There’s a bunch of annoying and weird boiler plate to configuring a timer. There are calculators online that make it easy:

https://deepbluembedded.com/arduino-timer-calculator-code-generator/

1. Determine what longest period you need is.
2. From that period, determine what prescaler you need to set.
3. Set up the clock in a setup() function.
4. Define the interrupt function. Keep it as simple as possible. The more it does, the more the timing can be affected. If possible just set variables and let the loop function do that rest based on the values set for those variables.

ISR(TIMER1_COMPA_vect)
{
  OCR1A += 41666; // Advance The COMPA Register to "schedule" the next interrupt if needed.
  // Code for what you want to do when the program is interrupted.
}

void setup()
{
  TCCR1A = 0;           // Init Timer1A
  TCCR1B = 0;           // Init Timer1B
  TCCR1B |= B00000010;  // Prescaler = 8
  OCR1A = 41666;        // Timer Compare1A Register. The interrupt will happen when the timer reaches this value.
  TIMSK1 |= B00000010;  // Enable Timer COMPA Interrupt
}

void loop()
{
  // ...
}

A Timer (8 or 16bit for most AVR boards) can only measure up to a certain period before resetting back to 0 based on the microcontroller’s frequency. The prescaler divides by some number to allow for timing longer periods. The limit of the number of periods is that largest value that can be represented in 16 bits (65535) or 8 bits (256).

(timer speed (Hz)) = (Arduino clock speed (16MHz)) / prescaler

See also https://www.instructables.com/Arduino-Timer-Interrupts/

An interesting discussion on if/how the prescaler to affect the clock resolution: https://arduino.stackexchange.com/q/4022

https://github.com/midilab/uClock/blob/main/src/platforms/avr.h