The Mathematics of Music: Tool’s Lateralus

Music is equal parts art and mathematics; however, some bands take this relationship to an extremely fascinating depth. Tool’s 2001 album, Lateralus, deals heavily with metaphysical themes built upon mathematical structures, such as the Fibonacci Sequence.

The Fibonacci Sequence

        The Fibonacci Sequence is a numerical pattern in which each number is the sum of the two preceding numbers. As an equation, it is expressed as Fn=F(n-1)+F(n-2), and it looks like this: 0,1,1,2,3,5,8,13… It is a sequence that has become particularly interesting due to its recurring presence in computer programming, nature, and in this case, music.

Fibonacci Fractal. (Source: Anders Sandberg http://www.flickr.com/photos/arenamontanus/)

The Golden Spiral

The titular track on Lateralus contains the most prevalent use of the Fibonacci Sequence. For one, it alternates between three unusual meters (9/8, 8/8, and 7/7) that together comprise the sixteenth number in the sequence (987).

More convincing is the vocal pattern of the lead singer during the first verse. The syllables in each line are sung as follows: 1, 1, 2, 3, 5, 8, 5, 3, 2, 1, 1, 2, 3, 5, 8, 13, 8, 5, 3. These ascending and descending sequences tie thematically to the “spirals” mentioned later in the lyrics by mimicking “The Golden Spiral”—a special shape that expands infinitely by a constant factor and it is the very factor the Fibonacci sequence presents.

The Golden Spiral. (Source: Helen Stevens http://www.flickr.com/photos/helen_stevens/)

“The Holy Gift”

        To go a step farther and incorporate the whole album into this theory, fans have rearranged the order of the tracks on the album into a similarly shaped sequence. The key to the order was placing track 13 in the middle and arranging the other tracks in additive pairs on either side. The songs  are said to match up with each other in a more sensible way, and makes for the “proper” order.

        Unconvinced? Here is a video, with song accompaniment, that makes a more in depth argument: 

Source:

https://math.temple.edu/~reich/Fib/fibo.html

http://www.peteofthestreet.net/sayz/C1151806467/E1494764863/

Nathan Repp is a writer for Scholar Hero, Inc.

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Daft Punk and the Introverted Celebrity

Rising above the fray of the MTV Video Music Awards, the enigmatic duo of Daft Punk offered an alternative presence to the confluence of celebrity.

Daft Punk somehow tows the line between immense notoriety and well-guarded secrecy. Some have compared their use of theatricality to that of Lady Gaga, but the mechanics are completely opposite. Lady Gaga’s music is heavily reinforced by her theatricality. Daft Punk’s theatricality is introverted, meant to shield themselves allow their music to stand alone.

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(Photo Source: Fabio Venni http://www.flickr.com/photos/fabiovenni/)

Despite their frequent attempts to remain cloaked from the limelight, most recently balking on an appearance on The Colbert Report, Daft Punk has been wildly popular team since the mid-1990s. Yet there are no public demands for them to discard their robotic exteriors and explain their actions. People only care about the music.

Daft Punk’s unique example of celebrity shows that it is possible to separate one’s personal identity and artistic craft in order to be popular. Of course, there are a confluence of other factors that influence celebrity, such as gender or race, but there’s comfort in knowing that some groups can exist solely for their musical talent.

It was even their lack of appearance on The Colbert Report that left an impact: http://www.colbertnation.com/the-colbert-report-videos/428372/august-06-2013/stephest-colbchella–013—daft-punk-d

Nathan Repp is a writer for Scholar Hero, Inc.

Remember, Remember, the 7th of September: Thrill Mill’s Thrival Innovation + Music Festival

Scholar Hero has been excitedly preparing for this upcoming Thrival Innovation + Music Festival on September 7th, our first opportunity to show off some of our hard work to the Pittsburgh public. As members of the Hustle Den’s inaugural cohort, we have been invited to join other startups and entrepreneurs to talk openly to attendees and potential investors about our products and future plans.

The Origins of the Thrival Festival

The Thrival celebration is actually an annual celebration organized by Thrill Mill, Inc., featuring several musical acts and festivities, all towards raising money for The Business Bout. Thrill Mill co-founder and chairman Luke Skurman http://about.me/skurman originally came up with the idea in 2005 to strengthen the Pittsburgh entrepreneurial community and reduce the pattern for the city’s young talent to emigrate to other larger cities. Years later, it is now one of the biggest networking events in the city.

Ultimately, The Thrival Festival is meant to close out the summer strong with entertainment and connection with the Pittsburgh entrepreneurial community. There will be food and drink available for attendees as well as live-performing musical artists such as De La Soul, RJD2, and Frightening Rabbit. Proceeds will go to Thrill Mill, Inc. to further support and incubate the next cohort of brilliant entrepreneurs.

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Scholar Hero’s Thrival Role

Scholar Hero will be one of the 13 Hustle Den companies to be stationed in Innovation Row at Bakery Square and delivering a brief pitch to potential investors at Google Pittsburgh. We will be showing prototypes of three products, all designed to assist scholars in creating and sharing their work:

·      Amino – A document assistance service helps structure ideas and data, preventing the writer’s block that comes with “blank page syndrome”

·      Synthesis – A document sharing service designed for acquiring rich community feedback.

·      Fusion – A mobile solution to “crowd-reviewing,” involving a gamified, ranking system.

You can read about all of the Hustle Den companies here. http://thrillmill.com/meet-the-teams/

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The Thrival Innovation + Music Festival is September 7th from 12:00pm to 10:00pm. More information can be found here: http://thrivalfestival.com/about/.

Help us celebrate those that choose make a difference. As Thrill Mill co-founder and CEO Bobby Zappala said: “You can’t change the size of Pittsburgh, but you can change how people think about it.”

Nathan Repp is a writer for Scholar Hero, Inc.