SBaGen -- Sequenced BinAural Generator
--------------------------------------

This is a utility, released under the GNU GPL (see the file COPYING),
that generates pink noise and binaural tones through your soundcard in
real-time according to a 24-hour programmed sequence read from a file.
It can also be used to play a sequence immediately, rather than
according to the clock, or even a combination of the two.

The original idea was to program a set of tones to play overnight as I
slept, hoping to improve dreaming, and dream-recall. This way, I can
also program a sequence to bring me up into alpha rhythms to hopefully
have a good start to the day. I'm still experimenting with all of
this, by the way.

Some of the more interesting uses (for me) of binaural tones I've read
about include: improving dream-recall, entering lucid dreaming,
facilitating meditation, accessing intuition, exploring consciousness.

USE AND EXPERIMENT AT YOUR OWN RISK !

If you make any changes or improvements to the code, let me know so
that I can keep a master copy of all the best bits. Also, if you come
up with any interesting tone-sets or sequences that you would like to
share, along with their story, let me know or post them on the mailing
list (see http://sbagen.sf.net/). I'm considering collecting people's
experiences together onto the site, if there is enough interest.

Jim Peters, Jan-1999
(updated Sep-2001 and Apr-2002)



Theory
------

The basic idea of binaural beats is that by applying slightly
different frequency sine waves to each ear, a beating affect is
created in the mind itself, due to the internal wiring of the brain.
If, in the presence of these tones, you relax and let your mind go,
your mind will naturally synchronize with the beat frequency. In this
way it is possible to accurately get into various brain-states, once
you know what the frequencies are.

It is also possible to play several different tones together, giving
several different beat frequencies, and programming quite a complex
brain-state based on several frequencies (in several different bands).
These complex mixtures of frequencies are the basis of the Hemi-Sync
(TM) process from the Monroe Institute .

For the complete theory of binaural beats and how they affect the
mind, it's best to see the Monroe Institute site, particularly the
pages at . I
know little more about binaural beats than what is explained in these
pages, so take a look.

I am just starting to experiment with this stuff, and I wrote this
utility to help me set up sounds and sequences to experiment on
myself. If you want to experiment with this, feel free to use my
utility, but don't blame me if you program it wrong and lose your job
because you were chilling comfortably in Theta until 11:00am and then
missed a vital meeting at work, or something like that.

You know what I'm saying -- USE AT YOUR OWN RISK ! If a little bit of
fun/risk puts you off, I believe that The Monroe Institute sells pre-
packaged tapes (although I've never tried them).

Some more theory. The oscillations in the brain are split into four
'bands' according to frequency:

Delta (0.5 to 4 Hz). This is normally generated in deep sleep, or
when unconsious. Those experienced in deep trance states can generate
these waves whilst remaining conscious.

Theta (4 to 8 Hz). This is the region between sleep and wakefulness,
in which *dreaming* and other dream-like (or 'hypnagogic') experiences
occur. It's that bit just before you actually fall asleep at night,
or just before you are really awake in the morning. They say it's in
this band that the unconscious talks to the conscious mind. It also
seems to be connected with psychic or ESP-type functioning.

Alpha (8 to 13 Hz). This is produced when you are awake and fully
conscious, but with your awareness focussed inside, such as when
trying to remember something, or when your eyes are closed.

Beta (13 to 30 Hz). This is normally generated when you are awake,
with the attention focussed outside, dealing with the outside world.
It is also generated when you are solving logical problems, such as
mental arithmetic.

It is interesting to note that in normal dreams, a combination of
Theta, Alpha and Beta waves are produced, just as if the person was
awake.

Anyway, it looks like Theta is the place to be, connected with all
kinds of ESP functioning, such as direct 'knowing', and other such
stuff. I'm sure I've been there many times, but I'm looking to
explore this area much further now using this utility.

References:

My source for a lot of the information on brain waves is the book:
"How to build a lie detector, brain wave monitor and other secret
parapsychological electronics projects" by Mike and Ruth Wolverton,
TAB books, 1981.

I became interested in The Monroe Institute and their activities
through the writings of Ken Eagle Feather, and from attending several
courses of his. He talks briefly about Hemi-Sync (TM) in "Tracking
Freedom", mentioning some of the 'Focus Levels' (tone-sets) discovered
by the Monroe Institute, which include ones related to out-of-body
experiences and even 'other worlds'. I believe he also talks about
some of his experiences on Monroe Institute workshops in his first
book "Travelling with Power", although I've not read it (yet).


