|
Accurate Lunisolar Calendar
Dear Calendar People,
The following would be a device useful for an observational lunisolar calendar.
The device consists of two gears that intermesh with each other or with a common gear.
The moon gear has 19 teeth.
The sun gear has 235 teeth.
One tooth on the moon gear is specially marked.
One tooth on the sun gear is specially marked.
Both gears are moved together each time there is a new moon. If this results in the specially marked teeth of both gears lining up, then a new year is started. So far, the Metonic cycle has been duplicated.
The Metonic cycle is a good approximation, but the year length is too long for the month length. So the following amends the above procedures:
The moon gear has two pegs that travel around the gear. The pegs at epoch start out together, and one is taller than the other. At epoch, the shorter one sits in the cog with the mark that's used to align with the sun gear. Each time the marks on the moon and sun gears line up, the tall peg is moved one cog. The cogs have only one hole used by both pegs, so when the tall peg catches up to the short peg, they trade places (the short peg is moved to where the tall peg was when the tall peg is moved).
If this last leap-frog operation results in the short peg landing in the marked cog, then the sun gear is advanced one cog.
This operation effectively introduces a leap month every 342 Metonic cycles. This gives a month:year ratio of:
19*342 : 235*342-1
One need not wait several thousand years for this device to be useful. The distance between the small peg and the mark is a measure of how far the year and month are drifting with respect to each other. You can extend that precision by using the long peg. Perhaps short and long hands, clock style, should be used instead, since we're familiar with that.
Victor
|
|
Re: Accurate Lunisolar Calendar
On 2009 May 19, at 18:06 , Victor Engel wrote: This operation effectively introduces a leap month every 342 Metonic cycles. This gives a month:year ratio of:
19*342 : 235*342-1
Irv replies: I assume that Victor meant year:month ratio, or else to invert the given fraction.
The last thing that the Metonic cycle needs is an extra leap month! Surely he meant that a leap month is omitted every 343 Metonic cycles? It looks like that, because of the minus one at the end of the given ratio. Indeed, the numeric value of his ratio, when inverted to actually show months:years, is slightly less than my 4366:353 cycle, so it seems that he targeted the mean tropical year or 365+31/128 days (exact value depends on the assumed lunation period) whereas I target the mean northward equinoctial year.
The very long cycle = 6498 years has exaggerated equinox wobble and medium-term drift because it takes a full cycle before it makes the one month correction. A smoother correction can be obtained by periodically delaying the leap month for a year (as done in the 353-year cycle with 4366 months), rather than omitting it entirely.
-- Irv Bromberg, Toronto, Canada
|
|
Re: Accurate Lunisolar Calendar
Dear Irv, I didn't give the units leading to the fraction, which is dimensionless, so you can flip it either way. Just to illustrate: year length : month length would be the inverse of year number : month number
As to whether the leap month is added or subtracted, it all depends on whether the driver is the year or the month. If it's the month as I described, yes, it is omitted. I still say it's an introduction of a leap month. Maybe I should say it's the introduction of an adjustment.
As far as target goes, I just wanted to see what one step more accurate than the Metonic cycle would yield. My goal was to use the numbers already inherent in the 19:235 ratio. Without extending the period ridiculously far, there were really only a small number of options, the most obvious ones being 18*19 and 19*19. I chose the former because it's more accurate. That it happens to come close to the mean tropical year is just an accident. I did not target it specifically.
I was expecting the delay remark, but I expected it from Karl and not Irv. I would like to see the mechanics of the delay, though. I formulated the scheme the way I did because the mechanics are simple. And as I said in my original post, you can tell exactly how far into the progression the device is by reading it like a clock. We don't worry about the large jump of an hour as we wait for the minute hand to go around. We can tell by how far around it is what the progress is.
Victor On Tue, May 19, 2009 at 9:05 PM, Irv Bromberg <irv.bromberg@...> wrote:
On 2009 May 19, at 18:06 , Victor Engel wrote: This operation effectively introduces a leap month every 342 Metonic cycles. This gives a month:year ratio of:
19*342 : 235*342-1
Irv replies: I assume that Victor meant year:month ratio, or else to invert the given fraction.
The last thing that the Metonic cycle needs is an extra leap month! Surely he meant that a leap month is omitted every 343 Metonic cycles? It looks like that, because of the minus one at the end of the given ratio. Indeed, the numeric value of his ratio, when inverted to actually show months:years, is slightly less than my 4366:353 cycle, so it seems that he targeted the mean tropical year or 365+31/128 days (exact value depends on the assumed lunation period) whereas I target the mean northward equinoctial year.
The very long cycle = 6498 years has exaggerated equinox wobble and medium-term drift because it takes a full cycle before it makes the one month correction. A smoother correction can be obtained by periodically delaying the leap month for a year (as done in the 353-year cycle with 4366 months), rather than omitting it entirely.
