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Answer: SYNCHRONOUS

by Azalea Weisblat

In this puzzle, we are presented with a series of diagrams with a lot of subdiagrams, with some regions highlighted in various colors.

The first thing we have to realize is that these are all depictions of various calendar systems. We might hypothesize this based on one of the calendars, like the Egyptian calendar, that divides a year into months into weeks into days, or by the number of 12s around, or by doing some careful counting and noticing a 365. Once we have this as a hypothesis, we can find confirmation by searching for some of the odder numbers of things, such as 361, in conjunction with the word “calendar”.

Once we've identified one or more of the calendar systems, we can start to determine what the different colors mean, which will help us identify more calendar systems.

Color Meaning Example
Cyan Leap days/months The month of Adar I, in the Hebrew calendar during a 13-month year, or St. Tib's Day in the Discordian calendar. Both are added to make the calendar line up more with the solar year more.
Dark red Removed days In the year 5781 in the Hebrew calendar, the last day of Kislev is removed so that Shabbat and Rosh Hashanah don't align.
Pale magenta Holidays and weekends In the Egyptian calendar, each decan ends with two days of rest.
Dark blue Mystery Hunt! In the Hebrew calendar, Mystery Hunt 2021 corresponds to 2–5 Shevat 5781. This is only marked in calendars where it is feasible to do so.
Green Extraction These will all be listed below.

Once we have identified most or all of the calendars, we can use the green-highlighted areas to extract a cluephrase.

Image Calendar First extract Second extract Indexed letters Notes
Bahá’í calendar 1 Kamál 4th Bahí KI The Baháʼí calendar has a 361-year cycle in which all the years are named in addition to a 361 (plus 4–5)-day year.
Hebrew calendar 1 Nisan Adar II ND When an extra month of Adar is added to the Hebrew calendar according to the Metonic cycle, Adar II is considered to be the original Adar, and Adar I the inserted month.
Calendar of Romulus 5 Ides Octobris   O The Romans counted including the day they counted up to, so what we think of as 4 days before the Ides, the Romans thought of as 5 days before. We don't actually know how long the months were in the original 10-month Roman calendar.
Discordian calendar Confusion 4   F The excellently absurd Discordian calendar breaks up the 365-day year into five seasons of 73 days each. Leap years are 2 mod 4.
Maya calendar 2 Wayeb' 1 Chikchan AC The Maya calendar counts its 260-day cycle (the Tzolkʼin) not by 20 chunks of 13 or 13 chunks of 20, but with a 20-day count and a 13-day count that go at the same time and thus only repeat every 260 days because 13 and 20 are relatively prime. The Maya considered the first day of a month in the Haab' year to be the “seating” of the month, and it was not numbered; day 1 is the second day.
Ancient Egyptian calendar IV Shemu 4 Mesore MO The Egyptian calendar is sometimes referred to as the “wandering year” because of how quickly it deviates from the actual seasons.
Tamil calendar 4 Kārttikai   T The sexagenary cycle used by various calendars in Asia is said to be derived from the 12-year orbital period of Jupiter.
International Fixed Calendar Sol 2   O The Kodak company used this calendar until 1989, which frustrated the friends and families of people working for Kodak, since they had a different idea of what day of the week it was. The large 100×4-part cycle in this diagram corresponds to the system of leap years used by every calendar in the Gregorian system.
Islamic calendar 1 Rajab   R The rules of when to add an extra day to an Islamic calendar month are determined not by mathematics but by astronomy. Thus, there is no exact repeating pattern of when each month will be 29 or 30 days.

Each extracted thing has a number and a word or some words. Indexing the numbers into the words, we get KIND OF AC MOTOR. The kind of AC motor that fits thematically with calendars is SYNCHRONOUS.

Author’s Notes

This idea initially came up when I was thinking about what a puzzle entitled “Rectangles” would look like, to complement the puzzles Circles and Triangles. However, my plans were foiled when the most thematic answer available came with a title constraint. We opted not to name the puzzle Equiangular Quadrilaterals and chose something less in keeping with the other puzzles but more subtle.