Glass Organ: Layout

Originally I arranged the glasses to go in ascending order from lowest to highest pitch. I found the configuration very good for playing melodies but not very good for playing harmonies. To remedy this I looked to Partch and copied his "Incipient Tonality Diamond" (see also, Just Intonation Scale Design). I set about arranging the glasses on my organ in a way that would maintain some aspects of the diamond and some chromaticism. Also I didn't want to reach over more than 4 glasses, and I didn't want any repeated notes because tuned glasses are a scarce resource.

By repeating rows or columns, one could tile the 9 odd-limit Tonality Diamond (see Glass Organ Tuning Part 1) in any direction. Notice that the diagonal of 1/1 makes a recognizable pattern when the table repeats.

Repeated 9 Odd-Limit Diamond (original diamond shown in white)

Because I have repeated my matrix, I still have all my original notes between the 1/1 diagonals. In the next table I have removed everything but my original ratios between the diagonal 1/1s.

Repeated ratios removed to reveal consolidation

I have removed the repeated 1/1s without sacrificing my row and column chordal relationships!

When playing the instrument, I discovered how nice it is to have notes arranged more or less chromatically. Especially when playing melody or matching another performer's note. If you try to follow the scale around the matrix chromatically, it is very confusing.

In my continuing quest for chromaticism, I tried changing the order of the rows and the columns. I noticed that if you shift the same rows as columns, you maintain the shape of your scale in the matrix! This is a very useful trick because it allows you to change the order of the pitches without changing the shape of the instrument.

"7" row moved above the "3" row

"7" column moved in front of the "3" column

Now, you can follow the ratios around the chart snaking around in a more or less chromatic fashion. Start from 10/9 in the lower right hand corner. Jump to the 9/8 in the middle of the top, and proceed diagonally to the right. From 6/5, jump back to 5/4 at the top and proceed diagonally down to the right again and so forth. Not perfect, but getting better.

Somehow in the course of all my experimentation, I reversed all the rows. This is not a problem and I left it in this explanation to show that it is possible.

Rows reversed

Here I considered my table a pattern again, and tiled it outward. This allowed me to slice my scale in a different way, again, maximizing chromaticism. I can do still better by taking a different slice of this pattern. First I'll expand it.

Expanded (previous table coverage shown in white)

Now I'll slice it.

New selection shown in white

I've just cleaned up the mess of extra ratios I created when I tiled and sliced in the previous 2 tables. Look at the chromaticism now!

Selection isolated (row labels removed)

The physical constraints of playing the instrument are always an important consideration. It was much easier for me to build a square glass organ than a trapezoidal one.

Imagine someone putting a heavy weight on top of the previous chart, to slide the highest columns of data downward. The matrix below is very similar to the layout of some of my first glass organs.

Vertically collapsed into a 4 row by 5 column grid

Not surprisingly, I got tired of thinking about the otonalities going diagonally down and right when I played the organ. Not to mention that I am right handed, and had to twist around to play them. That's when I thought it would be worth while to build a trapezoidal organ. You can think of this table shifting the previous one to the right like the leaning tower of Piza. Alternately, you could see it as the "Section Isolated" table rotated 45 degrees to the right. We have nearly reached the layout of my current organ.

Horizontally tilted to the right

You can move (more or less) chromatically by going left or right in any row. Upper-left to lower-right diagonals are still Otonal (major) and upper-right to lower-left are Utonal (minor).

Earlier, I mentioned eliminating duplicate notes, yet I kept the duplicate 4/3 and 3/2. It is very hard to find enough glasses for an organ like this without repeated notes. Not to mention the weight! I substituted the 1/1 and 2/1 for 4/3 and 3/2 respectively.

1/1 substituted back in

I could add extra pitches to any side of this layout and that is just what I did. Read on: Glass Organ Tuning Part 2.