Blind society timekeeping: observable natural cycles

The first step to figuring out a plausible system of timekeeping for my blind society is determining what natural cycles it could be based on.

Day and year
It's pretty obvious that day and year would both be observable. The day would be observable directly from day/night temperature variations and differences in the felt direction of the sun on non-cloudy days. It would also be observable indirectly through diurnal activities and phenomena in the living world - e.g. birds singing at dawn, flowers being open in the day and closed at night. Probably the natural time to mark the beginning of a day would be at a day/night boundary - either sunrise or sunset.

The year would be observable directly through differences in seasonal temperature/weather patterns; if they're in a sufficiently non-tropical location, it would also be observable through differences in day/night length; I'm not sure how noticeable differences in sun angle through the year would be. The year would also be observable indirectly through such things as plant growth and ripening, and animal migration and life cycles. It's not clear to me how you'd decide where to mark the beginning of a year, but I suspect animal and plant cycles would probably provide clearer marking points than weather and day length.

Lunar cycle: not observable
The moon, and thus the lunar month, would not be directly observable.

The lack of an obvious basis for a lunar month is interesting, because most Earth calendars have a month of some sort, whether it remains synchronized to the lunar month or not. There are, however, a few calendars that don't have months with lengths based on the lunar month; the ones I've seen use some other intermediate unit between days and years:

Akan calendar
Pentecontad calendar

There are also some other calendars that do include some reckoning of months, but also include a different sub-year group of days that is not dependent on the month:
Maya calendar
Javanese calendar

Other cycles
Although the lunar cycle would not be directly observable, the tidal cycle, which is related to the lunar cycle, would be. The society is located on an island in the ocean, so they would have experience with coasts and tides. What they would observe in tides depends on what kind of tides their location has. I learnt recently from Wikipedia that there are three main kinds of tidal patterns. Diurnal tides have one high tide and one low tide a day. Semidiurnal tides have two high tides and two low tides a day, with relatively similar heights for the highs and relatively similar lownesses for the lows. Mixed tides have two highs and two lows a day, but one high is significantly higher than the other, and one low is significantly lower than the other. My experience with tides is with mixed tides, and I had assumed they were universal. This map shows that most places in the world have either semidiurnal or mixed tides, so I can assume at least that my blind society would have experience with two highs and two lows a day. Of course, the point of bringing up the tidal cycle is that it's not exactly per day - a tidal day is longer than a solar day by about an hour. If I understand right, the tidal day and the solar day will resynchronize every month. Also, the relationship between the position of the sun and moon creates spring tides (when the tidal action of sun and moon is aligned at full and new moon) and neap tides (when the tidal action of sun and moon is crosswise at half moon). Tidal cycles might give a basis for the creation of a month or half-month period, but I'm not sure. It takes more to extract that from tidal patterns than from simple lunar phases. And how important the tidal cycle would be to them would depend on how much use they make of the ocean and intertidal zone.

Another observable cycle would be women's menstrual cycles. The length is approximately a month, but can vary considerably. And the timing is different for different women, so unlike astronomically-determined cycles, there's not a communally-accessible single standard.

I can't think of any other observable plausibly-useful natural cycles that are smaller than a year.

Small time units and echolocation
This observation is kind of irrelevant to the above thoughts about calendars, and is more relevant to the topic of time units smaller than a day, which I'm not really digging into right now.

They use echolocation. For sufficiently distant objects, this involves making a click and hearing a distinct echo a brief time later. Although their use of echolocation is so habitual that they usually primarily perceive the distance and location of the object, not the timing of the echo, I expect they would be able to be aware of the timing of the echo if they pay attention to it. This makes it likely that they would develop a concept of the speed of sound, and would be able to associate echo-times with distances. Since distances are easier to measure than times, it would be easy to speak about brief times in terms of the distance that echo-time corresponds to.

Blind society timekeeping: sub-year brainstorming

This post is for brainstorming ideas for how times smaller than a year but larger than a day could be reckoned in a blind society. It includes some ideas I'm sure I don't want to use, as well as ones I might.

Inherited months
One possibility is that they inherited a month-sized unit of time from the group they branched off from, and have maintained it, possibly with some modifications since they don't perceive the lunar cycle it was originally based on. I think this is a boring option, so I don't plan to use it.

