SLow harmonics

[Sam_Zen]

Maybe an open door, but I like to prove the direct connection between tonal harmonies as 'chords', and rhythmical patterns.
If you play a note and play the note one octave lower, it will be exactly half the frequency of the higher one.
And if the note is a sample, then, according to the old tape-recording rules, the note will also be twice as long.
Exactly the same rules of physics are valid for cycles in a much more lower frequency range : the rhythmic patterns.
I made an example module using the first half of the 'drumloop' sample by LPChip, made for the MP compo 2007 :
harmonicz

Don't just play the module, but open it, go to the pattern tab and click the 'replay pattern' (starting pattern '0'):
~ sample 1 is placed as C5. This sequence has a certain length. Related to the number of steps in the patterns, and the speed of the playback. The pattern has a default size of 64 steps. Because of wanting to have some room, I tuned the C5 with the playback speed, to have an end at the half, 32 steps. Appeared to be a 125/4 tempo. Of course I had to enter code C5 at step 32 as well to get a full repeat.
~ Ctrl_'1' (in patternrow) : C4 is added. An octave lower, so also double as long, taking the full 64 steps of the pattern.
~ Ctrl_'2' : The same possible with higher octave C6 : Twice as short, so the note has to be placed every 16 steps.
~ Ctrl_'3' : These three keys together
~ Ctrl_'4' : Playing with C7, having a length of 8 steps
~ Ctrl_'5' : Then, at channel 5, F4 is introduced. Not an octave, but a key within. To realize a full common repetition of the several 'notes', the pattern had to be extended to 192 steps, because F4 had a cycle-length of 48 steps.
~ Ctrl_'6' : Channel 6 added : F5. So with a length of 24.
~ Ctrl_'7' : Some variation

Of course the same is valid, if the drumloop is replaced by a sample of a single conga-stroke.

[CrazyAznGamer]

Whoa, this is cool. I knew about the doubling and halving of frequencies with each octave range, and I knew about the drumloop trick, but I didn't know F could be used to make it fit in a 48 tick environment.

[Sam_Zen]

Nice.
As an example of this phenomenon I made a recording using a simple Casio SK-1 KB. I sampled a tap on a conga included a bit of space, and set it in a loop to get a get a reasonable repetition under the default key. In the same way, the key an octave lower, if hit at the same time, or at the point of the next loop, would fit in the rhythm, but lower, and every two times.

In this piece I you'll hear the KB chords being played with some organ sound, but at the same time being played with the conga-sample under the same key-combinations.
Channels 2

Playing a chord with that conga-loop, it becomes clear, that the third note between the octave, if being a quart or a quint, is meaning a ratio of 2 : 3 or 3 : 4. This has a basic common of 12, so that's why number 48 comes into the picture.

EDIT : I've added some panorama codes to emphasize the different channels : harmonicz

[cubaxd]

Hi Sam.
Just wanna tell you that the link to the harmonicz file seems broken: 404

[Sam_Zen]

Thanks. I've corrected the sloppyness.

[rncekel]

Whoa, this is cool. I knew about the doubling and halving of frequencies with each octave range, and I knew about the drumloop trick, but I didn't know F could be used to make it fit in a 48 tick environment.

In fact, you can go further if you remember what the different notes are in `just intonation', although with well-tempered scales there will be a very slight and almost unnoticeable difference.
So:            1 tone = 9/8 (starting from C5, D5)
               2 tones = 5/4 (starting from C5, E5)
2 tones and a half = 4/3 (starting from C5, F5)
3 tones and a half = 3/2 (starting from C5, G5)
and if you go down, just invert the fractions.
So, if you start with a cycle of 64 ticks at C5, playing A4 would need 80 ticks.

[Sam_Zen]

2 rncekel
Great. More base-numbers.

although with well-tempered scales there will be a very slight and almost unnoticeable difference

Yep. This is the reason why I didn't set the sequences looping, but choose to repeat the startcode at the right position again.
If looped, then effects will be unnoticeable, but only on the short run. In each repeat of the two parallel sequences, the tiny difference will grow a bit, so theoretically there shall be a moment where it will become noticeable.