Mathematics and Music

 Mathematics and Music

January 13, 2026

2 Samuel 6:5

5Meanwhile, David and all the house of Israel were celebrating before the LORD with all kinds of instruments made of fir wood, and with lyres, harps, tambourines, castanets and cymbals.

In second Samuel, we see that King David utilized all kinds of musical instruments to worship the Lord. There are stringed instruments, winds instruments, both brass and woodwinds, and percussion instruments. But what enables all these types of  instruments to play together harmoniously? As we said briefly yesterday, It is because of the underlying mathematics that determines which notes and frequencies sound pleasing together. Let us go back to Pythagoras as see how he laid a mathematical foundation for music.

One story goes that it was as he was passing a blacksmiths shop that he noticed that two hammers ringing off of the anvil sounded good together. On closer inspection, he determined that one hammer weighted exactly twice what the other did, and the resulting sounds were the same note, but an octave apart. This established the first perfect interval, which is the octave, whose frequencies have a ratio of 2:1. You can demonstrate the same thing on a guitar by first plucking a string and then touching it at the halfway point (the twelfth fret). The tone will switch to the next higher octave. This is the first overtone. 

The next simplest ratio is the perfect fifth, which has a ratio of 3:2 and then the perfect third with a ratio of 5:4. Together these form the major chord which is the simplest and most harmonious chord. (In the key of C this is C, E, G and C2). This mathematical pattern repeats with increasing complexity, and all instruments are designed to produce these same notes so they create harmonious sounds when played together. In modern music, the standard musical scale has been divided into 12 equal half tones with A2=440 Hz. Without this mathematical precision, the instruments would just produce noise like the shofar, which is not tuned but just produces a shout or blast when blown.

There is much more to music theory, but this gives you a taste of the mathematical beauty and simplicity underlying musical harmony. Such beauty reflect the heart of God who created the universe to obey beautiful mathematical laws. This order illustrated His nature which calls order out of chaos (Let there be…). And without his guiding influence, which he delegated to us when He ordered Adam and Eve to take dominion over the earth, nature obeys the law of entropy* which results in a return to chaos. Therefore, there is something about making music and worshiping the Father that pleases the heart of God as it creates harmony and order. So let there be music and use it to worship God.

* The second law of thermodynamics introduces entropy, stating that the total entropy of an isolated system cannot decrease over time, implying that heat cannot spontaneously flow from a colder to a hotter body. Entropy is a fundamental physical quantity that quantifies the degree of disorder, randomness, or energy dispersal in a system. (grokipedia.com)

Donald Duck in Mathamagicland cartoon explains mathematical music to Donald:

https://youtu.be/hl6JDv4ZG7U?si=pNmmHoIc4O8Tnhrx