Installation for Windows users
------------------------------

Download the ZIP archive and unpack it somewhere suitable. Unpacking
it in C:\ seems a good idea to me, because that way it is easier to
find from the DOS prompt. Alternatively you could unpack it somewhere
else and/or move the directory to some other location you prefer.

To actually run the utility, you need to start up a DOS prompt, and CD
to the directory in which all the files have been unpacked. For
example (assuming version 1.0.10, and using '>>' to indicate the shell
prompt):

>> CD C:\SBAGEN-1.0.10
>> DIR/P

This should show a lot of files, including SBAGEN.EXE. If you are in
the correct directory, typing 'sbagen' should now give a welcome
message and a summary of the command's options. If so, everything is
ready.

>> sbagen

Thanks to the help of Dirk Cloete, Windows users now have a full set
of tone-set batch files to experiment with, equivalent to the t-*
scripts on UNIX and Mac OS X. These also appear in the same directory
(*.bat), along with the sequence files (prog-*) and other bits and
pieces.



Installation for Linux and other UNIX users
-------------------------------------------

(Mac users please skip forward to the Mac OS X section below)

Download the TGZ and unpack it somewhere. On Linux, the executable
can be built using the little 'mk' script:

>> ./mk

This script assumes GCC on Linux. If you're using something else,
please check the script and adjust it as necessary. There is also a
script 'mk-ansi' which strips out non-ANSI C stuff before compiling,
which may work if you don't have GCC. A user provided 'mk-netbsd' to
build on NetBSD. The other 'mk-*' scripts cover other possibilities
and other platforms -- see the comments in the files for more details.

On UNIX systems the code handles output to a stereo /dev/dsp device
using either 16-bit signed or 8-bit unsigned samples. Hopefully this
covers almost everybody's sound card, but if you have something else,
you will either have to modify the code yourself, or suggest
modifications to me. You can also output to a file, or to standard
output, if you wish -- see below.

Note that on low-spec machines, any heavy jobs you have running may
take CPU time away from the sound-generation, and cause gaps in the
output. You can try adjusting priorities with 'nice' and 'renice' to
improve the situation if you have this problem.

On my old Pentium-75, I could generate continuous 16-bit 44100Hz
output on 8 channels, and still only use 66% CPU-time, so even with
very old machines, you should be able to get some output, even if this
means lowering the output rate using the -r option.

Note that if you don't normally run with '.' in your PATH, you'll
probably want to install the 'sbagen' binary by copying it to
/usr/local/bin/. You'll need to log in as root to do this.

Once built, you can test the utility quickly using some of the t-*
scripts which generate various different tone-sets. The prog-* files
are sequences (see later), and the p-* files are Perl-scripts which
generate and run sequences.



Installation for Mac OS X users
-------------------------------

SBaGen was originally written as a UNIX tool, and it was adapted to
Mac OS X by using CoreAudio for audio output. For this reason it is
distributed as a TGZ archive, and it uses the text-mode OS X
'Terminal' application as its user interface.

Download the TGZ file for Mac OS X onto your desktop. Start up a
Terminal (you'll find it under Applications/Utilities/Terminal), and
type the commands below. (Note that I'm using '>>' to indicate the
shell prompt). Remember that you can save time typing by using the
Tab key to expand the filenames as you go (e.g. you can probably type
De for "Desktop"). Also, the version number you downloaded will
probably be different to this, so adjust it accordingly:

>> tar xvzf Desktop/sbagen-mac-1.0.10.tgz
>> cd sbagen-mac-1.0.10

This unpacks the files into a directory 'sbagen-mac-1.0.10/' in your
home directory, and moves into that directory. You can type 'l' or
'ls -l' to see all the files.

You also need to make sure that '.' (the current directory) is in your
$PATH. On 10.0 at least, it doesn't seem to be set up by default. If
you are running csh (which is the default in 10.0 and 10.1), type this:

>> setenv PATH "${PATH}:."

If you are running zsh or bash, however, type this:

>> export PATH="$PATH:."

Now, if you type 'sbagen', you should get a welcome message and a list
of command options. If so, then everything is ready.

