With his extensive writing, Rudhyar formalized theories behind the non-objective and symbolic expression of the TPG painters.  Referencing his relationship to the Transcendental group, he wrote in the preface to his book, Astrological Insights into the Spiritual Life: 

"During the Summer, 1938, while living in Santa Fe, New Mexico, I found myself close to several painters who had felt the need of forming an officially recognized group because they were all sharing an approach to Art definitely different from the more fashionable trends highly publicized in the big cities of the East Coast.  I participated in their discussion and their search for a name, and they finally adopted my suggestions, calling their group the Transcendental Painting Group.  I did not belong to the Transcendental Painting Group itself because at the time I had done no painting or drawing, but for a number of years, my musical career had been blocked by the antagonism of Neo-Classicists who since the late Twenties had come to control all openings in the music world, and being stimulated by my painter friends and that summer living in favorable conditions in Santa Fe, I felt the urge to draw and eventually to paint.  This I felt would somewhat take the place of music in my creative life." (Parker/Pasquine)

He was also a musician, and in 1913, when he was a teenager, some of his compositions were published.  Because of influence of TPG leader, Raymond Jonson, he also experimented with abstract, symbolic painting. 

Rudhyar was born in Paris and raised in a middle class family with the last name of Chenneviére.  He had poor health throughout his childhood, and because of limited physical activity, he "learned to value life through his inner spirit." (Blankenship, 24)  He attended the Sorbonne, majoring in philosophy, and graduated at age 16.

In 1916, when he was age twenty-one, he moved to New York City where he oversaw a radical, experimental multi-media performance, Metachory, at the Metropolitan Opera.  In New York, he became immersed in Zen Buddhist studies and western occult subjects including astrology mixed with psychology.  With the destination of Krotona, headquarters of the American division of Theosophical Society, he went to California in 1920.  He wrote articles for the magazine, American Astrology and began a publishing career with his 1936 book, The Astrology of Personality, establishing his reputation.
Spending time in Taos and Santa Fe in 1933, he met Raymond Jonson, organizer of the Transcendental Painting Group, and the two men found they had much in common intellectually and emotionally.  Not yet painting himself, Rudhyar gave Jonson a copy of seven of his published essays titled Art as Release of Power.  Future trips to New Mexico involved Rudhyar in the American Foundation of Transcendental Painting, the fundraising entity of the Transcendental Painting Group.  Rudhyar wrote many supportive articles, and his canvases reflected their ideas.

He died in San Francisco in 1985.

Sources: askART

Tiska Blankenship, Vision and Spirit: The Transcendental Painting Group, Exhibition Catalogue of the Jonson Gallery, University of New Mexico, 1997

Paul Parker, Collector and Scholar of the Transcendental Painting Group:
Among his sources are: Ruth Pasquine: 3 volume PhD (1000 pages) dissertation:  Dynamic Symmetry and Theosophy in the Art of Emil Bisttram

http://en.wikipedia.org/wiki/Dane_Rudhyar