letters of the alphabet with sections.
     The "Ode to Joy" could thus be described as AA'BA', with the 2nd and
     4th sections indicated with the "prime" mark to represent the slight
     change from the original "A."  And since the 2nd cadence is stronger
     then the first (because of its arrival on the tonic note), the AA'
     section could be considered as a section grouping and labelled as
     a larger "A." The overall form may thus be ABA:

     There is another way of viewing this structure, however. Because
     of the clear balance of measures, the second 8 measures (BA') might
     be grouped as an entity, thus making a two-part structure which
     could conceivably be labelled AA'.  This kind of ambiguity is
     common in making an attempt to pin down the details of patterning.
     The interplay between a sense of 3-part and 2-part organization
     produces an overall asymmetry which may be a factor contributing
     to the effectiveness of this very simple and straightforward piece.

     This kind of structural analysis reveals groupings of events which
     have been traditionally designated as phrases. A musical phrase,
     to quote Douglas Green in his "Form in Tonal Music" may be defined
     as "the shortest passage of music which, having reached a point of
     relative repose, has expressed a more or less complete musical thought."
     The qualifying terms here are very important, for the strength of
     cadences is relative, and the sense of wholeness is relative. This
     is certainly made clear by the Beethoven example. The first cadence
     in measure 4 is not as strong as that in measure 8, and the final
     cadence is the strongest of all.


    Mapping the overall structure of a piece of music provides insights
    into its sense of direction. A proper understanding of phrase struc-
    ture can aid the performer to think ahead to goal areas and to give
    them their proper emphasis. Composers can likewise gain understanding
    of how to shape their own creations to best effect.

    Just as an entire structure can be divided into sub-entities, so may
    those parts be divided. Examination of the details of the very first
    phrase or two may generate further insights into the music's workings.

    There are at least four significant aspects of organization here. The
    first is the coherency of pitch relationship.  All adjacent pitches
    are no more than an interval of a second. In melodies, this deploy-
    ment of pitches is called "conjunct." Conjunct motion is a natural
    outgrowth of vocal music because it is the easiest to remember and
    sing. It contributes to creating unity. Melodic intervals larger than
    a second are called "disjunct," and their use contributes to creating
    variety. We might question the balance of unity versus variety in
    this passage, since there are no disjunct intervals, but further in-
    vestigation uncovers other factors at work which may establish a
    better balance. <RET>

    The second significant aspect of organization here is choice of pitches
    occurring on strong beats versus those falling on weak beats. Those on
    strong beats (beats 1 and 3 in a 4-beat measure) outline the 1st, 3rd
    and 5th notes of a D-major scale. As we'll discuss in the greater detail
    in the chapter on harmony, this is the tonic chord, and it must in some
    way be given emphasis within the first few measures in order to thor-
    oughly establish the key center. That the first 4 measures cadence on
    a pitch not contained within this chord is the chief reason we sense
    a need to hear more. Any pitch other than the tonic is unstable, un-
    resolved, in relation to the tonic. Only the tonic note and the tonic
    chord are wholly stable. <RET>

    The third significant detail here is the specific contour formed by
    the choice of pitches and the overall pitch range formed by this con-
    tour. Most traditional melodies flow upwards and downwards in more or
    less standard patterns. Many begin with the tonic note, ascend some
    distance (often to the 5th or 8va), then return back downwards to
    tonic. Some start with tonic, leap upwards and descend. Some start
    high and move downward. In this instance, the initial pitch is above
    the tonic, there is a movement upwards followed by descent to the
    tonic. Combining elements of contour with intervallic movement from
    pitch to pitch results in a melody's overall range. Here it is an
    interval of a 5th, from the tonic to the 5th scale degree, which
    further reinforces the sense of key orientation. <RET>

    The subtle rhythmic deployment is the fourth important detail. In
    what would otherwise be a dull, plodding rhythm, Beethoven has intro-
    duced two chief factors of variety. The most obvious is the simple shift
    from the straight quarter notes to the dotted-quarter/eighth at the end
    of the phrase. Listen to what a slight but significant difference it would
    make if only quarter notes were used:

    The other factor is the offsetting of the repeated notes, which con-
    tributes to extending the length of time the 1st, 3rd, and 5th are heard
    This also creates a very gentle syncopated effect "across" the bar-line,
    highlights the 5th and the 3rd and thus strengthens the movement to the
    tonic note at the conclusion of the second phrase.


    While we examine these details, we may also observe relationships
    between one little idea and another. Quite clearly, the opening upward
    gesture (F#-G-A) is a unit which in some ways could be considered the
    "cell" from which the rest of the tune grows. The second measure pre-
    sents this cell in reverse order and "straightens out" the repeat,
    thus extending it one note downwards. We could consider this relation-
    ship either a mirror image or a retrograde (backwards). This kind of
    correspondance contributes to unity at the same as as to variety. The
    second measure is a form of varied repetition of the first.

    The 3rd measure re-initiates the same contour at a lower pitch level.
    This is likewise a form of varied repetition, specificically called
    "sequence."  Of course, it doesn't last very long here, otherwise
    we would be carried beyond the tonic note.

    It appears that cellular ideas, 3- or 4-note gestures, grow into
    parts of phrases, and these parts of phrases grow into larger en-
    ties, the phrases themselves. Phrases combine to make sections,
    and sections are joined to form entire works. There is, in fact,
    and entire branch of traditional music theory, form and analysis,
    devoted to studying these relationships and to labelling one part
    in relation to another. And we could continue examining this simple
    tune, making ever new discoveries regarding relationship of parts.
    What, for instance, is the specific relationship of the 3rd phrase
    to the first? We know it is contrasting. Of the most obvious items,
    are the fact that this section contains the only instants or disjunct
    motion, and that it reaches the lowest pitch in the whole of the tune.
    Also it contains the only occurrances of consecutive 8th-notes.  But
    are there factors linking it to the "A" section? Go back to page 3
    and listen again to the whole tune and make your own observations
    about this!


