Adan Neely‘s table of musical fractal equivalence.
The ratio is for the number of midi clips used to the number of midi clips that determine the duration. 57:32 means 57 midi clips condensed into the space of 32 midi clips.
One of theAbysmal Calendar’s functions is to facilitate scaling over orders of magnitude from seconds to epoch. Using the 24-hour day, the 24-day month, and 24–hōra year, (see: 360 day calendar) theAbysmal breaks linear time and pieces together a fractal, self-similar model of time.
Short version: the 360-day calendar does not include Leap Day (Jun 21), the New Year on Dec 21, or the four midquarter days: Feb 5, May 7 (6 in a leap year), Aug 6, Nov 5.
Calendar as Clock Analog
theAbysmal Calendar divides up the year symmetrically occording to the Seasons, providing a wide variety of divisions of the year into even numbers of weeks and months. For the purposes of relating the 24-hour day to the 365-day year, we use the 360 + 5 day model. The 365 days of the year (and the leap day) are divided into 360 calendar days and five (or six) days that fall outside of the calendar. We still experience the days – dawn to dusk to dawn – while the calendar takes a pause.
The five days excluded from theAbysmal 360-day year are:
Dec 21, Feb 5, May 7 (6), Aug 6, Nov 5 Jun 21 (Leap Day)
The remaining 360 days are arranged as 24 hōra of 15 days each, and 15 months of 24 days each.
the 24-hour day
86,400 seconds/day = 60 x 60 x 24 = 3600 x 24 = 360 x 240
I’ve chosen this particular clockface because it follows a number of patterns in common with theAbysmal Calendar:
begins counting with 0
covers a full 24 hours rather than twice 12 hours
places midnight at bottom
While we usually divide our day into 24 hours of 60 minutes of 60 seconds, we also observe half and quarter hours, periods in five-minute increments, a.m. and p.m. We haven’t really explored the full potential of dividing our day.
86,400 seconds/day = 27 x 33 x 52
There are so many ways to arrange these prime factors, however, the one that suits our purposes here are those that resonate with our 360-day year:
86,400 = 60 x 60 x 24 = 3600 x 24 = 360 x 240 = 24 x 15 x 240
In the course of a 24-hour day, there are 360 periods of 240 seconds (4 minutes), as there are 240 periods of 360 seconds (6 minutes).
theAbysmal Year
365 = 360 + 5 = 15 x 24 + 5
theAbysmal 24-hōra year
This particular visualization of theAbysmal Year follows a similar course to the clockface above:
begins counting with 0
covers a full 24 months
places Winter Solstice at bottom
While theAbysmal Calendar begins the day at Midnight and the year at the Southern Solstice at Dec 22, for the purposes of this exercise, let’s consider beginning both the Northern and Southern year at the Winter Solstice, Dec 21 and Jun 21 respectively.
There are two ways to arrange the 24-day month within the 360-day year: either as months of four 6-day weeks or three 8-day weeks.
theAbysmal 15-month year by 6-day week
The months illustrated above can be divided easily into quarters by 6-day week, whereas the months illustrated below can be divided by 8-day week. These reflect our use of 6-hour and 8-hour periods in scheduling our daily activity.
theAbysmal 15-month year by 8-day week
theAbysmal Calendar’s two principal models, then, are the 24-hōra year and the 24-day month.
Time by the Analogous Clock
When we look to relate the 24-hour day to the 24-day month and 24-hōra year, each of the days of the month and days of the hōra are themselves divisible by hours, minutes, and seconds.
24-hour day
24-day month
24-hōra year
1 day
24 days
360 days
1 hour
1 day
15 days
4 minutes
96 minutes
1 day
1 minute
24 minutes
6 hours
10 seconds
4 minutes
1 hour
1 second
24 seconds
6 minutes
4 seconds
1 minute
1 second
15 seconds
Table of equivalent times
We can further extend this equivalence to longer spans of time.
24-hour day
24-day month
24-hōra year
1 day
24 days
360 days
15 days
1 year
15 years
360 days
24 years
360 years
15 years
360 years
5,400 years
Table of equivalent longer times
What bends the mind is that 15 days of our typical experience is equivalent to 1 full year of 15 months as well as 15 years. 15 days is the duration of 1 hōra. So while we experience our 15-day hōra, it is a fractal for the 15-month year, and also for 15 years arranged by 24 hōra.
While we can further equate 15 years to a historical epoch of 5,400 years, theAbysmal uses a 5,200 year historical epoch. There’s nothing saying we can’t have both. The more ways there are to arrange time, the more it becomes a function of our mind and less an external truism.
Rethinking Time 