New Year’s Harmonics
2017 arrived with lots of work on every front. We bought tiles for our second floor and we’ve been starting to move steadily. A couple of friends visited us! 🤗 On the other hand, we got slightly sick since a brief change of temperature took us out of guard. I’ve mostly been studying Docker, categories and figuring my way around the technologies being used by the new team I will be joining in January (I will share more of them later on). In this post we’ll see several musical contents and relative scientific concepts, so let’s get through it.
Cheerful Meshuggah
Earlier this week, I was searching for a certain slow, smooth metal band in Spotify, and I found a song called “Cheerful Meshuggah”. This piece was composed by Dahfer Youssef, a Tunisian musician who’s worked on a variety of Jazz albums exploring outside the limits of traditional Jazz music, introducing elements from many different countries and cultures. It’s just now that I’ve learned about this artist, but a friend of mine says that his father has been admiring his works for quite some time. I guess it’s always good to discover the threads that have been inspiring the people around us ✌
We could think of this composition to be directly related to the suggested Metal band, but let’s be naive and avoid assumptions for fun. What do they have in common? Meshuggah is a variation of the Hebrew “məšugga” (Yiddish, Hebrew), which means “crazy”. There are little to no occurrences of music related to this word outside of the metal band and this outstanding Jazz match — so that’s a hint. However, the real evidence is that Cheerful Meshuggah doesn’t begin with any random group of notes, but with a drum sequence almost exactly like the song Straws Pullet At Random 🤘
There’s also a segment at the 53rd second that seems to resemble Rational Gaze’s main riff, at least to me 😜. Please let me know if you find any other match between those two.
The Album that embodies this work is named Diwan of Beauty and Odd. Here’s a short documentary on the band members and their experiences through the process of bringing life to this masterpiece:
Mr. Youssef uses this record as the medium to renew the concept of a Jazz quartet with fresh ideas like the tool he mainly uses: The Oud, a string but fretless instrument commonly used in traditional Middle Eastern Music.
Youssef also says that he is heavily inspired by odd meters because of the freedom they give, but he only uses them as long as they don’t sound odd. He says that music has to groove… like groove metal? I’ll see myself out 😸
Have you checked out Adam Neely’s latest video yet?
Over the course of the week I discovered the YouTube channel of Adam Neely, a bass player that teaches lessons through rabbit holes of knowledge he has gathered from the internet and his academic studies of music. I feel some urge on commenting everything I like about most of his content, but let’s leave that for another day. I haven’t even had the time to form a concrete opinion besides “WOAH DUDE”.
Here are some of the videos that I like from his channel (in no specific order):
- How and why classical musicians feel rhythm differently. And an after-edit, footnote, or answer to the responses he got on that video: Q+A #22 - Classical musicians still feel rhythm differently.
- What makes a song sound like Christmas?
- SUBHARMONIC Music (Anomalous Low Frequency Vibration).
- How to make 1 million dollars (as a musician).
- Steampunk black MIDI — The insane music of Conlon Nancarrow.
- Why Is Major “HAPPY”.
- Harmonic Polyrhythms Explained!
- The cult of the written score (Academic dubstep, and how sheet music affects how we listen to music).
- Quartal Melodies and Autotune (the intro music!).
Adam’s channel showcases his experiences and wanders in a way that is sound to the drive that most of us, netizens, have while we spend hours and hours navigating the vastness of the web. He’s never afraid to mention mathematical concepts that are used in music theory (or by musicians) to break away of the limits of their instruments and their relative status quo. For example, in the video about Conlon Nancarrow, Neely talks about Nancarrow’s interest on rhythmic relationships based upon irrational numbers, and even points to a paper which explains how such Studies can be performed by humans through approximations. On another of his videos, the one about Harmonic Polyrhythms, he begins by talking about the mass-energy equivalence (E=MC²), and how many features in reality are essentially the same form of energy occurring in different scales. He uses this information to make experiments and display how a 5:4 polyrhythm played on simple attacks on the kick drum at high enough speed is equal to a Major 3rd. These experiments are thrilling to me, for they are quite literally experiential learning, which (even if being virtual) expose a real-world experience from which he and all his viewers directly perceive a manifestation of different levels of the concepts being studied, using sound, animations and direct usage of tools in the process.
