Marking Rhythms (Miss It? Mark It! part 4)

Marking Rhythms (Miss It? Mark It! part 4)

This is the fourth article in a series about “marking music,” providing visual solutions to problems musicians encounter during practice. Our brains cannot remember everything. By carefully and consistently making marks in the music, musicians will learn music faster and with less frustration. This blog post will focus on how using pencil marks can aid in the learning of difficult rhythms.

Rhythms are the analytical, mathematical side of music making.

There is little grey area in interpreting rhythms. They are either right or wrong and learning them correctly from the beginning is critical.

My favorite way to mark rhythms involves drawing lines to represent the beats in a measure. I draw a short vertical line directly over the note that is to be played on the beat. The lines occur in the same place that my foot comes in contact with the floor when tapping the tempo.

rhythms visually organized - vertical lines show beats

Doppler’s Hungarian Pastoral Fantasy

In the above example, a have drawn vertical lines to represent where the beat falls in each measure. Notice that in the syncopations, the vertical line is drawn between the notes. When playing syncopated rhythms, it is important to feel the beat (or the foot hitting the floor) in the space between the notes. In this example, notes are played on beats 1 and 3 but not on beat 2.

Marking the beats can help with complicated rhythms. Consider this passage with a 9/8 time signature:

rhythms made easier by marking the music

from Danse de la Chèvre

This measure is made much more readable by adding in vertical marks over the large beats (dotted quarters). Visually, the organizes the measure into three distinct parts. By tapping my toe, I have kinesthetic feedback to tell me if my notes are starting on the right beat.

This is a simpler example from a student’s etude in 6/8 time:


etude in 6/8

In this example, I wrote in the numbers 1-6 for each of the eighth notes within the measure. This makes it easy to see how the notes relate. We could re-write this measure in 6/4 time with quarter notes and eighth notes to achieve the same rhythm and the same counting.

For the final example, I offer this example from the opening passage of Doppler’s “Hungarian Pastoral Fantasy.” I have added vertical lines to represent where each of the six eighth note beats occur in the measure. You will notice that there are longer lines over the two larger beats – the dotted quarter notes.

wild rhythms, organized

Doppler’s Hungarian Pastoral Fantasy

I am a visual and kinesthetic learner so marking my music with vertical lines to represent beats is essential. It graphically organizes the music into discreet packages that I can see and feel easily. Of course, this is not a new idea, nor is it one I created. In fact, I see these kinds of marks all the time in orchestra music used by professionals. I have developed a system that works for me. Now, go find one that works for you and use it consistently!

More ideas for marking music:


Chrome Music Lab – Acoustics Sandbox

Chrome Music Lab

Check out the Chrome Music Lab, a virtual playground for learning about acoustics.

Chrome Music Lab – Fun with Acoustics!

acousticsClick on something – anything – and interact with the pictures on the screen. There are no explanations, no words even. Jump into the musical sandbox and see the spectrogram of a flute.. or a harp… or even your own voice.

The interface is so simple and visual that people of all ages can learn about acoustics. You don’t need to be a musician to enjoy this website.



The Chrome Music Lab reminds me of The Exploratorium in San Francisco. It’s a giant building full of science experiments. My family spent an incredible day there several years ago with our kids, then six and four. I remember one exhibit in particular – it had a motor that was exposed and operational. Our youngest liked turning the crank and seeing all the parts move. I had a “lightbulb moment” about magnets and energy. Husband, who is a pro with small engines, was fascinated by some detail I didn’t begin to understand. All of us learned something new by playing with the exhibit.

The Chrome Music Lab is like this too. Playing with the monkeys and drums, I was reminded of the ethnomusicologist’s way of notating non-Western rhythms. My kids liked clicking on the silly monkeys and hearing the different sounds. Others might observe the visual spacing of the rhythms, as if the sounds were placed on a ruler. Each person will have a different understanding of the activity and unique insights.

Here are a few ideas for interacting with the Chrome Music Lab:

  • Try to guess the piece on the “Piano Roll” before hitting the play button.
  • Find the octaves in “Harmonics.”
  • Use “Arpeggios” to accompany yourself while singing simple songs like “The Wheels On the Bus” and “Twinkle Twinkle.”
  • Notice how the tune changes as you draw in “Kandinsky.” Art becomes music. Change colors for different sounds.

