Symmetry454
Symmetry454 is a rank-2 temperament that derives from the calendar by the same name, which was a proposed as a reform in 2004.
History
Symmetry454 calendar was developed in 2004 by Irv Bromberg. Unlike some of the previous calendar reforms, which proposed "null" days to even out the inconsistence of weekdays with months, Symmetry454 calendar employs a leap week to account for the inconsistency - each year is 52 or 53 weeks whole. What's more unique, each month is 4 or 5 weeks whole starting on Monday, resulting in dates such as February 35th.
The leap rule of Symmetry454 is defined by the following:
It is a leap year only if the remainder of ( 52 × Year + 146 ) / 293 is less than 52.
As such, it is an maximal evenness scale, therefore a MOS scale, and therefore can be used to produce a temperament. It is defined therefore in music through a 52 & 293 temperament.
Theory
Symmetry454's "first" comma is 225/224, meaning that it can be included in the collection of miscellaneous marvel temperaments. However, with the lack of commonality of a second comma between the 13 and 17 limits, it does not have a family yet.
Temperament data
In the limits below 13, Symmetry454 is a contorted 63 & 115 temperament.
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 225/224, 14700/14641, 16896/16807, 24192/24167
POTE generator: ~52/45 = 253.9315
Optimal ET sequence: 52, 241c, 293
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 225/224, 715/714, 2880/2873, 22750/22627, 60112/60025
POTE generator: ~52/45 = 253.9326
Optimal ET sequence: 52, 241c, 293