> “The musical drone, used in many spiritual practices, dilates time for both performer and listener, allowing them to temporarily exist outside of time. It is possible while in this state to renew our organs of spiritual perception and to not only experience but also to channel the enchantment in the world around us.” - Kim Cascone, “Transcendigitalism,” in *Sustain // Decay*

***

Our latest project, *Ratio*, explores the sonic realm of drones, combining some of the earliest ideas about music theory with modern digital concepts. Our personal history with drone music originates in our appreciation for artists like Pauline Oliveros, Elaine Radigue, William Basinski, and Taylor Deupree. Outside of electronic music, we’ve found inspiration in the use of drone in Buddhism, early Christian chorale musics, and the ragas of North India. While the framework of generative art often stimulates the intellect through its technical and conceptual inclinations, drone invites the listener to bypass a cognitive understanding of the work through its surface level simplicity. With little to contemplate about the music itself, the listening experience holds up a mirror to one’s inner space.

Early in the project, the question arose of how a digital work, developed through software rather than instruments, might participate in this sonic tradition and provide something new. When building a synthesizer in software, any frequency can be provided to the oscillator, including frequencies that exist between the standard notes of the 12 tone tuning system of Western Classical music. If we consider the underlying mathematics of a tuning system, the door is opened to new possibilities.

***

To understand how we arrived at our current tuning system, we must look to ancient history. Mesopotamian tablets dating from 1800BCE depict tuning systems for their harps and lyres suggesting that they were the first to understand and formalize harmony.

> \[...] there existed standardized tun­ing procedures that operated within a heptatonic, dia­tonic system consisting of seven different and interrelated scales. The fact that these seven scales could be equat­ed with seven ancient Greek scales (dating some 1400 years later) quite startled the scholarly community; and the fact that one of the scales in common use was equiv­alent to our own modern major scale seemed difficult for many to believe \[...]
>
> We also know that the Sumero-Babylonian musical system was exported at least as far away as the Mediterranean coast \[…] It is not a stretch of the imagina­tion to suggest that the ancient Greeks did, as Pythagoras said, learn Mesopotamian music theory—together with their mathematics—in the Near East.
>
> (Excerpt from Anne Kilmer, “The Musical Instruments from Ur and Ancient Mesopotamian Music”)

![An image of a Sumerian Lyre excavated from the archeological site for the ancient city Ur. Public Domain via Wikimedia Commons.](ipfs://QmfAd1jeBX55PM7wWfHq9uR81jEvstPcBAzm239tMj5fpL)

In ancient Greece, Pythagoras, Plato, and their students examined the relationship between mathematics and music, believing that music was a form of mathematics akin to geometry.

> Reportedly, Pythagoras experimented with the tones produced when plucking strings of different lengths. He found that some specific ratios of string lengths created pleasing combinations (“harmonies”) and others did not. Based on his careful observations, Pythagoras identified the physics of intervals, or distances between notes, that form the primary harmonic system which is still used today
>
> (Excerpt from "Music and Mathematics: A Pythagorean Perspective” - Edel Sanders)

The ratios 2:1, 3:2, and 4:3 took on particular significance, and would later become known as the octave, perfect fifth, and perfect fourth respectively. These ratios have a strong connection to the overtone series. Building a tuning system from these simple integer ratios based on the harmonic series is known as Just Intonation or Tuning, and Pythagoras’ tuning system is one example.

![The relationship between harmonic intervals, the frequency ratios between them, and how that corresponds to musical intervals in a Just Intonation tuning system.](ipfs://QmNdXHtdouxp81U1ZjgXJGxpuviwkXbqJ9EpehXxdss1Ve)

Building on these ideas, the *Ratio* algorithm designs chords where a single ratio, either 3:2 or 4:3, interconnects all frequencies. By using these ideal values, the consonance between frequencies is ensured. We further modify the stability of these “pure” ratios by allowing microtonal deviation, up to 3 [Holdrian Commas](https://en.wikipedia.org/wiki/53_equal_temperament#Holdrian_comma), which creates small amounts of tension and beating frequencies in the chord. By exploring harmony through mathematics, the project enables the creation of chords across the entire frequency spectrum, giving us access to chords which cannot be reached on traditional western classical instruments.&#x20;

In the diagram below, we compare the process of creating a chord using perfect fourths on the piano to the process used in *Ratio*. In our method, we can select an arbitrary frequency for the root, which lies between G2 and G#2. It should also be noted that a perfect fourth in [12TET](https://en.wikipedia.org/wiki/12_equal_temperament) (2^(5/12) = 1.334) is only approximately equal to 4:3.

![](ipfs://Qmf4uA4KS9hnGknRGqr9zyVJKRs636uF1NVyJqDmxzVszt)

We aim to create digital art which leverages the medium itself. The concept of time dilation is often used in the context of drone music, so in this work, we sought to manipulate time perception through a method unique to digital technology. The result was a freeze looper, a module which is constantly listening to the incoming audio stream, and when triggered, repeats the previously heard audio until switched back off. When used, the effect perfectly reproduces a short section of sound from the past and repeats it until freed, a process that cannot be replicated by real instruments or older technologies. This effect builds on our exploration of time as an essential, if not defining, component of audiovisual artworks in the generative art space.

The second custom effect is a texture module which utilizes techniques associated with digital recording and reproduction of sound. The module modifies the bit depth and sampling rate of the audio stream, while also producing glitches through the occasional dropped sample and introduction of dithering noise. By exploring the aesthetic of these purely digital techniques, we place the project firmly in the context of computer generated art.

![](ipfs://QmW17eXxyCEzf9DAVAMVG2ow4rveLJyJ9ajS4t9bNn9i1z)

> "It was an ancient idea that the whole number frequency ratios were important and gradually I pointed out in some of my theoretical writings that only whole number frequency ratios produce composite wave forms that are periodic. The brain analyzes information of a periodic nature better than any other kind \[…] with pure harmonic frequency ratios, you can establish profound psychological states.” - La Monte Young, creator of the [Dream Chord](https://en.wikipedia.org/wiki/Dream_chord)

# Recommended Listening

Enjoy this playlist of recommended listening, featuring ideas and artists mentioned in the article.

::embed-media[]{href="https://open.spotify.com/playlist/0Q1MYGTQm8s63AMwmROAPj?si=3f960c5de0694368"}

# Sources

[Kim Cascone, “Transcendigitalism” in *Sustain // Decay*. Void Front Press, 2017](https://www.amazon.com/Sustain-Decay-Philosophical-Investigation-Mysticism/dp/1540356574)&#x20;

[Edel Sanders, "Music and Mathematics: A Pythagorean Perspective”](https://www.unyp.cz/news/music-and-mathematics-pythagorean-perspective/)

[Kilmer, Anne Draffkorn. "The Musical Instruments from Ur and Ancient Mesopotamian Music." Expedition Magazine 40, no. 2 (July, 1998)](https://www.penn.museum/sites/expedition/the-musical-instruments-from-ur-and-ancient-mesopotamian-music/)

[Alan Licht, “A conversation with La Monte Young, Marian Zazella, and Jung Hee Choi”](https://daily.redbullmusicacademy.com/2018/07/la-monte-young-zazeela-choi-conversation)


Using our project, Ratio, as a starting point for a discussion around the intersection of time perception, the mathematics of musical harmony, and digital sound processing in the context of generative art.

Night Sea is a French-American duo working at the intersection of ambient music and generative audiovisuals. Their work focuses on the hypnotic and meditative experience of sound, combining textural atmospheres with subtle rhythms.

Digital Dream Chords - Musical Harmony, Time Perception, and Sound Synthesis

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