APU Triangle

The NES APU triangle channel generates a pseudo-triangle wave. It has no volume control; the waveform is either cycling or suspended. It includes a linear counter, an extra duration timer of higher accuracy than the length counter.

The triangle channel contains the following: timer, linear counter, length counter, halt flag, sequencer. The linear counter contains an internal halt flag and counter.

      Linear Counter   Length Counter
            |                |
            v                v
Timer ---> Gate ----------> Gate ---> Sequencer ---> (to mixer)

$4008	CRRR.RRRR	Linear counter setup (write)
bit 7	C---.----	Control flag (this bit is also the length counter halt flag)
bits 6-0	-RRR RRRR	Counter reload value
$400A	LLLL.LLLL	Timer low (write)
bits 7-0	LLLL LLLL	Timer low 8 bits
$400B	llll.lHHH	Length counter load and timer high (write)
bits 2-0	---- -HHH	Timer high 3 bits
Side effects		Sets the halt flag

The sequencer is clocked by a timer whose period is the 11-bit value (%HHH.LLLLLLLL) formed by timer high and timer low, plus one. So given the following:

• f_CPU = the clock rate of the CPU
• tval = the value written to the timer high and low registers
• f = the frequency of the wave generated by this channel

The following relationships hold:

• f = f_CPU/(32*(tval + 1))
• tval = f_CPU/(32*f) - 1

When the frame counter generates a linear counter clock, the following actions occur in order:

1. If the halt flag is set, the linear counter is reloaded with the counter reload value, otherwise if the linear counter is non-zero, it is decremented.
2. If the control flag is clear, the halt flag is cleared.

The sequencer is clocked by the timer as long as both the linear counter and the length counter are nonzero.

The sequencer sends the following looping 32-step sequence of values to the mixer:

15, 14, 13, 12, 11, 10,  9,  8,  7,  6,  5,  4,  3,  2,  1,  0
 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15

At the lowest two timer periods ($400B = 0 and $400A = 0 or 1), the resulting frequency is so high (over 20 kHz) that the mixer effectively receives a value half way between 7 and 8.