Showing posts with label Hexany. Show all posts
Showing posts with label Hexany. Show all posts

Wednesday, June 8, 2016

A 22 TONE 11 LIMIT CONSTANT STRUCTURE FORMED FROM A SPECIAL HEXANY STELLATION METHOD

This 22 tone scale of Wilson's believed to be from 1967 was found in a series of papers, charts and scales based  stellating Hexanies in  i have not seen before. One particular method resulted in the example below which seems to form the core of the scale above. Wilson took the 1-3-7-11 hexany and stellated it with 5 and /5 to complete the 8 basic triads found within which results in the 14 tone structure to the left. The result of this type of stellation has unexpected results. for instance 4 other hexanies are formed each which occurs twice.  All involve the added 5 plus three factors of the 1,3,7,11 set.  Because of the relationship of most of the added pitches to this stellate being 3/2 above and below, to form this 22 tone scale. 4 more hexanies also appear. The result is one of many 22 tone scales that contain a great variety of compact hexany subsets. 




Saturday, December 11, 2010

Hexany as a 12 tone meeting place

Here Wilson worked out the possibility of using a Hexany  as a meeting place between a harmonic and subharmonic series having no tones in common. the Second example here shows the two complementary series this time up the the 13 (or 15) (sub)harmonics still limited to 12 tones.