The NES sound channel guide 1.6
Written by Brad Taylor.
btmine@hotmail.com

Last updated: June 11th, 2000.

All results were obtained by studying prior information available (from 
nestech 1.00, and postings on NESDev from miscellanious people), and through 
a series of experiments conducted by me. Results acquired by individuals 
prior to my reverse-engineering have been double checked, and final results 
have been confirmed. Credit is due to those individual(s) who contributed 
any information in regards to the the miscellanious sound channels wihtin 
the NES.

A special thanks goes out to Matthew Conte, for his expertise on 
pseudo-random number generation (amoung other things), which allowed for the 
full reverse engineering of the NES's noise channel to take place. Without 
his help, I would still be trying to find a needle in a haystack, as far as 
the noise's method of pseudo-random number generation goes. Additionally, 
his previous findings / reverse engineering work on the NES's sound hardware 
really got the ball of NES sound emulation rolling. If it weren't for Matt's 
original work, this document wouldn't exist.


****************
* Introduction *
****************

The 2A03 (NES's integrated CPU) has 4 internal channels to it that have the 
ability to generate semi-analog sound, for musical playback purposes. These 
channels are 2 square wave channels, one triangle wave channel, and a noise 
generation channel. This document will go into full detail on every aspect 
of the operation and timing of the mentioned sound channels.


*******************
* Channel details *
*******************

Each channel has different characteristics to it that make up it's 
operation.

The square channel(s) have the ability to generate a square wave frequency 
in the range of 54.6 Hz to 12.4 KHz. It's key features are frequency sweep 
abilities, and output duty cycle adjustment.

The triangle wave channel has the ability to generate an output triangle 
wave with a resolution of 4-bits (16 steps), in the range of 27.3 Hz to 55.9 
KHz. The key features this channel has is it's analog triangle wave output, 
and it's linear counter, which can be set to automatically disable the 
channel's sound after a certain period of time has gone by.

The noise channel is used for producing random frequencys, which results in 
a "noise" sounding output. Output frequencys can range anywhere from 29.3 Hz 
to 447 KHz. It's key feature is it's pseudo- random number generator, which 
generates the random output frequencys heard by the channel.


*****************
* Frame counter *
*****************

The 2A03 has an internal frame counter. It has the ability to generate 60 Hz 
(1/1 framerate), 120 Hz (1/2 framerate), and 240 Hz (1/4 framerate) signals, 
used by some of the sound hardware. The 1/4 framerate is calculated by 
taking twice the CPU clock speed (3579545 Hz), and dividing it by 14915.


************************
* Sound hardware delay *
************************

Prior to resetting the 2A03, the first time any sound channel(s) length 
counter contains a non-zero value (channel is enabled), there will be a 2048 
CPU (1.79MHz) clock cycle delay before any of the sound hardware is clocked. 
After the 2K clock cycles go by, the NES sound hardware will be clocked 
normally. This phenomenon only occurs prior to a system reset, and only 
occurs during the first 2048 CPU clocks for any sound channel prior to a 
sound channel being enabled.

The information in regards to this delay is only provided to keep this 
entire document persistently accurate on the 2A03's sound hardware, but may 
not be 100% accurate in itself. I haven't done much tests on the behaviour 
of this delay (mainly because I don't care, as I view it as a inconvenience 
anyway), so that's why I believe there could be some inaccuracies.


************************
* Register Assignments *
************************

The sound hardware internal to the 2A03 has been designated these special 
memory addresses in the CPU's memory map.

$4000-$4003	Square wave 1
$4004-$4007	Square wave 2 (identical to the first)
$4008-$400B	Triangle
$400C-$400F	Noise
$4015      	Channel enable / length counter status

Note that $4015 is the only R/W register. All others are write only (attempt 
to read them will most likely result in a returned 040H, due to heavy 
capacitance on the NES's data bus). Reading a "write only" register, will 
have no effect on the specific register, or channel.

Every sound channel has 4 registers affiliated with it. The description of 
the register sets are as follows:

+----------------+
| Register set 1 |
+----------------+

$4000(sq1)/$4004(sq2)/$400C(noise) bits
---------------------------------------
0-3	volume / envelope decay rate
4	envelope decay disable
5	length counter clock disable / envelope decay looping enable
6-7	duty cycle type (unused on noise channel)

$4008(tri) bits
---------------
0-6	linear counter load register
7	length counter clock disable / linear counter start


+----------------+
| Register set 2 |
+----------------+

$4001(sq1)/$4005(sq2) bits
--------------------------
0-2	right shift amount
3	decrease / increase (1/0) wavelength
4-6	sweep update rate
7	sweep enable

$4009(tri)/$400D(noise) bits
----------------------------
0-7	unused


+----------------+
| Register set 3 |
+----------------+

$4002(sq1)/$4006(sq2)/$400A(Tri) bits
-------------------------------------
0-7	8 LSB of wavelength

$400E bits
----------
0-3	playback sample rate
4-6	unused
7	random number type generation


+----------------+
| Register set 4 |
+----------------+

$4003(sq1)/$4007(sq2)/$400B(tri)/$400F(noise) bits
--------------------------------------------------
0-2	3 MS bits of wavelength (unused on noise channel)
3-7	length counter load register


+--------------------------------+
| length counter status register |
+--------------------------------+

$4015(read) - length counter status register
-----------
0	square wave channel 1
1	square wave channel 2
2	triangle wave channel
3	noise channel
4	DMC (see "DMC.TXT" for details)
5-6	unused
7	IRQ status of DMC (see "DMC.TXT" for details)


+-------------------------+
| channel enable register |
+-------------------------+

$4015(write)
------------
0	square wave channel 1
1	square wave channel 2
2	triangle wave channel
3	noise channel
4	DMC channel (see "DMC.TXT" for details)
5-7	unused


************************
* Channel architecture *
************************

This section will describe the internal components making up each individual 
channel. Each component will then be described in full detail.

Device                        Triangle Noise  Square
------                        -------- ------ ------
triangle step generator              X
linear counter                       X
programmable timer                   X      X      X
length counter                       X      X      X
4-bit DAC                            X      X      X
volume/envelope decay unit                  X      X
sweep unit                                         X
duty cycle generator                               X
wavelength converter                        X
random number generator                     X


+-------------------------+
| Triangle step generator |
+-------------------------+

This is a 5-bit, single direction counter, and it is only used in the 
triangle channel. Each of the 4 LSB outputs of the counter lead to one input 
on a corresponding mutually exclusive XNOR gate. The 4 XNOR gates have been 
strobed together, which results in the inverted representation of the 4 LSB 
of the counter appearing on the outputs of the gates when the strobe is 0, 
and a non-inverting action taking place when the strobe is 1. The strobe is 
naturally connected to the MSB of the counter, which effectively produces on 
the output of the XNOR gates a count sequence which reflects the scenario of 
a near- ideal triangle step generator (D,E,F,F,E,D,...,2,1,0,0,1,2,...). At 
this point, the outputs of the XNOR gates will be fed into the input of a 
4-bit DAC.

The 5-bit counter will be halted whenever the Triangle channel's length or 
linear counter contains a count of 0. This results in a "latching" 
behaviour; the counter will NOT be reset to any definite state.

On system reset, this counter is loaded with 0.

The counter's clock input is connected directly to the terminal count output 
pin of the 11-bit programmable timer in the triangle channel. As a result of 
the 5-bit triangle step generator, the output triangle wave frequency will 
be 32 times less than the frequency of the triangle channel's programmable 
timer is set to generate.


+----------------+
| Linear counter |
+----------------+

The linear counter is only found in the triangle channel. It is a 7-bit 
presettable down counter, with a decoded output condition of 0 available 
(not exactly the same as terminal count). Here's the bit assignments:

$4008 bits
----------
0-6	bits 0-6 of the linear counter load register (NOT the linear counter 
itself)
7	linear counter start

The counter is clocked at 240 Hz (1/4 framerate), and the calculated length 
in frames is 0.25*N, where N is the 7-bit loaded value. The counter is 
always being clocked, except when 0 appears on the output of the counter. At 
this point, the linear counter & triangle step counter clocks signals are 
disabled, which results in both counters latching their current state (the 
linear counter will stay at 0, and the triangle step counter will stop, and 
the channel will be silenced due to this).

The linear counter has 2 modes: load, and count. When the linear counter is 
in load mode, it essentially becomes transparent (i.e. whatever value is 
currently in, or being written to $4008, will appear on the output of the 
counter). Because of this, no count action can occur in load mode. When the 
mode changes from load to count, the counter will now latch the value 
currently in it, and start counting down from there. In the count mode, the 
current value of $4008 is ignored by the counter (but still retained in 
$4008). Described below is how the mode of the linear counter is set:

Writes to $400B
---------------
cur	mode
---	----
1	load
0	load (during the write cycle), count

Cur is the current state of the MSB of $4008.

Writes to $4008
---------------
old	new	mode
---	---	----
0	X	count
1	0	no change (during the write cycle), count
1	1	no change

Old and new represent the state(s) of the MSB of $4008. Old is the value 
being replaced in the MSB of $4008 on the write, and new is the value 
replacing the old one.

"no change" indicates that the mode of the linear counter will not change 
from the last.


+--------------------+
| Programmable timer |
+--------------------+

The programmable timer is a 11-bit presettable down counter, and is found in 
the square, triangle, and noise channel(s). The bit assignments are as 
follows:

$4002(sq1)/$4006(sq2)/$400A(Tri) bits
-------------------------------------
0-7	represent bits 0-7 of the 11-bit wavelength

$4003(sq1)/$4007(sq2)/$400B(Tri) bits
-------------------------------------
0-2	represent bits 8-A of the 11-bit wavelength

Note that on the noise channel, the 11 bits are not available directly. See 
the wavelength converter section, for more details.

The counter has automatic syncronous reloading upon terminal count 
(count=0), therefore the counter will count for N+1 (N is the 11-bit loaded 
value) clock cycles before arriving at terminal count. This counter will 
typically be clocked at the 2A03's internal 6502 speed (1.79 MHz), and 
produces an output frequency of 1.79 MHz/(N+1). When the counter arrives at 
terminal count, an output spike will be generated by the counter that has 
the width of 1 CPU clock. This output frequency will then be fed to the 
appropriate device for the particular sound channel (for square, this 
terminal count spike will lead to the duty cycle generator. For the 
triangle, the spike will be fed to the triangle step generator. For noise, 
this signal will go to the random number generator unit).


+----------------+
| Length counter |
+----------------+

The length counter is found in all sound channels. It is essentially a 7-bit 
down counter, and is clocked at 60 Hz. When the length counter arrives at a 
count of 0, the counter will be stopped (stay on 0), and the appropriate 
channel will be silenced.

The length counter clock disable bit, found in all the channels, can also be 
used to halt the count process of the length counter for the appropriate 
channel, by writing a 1 out to it. A 0 condition will permit counting, 
unless the counter's current count = 0. Location(s) of the length counter 
clock disable bit:

$4000(sq1)/$4004(sq2)/$400C(noise) bits
---------------------------------------
5	length counter clock disable

$4008(tri) bits
---------------
7	length counter clock disable

To load the length counter with a specified count, a write must be made out 
to the length register. Location(s) of the length register:

$4003(sq1)/$4007(sq2)/$400B(tri)/$400F(noise) bits
--------------------------------------------------
3-7	length

The 5-bit length value written, determines what 7-bit value the length 
counter will start counting from. A conversion table here will show how the 
values are translated.

	+-----------------------+
	|	bit3=0		|
	+-------+---------------+
	|	|frames		|
	|bits	+-------+-------+
	|4-6	|bit7=0	|bit7=1	|
	+-------+-------+-------+
	|0	|05	|06	|
	|1	|0A	|0C	|
	|2	|14	|18	|
	|3	|28	|30	|
	|4	|50	|60	|
	|5	|1E	|24	|
	|6	|07	|08	|
	|7	|0E	|10	|
	+-------+-------+-------+

	+---------------+
	|	bit3=1	|
	+-------+-------+
	|bits	|	|
	|4-7	|frames	|
	+-------+-------+
	|0	|7F	|
	|1	|01	|
	|2	|02	|
	|3	|03	|
	|4	|04	|
	|5	|05	|
	|6	|06	|
	|7	|07	|
	|8	|08	|
	|9	|09	|
	|A	|0A	|
	|B	|0B	|
	|C	|0C	|
	|D	|0D	|
	|E	|0E	|
	|F	|0F	|
	+-------+-------+

The length counter's real-time status for each channel can be attained. A 0 
is returned for a zero count status in the length counter (channel's sound 
is disabled), and 1 for a non-zero status. Here's the bit description of the 
length counter status register:

$4015(read)
-----------
0	length counter status of square wave channel 1
1	length counter status of square wave channel 2
2	length counter status of triangle wave channel
3	length counter status of noise channel
4	length counter status of DMC (see "DMC.TXT" for details)
5-6	unused
7	IRQ status of DMC (see "DMC.TXT" for details)

Writing a 0 to the channel enable register will force the length counters to 
always contain a count equal to 0, which renders that specific channel 
disabled (as if it doesn't exist). Writing a 1 to the channel enable 
register disables the forced length counter value of 0, but will not change 
the count itself (it will still be whatever it was prior to the writing of 
1).

Bit description of the channel enable register:

$4015(write)
------------
0	enable square wave channel 1
1	enable square wave channel 2
2	enable triangle wave channel
3	enable noise channel
4	enable DMC channel (see "DMC.TXT" for details)
5-7	unused

Note that all 5 used bits in this register will be set to 0 upon system 
reset.


+-----------+
| 4-bit DAC |
+-----------+

This is just a standard 4-bit DAC with 16 steps of output voltage 
resolution, and is used by all 4 sound channels.

On the 2A03, square wave 1 & 2 are mixed together, and are available via pin 
1. Triangle & noise are available on pin 2. These analog outputs require a 
negative current source, to attain linear symmetry on the various output 
voltage levels generated by the channel(s) (moreover, to get the sound to be 
audible). Since the NES just uses external 100 ohm pull-down resistors, this 
results in the output waveforms being of very small amplitude, but with 
minimal linearity asymmetry. This linear asymmetery is hardly noticible, 
even with an oscillioscope.


+------------------------------+
| Volume / envelope decay unit |
+------------------------------+

The volume / envelope decay hardware is found only in the square wave and 
noise channels.

$4000(sq1)/$4004(sq2)/$400C(noise)
----------------------------------
0-3	volume / envelope decay rate
4	envelope decay disable
5	envelope decay looping enable

When the envelope decay disable bit (bit 4) is set (1), the current volume 
value (bits 0-3) is sent directly to the channel's DAC. However, depending 
on certain conditions, this 4-bit volume value will be ignored, and a value 
of 0 will be sent to the DAC instead. These conditions are as follows:

- When hardware in the channel wants to disable it's sound output (like the 
length counter, or sweep unit).

- On the negative portion of the output frequency signal coming from the 
duty cycle / random number generator hardware (square wave channel / noise 
channel). This means that while the channel is enabled (producing sound), 
the output of the channel (what you'll hear from the DAC) will either be the 
4-bit volume value, or 0. This also means that a 4-bit volume value of 0 
will result in no audible sound.

When the envelope decay disable bit is cleared, bits 0-3 now control the 
envelope decay rate.
"Envelope decay" is used to describe the action of the channel's audio 
output volume starting from a maximum value, and decreasing by 1 at a fixed 
(linear) rate. This fixed decrement rate is controlled by the envelope decay 
rate (bits 0-3). The calculated decrement rate is 240Hz/(N+1), where N is 
any value between $0-$F.

When the channel's decayed envelope reaches a value of 0, depending on the 
status of the envelope decay looping enable bit (bit 5, which is shared with 
the length counter's clock disable bit), 2 different things will happen:

bit 5	action
-----	------
0	The envelope will stay at 0 (channel silenced)
1	The envelope count will wrap-around; that is, the volume will go from 0 to 
maximum again on the next decay rate refresh clock, and continue counting 
down.

Only a write out to $4003/$4007/$400F will reset the current envelope decay 
count to a known state (to the maximum envelope volume=$F) for the 
appropriate channel's envelope decay hardware. Otherwise, the envelope decay 
counter is always counting down at the rate currently contained in the 
volume / envelope decay rate bits (even when envelope decays are disabled 
(setting bit 4)), except when the envelope decay counter contains a value of 
0, and envelope decay looping (bit 5) is disabled (0).


+------------+
| Sweep unit |
+------------+

The sweep unit is only found in the square wave channels. The controls for 
the sweep unit have been mapped in at $4001 for square 1, and $4005 for 
square 2.

The controls
------------
Bit 7   	when this bit is set (1), sweeping is active. This results in 
real-time increasing or decreasing of the the current wavelength value (the 
audible frequency will decrease or increase, respectively). The wavelength 
value in $4002/3 ($4006/7) is constantly read & updated by the sweep. 
Modifying the contents of $4002/3 will be immediately audible, and will 
result in the sweep now starting from this new wavelength value.

Bits 6-4	These 3 bits represent the sweep refresh rate, or the frequency at 
which $4002/3 is updated with the new calculated wavelength. The refresh 
rate frequency is 120Hz/(N+1), where N is the value written, between 0 and 
7.

Bit 3   	This bit controls the sweep mode. When this bit is set (1), sweeps 
will decrease the current wavelength value, as a 0 will increase the current 
wavelength.

Bits 2-0	These bits control the right shift amount of the new calculated 
sweep update wavelength. Code that shows how the sweep unit calculates a new 
sweep wavelength is as follows:

bit 3
-----
0	New = Wavelength + (Wavelength >> N)
1	New = Wavelength + (Wavelength >> N)!

where N is the the shift right value, between 0-7.

Note that in decrease mode, 1's compliment is being used to subtract the 2 
numbers, instead of the normal 2's compliment method.

On each sweep refresh clock, the Wavelength register will be updated with 
the New value, but only if all 3 of these conditions are met:

- bit 7 is set (sweeping enabled)
- the shift value (which is N in the formula) does not equal to 0
- the channel's length counter contains a non-zero value

Notes
-----
There are certain conditions that will cause the sweep unit to silence the 
channel, and halt the sweep refresh clock (which effectively stops sweep 
action, if any). Note that these conditions pertain regardless of any sweep 
refresh rate values, or if sweeping is enabled/disabled (via bit 7).

- an 11-bit wavelength value less than $008 will cause this condition
- the New calculated wavelength will always be tested to see if a carry (bit 
$B) was generated or not (if sweeping is enabled, this carry will be 
examined before the Wavelength register is updated). If carry equals 1, and 
the sweep unit is set to increase mode, the channel is silenced, and sweep 
action is halted. This doesn't happen in decrease mode.


+----------------------+
| Duty cycle generator |
+----------------------+

The duty cycle generator takes the fequency produced from the 11-bit 
programmable timer, and uses a 4 bit counter to produce 4 types of duty 
cycles. The output frequency is then 1/16 that of the programmable timer. 
The duty cycle hardware is only found in the square wave channels. The bit 
assignments are as follows:

$4000(sq1)/$4004(sq2)
---------------------
6-7	Duty cycle type

	duty (positive/negative)
val	in clock cycles
---	---------------
00	 2/14
01	 4/12
10	 8/ 8
11	12/ 4

Where val represents bits 6-7 of $4000/$4004.

The output frequency at this point will now be fed to the volume/envelope 
decay hardware.


+----------------------+
| Wavelength converter |
+----------------------+

The wavelength converter is only used in the noise channel. It is used to 
convert a given 4-bit value to an 11-bit wavelength, which then is sent to 
the noise's own programmable timer. Here is the bit descriptions:

$400E bits
----------
0-3	The 4-bit value to be converted

This is a conversion chart that shows what 4-bit value will represent what 
11-bit wavelength to be fed to the channel's programmable timer:

value	octave	scale	CPU clock cycles (11-bit wavelength+1)
-----	------	-----	--------------------------------------
0	15	A	002
1	14	A	004
2	13	A	008
3	12	A	010
4	11	A	020
5	11	D	030
6	10	A	040
7	10	F	050
8	10	C	065
9	 9	A	07F
A	 9	D	0BE
B	 8	A	0FE
C	 8	D	17D
D	 7	A	1FC
E	 6	A	3F9
F	 5	A	7F2

Octave and scale information is provided for the music enthusiast programmer 
who is more familiar with notes than clock cycles.


+-------------------------+
| Random number generator |
+-------------------------+

The noise channel has a 1-bit pseudo-random number generator. It's based on 
a 15-bit shift register, and an exclusive or gate. The generator can produce 
two types of random number sequences: long, and short. The long sequence 
generates 32,767-bit long number patterns. The short sequence generates 
93-bit long number patterns. The 93-bit mode will generally produce higher 
sounding playback frequencys on the channel. Here is the bit that controls 
the mode:

$400E bits
----------
7	mode

If mode=0, then 32,767-bit long number sequences will be produced (32K 
mode), otherwise 93-bit long number sequences will be produced (93-bit 
mode).

The following diagram shows where the XOR taps are taken off the shift 
register for each mode.

mode	    <-----
----	EDCBA9876543210
32K	**
93-bit	*     *

The current result of the XOR will be transferred into bit position 0 of the 
SR, upon the next shift cycle. The 1-bit random number output is taken from 
pin E, is inverted, then sent to the volume/envelope decay hardware. The 
shift register is shifted upon recieving 2 clock pulses from the 
programmable timer (the shift frequency will be half that of the frequency 
from the programmable timer (one octave lower)).

On system reset, this shift register is loaded with a value of 1.


