The Calendar and Pythagoras' Comma

We have noted a number of times that the months of the year were associated in antiquity with the total of twelve notes of the musical octave. There are, however, two slightly different kinds of months: the solar or calendar month which averages 30.44 days, making a total of 365.256 days per year, and the synodic lunar month of 29.5306 days, the duration of one moon cycle seen from the Earth.

Our Gregorian calendar based on the time the Earth travels one annual orbit around the Sun is and has been for many centuries the unquestioned authority, even before the re-discovery of the Earth as a round globe. Because of agriculture, machines, and especially for businesslike reasons, a mechanical and linear time concept is evident. "Time is money" is to be taken literally in its deepest application!

Actually, a far easier and more logical way to divide the solar year would be by thirteen 28-day months with one extra free day.

Right up to the 20th century pre-agricultural man, such as the Lakota, - A Native American tribe - has followed a vague or unfixed moon calendar. The fact is that during one solar year there is always a 13th lunation, which transits from one solar year to the next. The taboo nature of the number 13 seems to stem from the mysterious 13th moon.

There is an 11-day discrepancy between the length of the solar year of 365.242199 days and 12 complete synodic lunation’s of 354.36706 days.

The ratio of Pythagoras' comma is 531441 to 524288, the former figure being larger than the latter by the factor of 1.01364.

The ratio between the two years is the former figure being larger by a factor of 1.03073.

To express the closeness of the two ratios in a more graphic way, we can translate the ratios of the comma into calendar terms: 531441 is to the solar year of 365.256 days as 524288 is to the time period of 360.340 days.

This is about six days out from the precise 12 synodic lunation.

The two ratios - between the two years (solar and lunar) and the two types of musical scales (of perfect fifths and of equal temperament) - are astonishingly close to each other.

 The cultures of antiquity seem not to have missed this phenomenon of the cosmic comma. In ancient historical time the measurement of the year by means of solar months was considered holy and righteous, where as to keep time by the moon was both "incorrect and evil". The male power became associated with the sun, while the female was associated with the moon.

The Mayan calendar, on which the Mesoamerican civilizations was based, was made to apply to the dimension. The Mayan mathematical system had a fractal and exponential flexibility based on a dot-bar notation on 20’s rather than 10’s. The Mayan timing frequency was 13:20 and not our 12:60. Thirteen refers to the 13 galactic tones or power of creation, which were also encoded in the 13 moons or annual lunation's. Twenty refers to the 20 solar frequencies encoded as the 20 icons or solar seals. Upon this timing frequency was based the tzolkin or 260-kin "sacred calendar".

The Egyptian division of the circle into 360 degrees, subdivided into 12 parts of 30 degrees, provided the male priesthood of Egypt and Mesopotamia with the norm of their celestial oriented "male solar" hierarchies. This occurred some 5,000 years ago, at ca. 3000 BC.

By the time of the rise of the Christian Church, AD 500 – 1000, the Roman calendar of 12 months of uneven days in disregard of the lunation’s cycles was an established fact.

It is a tradition of time reckoning based on the Egyptian division of the circle, which is a division of space and not of time – and in which all taboos of the number 13 are fully incorporated.