>> sbagen

Note that you will have to do the 'cd' and 'setenv' every time you
start up a Terminal to run SBaGen. You can get around this by editing
startup files and so on, but that is too much for me to explain here.

For those new to the UNIX command-line, here are a few basic commands
you will need. I can't give you more than a taste here -- you'll need
to read up on this elsewhere if you need to know more.

Copying, moving and deleting files is done as follows:

>> cp old-file new-file
>> mv old-file new-file
>> rm file

You can view files using the 'less' command. For example:

>> less sbagen.c

Use 'q' to quit and arrow keys to move around. Other useful keys
include space, return, 'd', 'g' and 'G'. (Use 'man less' for full
docs). Don't be afraid to look inside things -- 'less' will warn you
if you are trying to look at a binary file. Remember that this is
UNIX -- you are supposed to be curious and poke around and try and
figure out how things work. For instance, most of the t-* and prog-*
files have extra information in the comments that you would not see
otherwise.

You can edit files using 'emacs', which is a very powerful editor.
For simple use, run it like this:

>> emacs t-alpha

Move around within the editor using arrows, ^A and ^E, save using ^X^S
and exit using ^X^C. If you want more info on this editor, type ^H or
^H 'i', or do a search on the 'net.

Remember that most non-interactive UNIX commands (including SBaGen)
and some interactive ones can be aborted using ^C (Ctrl-C). This is
the best way to stop SBaGen once it is running.

Also, on Mac OS X, you may wish to turn the volume up in the System
Preferences. However, if you turn it up *too* high, the audio may
start to distort (it will sound rougher), so watch out.


Invocation (all platforms)
--------------------------

One quick thing to note before we start -- whether you play these
binaural beats through headphones (as recommended by the Monroe
Institute, CenterPointe, etc), or through speakers, play them at low
to medium levels. My experience is that playing them too loud doesn't
improve the effect at all -- it just gives me a headache.

So, here we go. The following example commands should be typed at the
shell prompt provided by your operating system, prepared as explained
above.

>> sbagen

This gives the usage information, showing the version number and the
full list of options. Check this for any new features.

>> sbagen prog-chakras-1

This runs the sequence in file 'prog-chakras-1', starting playing
whatever should be playing at the current moment, according to the
clock time. The status-line at the bottom of the screen shows the
current time, and currently-playing tones/noise. The two lines
immediately above show the period of the sequence which is being
played -- these lines scroll up the screen as one period moves into
the next.

Remember that you can stop the utility using Ctrl-C on all platforms:
Windows, Mac OS X and UNIX. (Most UNIX users already know this, but
it seems that some Windows users don't).

To test a sequence (without waiting the full 24 hours for it to play
through), run with the -q 'quick' option:

>> sbagen -q 120 prog-chakras-1

This example runs the sequence at 120 times the normal speed. This is
quite useful to check that a new sequence is going to do what you
expect it to do.

To check that SBaGen has interpreted your sequence-file correctly, use
the -D option, which dumps a listing of the interpreted sequence
instead of playing it:

>> sbagen -D prog-chakras-1

To quickly test a particular tone-set continuously, use the -i
immediate option. This is good for experimenting with different
ideas. If your shell lets you recall the previous command with
up-arrow, you can quickly test and fine-tune a tone-set in this way
before putting it into a sequence:

>> sbagen -i pink/40 100+1.5/20 200-4/36 400+8/2

This incidentally, is an example of a complex brain-state built from
pink noise, to which is added three frequencies (1.5Hz, 4Hz and 8Hz)
each on an independant carrier (100, 200 and 400 Hz), at different
amplitudes (20, 36 and 2). This combination is supposedly something
like "body-asleep, brain-awake", assuming I've reproduced it
correctly.

While you're at it, try the alternate 'spin' effect. Not everyone
likes this, but in any case it's there if you want to use it:

>> sbagen -i spin:300+4.2/80

If you're having trouble with your soundcard or CPU usage, use the -r
option to run at a lower output rate. The tones still come out really
well even at 8000Hz, on my sound card at least, although the noise
suffers. For example:

>> sbagen -r 8000 -i pink/40 100+1.5/20 200+6/30

If your sound card doesn't support 16-bit output, you'll need to use
the -b option to select 8-bit output, for example:

>> sbagen -b 8 -i pink/40 100+1.5/20 200+6/30


For UNIX and Mac OS X, you'll find that there are a set of short
tone-set scripts (t-*) that you can run from the command-line. For
example:

>> ls t-*
>> t-alpha

All these executable tone-set scripts (t-*) accept additional options
and pass them onto SBaGen, so you can use the same options (e.g. -r
and -b) with these as well.