If you like his videos and you want to support him, please go to his Patreon page. It’s worthwhile, just watch his videos, like the one in which he talks about patronage.
Musical Numbers
Some of the key concepts in Music are natural occurrences of phenomenons that can be well described by Mathematics. For example, the non converging Harmonic Series perfectly matches the musical harmonics in string instruments. A string played without alterations represents a single tone, when it’s interrupted in it’s half (1/2) it represents the first octave, when interrupted at a third (1/3) of it’s length is a perfect fifth, and so it goes through the Harmonic Series, 1+1/2+1/3+1/4…
Another mathematical concept that can be experienced by studying music is the Golden Ratio. It consists of an irrational number that arrises in geometry by calculating the difference between two line segments, one of a length and another of b length, where a+b is to a as a is to b, or: (a+b)/a = a/b. This relation is always proportional to an irrational number named after the greek later phi (φ), and can be approximated to 1.6180339887498948482…
A spiral which growth is described by the phi (φ) constant can be closely approximated by tiling squares of side lengths equal to the sum of side lengths of those two squares previously tiled. This is known as the Fibonacci Sequence, where the next Fibonacci number F(n) is equal to the sum of the Fibonacci numbers F(n-1) and F(n-2). Thus constructing a sequence that starts with: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55… This sequence appears in nature everywhere (yes, even outside your first recursive script). For example, if you see a spiral in nature, you can be pretty sure it arises from the golden ratio. It can be seen in plants, hurricanes, galaxies and even in the DNA.
— ViHart has a triad of videos about the Fibonacci numbers and the Golden Ratio. If you’re curious and willing to spend some minutes entertaining yourself with beautifully explained mathematical concepts, please check them out: Doodling in Math: Spirals, Fibonacci, and Being a Plant, part 1, part 2 and part 3.
It’s not surprising that the numbers of the Fibonacci sequence, so closely related to the Golden Ratio, can be also found in music. For example, harmonics are described in octaves, fifths and thirds. Sylvain Lalonde also shows in this video how these numbers appear in both the Chromatic Scale and the Diatonic Scale:
GoldenNumber.net shows other occurrences of the Fibonacci numbers in music:
- There are 13 notes in the span of any note through its octave.
- A scale is composed of 8 notes.
- The 5th and 3rd notes of any given scale create the basic foundation of all chords and are based on a tone which are combination of 2 steps and 1 step from the root tone, that is the 1st note of the scale.
Additionally, there’s a close match to the Golden Ratio in musical frequencies. If instruments are tuned with the note A in 432hz, it’s fifth (or E) becomes 162hz, which is the number one and the first two decimal points of phi (φ). This is a polemic topic that is discussed ad nauseam in YouTube because in theory a pitch matching that of the universe can have good implications to our brainwaves and nature in general. Unproven theories like this must be taken with a grain of salt, but it’s never good to just accept what everybody does, like setting A to be 440hz. Here’s a fun video if you’re interested: HISTORY OF PITCH: 440hz vs 432hz, by FrankJavCee.
Even though our brains can be tricked by similarities, it’s impressive how mathematics can so closely represent nature in so many levels.
The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning.
— Eugene Wigner.
Gravitational Waves
This first week of January arrived with a couple of gifts given by the great YouTube Channel, Veritasium. Derek Muller presents us with the story behind Humanity’s breakthrough of discovering Gravitational Waves, the absurd engineering challenges the LIGO scientists went through, and how lucky they were to detect this event. The discovery celebrated a year old on September 14th, 2016, and Muller now offers us two fresh perspectives:
Along the lines of phi, music and astrophysics, this past week a YouTube user named Aubrey Meyer published a little video that quickly exposes many beautiful aspects hidden in phi (φ), and even dares to ask questions about the universe itself and our place within it. I had a blast watching it, so please check it out:
I will leave by evoking Tunisia, the mother country of the aforementioned Jazz player, Dahfer Youssef. This little country in the Mediterranean sea, sibling of Algeria and Libya, and far neighbor of Malta and Italy, is known for having a high human development index, for being the only full democracy in the Arab World, and for staring in this lovely bebop song called “A Night In Tunisia”. Here is an interpretation made by Cyrille Aimee and Diego Figueiredo:
