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All Unique Wave And Window Combinations

The previous page lays out ALL POSSIBLE combinations of waves and windows. This is a very thorough approach, and at the time I didn't know if I would find unexpected differences. But the results turned out to be very consistent, and therefore included a lot of redundancies.

This page restates in a single table all of the UNIQUE combinations of waves. In other words, I took all 512 possible combinations and eliminated everything redundant. I think it's nice to see all the possibilities on one page with no redundancies.

Test Procedure

The thing I need to explain here is how I figured out which wave and window combinations are UNIQUE. First, I started with a table showing all of the unique wave combinations:

000-000	000-001	000-010	000-011	000-100	000-101	000-110	000-111
001-000	001-001	001-010	001-011	001-100	001-101	001-110	001-111
010-000	010-001	010-010	010-011	010-100	010-101	010-110	010-111
011-000	011-001	011-010	011-011	011-100	011-101	011-110	011-111
100-000	100-001	100-010	100-011	100-100	100-101	100-110	100-111
101-000	101-001	101-010	101-011	101-100	101-101	101-110	101-111
110-000	110-001	110-010	110-011	110-100	110-101	110-110	110-111
111-000	111-001	111-010	111-011	111-100	111-101	111-110	111-111

The white squares are unique combinations, the pink squares are valid but are more easily achieved by using a single wave, and the blue squares are not unique because they are just reversed versions of waves already shown in white.

If you count them, there are 36 white and pink squares. You can run those 36 unique wave combinations through 6 unique window functions for a total of 216 unique wave and window combinations ( 36 x 6 = 216 ).

The illustration below makes the calculation visible all at once. It is an 8 x 8 x 8 cube, for 512 possibilities. I colored it according to the table above. You'll see that the front looks just like the table, but now it's been extruded back to account for the 8 possible windows. Note that Window 110 and Window 111 are shaded, because they are the same as Window 101.

To summarize, the 216 unique combinations are shown in the cube above. I have included all of the 216 unique combinations in the table below. Note that for the pink squares I have substituted the more simple single wave.

Findings

• It should be obvious that there are a lot more than 33 possiblities when using sysex.
• I think that a lot of these possibilities are not just junk, they are usable. They are especially good for people like me who like things that go buzz and squee.

Table Notes

• There is one single table below that lays out the 216 unique wave and window combinations.
• Each audio file in this table takes the basic wave combination shown at left and passes it through all eight of the window functions. The window functions go in order, so the first one you'll hear is WINDOW 000, the second is WINDOW 001, and so on.
• I am being lazy with the audio samples. Even though there are only six waves in every line, you will hear eight samples in every audio file. The extra two samples are the same wave combination going through WINDOW 110 and WINDOW 111. These samples are redundant to the one for WINDOW 101. However it would have been a waste of time and hard disk to create new audio files with those samples removed. Thanks for understanding.
• - Casio documented 33 possible wave combinations. Each of these original 33 is marked with the Panel icon.
• All other waves in the table are sysex only. I didn't mark them because there are so many of them.

Edited

• 11805.590 - page in progress
• 11809.629 - reviewed, add a few things

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