week 15: Kathleen O'Brien's

The Art

“Pentad” by Kathleen O’Brien
12 x 7.5, collage on Arches Cover;
From the series “The Mystery of Numbers”,
abstract watercolors, drawings, ephemera from an antique encyclopedia and Forget-Me-Nots.


O'Brien, "Pentad" watercolour, drawing, collage, 12 x 7.5"

O’Brien, “Pentad” watercolour, drawing, collage, 12 x 7.5″


The Music

“The Phi of five” (6:01 mins) © Helen Davey
for 5 voices, frame drum, egg shaker, lap harp, hackbrett (hammered dulcimer) 


Artist’s notes

Kathleen O’Brien

“Pentad”, from this series of Golden Rectangles, revisits one of my favorite subjects, Sacred Geometry, the development of numbers and related forms starting with one. The flatness of the basic forms are well suited to the flatness of collage. The method of construction of Pentad or Pentagram is complicated and was kept secret until Luca Pacioli (da Vinci’s teacher) published Divina proportione in 1509.

First one must create the Dyad from intersecting circles which creates the shared space, the vesica piscis. Next, once creates the Triad and triangle, then Tetrad and square. Using the points of the 4 previous forms one can draw the Pentad. Its geometry is seen often in nature, like the seeds of the apple, a starfish, and our own hands.

My Music

Focussing on the mountains in Kathleen’s artwork, “The phi of five” is a meditative pathway on five-ness. The meter is set in 5/4; I have used a hackbrett (Swiss hammered dulcimer) tuned to a C pentatonic (5-note) scale; the harmonic structure of this piece emphasises the consonance of the perfect 5th, unison/tonic and the octave (in equal temperament rather than Pythagorean or vedic tuning) which are all paramount in the first 5 notes of the overtone/harmonic series;

fibonaci sequence 2 on piano (www.astrosound.org)

fibonaci sequence 2 on piano (www.astrosound.org)



I’ve also used the first 5 numbers of the fibonacci sequence when the fundamental tone is C (as this diagram of piano keys indicates).




At the time when Pacioli revealed the golden ratio in his “Divina Proportion”, people believed that the world was flat and a firm dome – the firmament – separated the earthly waters from those above. As a “forget-me-not” to this time period, I took some Latin text from Hildegard von Bingen* where she describes the firmament. I’ve also referred to some of the key mathematicians who contributed to the development of the golden ratio (from Pythagoras ca. 490 – 430 BC) through to Paciolli (1445 – 1517).

For a person who finds it difficult to remember their own telephone number, researching the topic of sacred geometry was fascinating for me! Hope you too enjoy this collaboration of art and music. I’m interested to know what you hear/see in these artworks and welcome hearing from you via the comments section below; please feel free to share this around to anyone interested in cross arts projecrts, using the little icons below.

Sending you a high 5 and a Phi Pho Phip
(which is phi squared when A and B are vying for 5th in line for a Pho)


O'Brien, (detail) "Pentad"

O’Brien, (detail) “Pentad”

* Hildegard of Bingen, On the Planets and the Firmament. Excerpted from Causae et Curae: Kaiser 9:20; Moulinier 30:26–31:6; Kaiser 14:17, Moulinier 37:15–38:23

6 comments to week 15: Kathleen O’Brien’s “Pentad”

  • David

    I find this harmonic resonates with me.

  • Helen, this is such a beautiful mediation on 5. Being 6 minutes long helps me settle into the peacefulness of it. I especially enjoy the drum, shaker and harp sounds. It makes me so happy to inspire research into sacred geometry, and that you created this piece in 5/4 meter and the Fibonacci sequence as a result. This is new to me, so I am glad to add to my understanding of the golden ratio. The voices singing of the firmament are perfect. It made me smile to receive your high 5 and a Phi Pho Phip, and the same to you. Thank you so much for including me in your project.
    and I love feeding the fish!

  • Helen

    Kathleen, it was really stimulating to research this part of our history. Couldn’t resist incorporating Hildegard von Bingen’s text (although my Latin teacher would likely wince at my pronunciation); it just seemed fitting, in terms of honouring the scholars of that era and the extraordinary series of discoveries leading to our current understandings.
    Thanks for being part of project 52, and for feeding the fish!

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