Glass Organ: Basic Tuning

A random collection of notes will yield a great number of dissonances, and probably few, if any, consonances. In designing a system for the glass organ, I aimed first to maximize consonance. I began by making a list of small whole number ratios within an octave: 1/1, 2/1, 3/2, 4/3, 5/4, 6/5... It soon became clear that I could organize these pitches into a table with a column for each numerator and a row for each denominator:

9 Odd-Limit Tonality Diamond

Harry Partch often designed his instruments around a grid like this one. He called it the "Incipient Tonality Diamond." Read more about the Diamond and Harry's instruments in my Tuning section.

Even without using even rows or columns (except 2), several ratios show up multiple times in this table. 4/3 and 3/2 each show up twice because 9/6 = 6/4 = 3/2 and 8/6 = 12/9 = 3/2. Nine is the only column heading which is not prime (9 = 3 × 3), so some of its ratios reduce to simpler ratios (9/6 becomes 3/2, 12/9 becomes 4/3). 1/1 shows up 5 times in this table creating a diagonal line from the upper left to lower right hand corner.

I looked at this diamond and thought about building a glass organ with the glasses in a diamond configuration just like this chart. I had trouble finding enough glasses to tune to every note and it seemed wasteful to have 5 glasses tuned to 1/1. If I just took out the 1/1s and collapsed the table, I would ruin the row=major, column=minor aspect of this tuning. One of the unique and powerful side-effects of Just Intonation systems of this type. I began to look for ways to consolidate the rest of the pitches, yet keep the row and column, major, minor correlation that I wanted.

For more details on the layout please see my Glass Organ Layout page