Rhythm is the arrangement of sounds and silences in time (Wiki).
It is thus the duration aspect of music.
Rhythm notation:   the Meter is necessar to give the basic rhthm but it is not enogh for the description of the full rhythm
A Meter or Time Signature is f ex 3/4.
In this example 3 is the Beat number(or pulse) whereas 4 is the note used to represent one beat.
Beat is regular (there is no surprize) and is the display a pattern of accentuations. F ex in Waltz: 1,2,3  1,2,3  where 1 is accentuated.
On the piano, the beat is usually in the left hand while the melody is in the right hand, the high tone.
But also the melody displays a pattern of rhythm, motifs of rhythm (or “rhytmic figure”) which is recurring.
The full rhythm of the piece is evident only when both hands play it. The Meter is not enough.

But the right and left hand can interchange roles, and cooperate to create a feeling of rhythm.
The right hand often plays oranaments too. The ear has the ability to distinguish the melody from the kakaphony of tones ! if it cant, then the ornaments are just blurring the melody and that is not good music (unless the composer had the purpose to disguise any melody in the sense we understand it as tonal music).
Reading music notes could be difficult if you never heared that piece before,  and the music has lots of ornaments so you may have difficulties to see the melody. In such cases I always want to see the simple melody line, perhaps in a fake book or simplified version.

As an example:  look at time signature 3/4 ; here 1/4 is a beat unit.  1/4 is just a notation for a more convenient unit than the unit note.
Each bar (or meter) contains 3 beats of length 1/4. Thus the length of the bar is 3/4.
We can choose any notation for the unit. Thus, 3/4 or 3/2 or 3/8 are all equivalent !
This is not the case with mathematical fractional notation, i ex 3/4 and 3/2 are not equivalent!

What is a bar (or “measure”) ?
It is already mentioned above: a grouping of a number of beats, in this case 3 beats..
Bars, phrases, sections are divisions in time of the music, what we call “structure”.
The Blues has the structure ABC but AB form a unit, and C a separate unit.
But a melodic phrase is not a atime unit,  is not a rhythm

Syncopation is a general term for a disturbance or interruption of the regular flow of rhythm; a placement of rhythmic stresses or accents where they wouldn’t normally occur (Wikipedia)

  • Mathematics:  A fraction such as 3/4  is interpreted in math as 3 units of “fourths” , where a “fourth” is a name for the unit  just like cm is the name of a unit;  musical time signature shows us exactly this aspect of the fraction symbolism.
    A cm could be named ” a hundredth” but then it would be more abstract since we do not specify an absolute physical unit , i e the meter.
    The “fourth” is the “denominator” and the 3 is the “numerator”. The denominator is not just a name for a unit but also indicates an operation , i e divide the 1 by 4, the 1 is thus another unit,assigned to what we consider “the whole”, i e the “reference” (comparison).  Thus, the number 4 acts both as a name and as on operator!
    This is the meaning of “fraction” . But fractions  are a symbolism in math that goes beyond this interpretation with number of denominator units.
    Fractions is a symbolism that can represent ratios and rates too. And finally, fractions are a symbolism for “rational numbers” but that is another storry…
    This maybe is confusing at first.  It has to do with the basic principle that a unit (or group) can be arbitrarily chosen. We can have many units to play arround with and they are all related to 1, whcih is our reference for numbers.  A number is not absolute, it is relative.  The 1 is not “absolute”, like cm or km.  In math there are no absolute units, but only numbers.  In physics we can talk about km, cm, Celsius etc but not in math.
    Fractional notation is a great symbolism in math because it brings out this relative nature of numbers and has so many applications.Thus, I am thinking of the “fourth” notation as a unit.  The time signature 3/4 means I have 3 such units in a bar (which is represented by 1).
    2/4 = 1/2  means that you can choose different  “unit fractions”  to express the same amount.  The unit fraction could be 1/4 or 1/2 etc
  • The time signature should not confused with tempo.  F ex  4/6 means not a faster melody than 2/3.
    The absolute tempo needs a  to be given by a metronom.
    Notations for tempo in music are  “presto, allegro, allegretto, moderato, andante, largo, grave, adagio” .
    Tempo is measured in Beats Per Minute BMP and  a value is given for a melody f ex 120 means 120 BPM.
    We perceive this as fast since our own heartbeat is about 60-70.  A BMP below this is perceived as slow.
    Compare the Metronome to the Tuning Fork. Both are needed ot give the music absolute values in time resp pitch. Othewise, music is relative.
  • You should not play music with a Metronome on !!  that would make music a mechanical play.
  • Other tempo notations: accelerando, ritardando, rallentando, calando (both diminishing the loudness and tempo)


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