For Windows, these same tone-sets are available, translated into batch
files thanks to Dirk Cloete:

>> dir *.bat
>> t-brainstate-alpha

Try out some of these scripts/batch files to get an idea of some of
the possibilities.

For all platforms (UNIX, Windows and Mac OS X), the sequence files
(prog-*) can be used in the same way:

>> sbagen prog-NSDWS-example

Have a play with these sequences. Many of them are designed to run at
night, so you will hear nothing if you play them during the day. You
get around this by playing them immediately using '-q 1', or '-S' (run
from start):

>> sbagen -q 1 prog-NSDWS-example
>> sbagen -S prog-NSDWS-example

On UNIX and Mac OS X, there are also a few Perl-scripts which you can
run (p-*). These generate a sequence on the fly and then run it. For
anyone familiar with Perl, this is a good way to generate sequences
that are slightly different each night in a random way. For example:

>> p-nightly-sub-delta 7:30

This generates a night-time sequence in 'tmp-prog' with a wake-up time
of 7:30 and runs it. Naturally you won't hear anything unless it is
already night.


Outputting to a pipe or a file
------------------------------

You don't need to read this section if you are only interested in
outputting directly to the soundcard.

If you wish to pipe output on to some other utility, use the -O
option. When this is used, the real time is no longer checked, so you
can output to both real-time devices (such as a mixer daemon), or to a
file or effect utility. It is assumed that the eventual output device
will use exactly the frequency specified, or otherwise all the
frequencies and timings will be out.

The -o option can also be used to output directly to a file. In both
cases headerless raw data is output (to write a WAV file, see the -W
option below). For example, to pipe to bplay under UNIX, you could
use the following:

>> sbagen -r 8000 -O -i 100+0.92/30 200+4.2/15 | bplay -S -s 8000 -b 16

The -L option allows a time-limit to be set on the output. So, for
example, to output 45 minutes of data to a file, and then play it with
bplay, use:

>> sbagen -r 8000 -o out.raw -L 0:45 -i 100+0.92/30 200+4.2/15
>> bplay -S -s 8000 -b 16 out.raw

As an alternative to using -L, it is possible to use -S and -E to
indicate that the output starts at the start of the sequence file
rather than the real time (-S), and/or ends at the end of the sequence
file rather than going on forever (-E). It is also possible to start
at a particular clock time using the -T option.

A WAV file can be output if one of these options is used (-L or -S/-E)
using the -W option. This is used in conjunction with -o or -O.
Repeating the examples above using WAV files, we have:

>> sbagen -r 8000 -WO -L 1:00 -i 100+0.92/30 200+4.2/15 | bplay

and:

>> sbagen -r 8000 -Wo out.wav -L 0:45 -i 100+0.92/30 200+4.2/15
>> bplay out.wav

The -Q option may be useful to turn off the information that the
utility normally writes to the screen.

If you are using another utility (perl or whatever) to generate the
sequence-file, you can pipe it directly to the utility, and use '-' as
the filename. For example:

>> cat prog-chakras-1 | sbagen -

For those pushing the utility past its design limits, you may wish to
use the following options:

'-R rate' specifies the rate at which the sound parameters are
recalculated in Hz, the default being 10Hz. 10Hz is fine for a slide
that takes a minute, but if you are doing quick (1 sec) fades in and
out, you'll need a faster refresh to avoid clicks.

'-F fade_interval' specifies the time in ms over which a fade in or
out takes place. This is normally one minute (60000ms), which is fine
for slowly changing tone-sets, but you may wish to adjust this value
according to your needs.


Mixing in background sounds
---------------------------

There are also two options to allow you to mix in a background
soundtrack with the binaurals as they are generated. This is
generally regarded as a good idea, and this technique is used by both
CenterPointe and the Monroe Institute. The binaural beats are
generated at a low level (e.g. 200+4/1.0), so that they are only just
audible.

