Comments on Partch's Extended Diamond
Erv Wilson crossed paths with Harry Partch in the 60's and during this period supplyed the diagrams for the second edition for "Genesis of a Music". He suggested and helped build the Quadrangularis Reversum. One the features of this instrument is of doing appeggios going upward instead of downwards like the diamond marimba. He also donated the Bolivian Double Flute which would have a important role in Partch's" Delusion of the Fury".
What is important here is Wilson's observation of how Partch filled in the gaps of his 11 limit diamond and also how Partch would use his tuning in practice. Wilson noticed that both him and Novaro attempted to fill in the gaps of his tuning in a way where same interval is subtended by the same number of steps. Later Wilson would name these Constant Structures. While this is not possible with the 11 limit diamond without adding a extended number of notes, it is possble to do so if one allows two tones to act as variable degrees. Wilson stated that he heard and saw Partch use his tuning in a way consistent with a 41 tone system, substituting notes found in his tuning for ideal ratios.
PERSPECTIVES ON HARRY PARTCH'S EXTENDED DIAMOND offers Wilson papers on mapping Partch's tuning to a 41 tone matrix with possible ideas for other instruments. Included is George Secors suggestion for his generator and keyboard mapping others modified into what became known as his Miracle tuning.
ALTERNATIVES TO HARRY PARTCH'S EXTENDED DIAMOND shows Wilson alternatives to Partch's system. Pages 1-5 represent one 11-limit 41 tone system constant structure that is also bias toward a central point but expands secondary relationship the further one moves from the 1/1 in a unique and unnamed process that deserves further exploration. The complexity mentioned in page 6-10 refers to this chart
Page 11 relates to the alternative on page 1 in including the Indian 22 tone 5 limit matrix and is the 41 tone scale found on page 10-11 xen3b.pdf and xen3bappendix.pdf except spelled out a 3/2 lower.
'Eckland' is the first in a set of tunings that extend the diamond properties to 2 points instead of a single 1/1 mapped to a 31 tone keyboard pattern. Wilson commented that multiple diamonds offers both great modulatory resources but also yield many more repeatable tetrachords. Andrus adds 4 filler notes to Eckland and is mapped to a 41 tone keyboard. Andromeda shows mapping of two full diamonds with Cassandra showing the ogdoadic 13 and 15 limit diamond onto a 53 tone keyboard with charts of the closely related scales.
~Comments and Questions Welcome~