** 2 page regular features / 1400 words **

Hitting the right note

Fumbling with frequencies? Puzzled by pitch? Tune in with Shiuming 
Lai...

The last instalment of this series examined the technique of 
varying the playback speed of a recorded sound to make musical 
notes. This has some fundamental implications which are often 
overlooked, as demonstrated by many works found on the computer 
music scene - some of which are even composed by highly revered 
figures in their field.

Irrespective of the base technology (analogue or digital, the 
principle is the same), the absolute pitch of the resultant sound 
is only relative to that of the original from which it was 
synthesised. More specifically, it's a function of three 
variables: a note 
**ITALIC**
n
**/ITALIC**
, its base sampling frequency 
**ITALIC** b
**/ITALIC**

and output replay frequency 
**ITALIC**
r
**/ITALIC**.

** FUNCTION.GEM here **

One of the main flaws in the original Sound Tracker format was the 
omission of sample note information. Therefore, in order to make 
effective use of this system, we must establish a standard 
recording speed for a reference pitch. In digital terms this means 
a set sampling frequency. Although the word "frequency" is 
regularly used in relation to digital recording, it's important to 
differentiate between sampling frequency and signal frequency. To 
avoid confusion we'll say sampling "rate" henceforth.

The most common tracker format on the ST (4-voice Pro/Noise/Sound 
Tracker) uses a base sampling rate of 16KHz for C-3, the C note in 
the third octave. The table on this page contains the exact 
sampling frequencies, to the nearest Hertz, for the three-octave 
range (see boxout) of this standard.

Unfortunately, low-cost personal computer sampling systems tend to 
have a small number of preset rates. Even Soundlab (figure 1) with 
its fairly large range of sampling rates, can't quite match the 
ones we need.

ProTracker tips

This isn't as bad as it appears because the difference can be 
compensated for by software. One particularly powerful feature of 
ProTracker (supported by CyberSTrider and most popular tracker in 
the Maggie charts) is its resampling facility. It's also a cause 
of much head-scratching because ironically, the manual doesn't 
explain how to use it.

Press [Control]+S to open the sampling menu, shown in figure 2. 
You can see in the screenshot the mouse pointer is over the button 
marked E-2, which we will call our current sample pitch. The 
button below, marked C-2, is the reference pitch. All this means 
is, E-2 sounds like a properly tuned C-2. These two buttons are 
for data input (click on them to clear the entry, then enter a new 
note by pressing the appropriate key on the keyboard) - so the 
program can compute the correct shift from the specified tuning 
error.

From theory to practice

On the Reader Disk are some samples for you to play with. REF.SPL 
is a correctly-tuned reference sample, so load this first. Then 
load SAX.SPL into another, empty slot. This is a typical sample 
from a PD disk allegedly for use in tracker programs, and is out 
of tune. For demonstration's sake we'll use C-2 as our reference 
pitch; play a few notes of SAX.SPL until you match or nearly match 
REF.SPL at C-2.

It should be D#2. Now we've found the error we can enter the data. 
Going back to our previous explanation, this is "D#2 sounds like 
C-2" so make sure your current sample is the one you're going to 
modify, click the current sample pitch button and enter D#2. The 
reference is C-2 by default so you don't need to change that. Now 
just hit RESAMPLE.

The last practical experiment concerns sounds which are out of 
tune by less than a note even after resampling. For this, load 
CORK.SPL (a sound generated by Electronic Cow's Snippit Synth 
using a popping bottle cork as the grain wave table) then repeat 
the process of finding a note to match reference C-2. It's roughly 
D#2 again, so resample it as before.

Now adjust the fine tune controls - click on the VOLUME box in the 
sample parameter block to reveal the FINETUNE box. It's 
approximately -3. Once your sound is tuned, it's advisable to save 
it using ProTracker's extended IFF format, to preserve fine tune 
and loop values.