The soundtrack should be either in the form of a raw 16-bit stereo
file, or a 16-bit stereo WAV file. By specifying the -m option, the
given file is mixed with the generated binaural beats:

>> sbagen -m background.wav -i 200+4/1

Note that if the background sounds are too loud, then the addition of
the binaurals might cause clipping. However, when binaural beats are
mixed with a soundtrack, they are usually kept at a low level (e.g. /1
above, or even lower). Note that when the soundtrack file ends,
sbagen will stop playing.

The -m option in fact only handles raw 16-bit sound data, but if you
give it a filename ending with .wav, it will parse enough of the WAV
format to skip over any header data correctly. Don't expect sbagen to
do any format or sample-rate conversion for you, though!

The -M option allows raw sound data to be passed on the standard
input. This is useful in combination with an MP3 player. For
example, using 'splay' on UNIX, you can use an MP3 to provide the
background sounds as follows, for example:

>> splay -d - background.mp3 | sbagen -M -i 200+4/1

This has the advantage of not requiring a huge WAV file to be stored
on your disk.


Sequence-file format
--------------------

This section describes the format of the sequence files (the prog-*
files, for example). You'll need this if you want to modify these
files, or create your own sequences. For Windows users, you can edit
these files using EDIT or NotePad (or any simple text editor). Mac
users will have to use an editor that respects UNIX line-endings
(e.g. 'emacs').

Within the sequence file, blank lines, and any leading/trailing white
space are ignored. Comments are introduced with a '#', and extend to
the end of the line.

There are several types of entries that may appear in the file:

* Tone-set definition lines
* Time-sequence lines
* Block definition lines

These are described below. The example sequence-files (prog-*) are
useful to see how all these work together.

* The tone-set definition line. This takes the form of:

: ...

Examples:

theta6: pink/40 150+6/30
test10: pink/40 100+1.5/30 200-4/27 400+8/1.5
all-off: -

The name starts with a letter, and may continue with letters,
numbers, '_' or '-'. Following the colon is a list of one or more
tone-specifications. There are a maximum of 16 of these. (This can
be adjusted in the source code -- search for N_CH).

There are five types:

- # Channel not in use
pink/ # Pink noise
/ # Binaural tones
bell+/ # Bell sound
spin:+/ # Spinning phase shifted pink noise
wave:/ # Binaural tones using a user-
# defined waveform (see later)

The amplitudes are expressed on a scale 0-100. The total of all the
amplitudes in a tone-set should not exceed 100, or else there
will be distortion on output as the waveforms are clipped.

The pink noise is probably not 100% pure pink noise -- but it is
fairly pink, with everything from rumbling to hissing, and it
doesn't have too many noticeable distractions such as repeating
cycles or distant melodies or whatever. If you listen really hard,
though, you may be able to hear the fairies playing by the
waterfall.

The binaural tones are based on a carrier frequency (in Hz), which
should be in the range 100 to 1000. Frequencies above 1000-1500 or
so are of no use because the brain does not react to higher pitches
in the same way (see the Monroe Institute pages). The actual beat
frequency (which the brain responds to) should be in the
range 0.5 to 30 Hz. This corresponds to the ranges for Delta up to
Beta as described above.

The two tones generated are different by Hz, equally spaced
either side of . The should be + or -, and this
decides which channel carries the higher frequency. I don't think
this matters, but in case it does, you can change it here. So, for
example, 100+4/20 generates tones of 102 and 98 Hz, whereas 100-4/20
generates tones of 98 and 102 Hz.

The bell sound can be used to give cues and signals during the
sequence. A simple 'ping' is generated at the given frequency at
the start of the period in which the tone-set is used.

The spinning pink noise generates a binaural effect in a completely
different way, by shifting the phase of pink noise in opposite
directions for each ear, at a given beat frequency. In this case,
the first number is the width of the maximum phase shift from centre
in microseconds. Values from 100 to 500 seem good to me, although
you might want to experiment with this. The second number is the
beat frequency and the third is the amplitude, as above.

Binaural tones generated using wave work just the same way as
normal binaural tones. See the section later on for details.

Once a tone-set has been defined, it may be used in time-sequence
lines.