     Princlples of Analysis......................................p. 1

     Divisions of the Whole into Parts...........................p. 3

     Details of Melodic Sharping.................................p. 7

     Cellular Organization.......................................p. 13



     We have previously learned that a musical interval is the difference
     between two frequencies. This difference is expressed in terms of
     the numerical count from one pitch to, another together with a qual- 
     itative designation which enables describing the difference between
     two intervals which have the same count. Thus the interval from C3 
     to G3 is a Perfect 5th. The interval  C3 to E3 is a Major 3rd. And 
     the interval C3 to Eb3 is a Minor Third. Each of these intervals is
     one which we have discussed. We will now learn about others.


     One approach to learning intervals is to think of them in relation
     to a known pattern. The major scale is one such pattern. Its famil-
     iarity makes it useful for learning intervals. Because scale degrees
     are numbered, 1 through 8, the numerical designation of an interval
     from "prime" (or "unison") to "octave" is immediately at hand. In
     relation to the key note, any other scale degree may be labelled
     according to its position in the scale. The second scale degree is
     an interval of a 2nd in relation to 1; the 3rd scale degree is a
     3rd, and so on. In the major scale pattern these intervals have
     the following qualitative designations:

	 "H" = to hear key tone
	 "I" = to hear note within key (no larger than P8)
         "R" = ready to identify
         "N" = next 
         "Alt/F" = to save score to disk
         "+,-" = to advance or reverse pages

     Listen to key tone. Listen to 2nd pitch. Identify with number and
     quality. M for Major (M2,M3,M6,M7). P for Perfect (P1,P4,P5,P8).


     Once the quality of a given interval is known, altering the actual
     number of half-steps contained in the interval while retaining the
     numerical designation transforms the quality. We have previously
     learned, for instance, that a Major 3rd made smaller by a half step 
     (lowering the upper note, or raising the lower note) becomes Minor.

     The intervals just  learned are either Major or  Perfect. Here are 
     the "rules of transformation" involving these intervals:

       -Major intervals made larger by a half-step become Augmented
       -Major intervals made smaller by a half-step become Minor

       -Perfect intervals made larger by a half-step become Augmented
       -Perfect intervals made smaller by a half-step become Diminished

       -Minor intervals made smaller by a half-step become Diminished
       -Diminished intervals made smaller by a half-step become Doubly-
       -Augmented intervals made larger by a half-step become Doubly-

     I like to put these formulas into a simple code, in which ">" (greater
     than) means "made larger" and "<" (less then) means "made smaller."

               M > 1/2 = A
               M < 1/2 = m
               P > 1/2 = A
               P < 1/2 = d
               m < 1/2 = d
               d < 1/2 = dd
               A > 1/2 = AA

     Examining each of the intervals of the major scale with their half-
     step transformations leads to the following qualitative changes:

     This procedure reveals a difficulty we've encountered before: 
     enharmonic equivalents. The interval of an augmented second sounds
     the same as a minor third. How is one to know when to use which, 
     or, if identifying intervals aurally, which is which? As with most
     everything else within the realm of an art which is based upon the 
     manipulation of patterns, the answer is CONTEXT. 

     Understanding a given context requires knowledge of all the partic-
     ulars constituting that context. This is often a life-long pursuit.
     We can, fortunately, learn enough about the particulars early on
     to at least begin understanding the larger context and thus make
     decisions about specific usages, e.g. when an interval should be
     an augmented 2nd versus a minor 3rd.

     We have, in fact, seen this specific choice previously. Let's look
     at it again as an illustration.

     The largest context here is TONALITY.  Within the system of tonality
     there exists a pattern of pitches known as MINOR. There are three
     essential configurations of minor. To maintain the integrity of the
     pattern, the interval between the 1st and 3rd scale degrees in each
     of the three configurations is minor. In one of the configurations,
     namely HARMONIC MINOR, the 7th scale degree is raised from its
     "natural" pitch according to the key signature. This results in
     the interval of an augmented 2nd from the 6th to the 7th scale
     degrees. In the context of tonality and within the context of the
     minor scale, these two intervals are readily distinguished both in
     spelling and in sound. The minor 3rd sounds like a minor 3rd; the
     augmented 2nds sounds like an augmented 2nd, even though if heard
     in isolation each would sound identical to the other.


     The more ways we have of approaching a subject the more prospect
     there may be for understanding it. Another way of learning inter-
     vals is to count half-steps. Taking the intervals examined through
     the process of transformation above, we can construct a chart:

     Half-Steps:  0   1   2   3   4   5   6   7   8   9   10   11   12

     Interval:   P1  m2  M2  m3  M3  P4  A4  P5  m6  M6   m7   M7   P8
                     A1      A2          d5          d7  

     The top row of intervals are the most common. The second row are
     likely enharmonic equivalents. Other possibilities, like d2 as an
     enharmonic equivalent for P1 are rare. We have also exluded from
     this chart any spellings involving doubly-diminished or doubly-
     augmented intervals, which are also uncommon. You should under-
     stand how these may be derived, however.


     Another means of identifying intervals is  to see and hear them in 
     the context of the minor scale. The intervals which are different
     here from the major scale pattern are the minor 3rd, the minor 6th,
     and the minor 7th.

	 "H" = to hear key tone
	 "I" = to hear note within key (no larger than P8)
         "R" = ready to identify
         "N" = next 
         "Alt/F" = to save score to disk
         "+,-" = to advance or reverse pages

     Listen to key tone. Listen to 2nd pitch. Identify with number and
     quality.    M for Major (M2).    P for Perfect (P1,P4,P5,P8). 
     m for minor (m3,m6,m7).


     We have already had some practice in identifying intervals by ear,
     in the context of either the major or minor scale. Another way to
     hear isolated intervals is in association with the interval with
     which a familiar tune begins. Here are some examples:


     "H" = hear interval     "S" = see 2nd note     "R" = ready to identify

         At 1st prompt, enter QUALITY (P,M,m,d,A) and NUMERAL (e.g. P5).
   At 2nd prompt enter 2nd pitch (use bb for Double Flat, ## for Double Sharp)
   ("H" to hear again     "S" to see 2nd pitch on staff or to see name of note)

          "N" = next     Alt/F = save score     F =return to menu



     The word "rhythm"  is derived from a Greek  word meaning "measure, 
     measured motion." In  a general sense, rhythm  is the organization 
     of events into  patterns which are "measurable."  In music, rhythm 
     is the  organization of  time into  patterns of  relative loudness 
     versus relative quite.

