Math Simplified
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Math Simplified

A Celebration of Numbers and Seasons

Some More Music Into Math

(Or Vice Versa): If Pythagorean Tuning and Harmonic Series have it, so does Pascal’s Triangle.

Playing music on a keyboard (Source: Mathnasium)

A lot of people enjoy listening to music and love them but the math still falling behind as studies had shown. Although newer generations tend to view math as something important, still, more than 50% either hate or are indifferent to the subject but some promising result shows that students would like math more if they better understood its applications. For now, we can only hope that music and math will come into parity in the future. Who knows?

During a deep dive into my research on mathematics, I later found out that music has a strong connection with mathematics which dates back to antiquity. Pythagoras of Samos (c. 570 — c. 495 BC) had been mainly attributed to one of his famous discoveries on Pythagorean tuning (circa six century BC). Musical scales were shown to be mathematical in nature and linked to the Harmonic Series in some unpopular and perhaps vague connection but somehow the Harmonic, in general, cannot shy away from Pythagorean tuning.

Harmonic Series in Music (Source: YouTube)

The American Mathematical Society features the interconnectedness and majesty of music and mathematics through a video presentation with remarks from Santa Fe Institute mathematician and computer scientist Cris Moore and musical selections by the Santa Fe Symphony Orchestra with Principal Conductor Guillermo Figueroa.

Though Pascal’s Triangle was named after the French mathematician Blaise Pascal (19 June 1623 - 19 August 1662), other mathematicians before him had studied it in India, Persia, China, Germany, and Italy.

Animated Pascal’s Triangle (Source: Wikimedia)

The famous Pascal’s Triangle can still be traced back to Pythagoras through the Tetractys, a triangular figure consisting of ten points. Bizzare it could be that the works of Pythagoras and Pascal would find their connections in the field of music with a time lag of more than 1,000 years in their existence. But how?

The Tetractys (Source: Wikipedia)

The triangular patterns have something queer to show and if Pascal’s Triangle is viewed through the probing mathematical lens, the diagonals will communicate the figurate numbers or simplices.

Left-justified Pascal’s Triangle showing the Figurate Numbers (Source: Wikipedia)

What then?

Popular culture has it that the carol, Twelve Days of Christmas, and Tetrahedral Numbers found each other. The 12th Tetrahedral Number, which totals 364 is the number of gifts “my true love sent to me” during the course of all 12 verses of the carol, “The Twelve Days of Christmas”.

Number of gifts of each type and number received each day and their relationship to figurate numbers (Source: Wikipedia)

Yeah! Not only Christmas and carols remind us of a season but also some mathematical celebration we might as well.

Celebrating Christmas and math
Celebrating math, music, and Christmas (Source: Unsplash)

What's more, so?

Just recently, some amazing musical connections with Pascal’s Triangle had been forged by Jake Lizzio on the YouTube channel, Signals Musical Studio. You can watch their YouTube video: Making Music with Pascal’s Triangle + the LOCRIAN scale [RIFFING WITH MODES #7].

Making Music with Pascal’s Triangle + the LOCRIAN scale [RIFFING WITH MODES #7] (Source: YouTube)

Perhaps, few people could only deeply understand both math and music at the same time but to appreciate them both is something of a milestone for the human race. Discoveries and strange connections are surprises everywhere can happen. I couldn’t wait for more. Hope, you too!

Thank you for dropping by!




Simplified is a publication aiming at making mathematics accessible and enjoyable.

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Jonipol Esquillo Fortaliza

Jonipol Esquillo Fortaliza

My interests are polygamous in nature. Happily married to Mathematics but I still love Reading, Writing, and a lot more that attracts my pondering thoughts.

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