I've already told you about the hierarchy of long and short notes used to denote musical rhythm. See fig 1, August '78 issue.

You'll also remember that a 'time signature' is used at the start of most pieces of written music. This tells you what type of beat is being used, and how many of them there are in a bar, eg ³₄ — three crotchets per bar =

The bottom figure tells you the type of beat: 4 = Crotchet, and the top figure indicates how many of these per bar: ³₄ = three (crotchets) per bar.

Similarly, ⁶₈ = six quavers per bar, ⁷₁₆ = seven semiquavers per bar, etc.

When looking at the bottom figure, remember this table:

 2 = MINIM
 4 = CROTCHET
 8 = QUAVER
16 = SEMIQUAVER
32 = DEMISEMIQUAVER
64 = HEMIDEMISEMIQUAVER

and if anyone talks to you about ³³₃₅ time, laugh scornfully at them.

Now to continue; there are two ways of increasing the rhythmic value of notes. The first is by 'tying'. Let's say we wanted to have a note which lasted for five quavers — a semibreve (= eight quavers) is obviously too long to be helpful, but we can take a minim (= four quavers) and add the fifth quaver by tying it on.

Or, if a note which lasted three quavers was needed, we could tie a crotchet (= two quavers) to another quaver.

Ties are very useful in that they can span bar lines:

and by using them to tie together various types of notes, composite notes of any rhythmic value can be indicated.

The other way of increasing note-length is to use a dot. If you add a dot to a note its value is increased by 50%.

The whole 'table' of dotted notes looks like this:

These are especially useful in 3-type time signatures like ³₄, ⁶₈, ¹²₈ and ⁹₈.

[top image above] looks neater and is therefore easier to read than [lower image above].

Dots can be used in conjunction with ties as well:

Unfortunately dots cannot bridge bar lines in the same way as a tie;

is a mathematical impossibility (I hope you can see why!).

Really, rhythm is just a question of maths in many respects. Given a bar of fairly complex rhythmic structure, the best approach is to analyse it mathematically using your knowledge of note-lengths.

is a pretty simple grouping; one long note followed by two shorter ones. Most people can tap out four beats with their foot, and slap their thighs on beats 1, 3 and 4.

looks more intimidating, but can be worked out just as surely. The foot taps out nine quaver beats (not necessarily very fast) and the thigh is slapped on beats 1, 4, 6 and 7. (Remember that the time signature doesn't indicate the tempo, only the type of bar.)

Similarly, if you can hear a rhythm in your mind (or play a rhythm that you like) and want to write it down, try to reduce it to a mathematical formula. Every rhythm has some sort of beat running through it.

Try to play or tap out a series of equal beats and work out on which ones your particular rhythm falls. The foot-and-thigh method is particularly recommended by the author, and calamine preparations will bring fast, soothing relief to thighs badly chapped by a hard day's slapping out ⁶³₆₄ time.

Having glibly dismissed the entire question of musical rhythm as mere mathematics, and thus something which can be perfectly adequately worked out with pocket calculators, I would like to draw your flagging attention to rests. Rests are instructions not to play. Musicians working in West End theatres and night-spots are particularly fond of them, especially the ones that look like this:

Each note has its equivalent rest. A crotchet rest looks like below. When reading a bar like

the first, second and third beats are played, and the fourth is silent. A quaver rest is [see table], a semiquaver rest is [see table]. Here are the rests written alongside their equivalent note:

Rests can be dotted in the same way as notes, and again the dot adds 50% to the value.

So in a bar of ¹²₈, we might see:

The semibreve rest doubles as an all-purpose whole bar's rest, ie

In a piece where the time signature varies a lot, this is convenient, as [top image below] looks much neater than [bottom image below]:

and is much less likely to confuse someone reading a part. For long rests, say 32 bars silence,

to save space. The expression 'tacet' (Latin for 'shut up') is also used to indicate silence, as in 'tacet for 32 bars'.

When writing groups of notes like quavers or semiquavers, the 'tails' are often joined [top image below] rather than [lower image below]:

In a rhythm involving the use of crotchets, the smaller notes will often be joined in 'crotchet groups' ie

This can get more complex:
[first row left] is an abbreviation for [first row right] and
[second row left] is an abbreviation for [second row right]
[third row left] can be written [third row right]

Sometimes rests are included, as in [fourth row left]

Dots can occur, [fourth row right] and [fifth row left].

Joining the tails in this way means that the notes can be seen as a block, and as these blocks correspond to the beat of the bar, it makes reading a little easier.

[top image below] is a lot more manageable than [lower image below]:

Finally, triplets. These are written [first image right] or [second image right] (etc), and signify three notes to be played in the space of two.

[third image right] are three equal notes played in the space of [fourth image right] called a 'crotchet triplet'. A 'minim triplet' is written [fifth image right] and signifies three equal notes played in the space of two minims... and so on.

Occasionally triplets will occur inside a 'crotchet group', eg

Actually these quicker triplets, although they look a bit menacing, are far easier to play than the slow ones. Far harder is to play a slow triplet like

accurately. (Try it and see!)

Remember, if you have any problems understanding any of this, write to me c/o Sound International and I'll try to clarify any problems. Till next month, bonjour.