Ecologically-based timekeeping
Ecologically-based timekeeping reckons time of year based on cues in the living environment: things like when a certain plant grows shoots, when a certain plant flowers, when a certain plant has ripe fruit, when certain birds sing, etc. There are Earth calendars that involve ecological components. Older versions of the Hebrew calendar, and the version now used by Karaite Jews, determined the beginning of the month of Aviv by whether barley was ripe; if it wasn't, an intercalary month would be added. In many languages, months of lunisolar and solar calendars have names that reflect ecology; in some cases, especially with lunisolar calendars, these could reflect an earlier ecological basis for month determination. I can imagine several variants of ecologically-based timekeeping:

Informal ecological timekeeping
Informal ecological timekeeping takes note of ecological signs, and can talk about past and future times by referring to those ecological signs. It may or may not have an established sequence of ecological periods - the period when X is ripe followed by the period when Y is ripe, etc. But it doesn't have communally formally-defined transitions from one period to another. There's no communally-recognized first day of the next ecological period.

Formal observational ecological timekeeping
This turns informal ecological timekeeping into a system. There is a fixed sequence of ecological periods; when a new one starts is determined observationally in a way that can be shared with the whole (local) community, and the beginning of a new period is communally recognized. This could be by whoever notices that the period has begun telling others and getting confirmation of their evidence. It could be that there's someone who has a ritual timekeeping position who observes the signs and declares it to the community when a new period has begun. And there are probably other ways. In this kind of system, ecological periods will differ in length from year to year, and some ecological periods of the year may be significantly longer than others.

Idealized ecological timekeeping
In this system, units of time that were once based on ecological observation are given fixed lengths, and recur at the same interval year-to-year, regardless of whether they match with ecological observations in this particular year. (Intercalation of some sort will be necessary in order to keep the year roughly synchronous with the solar year.)

The variant of these that I am most likely to use is formal observational ecological timekeeping.

Divinely-given 7-day weeks
In an old version of Domil, I worked on an assumption that 7-day weeks are divinely-given, in Domil as well as on Earth; thus, all Domil societies used a 7-day week, whatever the rest of their calendar was like (unlike Earth, in which some societies have not traditionally used a 7-day week). I am not sure if I am still going to work on that assumption, but I might. I think a calendar system based only on days, weeks, and years is still probably a bit unwieldy - it feels like you'd probably want something larger than a week. Although, if you use seasons (quarter-year seasons), and count months within each season, that might work. More likely is that they use weeks in concert with ecological timekeeping.

Co-occurring weeks of differing lengths
As mentioned in previous posts, you can get an intermediate-sized unit by having two different "weeks" that run alongside each other, such as the Akan calendar with 6-day weeks and 7-day weeks which combine to make a 42-day "month". In some of my previous workings for Domil timekeeping systems, one society used concurrent 7-day and 12-day cycles, which combine to make an 84-day cycle. If I use a variant of this system for my blind society, I will use a 7-day cycle for one of them, but I'm not sure how long I'd make the other cycle be. The larger units could function as month-like units in correspondence with an ecologically-determined year start.

"Long weeks"
Some calendars have week-like units with arbitrary numbers of days that are significantly longer than a 7-day week. The Mayan calendar has a 13-day unit and a 20-day unit, which combine to create a longer unit, but the smaller units themselves are instances of what I'd think of as "long weeks". There could be a similar sort of "long week" that could serve a month-like purpose.

Groups of weeks
Weeks (assuming 7-day here, but in principle it could be other lengths) can be grouped into larger units, which could end up approximately month-sized. I suppose a fortnight is the smallest example of this. The Igbo calendar has 4-day weeks, with 7 weeks making a 28-day month. A calendar system I was working on a long time ago for another Domil people group had 7-day weeks, with 4 weeks making a 28-day month. Either way, 13 months of 28 days each makes a 364 day year, which would need some sort of intercalation to stay on track with the solar year. A 28-day month is close to a lunar month, but a bit short, so it wouldn't stay in sync. It is tidily in sync with weeks - a given day of the month would always fall on the same day of the week (at least as long as your intercalation added weeks or months, rather than filling up the year with a day (in normal years) or two (in leap years) that were outside the weeks and months). The rough equivalence with lunar months is probably where that number of weeks came from, but obviously it's not closely tied to the lunar cycle. 28 days is also close to the typical length of a menstrual cycle. I think a calendar system that was actively based on menstrual cycles would be really tricky to arrange, but I think it's much more plausible that if you have weeks in your calendar system already, you would notice that menstrual cycles lasted about 4 weeks. And I think that could provide a basis for choosing a 4-week grouping of weeks. An added bonus is that since it roughly corresponds to a lunar month, it will also roughly correspond to a tidal month.

Tidal months
They could have months based on observations of the tides. I'm not sure if these would more likely be full months or half-months.