Window Function And Combination Waves

2007-12-17

After I got done testing how the window function affects single waves, I immediately began wondering how the window function would affect combination waves.

About Combination Waves

The combination waves work a little bit differently than Casio's documentation would lead you to believe. I wrote a thorough description of it, with examples, a few pages back.

Test Procedure

I decided to do the MOST THOROUGH TEST POSSIBLE. I wanted to know how the window function affects combination waves. So I made patch dumps that combined EVERY WAVE with EVERY OTHER WAVE and then ran it through EVERY WINDOW. Then I took image snapshots of every combination, and audio samples of every combination. The results are below.

There are eight possibilities for WAVE 1, eight possibilities for WAVE 2, and eight possibilities for the WINDOW. That means there 512 possibilities to document (8³ = 512).

The problem with this approach is that I have included a lot of redundant waves. Out of the 512 combination possibilities, I estimate that only 216 of them are unique. So, yeah, the eight tables below include a lot of redundancies.

Window Function Demo—Combination Waves

There are eight tables below. Each table takes a basic wave, combines it with every other wave, and passes it through every window function. This serves as a demonstration that it is possible, via sysex, to combine all waves with all windows. There are no outages; everything is possible. It also serves as a map to show the results of these unholy combinations.

The first table takes WAVE 000 and combines it with all possible waves, and then passes each combination through all the different window functions. The second table takes WAVE 001 and does the same thing, and so on.

Each table is accompanied by audio files. Each audio file represents a row in the table above it. It takes the given combination of two waves, and passes it through each window function. The first sample will use WINDOW 000, the second will use WINDOW 001, and so on.

Key for each table on this page

The following key or legend applies to all tables on this page.

This option is available through the front panel.

This option is only available through sysex.

You'd be better off using a single wave, rather than this combination.
It is easier to imagine how the window functions affects single waves.

WAVE 000

This table shows WAVE 000 combined with every other wave, and passed through every window function.

WAVE 000, combined with every other wave, passed through every window
Click image to see full-size image

• Row 1 - WAVE 000 + WAVE 000, passed through all windows
• Row 2 - WAVE 000 + WAVE 001, passed through all windows
• Row 3 - WAVE 000 + WAVE 010, passed through all windows
• Row 4 - WAVE 000 + WAVE 011, passed through all windows
• Row 5 - WAVE 000 + WAVE 100, passed through all windows
• Row 6 - WAVE 000 + WAVE 101, passed through all windows
• Row 7 - WAVE 000 + WAVE 110, passed through all windows
• Row 8 - WAVE 000 + WAVE 111, passed through all windows

WAVE 001

This table shows WAVE 001 combined with every other wave, and passed through every window function.

WAVE 001, combined with every other wave, passed through every window
Click image to see full-size image

• Row 1 - WAVE 001 + WAVE 000, passed through all windows
• Row 2 - WAVE 001 + WAVE 001, passed through all windows
• Row 3 - WAVE 001 + WAVE 010, passed through all windows
• Row 4 - WAVE 001 + WAVE 011, passed through all windows
• Row 5 - WAVE 001 + WAVE 100, passed through all windows
• Row 6 - WAVE 001 + WAVE 101, passed through all windows
• Row 7 - WAVE 001 + WAVE 110, passed through all windows
• Row 8 - WAVE 001 + WAVE 111, passed through all windows

WAVE 010

This table shows WAVE 010 combined with every other wave, and passed through every window function.

WAVE 010, combined with every other wave, passed through every window
Click image to see full-size image

• Row 1 - WAVE 010 + WAVE 000, passed through all windows
• Row 2 - WAVE 010 + WAVE 001, passed through all windows
• Row 3 - WAVE 010 + WAVE 010, passed through all windows
• Row 4 - WAVE 010 + WAVE 011, passed through all windows
• Row 5 - WAVE 010 + WAVE 100, passed through all windows
• Row 6 - WAVE 010 + WAVE 101, passed through all windows
• Row 7 - WAVE 010 + WAVE 110, passed through all windows
• Row 8 - WAVE 010 + WAVE 111, passed through all windows

WAVE 011

This table shows WAVE 011 combined with every other wave, and passed through every window function.

