Behind the Notation: 10 Ways to Transform a Rhythm


There are a lot of composers out there using Noteflight, and your music is popping with great ideas. If you’ve come up with a theme you like, and you’re not sure what to do with it next, one of the most interesting things you can do is to repeat it while transforming the rhythm in each repetition. Put a few of these transformations together, and you’ve got a complete piece!

As an example, here is a simple theme you could transform rhythmically:

1. Diminution

Two of the most basic ways to transform it are to make it twice as fast, or twice as slow – but by changing the note values, not the tempo marking! For the “twice as fast” option, you are cutting the note values in half, in other words, “diminishing” them: that’s called “diminution.” For example, every quarter note (crotchet) becomes an eighth note (quaver), and every eighth note becomes a sixteenth (semiquaver). Applied to our example theme, that looks like this:
(just for fun, Example 1b shows a diminution that has also been altered a bit)

2. Augmentation

The opposite of diminution is “augmentation”: each note value becomes twice as long – “augmenting” it: every quarter becomes a half note, every eighth becomes a quarter, and so on. The result is that the tempo sounds twice as slow even though we have not changed the metronome marking:

3. Addition

Another great way to transform your melody is to add some new notes to it, while leaving the original ones in too. Compare this tune with the original: which notes have been added?

4. Subtraction

The opposite of addition, of course, is to leave some notes out:

Which notes are missing? Which note has been replaced by a rest? Which has been replaced by another note?

5. Retrograde

Another way to transform a theme is to play it in reverse, back to front. This is called “retrograde.” For example, in the original, the first four notes are quarter notes; in the transformations shown in Example 5, those four quarters “start from the end.”
Example 5 shows two different ways to do this. Ex.5a shows how to put all the notes and durations in reverse order. Alternatively, as in Ex.5b, you can keep the pitches in the original order, but reverse the order of the rhythmic durations.

6. Relative Durations

This next one is a little trickier to explain, but it can give you a lot of great options. Instead of thinking of the note values in the usual mathematical way, in which they are exact multiples of each other (for example “two eighths equal one quarter”), think of the note values in your theme as longer or shorter than one another in a loose, general way. You can be pretty inexact: look at your original and put each note into a general category like “long,” “longer,” “longish,” or “short,” “shortish,” etc. Then pick some other note values that are in the same general categories relative to each other, and replace the original values with those. For example, both a quarter note and a dotted quarter are “long” relative to an eighth note nearby, so they can go in the same “long” category and you can replace one with another while preserving the relative durations. Again, this is easier to see in notation than to explain in words!

Be creative, and don’t be too exact, and you can end up with a melody that still has the same relative set of note durations, but sounds different and fresh to the listener.

7. Displacement

This one’s pretty simple: just keep the original melody the same, but start a bit later – in this case, one eighth note later. However, if the melody is played alone, with no accompaniment, the listener won’t know you’ve displaced it, because they won’t hear that eighth rest at the beginning! So we’ve added a lower line with notes that give the beat: that way the listener knows that the melody has been moved off of the beat. You can choose any duration value to displace by: eighth, quarter, dotted sixteenth… it’s up to you!

8. Imitation

This is one of the most popular types of rhythmic transformation, used since Medieval times and probably long before that. If you’ve ever sung a round or a canon, you already know this one! Just have your theme enter again in a new voice/part/line, a few beats or a bar or two after the first one, and continue both of them so the theme overlaps with itself. Then you can add more entrances in other parts. This doesn’t work well for every theme, because the theme has to be constructed in such a way that it sounds good when it’s overlapped with itself. If it does sound good like that, then the theme can stay the same every time it enters, and that’s called a “canon.” If it doesn’t work as a canon, you can just change it a bit the second time it comes in, as long as it starts out the same. That’s called “free imitation.” Either way works!

You could also start the second rendition on a higher or lower pitch, using Noteflight’s Transpose feature to keep the notes consistent.

9. Change the Meter

There are at least two ways to transform a theme by changing the meter. First, you can keep all the notes the same, but move the bar lines, like this:

The downbeat is always the most accented note in any given bar, so moving the barline changes which notes are accented: in this case, the third note is now accented instead of the fourth one, and so on.
Another way to do this is to keep the same pitches accented as in the original, but to adjust some note values so you can fit the same number of notes into each bar as there were in the original. In this case we’ve squeezed them down to fit the same set of notes into less time (4/4 to 3/4), but you could do the opposite too.

10. Gradation

Last but not least, this is one of the trickier tricks in our bag. The musical example shows it more clearly than a written explanation can: notice how there are four sixteenth notes in the first bar. In each bar after the first one, we have moved those four sixteenths over to the left by one eighth note value, and we’ve adjusted all the other durations to fit.

In conclusion…

Here are all of the transformations we’ve described, together in one score:

We hope some of these ideas might be useful to you. Remember, they are not “rules” that you have to follow strictly, they are just “things you can do,” “tools in your toolkit,” or “tricks in your bag of tricks.” The possibilities are wide open. If you like one of these ideas but want to change it around, or do it inconsistently or haphazardly, or combine three of them, that’s your right as the composer!