diff --git a/software/glasgow/applet/audio/dac/__init__.py b/software/glasgow/applet/audio/dac/__init__.py
index 35cc400ea..cbfb0c42b 100644
--- a/software/glasgow/applet/audio/dac/__init__.py
+++ b/software/glasgow/applet/audio/dac/__init__.py
@@ -174,7 +174,7 @@ def add_build_arguments(cls, parser, access):
     def build(self, target, args):
         self.mux_interface = iface = target.multiplexer.claim_interface(self, args)
         if args.frequency is None:
-            pulse_cyc = 0
+            pulse_cyc = 1
         else:
             pulse_cyc = self.derive_clock(clock_name="modulation",
                 input_hz=target.sys_clk_freq, output_hz=args.frequency * 1e6)
@@ -182,7 +182,7 @@ def build(self, target, args):
             input_hz=target.sys_clk_freq, output_hz=args.sample_rate,
             # Drift of sampling clock is extremely bad, so ensure it only happens insofar as
             # the oscillator on the board is imprecise, and with no additional error.
-            max_deviation_ppm=0)
+            max_deviation_ppm=0) - 1
         subtarget = iface.add_subtarget(AudioDACSubtarget(
             ports=iface.get_port_group(o = args.pin_set_o),
             out_fifo=iface.get_out_fifo(),
diff --git a/software/glasgow/applet/interface/spi_controller/__init__.py b/software/glasgow/applet/interface/spi_controller/__init__.py
index 72b88c6a1..7081041ef 100644
--- a/software/glasgow/applet/interface/spi_controller/__init__.py
+++ b/software/glasgow/applet/interface/spi_controller/__init__.py
@@ -350,7 +350,7 @@ def build_subtarget(self, target, args):
                                          min_cyc=4),
             delay_cyc=self.derive_clock(input_hz=target.sys_clk_freq,
                                         output_hz=1e6,
-                                        clock_name="delay"),
+                                        clock_name="delay") - 1,
             sck_idle=args.sck_idle,
             sck_edge=args.sck_edge,
         )
diff --git a/software/glasgow/applet/interface/uart/__init__.py b/software/glasgow/applet/interface/uart/__init__.py
index f1feb8e63..530e4ba69 100644
--- a/software/glasgow/applet/interface/uart/__init__.py
+++ b/software/glasgow/applet/interface/uart/__init__.py
@@ -173,7 +173,7 @@ def build(self, target, args):
         # a build argument, even though the applet will never be rebuilt as long as you stay
         # above 9600.
         max_bit_cyc = self.derive_clock(
-            input_hz=target.sys_clk_freq, output_hz=min(9600, args.baud))
+            input_hz=target.sys_clk_freq, output_hz=min(9600, args.baud)) - 1
 
         self.__sys_clk_freq = target.sys_clk_freq
 
@@ -215,7 +215,7 @@ async def run(self, device, args):
         # Load the manually set baud rate.
         manual_cyc = self.derive_clock(
             input_hz=self.__sys_clk_freq, output_hz=args.baud,
-            min_cyc=2, max_deviation_ppm=args.tolerance)
+            min_cyc=2, max_deviation_ppm=args.tolerance) - 1
         await device.write_register(self.__addr_manual_cyc, manual_cyc, width=4)
         await device.write_register(self.__addr_use_auto, 0)
 
diff --git a/software/glasgow/applet/program/m16c/__init__.py b/software/glasgow/applet/program/m16c/__init__.py
index a1cdc643c..b809de4e4 100644
--- a/software/glasgow/applet/program/m16c/__init__.py
+++ b/software/glasgow/applet/program/m16c/__init__.py
@@ -332,7 +332,7 @@ def add_build_arguments(cls, parser, access):
 
     def build(self, target, args):
         self.__bit_cyc_for_baud = {
-            baud: self.derive_clock(input_hz=target.sys_clk_freq, output_hz=baud)
+            baud: self.derive_clock(input_hz=target.sys_clk_freq, output_hz=baud) - 1
             for baud in BAUD_RATES
         }
         max_bit_cyc = max(self.__bit_cyc_for_baud.values())
diff --git a/software/glasgow/gateware/clockgen.py b/software/glasgow/gateware/clockgen.py
index a88591ee6..da210054a 100644
--- a/software/glasgow/gateware/clockgen.py
+++ b/software/glasgow/gateware/clockgen.py
@@ -50,7 +50,10 @@ def __init__(self, cyc):
     def elaborate(self, platform):
         m = Module()
 
-        if self.cyc == 0:
+        if self.cyc <= 0:
+            raise ValueError(f"Invalid output clock period: {self.cyc}")
+
+        if self.cyc == 1:
             # Special case: output frequency equal to input frequency.
             # Implementation: wire.
             m.d.comb += [
@@ -59,7 +62,7 @@ def elaborate(self, platform):
                 self.stb_f.eq(1),
             ]
 
-        if self.cyc == 1:
+        if self.cyc == 2:
             # Special case: output frequency half of input frequency.
             # Implementation: flip-flop.
             m.d.sync += [
@@ -70,7 +73,7 @@ def elaborate(self, platform):
                 self.stb_f.eq(self.clk),
             ]
 
-        if self.cyc >= 2:
+        if self.cyc >= 3:
             # General case.
             # Implementation: counter.
             counter = Signal(range(self.cyc))
@@ -119,8 +122,8 @@ def calculate(input_hz, output_hz, max_deviation_ppm=None, min_cyc=None):
                              "cycles at input frequency {:.3f} kHz"
                              .format(output_hz / 1000, min_cyc, input_hz / 1000))
 
-        cyc = round(input_hz // output_hz) - 1
-        actual_output_hz = input_hz / (cyc + 1)
+        cyc = round(input_hz // output_hz)
+        actual_output_hz = input_hz / cyc
         deviation_ppm = round(1000000 * (actual_output_hz - output_hz) // output_hz)
 
         if max_deviation_ppm is not None and deviation_ppm > max_deviation_ppm:
@@ -148,7 +151,7 @@ def derive(cls, input_hz, output_hz, max_deviation_ppm=None, min_cyc=None,
                 clock = "clock"
             else:
                 clock = f"clock {clock_name}"
-            if cyc in (0, 1):
+            if cyc in (1, 2):
                 duty = 50
             else:
                 duty = (cyc // 2) / cyc * 100