(Thanks, James, for the link.)

Music and Math: Three Concepts for Understanding Rhythm

Music and Math

My job as a music teacher is to help students understand the basic elements of music. Rhythm is the most difficult of the “right-or-wrong” music elements (the others are articulations and pitches.) Mastering rhythm often requires multiple approaches. Connecting music and math is one approach.

We all have different learning styles. One model of learning suggests that we have a preference for visual, auditory, or kinesthetic experiences. Understanding where your strengths are in the visual-auditory-kinesthetic spectrum can direct you to helpful systems of learning. Here’s a link to the  VAK Learning Styles Survey .

Some students resonate with a kinesthetic understanding of rhythm. They need to feel the beat in their bodies. In the studio, we may use marching, bouncing balls, and/or conducting the music to help students internalize the beat. For kinesthetic learners, Dalcroze Eurythmics is helpful.

Other students prefer to hear the rhythms. These are auditory learners. The blog post “Rhythm Silliness” talks about the words I like to use to help students learn rhythm by ear. We use words like “Mississippi,” “peanut butter” or “R2D2” for sixteenth notes. We do a lot of playing rhythms together or I’ll play one measure and the student will play it back.

Visual learners often prefer a more analytical approach to learning rhythm. Charts and visual aids are helpful to folks who have strong visual skills. If you are one of these people, read on! This blog post is for you.

This blog post will show three mathematical concepts and how they contribute to a deeper understanding of the division of the beat.


5th grade math and music

math workbook

My son brought home his fifth grade math book last night. This is from an introduction page to a unit on fractions. This page clearly shows the relationship between music and math. It even points out that the time signature looks like a fraction. By adding the note values at the bottom of the page, students can figure out where the barlines are supposed to be.

A word of caution: I have observed that younger students can be confused about fractions. They think that if a pie is divided into two parts, there must be more pie because two is more than one. For this reason, I don’t use fractions with young students until they have studied them in math at school. I have had the most success using rhythm words to teach rhythm to young students.

However, once a student understands fractions, the concept is easily applied to music and deepens the student’s understanding of how the beat is divided into equal parts. Notes that are tied together become easy math problems. (1/4+1/4=1/2) Students who understand fractions have an easier time subdividing the beat, as they have to do when the eighth note is the value that gets one beat.


I love to cook and sometimes I have to double of halve a recipe. This calls for an understanding of fractions and ratios. Take a look at my measuring cup:

music and math in the kitchen

measuring cup

If you look closely, you can see that there are lines for 1/4 cup, 1/3 cup, 1/2 cup, 2/3 cup, 3/4 cup, and the top is one whole cup. Imagine that this one cup of flour is a quarter note. That note can be divided in many different ways. Three 1/3 cups = 1 cup in the same was as a triplet will divide a quarter note into three equal short notes. I like to think of the image of this measuring cup when working on rhythms that switch between eighth notes and triplets. I have a clear mental image of how triplets in one instrument and sixteenth notes in another will line up.

Music and math makes great cookies!


Daniel Buckvich, professor of music at University of Idaho has an innovative system for teaching rhythm, which he calls “Measured Music.” I became familiar with his ideas as an undergraduate student at The Ohio State University. It was one of those great “AHA!” moments when I opened the book and saw for the first time the visual representation of my mental concept of rhythm. Buckvich’s “Measured Music” system begins with a ruler, something with which we are all familiar. (I should note that this ruler is in inches, so if you are a metric person, this might not be as helpful.)

music and math

from Measured Music

A ruler has whole numbers (1, 2, 3, and so forth) that indicate inches. The inches have smaller divisions also. The longest line is at the half-inch mark. Shorter lines indicate the 1/4 and 3/4 inch. Finally, the smallest lines divide the 1/4 into 1/8 (and sometimes 1/16).

Buckvich’s system also uses small circles, like mini pies, to show the subdivision of the beat. Sometimes the smallest subdivision is 1/2, other times it is 1/3. In the above example, you will see that it is 1/4 or the sixteenth note. Below is a page from later in the book showing complex rhythms. I love how visual this music and math system is.

music and math

another page from Measured Music

If your brain isn’t wired for this kind of math, that’s totally fine. You likely need another system for internalizing the pulse and subdividing the beat. As I mentioned earlier, there are other systems for teaching rhythm that are good for kinesthetic and auditory learners.