* Time-sequence lines. These take the form of:

[] [->]


Examples:

16:00 theta6
NOW theta6
+00:03:30 == theta4 ->
NOW+04:00 <> theta4
12:00 theta-bursts

In it's simplest form, this specifies a clock time, and which
tone-set should be played at that time. This tone-set continues
until the next clock-time that is specified.

Time-sequence lines should always appear in order -- you will get an
error if things appear out of order.

More complex examples give time relative to the program start time
(NOW, or NOW+04:00), or relative to the last absolute time mentioned
(+00:03:30). They also use different varieties of fade-in or
fade-out (== or <>), and use '->' to slide to the next time-
sequence. You can also name blocks instead of tone-sets. These
more complex options are described below.

Take a simple example such as this one:

11:00 theta6
12:00 alpha8
13:00 alpha10
14:00 off

This indicates three tone-sets that will play for an hour each
between 11am and 2pm. The tone-sets do not change suddenly on the
hour. Rather, SBAGEN starts to fade out one tone-set 30 secs before
the hour, fading in the next for the first 30 secs of the next hour.

By default, SBAGEN will attempt to keep common things playing from
one tone-set to the next. So if, for example, all of them use pink
noise on the first channel, then this will keep on playing the whole
time, whilst the tones that change will fade out and in.

To change the fading in/out behaviour, include a
specification before the name. This consists of two characters, one
for fading in this tone-set, the second for fading it out. The
fade-in character may be:

< Always fade in from silence.

- Fade from previous to this, fading out all tones not
continuing, fading in all new tones, and adjusting the
amplitude of any tones continuing.

= Slide from previous to this, fading out all tones ending,
fading in all new tones, and sliding the frequency and
adjusting the amplitude of all other tones.

As an example, using '=' you can smoothly slide from a 4 Hz
frequency all the way up to a 12 Hz frequency, rather than fading
one out, and fading a new one in. The fade-out characters are
similar, and may be:

> Fade out to silence
- Fade to next, as above
= Slide to next, as above

What fades/slides actually occur between two tone-sets depends on
what both of them are asking for. If one wants to fade out to
silence, then the other one can't slide to it. They both have to
want to slide for this to occur.

The default specification is '--', which means
keep playing anything that is the same frequency (adjusting the
amplitude if necessary), but fade everything else in or out.

By default fading and sliding only occur during the 60 second period
within 30 seconds either side of the change-over time. However,
using '->', the entire period from the start time to the time on the
next time-sequence line becomes a transition period. This way you
can have a gentle frequency slide that goes on for an hour, if you
like:

15:00 == theta4 ->
16:00 == alpha10

Assuming these tone-sets do what their names suggest, this will
produce a gentle change in binaural beat frequency from 4 Hz up to
10 Hz over the hour from 3pm to 4pm.

The time-specification in its simplest form may be in the form
'hh:mm' or 'hh:mm:ss'. This counts as an absolute time.

Another form of time-specification is 'NOW' which indicates the time
at which SBaGen was started. This is useful for sequence-files that
are intended to play from the time that they are run, rather than
always at the same time of day. 'NOW' is another absolute time.

The other form of time-spec is a relative time, either '+hh:mm' or
'+hh:mm:ss'. This, if used alone, is taken relative to the
last-mentioned absolute time, for example the three relative times
below are all relative to 'NOW', the last-mentioned absolute time:

NOW+00:10 theta4
+00:20 off
+00:30 theta4
+00:40 off

Any number of relative times may also be used with an absolute time,
to modify it, for example 'NOW+04:00+01:12:04' or '12:00+00:00:20'.

* The block definition line. This introduces a set of lines, and
takes the form:

: {

::
}

For example:

theta-burst: {
+00:00 theta4
+00:10 off
}

A block definition associates a name with a group of time-sequence
lines. All the time-specs on these lines should be relative,
because when the block is called on, all the times will be combined
with the time-spec from the calling line.

For example, using the above definition:

NOW theta-burst

expands to:

NOW+00:00 theta4
NOW+00:10 off

Or for another example:

+01:00 theta-burst

expands to:

+01:00+00:00 theta4
+01:00+00:10 off

This should be enough information to allow you to design and write
your own sequences now. Playing around with the example sequences
(the prog-* files) will also probably help.

Happy experimenting !!

