Waveform Palindrome Music Technique: Part 1
Tutorial, as a lair o' Tut
In this three part tutorial, I will describe some of the basic techniques I used in composing waveform palindrome music. As I am primarily interested and most proficient at composing electronic music, I will be writing with the understanding that you will be entering notes in a sequencer and will have the waveform available to manipulate. I imagine accoustic waveform palindrome music could also be produced, although the it would of course have to be turned into a palindrome during mixing, after recording.
Please pardon also any misused terms. I'm rather shakey on some musical terms, as I've had very little need to use them, and have not spent very much time book-learning traditional music theory. Also, if you are used to composing using traditional score-notation, I should tell you now that that renders writing acceptable waveform palindrome music nearly impossible, as note-ending times in such notation are too imprecise. Instead, a piano-roll or matrix view is prefered.
The Basics
Before we begin, let's first look at the waveform of a palindrome track.
As you can see, the waveform of this palindrome song (I Prefer Pi) is perfectly symmetrical. The reason should be fairly apparrent. Since the waveform is the same when it is played backwards, it would have to look the same on both sides of the center line of symmetry. If one were to place a mirror in the center of the waveform, he would see that the reflection was the same as the other side. Everything you see in a mirror is reversed. If I had only the first half of the palindrome song image presented, you could generate the second half by putting a mirror up against the screen. Thus, the basics of making waveform palindromes is doing just what the mirror in our example did: appending a reversed copy of a sound onto the end of that sound. This will make any sound into a palindrome. That is what I call a forced palindrome. Since there seems to be relatively few waveform palindromists (only me, to the best of my knowledge), the term forced palindrome, as with all other original terms found in this site, is about as official as you can get.
Variations on the Forced Palindrome
There are several variables available to alter when creating forced palindromes. The first and most important is the offset. The offset is a positive number, usually between zero and one. If one were to force a palindrome in the manner described above, the offset would be equal to one. However, if the new, reversed waveform was copied then mixed equally with the original, the offset would be zero. Offset that are equal to a value greater than one are seldom used as they would create a blank space in the final palindrome.
Now the palindromist has one more option available when he or she uses a forced palindrome. The palindromist can use crossfade the original with it's counterpart and still create a perfect palindrome. And the slope of the crossfade is also adjustable, just as long as it remains identical in both the sound and it's reversed copy.
In the image above, a stereo version of the waveform in Figure 1 was copied, reversed, then crossfaded with the original. The shaded region represents the area in which both waveforms are heard simultaneously, and the two lines forming an "X" shape demonstrate the volume of each of the sound clips. As you can see, the waveform shown in Figure 2 is perfectly symmetrical. The two clips can overlap to any degree and crossfade with any slope and still create a palindrome.