     Just as space is made perceivable and measurable by objects differ-
     entiating  one location  from  another, so  time  is perceived  by 
     relationships of events: the heart contracting  and expanding; the 
     sun appearing  overhead or setting; the  sound of a drop  of water 
     falling, then another...and another... Of course, all these events 
     are spatial as well as temporal, and in our associating the two we 
     comprehend the elementary continuum which they form.

     In less formal language, rhythm is the "swing" of things, the flow 
     of events  as they  relate one to  another. Rhythm  is felt  to be 
     generative. It propels events, gives  life to them, stimulates our 
     sense that the elements of life create patterns.  Rhythm occurs at 
     all levels of our experience: the cycles of our lives, our heart's 
     pulse, the hours,  days, weeks, and months into which  we make the 
     divisions of our time; changing seasons; design of flowers, magne-
     tic fields, snowflakes,  galaxies... This may be  why the rhythmic
     patterns of sound in music have such a fundamental effect upon us.
     Musical rhythm is  the articulation of time,  which resonates with
     all the other rhythms we instinctively understand.

               Rhythm, pulse, cycles of the seasons, the days,
               our blood, life and death, questions of why and
               how and what shaped into communal expressions
               danced and sung and pounded out on drums; rhythms
               and sounds and silences and gestures groping for


     The relatively longer versus shorter sounds of words have been
     traditionally represented by    = long and   = short.

      <1> = Enter text. At prompt, write a text no longer than one line
            with a maximum of 20 syllables. <RET>
      <2> = Enter number of syllables in text. <RET>
      <3> = Enter "S" for Short, "L" for long, trying to produce an
            approximation of the rhythm of your text.
      <P> = Play rhythm.

      [You may continue above sequence as many times as you like.]


     In music,  time is  measured by  rhythm, an  articulation of  time
     created by  contrasts in  relative loudness  or intensity  levels.
     These contrasts cause pulses to occur, which may be either regular
     (periodic) or irregular (nonperiodic).

     Pulse is distinguished by difference between emphasis (oomph!) and
     de-emphasis (pah) or any combination of these contrasting events:

     We know that  this computer is not capable  of varying loudnesses,
     so the sense of emphasis and de-emphasis just heard was created by
     varying pitch level.  This reinforces the notion  that we perceive
     rhythmic patterns through differences.

     We are most familiar in traditional  music with regular pulse, the
     articulation of  time into  periodic recurrence  of stress  versus
     nonstress.   But  rhythm  may   also  be  nonperiodic--stress  and
     nonstress occuring irregularly--and much of the beautiful complex-
     ity of primal music, as well as the exciting tensions of twentieth-
     century Western music, is created  by diverging from regularity of
     pulse.  <RETURN>

     Pulse is just what we understand it to be in relation to our heart
     beat:  contraction and  expansion (called  systole and  diastole).
     Pulse is a basic aspect of music which occurs on several levels: a
     piece of music  as a whole is a  kind of pulse in  relation to the
     relative silence  which surrounds it;  there is  usually sectional
     division of structure  within the music which  creates large-scale
     pulses of contrasting intensity; and there is a basic pulsation of
     sound  which we  commonly  refer  to as  the  beat,  which is  the
     ongoing,  second-to-second, propelling  rhythmic  force of  music,
     providing  the basic  sense of  motion through  time essential  to
     Western music.  The beat is  what we clap  our hands or  stamp our
     feet to,  and it  is this  level of  rhythm for  which we  need to
     formulate principles of notation in order to read and compose music.


     1. Beat Groupings

     As has  been stated, rhythm in  music requires the  alternation of
     sound  and  silence, or  relative  change  in loudness  levels.  A
     metronome produces such an alternation. <RET> [any key to stop]

     You have just heard a regular and constantly intense pulse juxta-
     posed with silence.  These pulses are undifferentiated.  But if we
     listen for any length  of time, chances are that we  begin to hear
     them in  groups, most  likely in 2's  or 3's.   Listen again  to a
     series of  beats and hear  how easy it  is to change  from hearing
     them in groups of 2 to groups of three. <RET> [any key to stop]

     It is possible to hear these beats in larger groupings, of course,
     but one must consciously  add the beats up to 4 or  5 or 6.  These
     larger groupings are more likely heard as combinations of 2 or 3.

     Undifferentiated beats  are essentially  as meaningless  to us  as
     eternal silence or  featureless space.  Things seem  to come alive
     only when we perceive change.  So it  is with rhythm.  Just as the
     ear imposes patterns on consistantly  intense beats, so when music
     is composed,  beats are traditionally  organized into  patterns by
     emphasising certain  beats and underplaying  others.  And  just as
     the ear most readily organizes  undifferentiated beats into groups
     of 2 and 3, so does composed  music most readily deploy these beat
     patterns.  Longer  groupings are  possible, but  just as  with the
     imagined groupings, them are most often heard as combinations of 2-
     and/or 3-beat groupings.

     A beat grouping, in the terminology of music, is called a measure.
     In traditional notation, the measure symbol is a vertical line--the
     measure or bar line.  <RET>

     A 2-beat measure is duple, a 3-beat  measure triple, and so on. In
     the heirarchy of rhythmic levels, the measure is the next duration-
     al level up from  the beat (the next longest). In  other words, if
     the first  beat of  a measure is  listened to as  such, it  can be
     heard as  establishing a new pulse  at a longer duration  than the
     beat: <RET>

     If, on every  4th measure, say, the  elements of a piece  of music
     were to combine to emphasize the  first beat of that measure above
     any other  beat, yet another  level would be  established--a pulse
     every 4 measures: <RET>

     This latter  grouping of four measures  could be called  a musical
     phrase.  How  phrases are  grouped determines  the larger  musical
     structure. The  sense of the different  levels on which  rhythm is
     operating is  important for understanding  how patters  of rhythms
     may be built up to shape an entire piece of music, contributing to
     a sense of  forward motion, fullfilling a  listener's expectations
     or thwarting them.


