FOR THE CURIOUS CELLIST

Dotted Rhythms

Dotted rhythms are a curious phenomenon from several different points of view: technical, musical, mathematical, ………… and perhaps even philosophical. What then is the significance of dotted rhythms in the musical language? Which bowings are best and why? Why are they considered “French Style”? Are they always “French Style”? Are there different degrees of dottedness (dottiness)? But we had better start with the ultimate and most basic question: what is a dotted rhythm?

To go directly to some practice material and jump these theoretical discussions, click here:

Study Material for Practicing Dotted Rhythms

DEFINITION OF A DOTTED RHYTHM?

If we try and count how many dotted rhythms there are in a certain piece or movement, we quickly realise that, unfortunately, the definition of what is (and what isn’t) a dotted rhythm is not as simple as we may have initially thought. Let’s start by looking at what is definitely not a dotted rhythm.

WHAT IS NOT A DOTTED RHYTHM

When each pulse of a mini-group of binary or triplet pulses has a newly articulated note on it, then the group is “undotted”.

In the above examples, we could replace any note with its full semiquaver (16th note) subdivision without changing the “un-dotted” nature of the figures. This means that any half-note can be replaced by eight 16th notes, any quarter-note by four 16th notes, and any eighth-note by two 16th notes.

WHAT IS A DOTTED RHYTHM

Prolonging a note over the next pulse in the group, so that we are taken across to the following pulse without a new articulation, is what leads us into the new and wonderful worlds of both dotted rhythms and syncopations.

The above examples are classic, unambiguous dotted rhythms, but the following variants ….. ???

Here we might have a doubt about whether these really are “dotted rhythms” but in fact, these examples are the same as those just above them, with the only difference being that our “short note” has been subdivided into two.

REVERSE DOTTED RHYTHMS

We tend to think of a dotted rhythm as having a small note tucked onto the end of a large note, a little bit like a child following an adult. This is definitely the most common form of dotted rhythms, but sometimes the roles are reversed and it is the child who leads the adult:

THE DIFFERENCE BETWEEN A DOTTED RHYTHM AND A DOTTED BOWING

A dotted rhythm doesn’t necessarily mean a dotted (articulated) bowing. We can have a dotted rhythm in the left hand combined with a totally legato bowstroke:

CREATION OF (SOMEWHAT DILUTED) DOTTED EFFECTS BY THE BOWING EVEN WHEN NOTE VALUES ARE NOT DOTTED

A dotted effect does not have to be purely rhythmic: it can also be created in a passage of constant equal (undotted) rhythmic values by a combination of the asymmetrical melodic line contours reinforced by our bowings (articulations).

CREATION OF VERY DILUTED DOTTED EFFECTS EXCLUSIVELY BY THE MELODIC LINE

In the above example, the melodic line contours were reinforced by our asymmetrical bowing, and the combination of these two mutually reinforcing factors contributed to the creation of the notable dotted effect. An even more diluted dotted rhythm effect occurs when the melodic pattern (contours) of totally undotted notes is played without the reinforcement of the asymmetrical bowings. Even with totally undotted, symmetrical bowings, the melodic line alone can still create a somewhat dotted effect:

DIFFERENT DEGREES OF DOTTINESS

From all the above we can see that a dotted rhythm is not a binary, either-or affair: there are different degrees of dottedness. This concept will be looked at in greater detail further down the page.

THE SIGNIFICANCE OF DOTTED RHYTHMS IN MUSICAL LANGUAGE

The dotted micro-units of two notes (or three notes in compound time) are asymmetrical, lopsided, and unbalanced. Undotted rhythms can be compared to normal walking or running: the pace can be fast or slow but the rhythm of the steps is regular and metronomic. In other words, each step is equidistant from the one before it, each step coincides with a rhythmic pulse, and no pulses are “missing”. In contrast to this, dotted rhythms are the equivalent of skipping, dancing, or (in extreme cases) of Monty Python’s “Silly Walks”.

The simple fact of adding the dot gives a new and instantaneous vigour and interest to the note progression: now one note (the short one) is an upbeat to the next and the rhythm comes alive. Dotted rhythms add interest, expression and tension/release to music. The particular tension and release patterns inherent in dotted rhythms have parallels in human movement: as mentioned above, adding the dot is what we do when we change from running to skipping, from walking to lilting, from marching to dancing.

