The 260-Day Gear Wheel Principle

How the 20 × 13 cycle interlocks to form an endlessly unique rhythmic pattern

The Two Gears

Imagine two interlocking gear wheels: an outer ring with 20 teeth (the 20 Day Signs) and an inner ring with 13 teeth (the 13 Galactic Tones). With each step forward, the combination shifts. Since the least common multiple of 20 and 13 is 260 (lcm(20,13)=260), it takes exactly 260 steps to return to the exact same 'Day Sign + Tone' combination.

This is precisely why Kin numbers range from 1 to 260: a Kin is the position index of this specific combination within the cycle, rather than the day number of a Gregorian calendar year.

Relationship with the 365-Day Solar Calendar (Haab)

Traditional Mayan chronology also includes the Haab, a 365-day solar calendar used for agricultural and seasonal tracking. The 260-day Tzolk'in and the 365-day Haab run concurrently, forming a much larger alignment cycle when they meet (such as the 52-year Calendar Round).

mayakin focuses exclusively on the Tzolk'in layer: Natal Kins, Daily Kins, 13-day Wavespells, and Yearly Flows are all derived from this layer. You do not need to master the Haab first to fully utilize the core features of this site.

What 260 Days Means to the Individual

A period of 260 days is roughly equal to 9 months, closely mimicking the human gestation period, which is why many modern interpreters view it as an 'inner growth cycle.' Regardless of whether you adopt this symbolism, the 260-day cycle remains mathematically concrete: the same Gregorian date usually corresponds to a different Kin each year (unless it happens to align perfectly with the 260-day interval).

In the next article, we will break down the Kin number into two readable dimensions: 'Day Sign' and 'Tone'.