     1. "H"= (H)ear tune which has periodic rhythm. You may listen to
        tune as many times as you wish, using  "H".
     2. "R"= ready to enter the number of beats you perceive per grouping
        (measure). You get only 1 chance here, since your options are so
     3. At the next prompt, enter the number measures in a phrase.
     4. "N"=(N)ext tune - up to 10.
     5. "P"=(P)rior tune

     Beat Divisions

     Careful listening to the tunes in the above exercise will have re-
     vealed a couple additional pieces of information. One is that most
     phrases in common  tunes are either 2 or 4  measures long. Another
     is that what is perceived to be the main beat is sometimes divided
     into shorter sub-pulses.  In fact, the sub-pulse  may occasionally
     be confused with  the beat, depending upon the  tempo (beat rate).
     In slow tempos, the sub-pulse may assume  the role of the beat, in
     the same way that at very fast tempos, the first beat of each meas-
     ure may be heard as the beat. <RET>

     Just as a measure may have, at  its simplest ordering, either 2 or
     3 beats, so a  beat may be divided most simply into  either 2 or 3
     sub-pulses. If  the beat is divided  into 2 equal  sub-pulses, the
     division is  simple; if into 3  equal sub-pulses, the  division is
     compound. <RET>

     By varying combinations  of divisions of the  beat, beats, measure
     lengths, and phrase lengths, a great variety of rhythms is possible.
     In most  traditional music of  the Western European  heritage, the
     phrase length, measure length, and beat length remain fairly con-
     stant, but  even with the  permutations possible at  the sub-pulse
     level, tremendous rhythmic interest can be generated.


     1. "H"= (H)ear tune which has periodic rhythm. You may listen to
        tune as many times as you wish, using  "H".
     2. "R"= ready to enter the perceived divisional value of the beat:
         SIMPLE, or COMPOUND>
     3. "N"=(N)ext tune - up to 10.
     4. "P"=(P)rior tune.

     Non-Periodic Rhythm

	Beats, measures,  and beat  divisions, as  just discussed,  are
     categories of  periodic rhythm, all relating  to a steady  rate of
     pulsation. Non-periodic rhythm has no steady underlying pulse rate
     and therefore  does not require  symbols for measures,  beats, and
     beat division. Or  if these symbols are used, some  factor must be
     added which allows for a changing rate. If a composition is con-
     ceived in which great flexibility of pulse is desired, it is easier
     to accomodate this  with newly designed symbols  and instructions.
     For instance,  an accellerating series  of articulations  might be
     represented by a  "time" line, read from left to  right, with dots
     standing for the articulations. Thus:

	    .    .    .   .   .   .  .  .  . . . . ........

     visually suggests a slow rate gradually getting faster. The inter-
     pretation of this could not be precise,  and it is this very issue
     which underlies non-periodicity. To precisely control non-periodi-
     city requires extraordinary notational as well as performing skill
     and the results, for the most part, are no better than approximat-
     ing the same effect with a less precise system. Hit <RET> to  hear
     interpretation of the above notation.

     Levels of Rhythmic Activity

     The beat is the most basic level rhythmic activity. It is at this
     level that we tap our foot, snap our fingers...dance. Measures (beat
     groupings) are a "higher" or "macro" level of rhythmic organization,
     and beat divisions are "lower" or "micro" level.

     Our perception of the level of rhythmic activity is entirely
     dependent upon our  perception of tempo (the rate of the beat,
     measure in beats per minute). <RET>

     This tune is in 3 beats per measure with simple division. Each note
     heard is a beat length. At this slow tempo, we are likely to start
     hearing the divisional value (half the beat length) as the beat. At
     tempos slower than around 50 bpm, we would not tap our feet to the
     designated beat, but to the division of the beat. <RET>

     The measure at this tempo is clearly heard. At rates anywhere from
     about 60 to 140 bpm, we have no difficulty responding by matching
     toe-tapping to the beat. <RET>

     Now the tempo is fast enough that we hear each beat as a division,
     and we group these into "the beat". Since there were 3 per measure,
     we now hear 3 units per beat and thus have compound division. Note
     that you may now hear 2 of these units per measure.






					     (John Cage)


     Brief Review - Periodic rhythm is organized into measures of 2, 3,
     or more beats. Beats are divided into 2 or 3 sub-pulses. If a beat
     is divided into 2 equal parts, the division is simple. If the beat
     is divided into 3 equal parts, the division is compound.

     Labelling Measures

     Combinations of particular numbers of beats in a measure and how
     each beat is divided determines how measures are labelled. A 2-
     beat measure is called duple; 3-beat measure = triple; 4-beat meas-
     ure = quadruple; 5-beat measure = quintuple, etc.

     REMEMBER: If the basic beat is divided into 2, the beat is simple;
     likewise the measure having simple division of the beat. If the
     basic beat is divided into 3, the beat is compound; likewise the
     measure having compound division of the beat.

     Thus, a measure containing 2 beats (duple), which are divided into
     2 sub-pulses (simple) is labelled duple simple. Duple and quadruple
     measures, either simple or compound, are often difficult to distin-
     guish with the phrase structure of the piece providing the only
     basis upon which to make the distinction.

     A measure containing a given number of beats (2,3,4, etc), each of
     which is divided into 3 sub-pulses would be a duple, triple, quad-
     ruple, etc., compound measure.  Compound meter will be discussed
     at greater length later.


