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Heavenly Harmony and Musical Patterns

Why do harmonious musical intervals pervade the universe?

We see the ratio of 2 to 1 in both orbits and music. Saturn’s moon Mimas is in a 2 to 1 resonance with a region of Saturn’s rings. For each of Mimas’ orbits around Saturn, particles in a region of its ring orbit twice. As a result, Mimas is very regularly pulling on those particles gravitationally, creating the noticeable gap in Saturn’s rings.

The moons Europa and Io have a 2 to 1 ratio. For every time Europa goes around Jupiter, Io goes around twice. This 2 to 1 frequency ratio is the octave in music (as we show in brief video below).

Cut a pipe length in half and the resulting note we hear sounds very similar, but higher, what we call an “octave” higher.

When the pipe is twice as short it has twice the frequency. That sounds like the same note to our ears, but higher.

If you shorten a pipe to 2/3 of its original length we hear the new note as a “perfect fifth” higher than the original.

Now starting with that shorter pipe length, if you again reduce the pipe to 2/3 its previous length you get a perfect fifth higher again. Each consecutive pair of perfect fifths sound harmonious together. It so happens that you can continue this 2/3 division to produce 12 perfect fifths (corresponding to all 12 notes of the scale). After 12 fifths the pattern repeats, and cycles through the same series of notes, but octaves higher and higher. But you can lower each note by an octave by doubling the length of the pipe.  If you work all this out, you will find that this is a simple way to think of why we have 12 notes in a scale.

The first image below shows the simplest and most common way to play the pan pipes. Make a slight smile and purse your lips. Make a small opening between your lips. Place the pan flute against your bottom lip and direct air into the pipe’s tube.

You can also use a second but smaller straw to direct air into the larger straw as shown in the video below. The other video shows a mouthpiece you can make with a flattened straw.

These ratios 3 to 2, 2 to 1, and so on, appear in in the heavens as well, as we mentioned. This led early scientists to many insights and speculations about heavenly harmony, or the “music of the spheres.”

Here we see that not only does Io go around Jupiter with twice the frequency, but Europa’s orbit has twice the frequency of Ganymede. This is like three octaves in music.

Coding Music in Scratch

The simplest code we did in Scratch makes a playable Xylophone. It has each Xylophone key as a different Sprite. Each sprite has only one line of code, when this Sprite clicked, play note ___. Each sprite just has a different note and different look (size and color).

Here’s our Keyboard using clones. You can play notes by touching keys, in one of several musical instruments.

Also see our interval and chord player in Scratch.

The above is the simplest code, for a beginner. It is simple because there so little code, really just one command for each sprite.

But you also can make clones of sprites, one clone for each note. This has many advantages. Here’s our Keyboard using clones. You can play notes by touching keys, in one of several musical instruments.

Also see our interval and chord player in Scratch.

We also created a playable keyboard using clones. You can change the instrument.

Also see our interval and chord player in Scratch. Below is a snapshot of the screen.

Here is the code for the interval and chord player. The simple major and minor cords need very little code.  The great bulk of the code is for the key signatures.

Musical patterns include polyphony and polyrhythm. The opening of Jupiter from Holst’s the Planets is an elegant polyrhythm of 3 against 2.

Here’s our code for the lead instrument in the introduction.

Below is code for the second instrument.