Week 2 - Math and Art

 Art and Mathematics 

    The intersection between art and math is one that is often overlooked and avoided due to the seemingly unbreakable barrier between the two. In reality, the two subjects are far more intertwined than what is seen at first glance. An example of the dependency of art on math is the calculations behind frequency and pitch in music. In my hometown Portland Oregon, the climate tends to be cold and dry for most of the year. Although the humidity rises a bit in the summer, it generally never reaches above 60%. For this reason, mathematicians have generally found that the ideal pitch to tune to is an audio frequency of 440Hz. After being used to tuning to this frequency for most of my life, I attended a summer music camp in North Carolina, where the weather was consistently in the 90s and the humidity averaged at around 85%. This caused significant changes for my instrument that forced me to adjust to the sudden change in climate. Interestingly, I found that the orchestras in these climates tuned to a frequency of 441Hz rather than 440Hz. I hadn't given this anomaly much thought back then, but after this week's lecture topic, I decided to do more research on why that was the case. I discovered that metal strings have a tendency to go flat with increasing temperature, which is why the orchestra will initially tune to a higher frequency, to negate the effects of becoming too flat over the course of the performance. The higher temperatures cause the wood of the instruments to expand and lose resistance. This causes changes to the sound post, which will ultimately affect the sound. The methods for fixing this issue such as tuning to a higher frequency and keeping humidifiers in the instrument's case would not have been viable without the mathematical calculations behind them. 

https://introcs.cs.princeton.edu/java/assignments/dsp.html

https://www.mathnasium.com

    Another topic from this weeks lecture that interested me was the Golden Ratio, which is the ratio of 1:1.618. Because this ratio appears so much in nature, many use it to create art and architecture that is appealing to the eye. I find it very interesting that it's a principle that can be found in the natural world as well as in manufactured objects. Some examples of the ratio in nature include flower petals, shells, and galaxies, which are all pleasing to the eye. 

https://www.mathnasium.com

The intersection of art and mathematics is one that is so prevalent in both cultures and adds so much to the world today. 

Sources

Burk, Phil. “Chapter 1: The Digital Representation of Sound, Part One: Sound and Timbre.” Music and Computers, musicandcomputersbook.com/chapter1/01_03.php.

Mann, Adam. “Phi: The Golden Ratio.” LiveScience, Purch, 25 Nov. 2019, www.livescience.com/37704-phi-golden-ratio.html.

Mnatzaganian, Sarah. “Humidity and Cellos.” Aitchison & Mnatzaganian Cello Specialists, 12 Jan. 2021, www.aitchisoncellos.com/humidity-and-cellos-2/.

Neil. “Why Does Pitch Change with Temperature?” The Horn Guys, www.hornguys.com/blogs/horn-guys-blog/15338265-why-does-pitch-change-with-temperature.

“Why Stringed Instruments Don't Stay Tuned.” Meadowood, www.meadowoodmusic.com/care-tip-33#:~:text=Metal%20strings%20generally%20go%20flat,humidity%20climbs%20(wood%20swells).