     Notation of the Beat
      Its Division and Subdivision
       The Time Signature

     A system of noteheads, stems, flags and beams, has been standard-
     ized to notate rhythm. These symbols are used to indicate relative
     duration of tones. Any one of  these may represent the basic pulse
     or beat,  depending upon  the time  signature, which  is discussed
     below.  The notehead  most commonly  associated with  the beat  in
     simple-division measures is called a quarter note:

     "H" to  hear above tune. Observe,  by listening, that  the quarter
     note does indeed represent each basic  pulse (at the given tempo).
     There is also  a regularly occuring accent every  2 quarter notes,
     and  thus a  measure (or  bar) line  is drawn  to distinguish  one
     grouping from another. The true meaning  of the measure line is to
     indicate where  a point of natural  stress occurs. The  numbers at
     the beginning of  the tune comprise the time  signature. In simple
     division measures, the upper number  indicates the number of beats
     per measure,  while the lower number  represents the kind  of note
     designated as the symbol for the beat, in this case a quarter note.
     (Please note that the time signature  is not  a fraction; there is
     no divider line  which would indicate that the upper  number is to
     be divided  by the  lower number, although  the lower  number does
     represent a fractional durational value).


     H=Hear (to hear example)       P=Prior (prior example)
     N=Next (next example           R=Ready (to input information)
     + = Next page, as usual        - = Previous page, as usual

     Use above keystrokes to hear examples (5) and answer questions.
     Note that some of the tunes do not begin on the first beat of a
     measure, but with a pickup beat (anacrusis, or upbeat); the pickup
     is unstressed and has the effect  of leading into a stressed beat,
     as in the sentence "Oh I've been workin' on the Rail Road..."

			      "down" beat - 1st of measure

     The quarter note is normally divided into two equal sub-pulses:

     The note with the single flag  is an eighth-note. The quarter note
     thus has  a simple  division, and  so the  above tunes  are either
     duple simple, triple  simple, etc., depending on  how many quarter
     notes (beats) there  are in the measure.  The further sub-division
     of the quarter note is indicated below.

     (Note: the  beam joins two or  more flagged notes together  into a
     unit; as a  general rule, it is  a good idea to  beam all possible
     single-beat units, so that they are perceived as a unit; sometimes
     4 eighth-notes are beamed together as a 2-beat unit, and sometimes
     8 sixteenth-notes).

     Most tunes,  including ones  above, do  not have  articulations on
     every beat. There are inevitably times  when one wishes to sustain
     a tone for longer than a quarter note (or a single beat). The quar-
     ter note  bears the same  relations to longer-duration  notes that
     division of the quarter note bears  to it. Two quarter notes equal
     a half-note; two half-notes equal a whole-note, etc., as shown below.

     You've probably noticed by now that  in several of the tunes cited
     as examples,  not all  of the notes  bear the  standard durational
     relationship of 1:2 (quarter to eighth, eighth to sixteenth, etc),
     but rather  have a  1:1.5 ratio,  and that  these notes  have dots
     after them. The dot following a notehead lengthens the duration of
     the note being  dotted by half again  as much. Put more  simply, a
     dot lengthens a note by half the length of the note being dotted.
     A new symbol,  the tie, is employed in the  following examples. It
     joins notes together as single durations.


     For every notehead value that may  exist, there is a corresponding
     rest value (no sound).  These are exhibited below.

     Dots are added to rests in the same way as they are to noteheads,
     to lengthen the duration of the rest by half the time of the rest

     Writing and Reading Rhythms

     Whatever the durational values of notes or rests may be, they must
     add up  to the number of  beats designated by the  time signature.
     Among  the very  first things  that needs  to be  dealt with  when
     deploying rhythm is thus to make  sure there are the proper number
     of durations in  each measure. A second "rule  of thumb" regarding
     rhythmic notation is  to try, in the notation, to  show where each
     beat is. In 4-beat measures, another level of organization may be
     perceived: 2-beat  units. These issues  will become clearer  as we

     As with any aspect of music, intellectual comprehension of funda-
     mentals is not the same as performance, "doing" the music, either
     composing or performing. Performance necessitates a body/mind co-
     ordination that  demands practice. While  some people may  have an
     inate sense of  rhythm, anyone, with practice, can  improve her or
     his rhythmic skills. Also, the reciprocal processes of writing and
     reading rhythms within the traditional system demands experience.

     The main issue in  both the notating and reading of  rhythms is to
     determine where the beat is, and to feel this beat in an internal-
     ized physical and consistent way. The  biggest problem I have seen
     in working with students as composers is that few have approached
     understanding  rhythm in  a disciplined  enough way  to achieve  a
     sense of  feeling accurately  the rhythms  they are  imagining. So
     when it comes to writing their  pieces, rhythmic notation is often
     sloppy. This applies also to beginning music students who perhaps
     respond instinctively  to rhythm,  but who have  not had  to think
     much about what they are actually  responding to. Because of this,
     I generally  recommend the  use of a  metronome when  learning and
     practicing rhythms, to assure consistency. Flexibility, that marv-
     elous ability to bend and shape music spontaneously and individu-
     ally, can come after one has acquired skill in maintaining rhythms

     The first premise in writing and reading rhythms is: feel the beat
     consistently. Then: sense the beat groupings, the number of beats
     that may comprise a measure. Next: sense the divisions and subdi-
     visions of the beat. And always remember: keep everything regular
     (a consistent,  periodic beat).  It is much  better to  start very
     slowly,  maintaining  accuracy  and relative  proportion  of  note
     values, than  to attempt to do  something too quickly  and thereby
     continually alter the duration of the given beat.

     In notating rhythms, to state it  from a slightly different angle,
     the prinicple is:  make absolutely clear where each  beat is. This
     is done by  grouping rhythms by beats, and with  a few exceptions,
     this means in  such a way that  each single beat and  its division
     and subdivision units are readily seen.


     Listen to the  following  examples (5), with  particular attention
     directed to the number of beats per measure and the beat division.

     You will observe above standard 2 and 4-beat measures with more or
     less obvious tripartate beat division. These tunes are thus in com-
     pound meters.  Because the notehead  value designated as  the beat
     needs to be divided into 3,  compound meters use dotted values for
     the  beat.  And because  a  dotted  note  is  the beat,  the  time
     signature itself cannot state directly the true number of beats in
     the measure.

