Tempo and Rhythm in Cassandra’s Dream Song

In previous posts on Ferneyhough’s music, I describe my approach to his complex rhythms. It is worth noting again that his music is not pulse based; rather, the measure is considered a “domain of a certain energy quotient”.

In Cassandra’s Dream Song we are presented with freedom from measures, time signatures, or metronome markings. The Italian indications often refer to character more than actual speed: lento analitico, grazioso e rubato, molto rigoroso. So how fast do we play it? I can give no answers, but hopefully my ideas can give a clue as to what may work for you.

If you carefully sketch the rhythm of a passage, the spatial relationships become apparent. Here is a very old sketch I did of line 6. I attempted to make measures out of the gestures – an idea I later abandoned in favor of pure spatiality:

Rhythmic sketch line 6

Old rhythmic sketch line 6

Personally, I find this line is often performed too fast. I am guilty of this as well. Who doesn’t get excited by those closely-written, many-beamed tuplets at the end? But if you look carefully, I believe there is a compositional reason for those multi-beams. The beginning of the line has a sort of quarter-note feel to it. Under the first heavy arrow (indicating ritardando),  the eigth-note becomes the rhythmical basis of movement (see, I try to avoid the word “pulse”, but maybe I am being too pedantic). By the A-natural things have slowed way down: lento molto con forza! (Composer’s exclamation point). That is one very long note, relatively speaking. By this time, like a compositional microscope, the rhythmical basis has magnified to the level of the 16th note. And then there is another ritardando! (The heavy arrow). It is as if we are being drawn even further through the lens of this microscope, experiencing progressively smaller units of the beat as time proceeds. Finally, we come down to the “atomic” level of the piece. It is an amazing ending.

After analyzing several lines like this, I abandoned the idea of imposing measures and transferred  the sketches to graph paper in order to see the accuracy of spacing as clearly as possible. Here is an example of line 4:


Rhythmic graph line 4


I did all this work not only to have a chance of playing the rhythms accurately, but as a crucial step in deciding: how fast? You have to find which notes are really the fastest (sometimes not the ones that look the fastest), and go from there. How fast you play will be an individual decision. I am not convinced there is a global metronome marking that works for the entire piece, but maybe someone else has another opinion. I do think the flow should be consistent within an individual line – with close attention if there are indications of change.

In this entry, I present these sketches so that if you are interested in the piece, you can have a go at it yourself. The rest of the sketches are too large and lightly written to scan well. Please don’t ask me to scan or photograph the rest and post them (and not every line has been analyzed). However, I am happy to show them in person.


Polyrthythms IV – Practicing Tempo Modulation

This is a continuation of my previous post, where I use Taffanel/Gaubert’s Exercises Journaliers no. 1 to practice polyrhythms. Check that out before trying these! It will give you the correct placement in the measure for 4:3 and 4:5, which I have not notated here.

In these exercises, the metronome stays the same but the player has to change gears. I like to use this as an articulation exercise. You can shift from single tonguing to double tonguing as the tempo changes (but the metronome doesn’t). It keeps you on your toes.

Set your metronome to a 3-beat pattern. The suggested tempo is a quarter note=45 but you can start slower if it helps. You’ll need to start on the third beat for this to come out right. I love the fact that this pattern gives you an added rest for breathing!

The following variation puts the polyrhythm first. If you are doing this as an articulation exercise, it is good to start with double tonguing and then go to single tonging. I find this shift to slower tonguing more challenging.

Here is another variation going against a 5-beat pattern. Set your metronome to reflect that, at quarter note=75 (or slower if that helps). For this to come out right, start on the second beat. (This pattern gives you an eighth note for breathing, hooray!)

And here, a variation starting with the polyrhythm.

I hope these exercises will be of some use. Please post a comment if you have questions. I have had various comments regarding the notation of these exercises. There are more detailed ways of notating them but I find the notation above gets the concept across. In the end, you don’t need the notes to perform the exercises. My goal in this was to use melodic material to develop a sense of rhythmic phrasing.

