|On tuning & creativity: Throughout history we have thought up many visual, numeric, and verbal ways to represent the beautiful vibrations that make up music...their direct speeds, the ratios between them and even ways to show how to tamper (temper) them. The earliest written tuning instructions come to us from the time of Hammurabi and are written by cuneiform in the language called old Babylonian. An example of this in the British Museum (U. 7/80) uses the term "unclear" to refer to the tri-tone, and recommends making it "clear" by sequentially raising tones by a half step. The reverse side of the tablet tells how to lower the "unclear" ones until all seven steps are returned to the original.
Pythagoras is said to have brought the "monochord", or single string, from Mesopotamia and/or Egypt. This method is as useful today as it was several thousand years ago. Today using the metric system for marking off the proportions on a meter-length string, and then sounding them will produce the actual musical relationship intended. These can be transferred to any tunable instrument. Our luscious heritage from Claudius Ptolemy, Didymus, Avicenna, Al Farabi, Werckmeister, Kirnberger, Stanhope and a multitude of others are all available by this sure and simple method. Popular in more recent times is the graphic circular method, showing 12 "fifths" either "just"... correctly tuned to a three to two... or altered a little by widening or narrowing. Lines crossing the circle are almost always just major thirds, and in this reminding us that Europe had a "thing" for the major third and in its keyboards altered other intervals to attain it at large so to speak. Meantone temperament was a result of this.
Although for several centuries keyboards were made that presented more than twelve tones, the hypnosis of twelve has continued, and continues to spread wherever "Western" culture settles in. Even here there are apostates. The important composer Harry Partch built an entire orchestra for his works written in a forty-three tone scale. Younger people still do this and, in addition, tend to show tunings by means of "lattices."
In this fine recording of my keyboard works, Linda and I have become a part of such apostasy from the dull grey of industrial twelve tone equal temperament and worked together to take back to ourselves as artists the natural right to tune pieces in ways that are fitting, appropriate, or enhance musical beauty.