--------------------------------------------------------------------------------



(VERY) EXPERIMENTAL FEATURE: User-defined waveforms
---------------------------------------------------

This is a more complex form of binaural synthesis (maybe too complex!),
and right at this moment, I'm not sure whether it really works or not
either, so this section is only for die-hard (b)leading-edge hackers
and experimenters. The code is in place to do this synthesis, but it
might still have bugs or other problems. If you're still interested,
read on ...

The purest form of binaural beat synthesis is based on two sine waves
of slightly differing frequency. The interference between these two
within the brain generates a resultant wave with a slow modulation.
Assuming the interference within the brain is similar to normal wave
interference, then the resultant amplitude wave is shaped by what
looks like a full-wave rectified sine wave (like the +ve half of a
sine wave repeated endlessly).

There is a line of thinking that suggests that if we replace this
amplitude envelope with one based on the shape of a measured
brain-wave, then we should be able to reproduce that brain-wave in the
brain -- i.e. we play a measured alpha wave to entrain the brain
precisely to an alpha wave. Does this work ? I really don't know.

This is how it is used in the sequence-file. You provide the shape of
the brain-wave to the program in a waveform definition line:

wave<2-digits>:

There can be at most 100 waveforms defined in a sequence, numbered 00
to 99. For example:

wave00: 0 5.5 10 8 10 7.2 4.7 2

The samples are values from the waveform shape taken at regular
intervals over one cycle. They can be in any units you wish --
floating point numbers, negative, whatever -- and there may be as many
samples as you wish (currently only limited by line length). They
will be rescaled to fit between the amplitudes of 0% and 100% and
smoothed using a sin(x)/x function. See here for more details on the
smoothing used:

http://www-ccrma.stanford.edu/~jos/resample/

This waveform now becomes the amplitude envelope of any binaural tones
generated from it:

wave00:200+4/50

This is just the same as 200+4/50, except it uses the new waveform for
the amplitude envelope.

That's all you need to know to be able to use it. All you have to do
now (according to the theory, at least) is to go and measure some
waveforms -- off the 'net if like most of us you don't have an EEG --
feed them into waveNN: lines, and then play them at appropriate
beat-frequencies.

Well, that's the theory, but not everything seems to be working
according to plan from my experiments. Here is the basis on which the
code works to generate the tones:

If you take the 0-100% scaled and smoothed amplitude waveform, and
draw it twice, and invert the second version, you have a wave that can
be played at audio frequencies. If you play this in the left ear at
102Hz (for example), and in the right ear you play the same thing at
98Hz BUT WITH THE SAMPLE REVERSED, then in theory you should get the
correct amplitude envelope. Here is the mathematical basis for this
(from the mailing list):

> Let's say we have a brain-wave waveform of f(T) (T is theta),
> expressed as a fourier series (using complex maths because it's
> easier):
>
> f(T) = sigma(n= -inf to +inf) ( Cn . e^(inT) )
>
> What we want to end up with is a resultant function something like
> this:
>
> g(t) = sigma(n= -inf to +inf) ( Cn . e^(inbt) . 2 cos nat )
>
> where 'a' is the resultant carrier frequency (in rad/s here), and 'b'
> is the beat frequency. This means that the phase information is
> connected with the beat waveform, and the phase of the carriers are
> fixed. The factor 2 comes in handy lower down:
>
> g(t) = sigma(n= -inf to +inf) ( Cn . e^(inbt) . (e^(inat) + e^(-inat)) )
>
> g(t) = sigma(n= -inf to +inf) ( Cn . e^(in(b+a)t) + Cn . e^(in(b-a)t) )
>
> g(t) = f((b+a)t) + f((b-a)t)
>
> So we just need to play the original waveform at frequencies (b+a) and
> (b-a). But 'b' will typically be small (1-30Hz), and 'a' will be
> large (100-1500Hz). So (b-a) is negative, which means playing the
> sample backwards.
>
> So if we play the required brainwave forwards at the higher
> frequency, and backwards at the lower frequency, it should all come
> out with what we want.

However, with my experiments I don't get the expected resultant
amplitude envelope. I get bits of it, but not a perfect result.
What's going on, I don't know. Anyway, if you're up for experimenting
with this, at least the code is there now for you to play with and
modify. If you make any progress, let me have the improved code, and
I'll include it in the next release.

Cheers --

Jim

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