If the above music and math concepts work for you, great! Use them to deepen your understanding of the division of the beat. Visually overlay a ruler, a measuring cup, an apple pie over difficult rhythms. Continue to explore how the fractions can be overlaid and be prepared for some “Aha!” moments of your own.

Music is a beautiful, mathematical marvel. If you liked this post, you may also be interested in learning about the math concepts behind the harmonic series, music theory, acoustics, and instrument design.

Mental Practice

Mental practice can be as effective as physical practice in music.

That sounds crazy, right?! You wouldn’t train for a marathon by sitting on your couch and thinking about running 26.2 miles. It seems counterintuitive that we can practice music without making a sound or even having an instrument in our hands. But practicing away from the instrument can be as effective or maybe even more effective than practicing with the instrument.

mental practiceIt’s not always practical to play an instrument. You can’t whip out a trumpet on an airplane; your boss might not appreciate the sound of an oboe during a break at work. However, it’s not difficult to find a quiet spot to look at sheet music. If you get in the habit of carrying music with you, like a novel, you can find excellent opportunities for mental practice throughout the day. Perhaps you have a doctor’s appointment that will interfere with your normal practice time or maybe a nasty chest cold is inhibiting your ability to work on the vocal solo you need for an audition. Mental practice will help you make progress toward your musical goals.

There are four major areas where mental practicing is superior to physical practicing.

1. Tapping Rhythms. The most obvious thing to practice away from the instrument is rhythm. I like to tap the rhythm on my leg as I watch the music. Some people like to clap, snap fingers, or say a nonsense syllable like “ta.” For added difficulty, try tapping the beat with one hand and the rhythm with the other. (Remember, the beat is the constant pulse of the music whereas the rhythm is how the beat is divided.) Maybe you like to count out loud. That works too. Or you can tap your toe to the beat and clap the rhythm. Continue changing it up by using simple rhythm instruments like a hand drum or castanets. Adding the metronome is always a good idea. (For more ideas on how to use the metronome, see an upcoming blog post.) The way you tap the rhythms is limited only by your imagination. Remember, the more fun you have, the better you will learn the material.

2. Sizzling Articulations. For wind players: Reinforce proper articulations by practicing them away from the instrument. Make a loud hissing sound by blowing air through your tongue and teeth, like a snake. You will be able to use your tongue to articulate the notes and the hissing sound will create resistance similar to your instrument. However, by focusing on just the skill of articulating (not tone or fingerings), you will be better able to catch and fix mistakes. For string players: mimic holding the bow in your right hand and practice the changes of direction.

3. Ghost Hands. Sit comfortably with music in front of you. Place your hands on your knees or in your lap. Now imagine that your arms are moving into playing position. In your mind, feel the instrument under your fingers. Now begin to hear the piece in your mind. Imagine your fingers moving, playing the piece flawlessly. Remember, you aren’t actually moving your fingers nor are you singing the music, but the image should be strong enough that you can hear it in your mind and your fingers “feel” the movements.

mental practice

piano fingers

4. Visualizing the Performance. One to two weeks before a recital, competition, or audition, try to imagine what the performance day will be like. Think about all the minor details, such as what you will be wearing and what the room might look like. Imagine yourself looking confident and calm as you walk onstage. Try to anticipate anything goofy that might happen. Plan for the worst and you’ll be surprised at how smoothly the performance actually went. I have found that the unexpected events can really throw things out of whack, but if you’re ready for anything, nothing will make you lose your cool. Imagine a judge writing with a squeaky pencil and a deep scowl on her face. Think about how you might feel if you get lost on the way (and then add some extra time to your travel plans.) Breathe deeply while you visualize and reassure yourself with positive self-talk. Don’t dwell on the negative, however. Spend most of your time visualizing a perfect performance and a deep sense of satisfaction.

In all of the above exercises, make the images as vivid as possible. Add as many details you can – the way it feels, the sounds, colors, maybe even the smells. It may take a little practice to hear the music loudly in your head. Start with small passages if you find your mind wanders. (For more help on focusing the mind, see my bog article on Concentration Exercises.)

Athletes believe in mental practice. So do surgeons. If you don’t believe me, read the articles “Mental Practice for Musicians,” “Mental Practice Makes Perfect,” and “The Benefits of Mental Practice.” I also recommend the book The Inner Game of Music