     The most common notehead value for a  beat in compound time is the
     dotted  quarter. A  two-beat measure  would contain  two of  these
     units; a four-beat measure four of them, and so on. But convention
     doesn't allow us to notate this thusly:

     While this might be logical, the  given system rather calls for us
     to notate compound division meters as  if they have three times as
     many beats, with the upper number  thus representing the number of
     divisions in a measure and the lower number indicating the kind of
     durational value  which represents  the division  rather than  the
     beat. A two-beat compound-division meter, using the dotted quarter
     as the beat, is thus, as represented  in the common folk tune "The
     Irish Washerwoman:"

     Because the tempo  is sufficiently fast here,  rather than hearing
     each eighth-note as a beat, we  hear the eighth-notes grouped into
     threes.  All  compound  division  meters   have  an  upper  number
     divisible by 3 (except 3 itself, which is usually grouped with the
     simple-division meters).  Dividing the upper  number by  3 reveals
     the number of  beats in the measure,  while adding 3 of  the lower
     number values together reveals the notehead value of the beat.

     The relationship of the dotted quarter to its division and subdi-
     vision is as follows:

     Note that the subdivision of a compound beat traditionally divides
     the division into 2, not 3.

     The relation  of the  dotted quarter to  larger duration  notes in
     compound meters is:


     H=Hear    N=Next    P=Prior   R=Ready    A=Answer    +,- per usual

          H.= dotted half      Q.= dotted quarter    Q= quarter
            E.= dotted eighth     E= eighth      S = sixteenth

     Listen to example. When ready, hit "R" and enter durational values.
         (4-beat pattern is preceded by 4 beats to establish tempo).


     If rhythmic structures contain sub-pulses that are half the length
     of the beat,  the meter is simple;  if the sub-pulses are  a third
     the length  of the beat,  the meter  is compound. For  variety, in
     simple-division  meters one  may  occasionally  employ a  compound
     division unit, and vice-versa.  This  is technically considered to
     be a "borrowing" of the common division from the "opposite" config-
     uration, simple/compound. Such borrowings must be specially marked.

     When  in a  simple-division  meter,  the compound  "borrowing"  is
     called a triplet. The comparable unit in a compound-division meter
     is a duplet.



     With sharps and flats (accidentals), it  is possible to notate all
     twelve distinct half-step increments within the octave. To do this
     however, it  is necessary to know  that basic notes on  the 5-line
     staff are not all equi-distant from one  to the next. If there are
     only 7 basic  notes, it is obvious that the  distance between some
     of these adjacent pitches must be more than a half-step. The dis-
     tance from one frequency (pitch) to another is known as an inter-
     val. The half-step  is the smallest interval  in twelve-tone equal
     temperament. By  custom, only  two adjacent  pairs of  pitches are
     separated by an interval of a half-step. These are the intervals E
     to F, and B to C, in whatever octave range they appear:

     Two half-steps comprise a whole step. All of the basic-note inter-
     vals of adjacent pitches, except those mentioned above (E to F and
     B to C) are whole-steps.

     The way  a note appears on  the staff ("basic," with  sharp, flat,
     natural, etc)  is its  spelling. Given  twelve pitches  within the
     octave, and the flexibility of applying accidentals to basic notes,
     it's readily apparent that the same pitch can be spelled in differ-
     ent ways. For instance, D-sharp and E-flat are the same frequency,
     but  are spelled  differently. The  reason  for these  alternative
     spellings will become clear in later discussion of pitch patterns.
     Tones which sound  the same but which are  spelled differently are
     enharmonic equivalents.

     The Chromatic Scale

     When all  12 notes within  an octave are  sounded as a  scale, the
     distance between each adjacent note is a half-step. This scale has
     the name chromatic, in analogy to  the word chroma, meaning color.
     In spelling an ascending chromatic scale, it is customary to spell
     the appropriate half-steps with sharps:

     Conversely, a descending chromatic scale is spelled with flats:

     Half-steps  which result  from accidentalizing  a  basic note  are
     chromatic  half-steps. Do  not confuse  this  term with  chromatic
     scale.  Chromatic half-steps  may occur  within  a melody  without
     being part of a chromatic scale. <RET>

     Half-steps that are chromatic involve no  change of line or space.
     If adjacent half-steps are from a line  to a space,or from a space
     to a line, they are diatonic: <RET>


     The screen below displays the basic note pattern for the major scale.
     The pattern is WWHWWWH. Your assignment is to construct this same
     pattern beginning at each successively higher basic note.

     N = next pattern to enter. Beginning pitch is shown.
     P = prior pattern.
     R = ready to enter. At prompt, enter each note name, with necessary
         # or b (lower case B). Leave no spaces and enter in either
         lower or upper case. 3 chances allowed on each pattern.
     H = hear notes.
     S = see answer.


     The  previous exercise  introduced  you to  a  pattern of  pitches
     referred to  as a  scale (from scala,  "ladder"). We've  all heard
     scales practiced by budding musicians and know how tedious, boring
     and unmusical they  are. While practicing scales  on an instrument
     is a  useful means of  acquiring technical proficiency,  we rarely
     hear scales as componants of actual pieces of music. From the point
     of view  of analysing  music, scales  are abstracted  "pitch sets"
     which help us to better understand pitch organization.

     For the past 400 or so  years, composers working within traditions
     developed in Western Europe have focused upon a means of organizing
     pitch materials  known as  "tonality." The  fundamental notion  of
     tonality is  that within any given  piece, there is a  single tone
     which functions as  a kind of center of gravity.  This single tone
     is called  the TONIC. The other  pitches (within the  framework of
     the 12 pitches of equal temperament)  all have a tendency to sound
     unstable (up in the air?) in relation to this tone.

     Tonality is an issue we will  continue to examine. For the moment,
     however, we'll look at it in the context of some particular scalar
     patterns. Look  at and  listen to  the following  tune, the  first
     segment of the familiar "classic," Somewhere Over the Rainbow.

     Given the conditioning  we've experienced by way  of hearing tunes
     in the  tonal system,  you should have  no difficulty  hearing the
     beginning pitch, C, and especially the same pitch used at the end,
     as the  "center of gravity" among  all the other pitches.  This is
     the tonic note,  one which I sometimes refer to  as the generating
     tone. If we write this pitch down  on a staff  and then deploy the
     other pitches in ascending order 'til we reach the octave, we have
     the pitch set from which this piece is made. This is, as you know,
     a scale.