WAVE 011, combined with every other wave, passed through every window
Click image to see full-size image

• Row 1 - WAVE 011 + WAVE 000, passed through all windows
• Row 2 - WAVE 011 + WAVE 001, passed through all windows
• Row 3 - WAVE 011 + WAVE 010, passed through all windows
• Row 4 - WAVE 011 + WAVE 011, passed through all windows
• Row 5 - WAVE 011 + WAVE 100, passed through all windows
• Row 6 - WAVE 011 + WAVE 101, passed through all windows
• Row 7 - WAVE 011 + WAVE 110, passed through all windows
• Row 8 - WAVE 011 + WAVE 111, passed through all windows

WAVE 100

This table shows WAVE 100 combined with every other wave, and passed through every window function.

WAVE 100, combined with every other wave, passed through every window
Click image to see full-size image

• Row 1 - WAVE 100 + WAVE 000, passed through all windows
• Row 2 - WAVE 100 + WAVE 001, passed through all windows
• Row 3 - WAVE 100 + WAVE 010, passed through all windows
• Row 4 - WAVE 100 + WAVE 011, passed through all windows
• Row 5 - WAVE 100 + WAVE 100, passed through all windows
• Row 6 - WAVE 100 + WAVE 101, passed through all windows
• Row 7 - WAVE 100 + WAVE 110, passed through all windows
• Row 8 - WAVE 100 + WAVE 111, passed through all windows

WAVE 101

This table shows WAVE 101 combined with every other wave, and passed through every window function.

WAVE 101, combined with every other wave, passed through every window
Click image to see full-size image

• Row 1 - WAVE 101 + WAVE 000, passed through all windows
• Row 2 - WAVE 101 + WAVE 001, passed through all windows
• Row 3 - WAVE 101 + WAVE 010, passed through all windows
• Row 4 - WAVE 101 + WAVE 011, passed through all windows
• Row 5 - WAVE 101 + WAVE 100, passed through all windows
• Row 6 - WAVE 101 + WAVE 101, passed through all windows
• Row 7 - WAVE 101 + WAVE 110, passed through all windows
• Row 8 - WAVE 101 + WAVE 111, passed through all windows

WAVE 110

This table shows WAVE 110 combined with every other wave, and passed through every window function.

WAVE 110, combined with every other wave, passed through every window
Click image to see full-size image

• Row 1 - WAVE 110 + WAVE 000, passed through all windows
• Row 2 - WAVE 110 + WAVE 001, passed through all windows
• Row 3 - WAVE 110 + WAVE 010, passed through all windows
• Row 4 - WAVE 110 + WAVE 011, passed through all windows
• Row 5 - WAVE 110 + WAVE 100, passed through all windows
• Row 6 - WAVE 110 + WAVE 101, passed through all windows
• Row 7 - WAVE 110 + WAVE 110, passed through all windows
• Row 8 - WAVE 110 + WAVE 111, passed through all windows

WAVE 111

This table shows WAVE 111 combined with every other wave, and passed through every window function.

WAVE 111, combined with every other wave, passed through every window
Click image to see full-size image

• Row 1 - WAVE 111 + WAVE 000, passed through all windows
• Row 2 - WAVE 111 + WAVE 001, passed through all windows
• Row 3 - WAVE 111 + WAVE 010, passed through all windows
• Row 4 - WAVE 111 + WAVE 011, passed through all windows
• Row 5 - WAVE 111 + WAVE 100, passed through all windows
• Row 6 - WAVE 111 + WAVE 101, passed through all windows
• Row 7 - WAVE 111 + WAVE 110, passed through all windows
• Row 8 - WAVE 111 + WAVE 111, passed through all windows

Summary

There are a lot of possibilities for interesting and new wave shapes. I documented all 512 possibilities in case they were unexpectedly different. For instance, would you get a different result by changing the *order* of the two waves? After studying the results, I found that things like that didn't matter, and there was a lot of repetition.