If at this stage you're thinking resampling is a lot of hassle, 
how many times have you written a track then tried changing the 
instrument? If the one you composed with was not properly tuned, 
you're faced with worse problems, especially if you want to 
evaluate the piece with a number of other instrument sounds.

In fact, there has been at least one case of a tracker module's 
score being translated into conventional musical notation for a 
pianist, and when it was played for real it sounded completely 
off. The piano was not to blame as it had been subject to regular 
tuning checks, so I hope that consolidates the point. It's worth 
every effort to knock samples into shape before commencing any 
real work.

** Boxout 1 **
Only three octaves?

In isolation it seems musically inadequate - however, three 
octaves is a deliberately imposed limit of a tracker's 
pitch-shifting ability (some have four, maybe five), rather than 
the range the hardware can reproduce. A digital recording can only 
be pitch-shifted so far, before its finite resolution deviates 
from the original source to the extent it begins to sound terribly 
artificial in comparison. That's the engineering viewpoint. On the 
other hand, in an artistic sense, excessive resampling can create 
some very unusual sounds, so by all means try it and hear.

Noise Tracker users try bumping a sample up or down a few octaves 
(figure 3) while ProTracker people can use the resampler to get 
the same effect; make the current sample pitch an octave more or 
less than the reference and resample. Repeat this several times, 
as the current sample pitch button changes to match the reference 
pitch after each resampling operation.

Multi-sampling

This is a technique used by synth manufacturers when sampling a 
real instrument, to overcome the aforementioned problem. It simply 
involves sampling a number of notes along the musical scale of the 
instrument. Upon playback from the synth, interpolation fills in 
the ones in between to recreate the whole range of notes, far more 
accurately than can be achieved with a single sample for the same 
range.

You can apply the same method when recording instruments for 
trackers, with the advantage you only need sample for the range 
you will use.
** /boxout 1 **


** Boxout 2 **
Resampling: pitfalls

Bear in mind not all sounds are suited to this kind of treatment 
as it introduces digital artefacts (giving a tinny quality). Those 
with plenty of harmonics and distortion will mask it out to an 
extent. This is actually true of normal ST/Falcon tracker replay 
too, which is essentially real time non-destructive resampling, 
with the processed sample data routed to the audio output system 
rather than overwriting the source stored in memory.

One Atari software developer with notable expertise in digital 
synthesis is Softjee in France. Its products use base note 
information as discussed earlier, to avoid having to make a 
second-generation resample.
** /boxout 2 **

** Boxout 3 **
Alternative systems

The ill-fated TCB Tracker from the Swedish demo masters broke new 
ground in ST tracker programming back in the early '90s. Its 
concept and design was more or less identical to the more 
established Sound Tracker format, differing in its file structure 
and use of 20KHz base speed. Some years down the line, when 
another Swedish group started work on an 8-voice tracker, 
Octalyser, it was decided to include both 16KHz and 20KHz, as well 
as a new, 25KHz base speed option. The latter enabled the use of 
samples recorded at 50KHz.
** /boxout 3 **

** Images and captions **

** SOUNDLAB.GIF
Figure 1: Soundlab - fairly flexible sampling/resampling speeds.

** PT_RESAM.GIF
Figure 2: Resampling to an accuracy of one note in ProTracker.

** NOISETRK.GIF
Figure 3: Noise Tracker's octave shift, in the SAMPLER menu.

** Table in comma separated variables (CSV) format **
Sound Tracker standard sampling frequencies (KHz)

Note,Octave 1,Octave 2,Octave 3
C,4.181,8.363,16.726
C#,4.430,8.860,17.720
D,4.697,9.395,18.839
D#,4.971,9.943,19.886
E,5.279,10.559,21.056
F,5.593,11.186,22.372
F#,5.926,11.852,23.705
G,6.279,12.559,25.031
G#,6.653,13.306,26.515
A,7.046,14.092,28.185
A#,7.457,14.914,29.829
B,7.901,15.838,31.677
** /table **

** Reader Disk files **
** CORK.SPL
** REF.SPL
** SAX.SPL