Homemade Musical Instruments — Pythagorean — Pythagoras

Musical Fraction Tubes

You can build your own musical instrument based on a simple set of fractions  and this page will show you how!  It includes: 1) Virtual Fraction Tubes you can play right now on your computer; 2) directions on how to build a 5-note set of Fraction Tubes; and 3) information on building and playing an 8-note set of Fraction Tubes  including step-by-step instructions, playing tips, beginning exercises and songs, and music you can play with two to four people.  So take a couple of minutes, play the Virtual Fraction Tubes, learn how to make your instrument, and discover all of the great songs you can play with fractions.

Virtual Fraction Tubes

Our Virtual Fraction Tubes play the 1st, 2nd, 3rd, 5th & 6th notes of the Major Scale.  It's called the Pentatonic Scale (see below). 

As you will hear, the longer the tube, the lower the pitch the shorter the tube, the higher the pitch.  

Start by clicking your mouse on each tube (below). Then, choose a song and start playing.  The sounds you hear are produced by tapping a pencil on the top of each tube.  If you would like to make this instrument, just follow the directions below.

Choose a Song to Play

Building a 5-note set of Fraction Tubes

Begin by getting approximately 5 feet of class 200 - 3/4 inch PVC sprinkler pipe.

  Fractions Inches Centimeters  
A 1 14 13/16 37.7 1
B 8/9 13 3/16 33.5 2
C# 4/5 11 7/8 30.2 3
E 2/3 9 7/8 25.1 5
F# 3/5 8 7/8 22.6 6

1) Cut the tubing into the five sections listed on the left.

2) Place a 1" X 1" chipboard square (from a cereal box) over one end of each tube.

3) Cover each chipboard square with a 2" X 2" square piece of duct tape.

4) Wrap about 15 inches of duct tape around the set as shown on the right.  Tap on the tops of the tubes with your fingers or lightly strike with a pencil.

If you would like to build an 8-note set that plays many more songs, see below.

Building an 8-note set of Fraction Tubes

My daughter and I have created a special resource on building and playing Musical Fraction Tubes based on Pythagorean fractions!  It includes step-by-step instructions, exact measurements, sheet music, and play-along music tracks.  It has everything you need to be successful with your project, from beginning exercises to duets and quartets you can play with your friends.  Just like our homemade water bottle xylophone, glockenspiel, panpipes, and melodic tube drums, our Fraction Tubes are tuned to play an 8-note scale in the key of C.  Playing all of these instruments together, you have an instant homemade instrument band with musical arrangements that work for everyone!  Check out all the songs these instruments will play  — they're in the table of contents.

“Building and Playing Musical Fraction Tubes”
by Phil & Sarah Tulga



Phil’s daughter, Sarah, shows you how to make and play a great sounding instrument based on Pythagorean fractions. This 8-note set is tuned to the key of C and can be easily played with your fingertips or a pencil. Sarah shows you how to prepare your materials, and guides you step-by-step in assembling your own set of Musical Fraction Tubes.

You will also learn special exercises to develop your playing technique, and some great songs to play by yourself and with your friends. To help you learn faster, Phil and Sarah have included both sheet music and play along tracks for each song.

It's the perfect project for scouts who are making a homemade instrument.  In fact, you will see many scouting songs in this package.  Homeschoolers will also enjoy the project as a cross-curricular activity on math, measurement, music, and the physics of sound.

This complete package (including step-by-step instructions, playing tips, exercises, songs, duets, and quartets) costs only $14.95.

To download this PDF book on "Building and Playing Musical Fraction Tubes" along with all the music tracks, just click the "Buy Now" button below.


Table of Contents



I. Preparing your materials
II. Building your Fraction Tubes
III. How to play your Fraction Tubes
IV. Playing techniques
     - Scale
     - Counting Rhythms
V. Beginning songs
     - When the Saints Go Marching In
     - Lightly Row
     - Go Tell Aunt Rhody
     - Matarile (folk song from Mexico)
     - Oh Susanna
VI. Intermediate songs
     - Ode to Joy (Beethoven)
     - Song of the Dragon (Chinese New Year song)
     - Camptown Races
     - Oh My Darling Clementine
     - Tue Tue (folk song from Ghana)
     - This Land is Your Land
     - On Top of Old Smokey
     - Daisy / Bicycle Built for Two
     - Home on the Range
VII. Playing with a friend
     - Hot Cross Buns (duet)
     - Mary Had a Little Lamb (duet)
     - Yankee Doodle (duet)
     - Good Night Ladies (duet)
     - Shoo Fly, Don’t Bother Me (duet)
     - Jingle Bells (duet)
     - Jolly Old St. Nicholas (duet)
VIII. Playing with four or more
     - Row Row Row Your Boat (4-part round)
     - Frère Jacques / Are You Sleeping (4-part round)
     - Taps









Copyright © 2005-2020 Phil Tulga

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