Undotted rhythms are more mechanical, regular, steady and serious. When we are working hard, we are often “undotted” (participating in a race, or doing “serious” training, for example). When we are fooling around, literally “playing” (or dancing) we are often more dotted. Our english word “dotty” – normally meaning a sort of charming, silly, harmless craziness or eccentricity – is also often a good description of the effect of dotted rhythms. The dot usually gives music more character, most often making it more graceful, playful and delightful. To illustrate this influence of the dot, try playing Fred Wilson’s Hornpipe (Irish folkmusic) to children, firstly without, and then with the dotted rhythm. Normally they will squeal with laughter and delight with the dotted version!

At the beginning of Stravinsky’s Pulcinella ballet music (on which our Suite Italienne is based), the opening theme comes twice. Each appearance is identical, except for one “tiny” dot that is “missing” in the first presentation. Let’s compare the characters of the two forms:

Once again, “what a difference a dot makes”! The dot is what makes this melody truly italian: lively, playful, frisky etc. It seems inconceivable that the young neopolitan Pergolesi could have written this theme without that second dot: it’s just too “square” sounding. But it is easily conceivable that the dot could have been lost accidentally during the transcription process. Certainly, Piatagorsky would seem to have been in agreement with this idea because in the cello transcription that he made with Stravinsky of this piece (Suite Italienne) the theme is dotted both times, unlike in the violin transcription.

At slower speeds, dotted rhythms can give a mannered, courtly, lilting, even teasing character. This is especially so when we wait – to great effect – till the absolute last moment, before playing the short note (see “double-dotting” below). The Allemande from Bach’s 5th Cello Suite illustrates well this type of dotted rhythm. At faster speeds, dotted rhythms usually give a skipping, rollicking, sparkling, sprightly, crisp, playful, dancing character. The first movement of Schubert’s Piano Trio nº 1 in Bb is full of examples of this type of dotted rhythm.

In all of these above cases, the effect of the dotted rhythm is lightening and delightful, but it is not always like that. If we don’t relax the pressure on the long note, then rather than creating a lilting alternation of tension and release, the effect of the dot can be to actually to augment the tension. Playing dotted rhythms in this way, especially at faster speeds, loudly, and when the dotted pattern repeats itself relentlessly, can create great intensity. We can find many examples of this in the driving, intense music of Beethoven, such as in the first movements of both his 7th Symphony and his Quartet in f minor Opus 95. This use of the “intense dot” can be taken even further, to create maniacal, sinister and violent effects such as in the following example by Berlioz:

berliozdottedhammered

“FRENCH STYLE” VERSUS “GERMANIC STYLE”: DOTTED VERSUS UNDOTTED

With the exception of the ultra-intense “Beethovenian” dot mentioned above, dotted rhythms tend to lighten the music, independently of whether the movements are fast or slow. The frequent use of dotted rhythms, especially in Baroque music, is considered “French Style” because of the character it gives to the music: sprightly, capricious, flirting, lightfooted or nervous, impetuous, excitable. When Paul Tortelier used to take his little trade-mark skip up onto the soloist podium, we could also call this an excellent example of a “French dot”.  Undotted rhythms on the other hand, at any speed, have a more steady, predictable character. They can be slow and stately, or sprinting and driven, but are usually more “serious” and therefore referred to (in Baroque music) as “Germanic Style”.

Look at the following table and you can see why Bach’s Fifth Cello Suite is considered to be in the “French Style”. It has more dotted rhythms than all the other suites combined !

