Toccata Blocks: A Tool To Help Teach Rhythm

Version 2No matter what method you use to teach music, be it Kodaly, Orff, or any other, when it comes to music reading there are certain aspects of our music notational system that are counter-intuitive and confusing to students who are just beginning. One of those difficulties is often the irrelevance of how the notes are spaced on the page. Students naturally assume that notes that are closer together go faster, and notes that are spaced further apart go slower. They will even carry this into the same note value. For example, they will think that quarter notes spaced closely together go faster than quarter notes spaced further apart. The concept of how the note head, stem, and/or beam are drawn can become overlooked, leading the student to make frequent rhythmic errors.

It is always good pedagogy to start from where students are and work from there to where you want them to arrive. Rather than dismiss using spacial perception as wrong, why not take advantage of children’s intuitive ability to perceive spacing in teaching them to read note durations accurately? Catherine Schane-Lydon has invented Toccata Blocks that do just that.

toccata blocks

The basic set includes blocks with time signatures and notes on blocks that fit onto a provided easel. The easel is exactly the width of the blocks for a time signature and the correct number of beats of notes. A whole note block is the width of four quarter note blocks or four paired eighth note blocks. Single eighth note blocks are half the width of quarter note blocks and so forth. There are easels for simple and compound time signatures. Once an easel and time signature are chosen, the child builds a measure of rhythm by placing blocks on the easel. If the easel is less than filled, the child knows more notes are needed. If the easel is over filled, with a block hanging over the end, the child knows there are too many beats. This design makes building rhythms self-correcting because the child knows when he or she has done it right because the blocks will exactly fit across the easel.

I gave a set to students in middle school, and students in 2nd grade. An 8th grader said, “it [toccata blocks] helped me learn how the notes go together.” A 2nd grader remarked, “making rhythms is fun with these blocks. I got it wrong at first, but now it fits.”

I also used my set of Toccata Blocks to do a full class demonstration. I began a rhythm and then called on student to finish the measure. After each addition of a block, I asked the class if the measure was finished. “Do the blocks fit perfectly?” The children would look and respond, then give me suggestions on what block I should put in next. If the next block hung over the end, they were quick to reject that choice and make another of a shorter note duration. Almost every student I gave these blocks to to use immediately understood how they worked, and were able to correctly create a measure of rhythms.

Of course, I want students to write rhythms on conventional music paper, so it was important for me to make sure they took note of what notes they were using, and didn’t just fill up the easel randomly. So I had them tell me with each block they added how many beats that block added, how many beats they had, and how many more they needed. It was helpful to them to learn the note durations, and it delighted our school math coach!

Once they wrote original rhythms on paper, they could go back to the Toccata Blocks to check their work. They would exactly place what they had written on the easel, and see if it properly filled the easel or not. If not, they could not make corrections with the Toccata Blocks, they had to make corrections on their paper, and then return to the Toccata Blocks to again check their work.

With the length of the blocks proportional to the duration of the note, it is also possible to use the blocks as prompts for creative movement. The whole note block is long, and so a long, extended movement is called for. The quarter note blocks are short, so they call for smaller movements. Turning this into a movement game, children draw blocks like playing cards, then begin walking around the room. If a whole note is drawn, one giant step that takes four beats is taken. If a quarter note is drawn, then four smaller steps that traverse the same distance as the child who took the giant step is taken. Using them in this way helps students deepen their understanding of why the blocks are different lengths, and how the various note durations relate to each other.

Students worked well in small groups finding blocks to add to a group composed rhythm. I have learning centers set up in my classroom, and the Toccata Blocks make a good basis for such a center. With my older students, students who have composed a rhythm on the Toccata Blocks can then take it to students working on the keyboard to add pitches to the rhythm, making a short, one-measure melody. This rhythm then can become the basis for extending a melody.

The blocks are made of durable hard plastic. I anticipate that they will stand up well to classroom use. There is also a CD included with rhythms for students to build with the Toccata Blocks, taking dictation from the CD. The basic set includes quarter and eighth note durations in simple and compound time signatures. Supplemental sets add sixteenth notes to the basic set. Each block has a note on one side and the equivalent rest on the reverse side, so students can learn both notes and rests together. Toccata blocks are suitable for students in second grade and older, though one must be aware that many of the blocks could be a choking hazard for children prone to put such things in their mouth. I have had encouraging success with Toccata Blocks. They are certainly worth looking into. For more information, go to toccatablocks.com.