     This particular pitch set should sound  (and look) familiar. It is
     one of the most common pitch sets of tonal music, known as a MAJOR
     SCALE. The whole-step, half-step pattern, in ascending order, is:


     In the first window, you can  cycle through 5 examples of sections
     from common tunes  which use major pitch sets. You  can hear these
     tunes by hitting "H", cycle through them by hitting "N" (for next)
     and "P" (for prior). Use the Up/Dn  Arrows to set the cursor on the
     line or space  (in the second window)  of the pitch you  deduce is
     the tonic  note in the  given example. Hit <ENTER> when ready...

     If you  are  right, the  rest of  the pitches will appear in
     ascending order  to form a  scale. Examine this scale to determine
     indeed,  consists of  the correct pattern for MAJOR. If you're not
     right, you get one  more chance before being given the answer.


     Understanding  scale patterns  can be  enhanced  by a  preliminary
     expansion of  knowledge of  intervals. A  musical interval  is the
     frequency difference between one pitch and another. In traditional
     terms, this  difference is expressed  as the numerical  count from
     one  letter-name to  another, including  the  starting and  ending
     letter-names in  the count. Thus,  the interval from  C to D  is a
     2nd, C to E  a third, and so on. And since  the same frequency may
     be spelled in more than one way (enharmonic equivalents), there re-
     sults different varieties of  the same numerically-named interval.
     The interval C to  E is, numerically, a 3rd. So  is the interval C
     to  E-flat. The  former contains  4 half-steps,  while the  latter
     consists of only 3 half-steps. C to E  is a MAJOR 3RD. C to E-flat
     is a MINOR 3RD. The interval C to D is a 2nd. So is the interval C
     to D-sharp. C to D contains 2 half-steps (thus a whole-step); C to
     D-sharp is 3 half-steps.  C to D is a MAJOR 2ND.   C to D-sharp is
     an AUGMENTED 2ND. This latter interval  sounds exactly the same as
     a minor 3rd, but is spelled  differently. Thus these two intervals
     are enharmonically equivalent.

     A musical  interval has  two designations.  One is  numerical. The
     other  is  qualitative.  We will  discuss  these  designations  in
     greater detail later. For now, there is one interval in particular
     which is most  helpful in further understanding scales.  It is the
     PERFECT 5TH. The interval from the first scale degree in the major
     scale we have been considering (the TONIC, or generating tone) and
     the 5th scale degree (called the DOMINANT), is, numerically, a 5th.
     This can be readily deduced in the C-Major scale, for instance, by
     counting C-D-E-F-G, a count of 5.  IN ANY MAJOR SCALE, THE QUALITY
     PERFECT. The perfect 5th contains 7 half-steps.

     The perfect 5th is a useful interval for examining certain relation-
     ships among scale patterns. These relationships are the fundamental
     building-blocks of  tonality: KEYS.  Any tonal  piece of  music is
     said  to be  in a  particular  key. The  key  is the  name of  the
     generating tone. For example, if a tune's tonic note is C, and the
     pitch pattern is Major,  the key is C-Major. As we  have seen, the
     key of C-Major needs neither sharps nor flats. It is the "basic-note"
     pattern for the major scale.

     In EXERCISE  1 you "built"  a major  scale beginning on  the basic
     note G.  You would  have determined  that this  scale necessitated
     raising  the  F a  half-step  (F#)  to replicate  the  major-scale
     pattern. You also  made a major scale beginning on  D. The D-Major
     scale uses  both an  F# and  a C#.  Now you  can begin  seeing the
     pattern in which sharps are added. If you "project" upwards by the
     interval of  a perfect 5th you  arrive at the next  "sharped" key.
     Each successively arrived  at key adds a sharp, and  that sharp is
     added to  the 7th scale degree.  This pattern forms the  basis for
     what is  known as the CIRCLE  OF 5THS, a commonly-used  device for
     learning key relationships.

     We do run into a problem in this circle of 5ths. Any keys beyond 7
     sharps need double-sharps. This is  very cumbersome. The remedy is
     to respell a key using flats. This usually is done when the use of
     6 sharps is  reached (F#-Major) because the  respelling produces a
     key with 6 flats (Gb-Major):

     Now, if  we continue on with  the circle of 5ths,  spelling scales
     with flats, we note that adding a sharp to the 7th scale degree is
     equivalent to  elliminating a flat.  The circle is  completed when
     all flats are gone, and the key of C-Major is reached.

     Another way to approach the keys  which employ flats is to project
     downwards by perfect 5ths. From the  key of C-Major, the next key,
     with one flat, is  F-Major. You spelled this as the  only scale in
     EXERCISE 2 with a flat. To  make the correct whole-step, half-step
     pattern for major beginning  on F, the 4th scale degree  has to be
     flatted. F-Major  therefore has one flat,  Bb. A perfect  5th down
     from  F is  Bb. The  new flat  added is  Eb. The  counterclockwise
     series in the circle of 5ths adds flats:


     If a  piece of music  is tonal and  therefore cast within  any one
     given key,  it will consistently use  a given number of  sharps or
     flats.  Rather than  employing accidentals,  having  to write  the
     sharp or flat every time it is called for, the sharps or flats are
     written at the beginning of each staff line as a key signature.

     The placement of the sharps or flats follows a consistent pattern:

       Enter signature for given major key.
       ARROW KEYS = move cursor to proper location
          # (or 3)=SHARP     b (or B)=FLAT     E=ERASE (reverse order)
          ENTER = when you think you have proper signature
          M=more (continue as long as you wish)
          Alt/F = to store score to disk      +,- = next or prior page


     Examine the following tune to determine its key tone:

     All of the clues discussed with regard  to the major scale lead to
     the conclusion that this tune's tonic note is A. Deployment of the
     other pitches  to generate a  scale produces a  basic-note pattern
     with a different configuration from major: WHWWHWW.

     This pattern is, in the system of tonality, the complement to major:
     MINOR. The most crucial difference between the two patterns is the
     quality of  the 3rd scale degree.  The interval between  the tonic
     note and the 3rd in major contains 4 half-steps and is referred to
     as a  Major 3rd.  The distance  from the  tonic to  the 3rd  scale
     degree in minor  consists of only 3 half-steps and  its quality is
     labelled minor.

     There are traditional learned associations  with the difference in
     quality between  these two patterns.  Major scales, keys,  and the
     major 3rd  are "bright,"  "cheerful," "open,"  "up-lifting." Minor
     scales, keys, and the minor  3rd are "sad," "poignant," "doleful,"
     "closed." Whatever  associations you may  have, the  difference in
     sound is distinct. If you perceive sounds in terms of colors (syn-
     esthesia: one type  of stimulus producing a  secondary sensation),
     you  may even  "see" different  colors in  association with  major
     versus minor.

     Transposition of  the minor scale pattern  via the circle  of 5ths
     reveals the respective key signatures for minor. At the same time,
     another method  for deriving minor  signatures is exhibited.  If C
     major has  no sharps  or flats  in its  signature and  A minor  is
     similarly disposed, C  major and A minor have  the same signature.
     Since A is  the 6th scale degree  of C major, you  can deduce that
     every major  key has a related  minor which shares  its signature,
     found on its 6th  scale degree. This is a common  way for learning
     minor keys, in association with  major. Cycling through the circle
     of 5ths  corroborates this relationship. Note  that it is  now the
     2nd scale degree which is raised  in each successive scale, rather
     than the 7th.

     Again, we encounter the problem of needing to use double sharps if we
     were to continue with the above process. Conversion to flats when
     6 sharps are reached will result in the enharmonically equivalent
     scale of Eb minor.


     Minor key signatures have the same patern as major. Hit "B" (b) to
     see the flat keys, "#" to toggle to sharp keys.

       Enter signature for given minor key.
       ARROW KEYS = move cursor to proper location
       #(or 3)=SHARP      b(or B)=FLAT      E=ERASE (reverse order)
       ENTER = when you think you have proper signature
       M = more (continue as long as you wish)
       Alt/F = to store score to disk        +,- = next or prior page


     Here's  an English  folk song  which  is clearly  in minor.  Note,
     however, the use of accidentals.

     For reasons having to do with the  sense of direction of a melodic
     line and underlying harmonic implications, strict adherence to the
     notes called for  by the signature of  a minor key is  rare. There
     are two  common variants of the  minor scale pattern.  The example
     above refers to both.

     If a tune is  in minor and the melodic contour  contains a segment
     which ascends  up through  the 6th  and 7th  scale degrees  to the
     tonic note,  it is common  for these pitches  to be raised  a half
     step. If the  melodic contour, however, is  descending through the
     7th to the 6th and on downwards, it is standard practice for these
     pitches  to be  in  their "key  signature"  positions. "The  Three
     Ravens"  has a  measure  demonstrating the  latter,  and the  last
     measure exhibits the  trait of the 7th raised a  half-step to lead
     to the tonic.

     The  scale abstracted  from  this pattern  is  called the  melodic
     minor. As a scale  pattern, it raises the 6th and  7th a half-step
     from "key signature" position when  ascending, while lowering them
     back down to "correct" spelling when descending.

     Very  few melodies  actually appear  having the  exact pattern  of
     ascending 6th-7th-tonic, then tonic-7th-6th, but a variety of uses
     could  be construed  as  fitting the  basic  framework of  melodic
     minor. Even  without this  specific pattern,  however, unless  the
     melody is a direct linear descent through  the 7th to the 6th, the
     7th scale degree is nearly always  raised, especially if this note
     is  going  to be  harmonized  by  the  Dominant triad  (the  chord
     constructed from  the 5th scale degree  of the given  key) because
     this chord sounds best (in the system of tonality) if it is Major.
     In a minor key, the dominant  triad would "naturally" be minor, so
     its "third" needs to be raised a half-step to make the major chord.
     The "third" of the  Dominant triad is the 7th scale  degree of the
     given key.

     Abstracting from a minor key the pitch set which uses a raised 7th
     results in the  scale pattern called harmonic  minor. This pattern
     is  the same  ascending as  descending,  with a  7th scale  degree
     raised a half-step.  As you can hear, this scale  has a distinctly
     Eastern European  "flavor," which results  from the  augmented 2nd
     interval  between the  6th  and 7th  scale  degrees.  As a  strict
     melodic  contour, this  is not  common to  most traditional  minor
     tunes. In  this instance,  one can understand  directly how  it is
     that a scale pattern is an abstraction.

     There are,  then, three common variants  of minor pitch  sets. The
     one based upon  the key signature, without  accidentals, is called
     natural minor. It is the "model"  scale from which the melodic and
     harmonic minor are derived.


     "P"= play scale.   "M"= more.   Alt/F= save score.
     "R"= ready to identify quality. At prompt, enter MAJOR, NATURAL, MELODIC,
        or HARMONIC (upper or lower case). At 2nd prompt, spell scale in
        ascending and descending order, USING CAPS with no spaces
        (e.g. ABCDEF#G#A-AGnFnEDCBA for "A Melodic Minor" - note hyphen
        between up/down and lower-case N for "natural"). "##" for double sharp.
     "M"= more.  Alt/F= save score.

Directory of PC-SIG Library Disk #3471

 Volume in drive A has no label
 Directory of A:\

RHYTHM   MNU      1312   7-07-89   8:07a
RHYTHM   TBC     89148   2-17-90   9:11p
RHYTHM   TXT     25490   1-22-90   3:54p
SCALES   MNU       973   8-17-89  11:37a
SCALES   TBC     94799   3-31-90   4:08p
SCALES   TXT     18193  10-03-89   4:04p
INTERVAL MNU       679   7-10-89  10:37a
INTERVAL TBC     51253   1-22-90   1:40a
INTERVAL TXT      7531   7-10-89  10:13a
ANALYSIS TBC     30451   1-22-90   7:38p
ANALYSIS TXT     12013   7-10-89   5:24p
       11 file(s)     331842 bytes
                       25600 bytes free