Polyrhythm III Exercise with Taffanel/Gaubert

Here is the third of my posts on rhythm. You can read the first post here and the second here. I wouldn’t proceed here unless you can perform the exercises of these previous posts.

What I like about using Taffanel/Gaubert no. 1 from Exercices Journaliers is that it is a melodic study. In my first post, I emphasize the need for rhythmical phrasing, and the goal of playing rhythmically and not mechanically. One way of developing this, I think, is to develop your own strong, steady sense of pulse. This is something different from practicing with a metronome. If you test and develop your sense of pulse against the metronome’s ticking, it will grow stronger.

If you take the basic 4-beat pattern of TG no. 1 and set your metronome to a 3-beat pattern at tempo 45, it could fit together like this:

And if you take the basic 4-beat pattern and set your metronome to a 5-beat pattern at tempo 75, it could fit together like this:

You may have noticed that in both examples the 16ths are the same speed, only the metronome setting is different.

An interesting way to practice Taffanel Gaubert nos. 1 and 2 is to first play with the metronome at a quarter note = 120. Play a number of patterns until you feel comfortable with the speed, then continue but change the metronome to a quarter note = 45 and play the 4:3 pattern. When you feel comfortable with that, change the metronome to a quarter note = 75 and play the 4:5 pattern.
This is a wonderful way of practicing groove!

In my next post, I will use these same sort of exercises to practice tempo modulation.

Polyrhythm II

To read my first post on how to figure out polyrhythms, click here.

To internalize an unfamilar polyrhythm, I suggest the following steps:
1) clap and tap the rhythm away from your instrument
2) play it on your instrument, using a single pitch (no moving notes yet)
3) if it’s a difficult passage, play it using simplified material (a simple scale pattern)
4) play as written

Here is a written-out variation on how you can practice a scalar passage 5:4.
Your first step (not shown here) could be to play repeated sixteenths (here, it would be repeated F’s) and accent every 5th one.
The first line shows how groups of 5 sixteenths fit into a 5/4 bar.
The second line fills in the ties with moving sixteenths.
The third and fourth lines are played the same but notated differently. It’s good to practice both.

When you have an even number against 3, I find it easy to feel or visualize the second half of the second beat. It serves as a goal-post, or check-point. Here is an exercise similar to that above, but with 4:3.
Remember, your first step (not shown here) could be to play repeated sixteenth F’s and accent every 3rd one.

Here are some further exercises with even numbers against 3.  If it helps, focus on the back of the second beat.

In the next post, I will take the scale patterns from Taffanel/Gaubert and fit them into a polyrhythmic pattern.

Polyrhythms I

This is the first of a series about practicing complex rhythms related to a pulse, a.k.a. polyrhythms.

Why bother practicing polyrhythms? Some of us have been taught that our metronome is our best friend, but how useful is it really? Do we bother to listen to it? If we do, does it ensure us a good sense of rhythm? If some of us were honest, we would admit that we do not want to listen too closely, for fear of being labeled mechanical. After all, we want to play rhythmically, not mechanically. How to do this?

What I suggest is a method to develop rhythmical phrasing through the study of Taffanel/Gaubert’s study no. 1 from Exercices Journaliers. (I choose this because most of you reading this are flutists, and it is best to apply these ideas to something that is already familiar.). But this introduction will first cover the basics.

A well developed sense of rhythmical phrasing can help whether you want to become the next star beat-boxer or want to keep a steady Scherzo from Mendelssohn’s  A Midsummer Night’s Dream.

You will need a metronome that can be set to a simple beat pattern (2/4, 3/4, etc.), and a willingness to feel a bit clumsy at first.

The following examples use simple mathematics to see visually where your pulse is against the metronome’s (or your partner’s). It is a graphical guide to help develop a FEEL for the polyrhythm.

Given polyrhythm a:b, where b = metronome beats and a = your beats, there are two ways of figuring it out:

1) Take the b number of metronome beats and divide it into units of a, then clap or play every b number of these units. Let’s take the example where a:b = 3:2(three against two). In standard notation it looks like this:

Now take two (b) metronome beats, divide them into units of three (a),
Now clap or play every two (b) of these units as shown by a crossed note head:

2) The second way to figure a:b  is to multiply a times b, in this case 3 times 2. This gives us six:

Now divide this 6 into a (3). That gives us two, so mark every two pulses with an O on top. Then divide 6 into b(2) . This gives us 3, so marks every 3 pulses with an X on the bottom.