 

Musical Fractions That Make Sense

Version 2The nomenclature we (except for those who use the quaver family of names) really is not very useful. Whole note, half note, quarter note, eighth note, and sixteenth notes are the terms by which teachers, both of music and of other subjects, connect music to fraction arithmetic. As far as it goes, they are correct. All of those names, that is, quarter, half and so forth are fractions, but fractions of what? They are fractions of a measure in common time. Because those names only apply to four-four meter, their meanings are irrelevant to every meter except four-four. What’s more, I’ve never, in 31 years of teaching, found a student for which knowing a quarter note was one quarter of a whole note really helped him or her perform the more accurately. Of much more value is that the quarter note is, at least frequently, equal to the pulse of the music; the ictus, the beat the coincides with what an ensemble conductor is conducting.

From there, it is helpful to know that eighth notes are two equal divisions of the quarter note pulse. It is not at all helpful to know that one eighth note is one eighth of a measure in four-four time, and, as I have pointed out, even less helpful if the child is not performing music in four-four meter. Eighth notes are the division of the quarter note pulse into two equal parts, or the dotted quarter note pulse into three equal parts. Stated as a fraction,  one eighth note is either one half or one third of an ictus beat. That is the sort of musical fraction that is helpful. There are two or three sounds of equal duration during each pulse. That is helpful, because musicians mostly divide beats, not measures. Quarter note pulses can be further divided into four equal durations, and dotted quarter note pulses can be further divided into six equal durations. When this occurs, those divisions of the beat are called sixteenth notes, and each sixteenth note is either one-fourth or one sixth of a beat. Even this fractionalizing is of limited value, because the performing musician is not measuring individual durations in relation to the beat, he or she is gauging how to evenly distribute a number of sounds over a single pulse. Nevertheless, fractions of a beat are more useful than fractions of a measure. Every note value less than the value of the ictus is a division of the beat, and the process by which beats are divided are an example of the mathematical operation of division, which includes fractions.

Notes that are longer than the duration of the ictus are elongations of the beat, and the process by which beats are elongated are an example of the mathematical operation of addition, including adding fractions. Once more, we don’t really care that a half note is half of a measure in four-four time, or that a whole note occupies the duration equal to an entire measure in four-four time. We do care that a half note is the duration of two ictus beats added together, and that a whole note is the duration of four ictus beats added together, though in both cases the quarter note must be the ictus for this to be true.

It is useful to think of note values as not only fractions of the ictus, but also as fractions of note_hierarchyeach other. Practicing sixteenth note passages while audiating an eighth note beat in a piece where the quarter note is the ictus, a practice referred to as subdividing, is used by many students and teachers as an effective way of achieving rhythmic evenness. Such thinking also facilitates shifting the ictus from, for example, the quarter note to the half note when the feel of the music suggests as much. This often happens when the composer transitions the music from a rhythmic section that is best understood in quarter notes, to a broad melody that comfortably soars above all in half notes. Understanding that those still present quarter notes are each half as long as the now predominant half notes makes the shift natural and enjoyable.

Thinking of note values as fractions of other note values also facilitates understanding rhythm when the ictus is not the quarter note. Knowing that  a quarter note is half of a half note, and that an eighth note is half of a quarter note makes dividing or elongating the half or eighth note ictus possible, and the concept of divisions and elongations of the beat transferable. Indeed, it is important for students to understand once they have begun to read music that any note value can be the ictus, and that it follows that any note value can be divided or elongated. Indeed, a whole measure can be the ictus, and a half note a division of the beat. It is also important to understand that before students begin to read divisions or elongations of the beat, they must learn them aurally, so that when they do read them, they have a sound to associate with what they see. Music Learning Theory (Gordon) and Conversational Solfege (Feierabend) both provide well researched and classroom tested procedures for doing this.

We cannot conclude our discussion without raising the issue of meter signatures. Though these look like fractions, and are frequently wrongly notated in texts as fractions and aurally referred to as fractions as in “three quarter time,” they are not fractions. Three-four meter does not indicate three fourths of anything. Instead, it is a convenient way of indicating that there is the equivalent of three quarter note durations in each measure of music. There is no way of knowing from a meter signature how the ictus is divided, whether into two or three divisions, nor is there any way of knowing what the ictus is. The bottom number of the meter signature may, and often does coincide with the ictus, but it frequently does not as well. That said, more often than not a meter signature with a 4 as the bottom number and a number evenly divisible by two but not three as the top number  has beats divided into two equal durations, and a meter signature with an 8 as the bottom number and a number evenly divisible by three as the top number has beats divided into three equal durations, though eight-eight meter is an exception to this (see Toccata by Frescobaldi).

Attempts to correlate music with Common Core Mathematics with fractions can be made with note value nomenclature, but such connections are not helpful or even confusing to music students. Connections between music and fractions are more advantageously made concerning fractions of ictus beats and fractions of other note values. While traditional nomenclature can and does continue to be used, the bases for names such as quarter and half notes is only relevant to four-four meter.