FREQUENCY OF DOTTED RHYTHMS IN THE BACH CELLO SUITES

SUITE 1

SUITE 2

SUITE III

SUITE IV

SUITE V

SUITE VI

PRELUDE

0

10 (16)

0

3 (6)

Prelude  44 (52)

Fugue    2

0

ALLEMANDE

18

14

3

0 (1)

78 (82)

33 (45)

COURANTE

3

2 (6)

0 (4)

0 (2)

34

0

SARABANDE

7 (9)

4 (19)

10

43 (44)

0

31 (43)

GALANTERIE I

0 (2)

0 (1)

0

0

0

0

GALANTERIE 2

0

0

0

0

0

0

GIGUE

0

0

0

0

63

0

TOTAL

28

30

13

46

221

64

 

When we try and count exactly how many dotted rhythms there are in a certain piece or movement, we quickly realise that, unfortunately, the definition of what is (and what isn’t) a dotted rhythm is not actually completely precise. This is why in the above table some numbers are in brackets (these numbers include the “doubtful dots”). See below for a further discussion about this subject.

In Bach’s Partitas and Sonatas for Solo Violin, several of the movements also stand out for being extremely dotted: the First Movements of the B minor Partita and the C major Sonata each have more than 100 dotted rhythm figures.

FRENCH STYLE: THE “DOUBLE-DOT”

What really gives a strong  “French style” however is when we decide to “double dot” these dotted rhythms. This is optional, but was in the Baroque period perhaps an automatically assumed way of playing these rhythms, in the same way that we nowadays automatically (hopefully) play “swing” music syncopated, even though is traditionally written out “square”. Thus in some Baroque music we can choose between playing in the German style (as written) or in the French double-dotted style in which the semiquavers (16th notes) are played late and as semidemiquavers (32nd notes) as in the following examples taken from Bach’s Fifth Suite.

Actually, this “double dot” is often not what it says it is. Rather than playing the short note twice as short as written, we often make a compromise which converts the semiquaver (16th note) into a triplet semiquaver (a 24th note?) rather than the ultra-short semidemiquaver (32nd note).

rhythmdbledottriplet

For more examples of this “double dotting” see the article about Bach Cello Suite Nº 5, and especially the discussion about the Gigue.

DEGREE OF DOTTEDNESS

At the beginning of this article, we saw that a rhythmic figure is not just simply “dotted or not dotted”. Not only can there be a certain ambiguity as to whether or not a rhythm is dotted, but also an unambiguously dotted rhythm can be more or less intensely dotted, and any particular musical passage can have a greater or lesser frequency of dotted figures within it. Let’s look now in greater detail at the questions of:

  1. how dotted is any particular dotted figure?
  2. how dotted is any particular passage?

HOW DOTTED IS ANY PARTICULAR DOTTED FIGURE ?

The degree of dottedness of any particular dotted figure depends on the degree of shortness of the short note in relation to the lengths of the long notes The greater this difference, the more intense will be the “dottedness” of the rhythm as the following examples will show. When we “doubledot” we halve the length of the short note, which has the effect of “doubling” the dottedness. In these examples, we progress from only very slightly dotted to extremely dotted. The two rows of music show identical rhythms, just notated differently. The numbers show the relative lengths of the long and short notes.

We could also use one single number to show the relation between the length of the short note and that of the entire dotted figure. For the above progression this would give the following numbers:

1/2.5    1/3     1/4     1/6     1/8    1/12     1/16

Triplet dotted rhythm figures (𝅘𝅥 𝅘𝅥𝅮) are more relaxed (less intensely dotted) than quadruplet (𝅘𝅥. 𝅘𝅥𝅮) figures and we have to be careful in a lot of classical music (in contrast to pop, swing, jazz etc) to “not let our quads become tripe”. Or, in other words, to keep our dotted rhythms crisp and tight (quadrupletised), not letting them relax into laid-back triplets. A  piece to play to work on this potential problem is the Courante from Bachs D minor Partita for solo violin, in which the alternation of triplet quavers with dotted quaver/semiquaver figures is constant.

HOW DOTTED IS ANY PARTICULAR PASSAGE ?

Apart from the degree of dottedness of any particular dotted figure, we can also look at how dotted is any particular passage. This is determined by the frequency of the dotted figures.

TECHNICAL PROBLEMS ASSOCIATED WITH DOTTED RHYTHMS

Non-legato dotted rhythms, especially when they are fast and repeating, can pose significant problems for the bow (bow division) because of their asymmetry. For the left hand, all fast dotted passages, whether legato or non-legato require special attention being given to their fingerings in order to plan as much as possible for the major changes in both left and right hands to occur after the long notes rather than after the short notes. These fingering problems are looked at on the following page:

Fingering Dotted-Rhythm Passages

Let’s look now at the bow division problems.