The “O”s are the rhythm you play or clap, the “X”s are the metronome beats.

Here is a more complicated example: 5:7

Let’s see how it looks using the first method: given a:b, divide b (7) into units of a (5) :
Now clap or play every b of these units (7) notated by a crossed note head:
Try writing this example using the second method. (Begin by multiplying 5 x 7.)
The next installation will give practical exercises on how to feel 5:4, and any even number against 3.
For more practice, see Peter Magadini’s Polyrhythms, the Musician’s Guide, Hal Leonard Publications, 1993
If you would like a pdf of this information in English or German, please leave a comment.

Tips for Complex Rhythms à la Ferneyhough’s Superscriptio

Below is some advice for works by composers (such as Brian Ferneyhough) who use complex rhythms not based on pulse-centered activity. I spoke with Mr. Ferneyhough about this subject and he was very clear that in his music, the measure is a “domain of a certain energy quotient” not related to a pulse.

In other words, a measure can be interpreted as an “area of activity”. The level of activity can easily be reckoned using the starting tempo. From there we can calculate the length of any measure or individual note through simple mathematics.

So if the rhythm cannot be felt as a pulse, one can at least memorize the speed in which it is supposed to happen. Surprisingly, it’s sometimes much slower than one thinks!

Ferneyhough’s Superscriptio for solo piccolo is a good example. The basic tempo is an eighth-note at 56. This means a whole note in 4/4 equals 7, because there are 8 eighth notes in a 4/4 bar, and 8 divided by 56 = 7.

From this number 7 you can deduce all the “odd” time signatures that are not based on divisions of the eighth note. An eighth note quintuplet (or a “1/10” bar) will equal 70 because there are 10 quintuplets in a 4/4 bar (7 x 10 = 70). To find the length of a 3/10 bar you would divide 70 by 3. If you have a 5/10 bar you would divide 70 by 5. An eighth note triplet (or a “1/12” bar) will equal 84 because there are 12 triplets in a 4/4 bar (7 x 12 = 84). To find the length of a 3/12 bar you would divide 84 by 3, and to find the length of a 5/12 bar you would divide 84 by 5.

What if the compound rhythms are stacked on top of each other, as in Ferneyhough’s other works? This is an imaginary example:
Let’s imagine as in Superscriptio the starting tempo is an eighth-note at 56. The last six 16ths (at the end of the bar) roughly equal two 16th-note triplets at 64. The nine 32nds under the 9:5 are roughly equal to three sets of 32nd triplets going at 116.

It could have been notated thus (among other possibilities):

Here’s the math:
From above we know that a 1/10 bar equals 70.
A 4/10 bar will equal 17.5 (70 divided by 4 = 17.5).
Each 11-tuplet will be 192.5 (17.5 x 11 = 192.5).
There are 6 of these 11-tuplets at the end. If we think of them as two 16th-note triplets, divide 192.5 by 3 = ca. 64

5 of those 11-tuplets equals 38.5 (192.5 divided by 5 = 38.5).
In the 9:5, if you think of the 9-tuplets as 3 sets of 32nd triplets, those triplets go at ca. 116 (38.5 x 3 = 115.5)

A click track will ensure accuracy without a doubt. However, if you opt for another approach, try the following: memorize the speed of each bar by practicing related bars together. Keeping Superscriptio as an example, you can practice all the bars based on “1/12” while keeping the metronome at tempo 84. (Yes, you will be jumping from measure to measure, or page to page.) Then do the same for all the “1/10” bars, then “1/8” etc. You are not trying to achieve musical continuity yet, this is just an exercise to help relate all the bars with this tempo, and to keep them consistent. When you finally put the piece together, your “internal conductor” will hopefully have a kinesthetic memory of the pulse of each measure and make the tempo changes accordingly.

Also see my post Seminar with Brian Ferneyhough.
Other thoughts?