BOW DIVISION IN NON-SLURRED DOTTED RHYTHMS

1: DUPLET DOTTED FIGURES AND THE NEED FOR “HOOKED” BOWINGS

Because of their unsymmetrical nature, finding a good bowing for duplet (not compound-time) dotted rhythm passages requires a little thought.

If we try to play any extended passage of repeated duplet dotted rhythms simply “as it comes” (using a new bow for each note), we will find two things happening involuntarily:

  • our bow is rapidly propelled to the frog or to the tip and/or
  • we are giving unwanted accents on the short note in order to try and avoid the above effect

These two problems occur because we are making repeatedly several steps in the one direction (usually in the down-bow direction) and only one back in the reverse (up-bow) direction. This means that it is mathematically extremely difficult to stay in the same part of the bow. If we have time to lift our bow off the string before (or after) the short note, then this allows us to retake the bow (bring it back in the air to where we want it) and we can do the bowing “as it comes” without any problems.

It is in those passages with repeated duplet dotted rhythmic figures in which we can’t lift our bow off the string to retake that our problems with bow division occur. Here we need to use “hooked” bowings. With hooked bowings, each pair of dotted figures neutralises each other with respect to bow displacement, and the net effect on the bow position is zero: in other words, we automatically and naturally stay in the same part of the bow. Hooked bowings are traditionally notated by a slur and a dot, but this can be ambiguous sometimes (for example when the short note is connected [legato] to the following note, or in inverted dotted rhythms) so we could also use a dashed-slur to better indicate hooked bowings.

1.1: HAMMERED DUPLETS

A special bowing case is the ricochet “hammered” bowing that we use sometimes to give the crispest ultra-percussive dotted rhythms:

berliozdottedhammered

Whereas a “hooked” bowing would allow the long note to actually sound longer, this hammered ricochet bowing keeps all the notes equally short. There is nothing graceful or playful about a dotted rhythm when played in this manner!

This may seem like a “backwards” bowing – don’t we normally play our short up-beats on an up-bow? Well yes, we do …….. but only when the note after the short upbeat needs to be played longer. In very fast dotted-rhythm passages in which both up and down beats need to be short, this “backwards bowing” allows us to get into an effortless, self-sustaining loop, in which the wrist is making its favourite anti-clockwise circles (which is what helps the bow to bounce effortlessly- see Spiccato). Try the same passage (or the same rhythm on any series of notes) with the opposite bowing and you will see how it suddenly becomes very hard work. Suddenly we are fighting against the natural tendencies of the bow. Now it no longer wants to bounce and, what’s more, it now wants to take us out away from the frog. André Navarra, curiously, preferred these “hard-work-bowings”.

2: COMPOUND-TIME DOTTED FIGURES

The compound-time dotted rhythm figure, however, has exactly the opposite characteristics to the binary version. When played “as it comes” the bow doesn’t gradually work its way out to one end. This is because each pair of figures has a neutral effect on the bow’s position, and thus the bow comes back automatically to where it started. When we do this figure with the hooked bowing however we are taking always several steps in one direction for only one step in the other so it is here, unlike with the duplet hooked bowing, that we are entering into unbalanced territory and need to be careful not to give unwanted accents on the last note of each figure.

hookedbalancedorunbalanced

When played with the hooked bowing and at high speed, the compound dotted figure can easily mutate into an unwanted duplet version

To avoid this mutation, we can either make the supreme effort to play the short note always as late as possible or we can play the bowing “as it comes”.

RIGHT-HAND PRACTICE TIP FOR FAST DOTTED RHYTHMS

It can be helpful to practice fast dotted rhythm passages without their “short notes”. This helps us to reinforce the basic bowing and rhythm of the “main notes”and to keep the little ones “little”.

HOW FAST IS TOO FAST FOR DOTTED RHYTHMS ?

The most intense, concentrated, dotted passages are those in which we have an endlessly repeating, tight quadruplet dotted figures (not compound time or triplet) at top speed. We can do them either hooked or with our down-up bowings (as in the Berlioz example above but much much lighter).