-- Irv Bromberg, Toronto, Canada
|
|
Re: Accurate Lunisolar Calendar
Hi Vic, I have designed already the moon gear and my wife wears it golden on her ears. servus sepp
Am 20.05.2009 um 00:06 schrieb Victor Engel: Dear Calendar People,
The following would be a device useful for an observational lunisolar calendar.
The device consists of two gears that intermesh with each other or with a common gear.
The moon gear has 19 teeth.
The sun gear has 235 teeth.
One tooth on the moon gear is specially marked.
One tooth on the sun gear is specially marked.
Both gears are moved together each time there is a new moon. If this results in the specially marked teeth of both gears lining up, then a new year is started. So far, the Metonic cycle has been duplicated.
The Metonic cycle is a good approximation, but the year length is too long for the month length. So the following amends the above procedures:
The moon gear has two pegs that travel around the gear. The pegs at epoch start out together, and one is taller than the other. At epoch, the shorter one sits in the cog with the mark that's used to align with the sun gear. Each time the marks on the moon and sun gears line up, the tall peg is moved one cog. The cogs have only one hole used by both pegs, so when the tall peg catches up to the short peg, they trade places (the short peg is moved to where the tall peg was when the tall peg is moved).
If this last leap-frog operation results in the short peg landing in the marked cog, then the sun gear is advanced one cog.
This operation effectively introduces a leap month every 342 Metonic cycles. This gives a month:year ratio of:
19*342 : 235*342-1
One need not wait several thousand years for this device to be useful. The distance between the small peg and the mark is a measure of how far the year and month are drifting with respect to each other. You can extend that precision by using the long peg. Perhaps short and long hands, clock style, should be used instead, since we're familiar with that.
Victor
|
|
Re: Accurate Lunisolar Calendar
Some parts of this message have been removed.
Learn more about Nabble's security policy.
Dear Victor, Irv and Calendar People
From: East Carolina University Calendar
discussion List [mailto:CALNDR-L@...] On Behalf Of Victor
Engel
Sent: 19 May 2009 23:07
To: CALNDR-L@...
Subject: Accurate Lunisolar Calendar
Dear Calendar People,
The following would be a device useful for an observational lunisolar calendar.
The device consists of two gears that intermesh with each other or with a
common gear.
The moon gear has 19 teeth.
The sun gear has 235 teeth.
One tooth on the moon gear is specially marked.
One tooth on the sun gear is specially marked.
Both gears are moved together each time there is a new moon. If this results in
the specially marked teeth of both gears lining up, then a new year is started.
So far, the Metonic cycle has been duplicated.
I’ve had difficulty understanding this. If moved
together means moved together by one tooth, then it’d would take
235*19=4465 new moons, which is about 361 years to the two marked teeth to come
together. I am aware that if the moon gear wheel were turned one revolution per
lunation, the sun gear would turn about once per year and its marked tooth reaching
the moon gear wheel would mark the new year.
I now think what Victor meant by moved together was that
the moon gear wheel was turned one complete revolution each new moon.
An alternative (to one complete revolution on the new moon) is
to move it one tooth every 2nd, 3rd , 5th, 6th,
8th, 9th, 11th, 12th, 14th
day after a new moon and likewise for the following 14 days, then one more
tooth on the new moon to complete one revolution of the moon gear wheel.
Another alternative is to move the wheels one tooth according
the same 14-day cycle till 26 cycles have passed then for a common year move
one tooth the next (and 365th) day to complete a year and in a leap
year move one tooth the next but one (and 366th) day to complete a
year. The moon gear wheel would turn close to once per lunation.
However the lining up of the marked teeth on both the moon and
sun gear wheels would occur just once every 19 years.
The Metonic cycle is a good approximation, but the year length is too long for
the month length. So the following amends the above procedures:
It can be corrected by making the sun gear wheel slip one tooth against
the moon gear wheel , so the sun wheel turns one tooth, the moon gear
wheel does not turn.
The moon gear has two pegs that travel around the gear. The pegs at epoch start
out together, and one is taller than the other. At epoch, the shorter one sits
in the cog with the mark that's used to align with the sun gear. Each time the
marks on the moon and sun gears line up, the tall peg is moved one cog. The
cogs have only one hole used by both pegs, so when the tall peg catches up to
the short peg, they trade places (the short peg is moved to where the tall peg
was when the tall peg is moved).
If this last leap-frog operation results in the short peg landing in the marked
cog, then the sun gear is advanced one cog.
This operation effectively introduces a leap month every 342 Metonic cycles.
This gives a month:year ratio of:
19*342 : 235*342-1
One need not wait several thousand years for this device to be useful. The
distance between the small peg and the mark is a measure of how far the year
and month are drifting with respect to each other. You can extend that
precision by using the long peg. Perhaps short and long hands, clock style,
should be used instead, since we're familiar with that.
It seems that by each tooth of the moon gear wheel there is a
hole in which a peg may be placed and the pegs are moved once every Metonic
cycle so completing a cycle once every 342 Metonic cycles after which the moon
gear wheel is turned one revolution backward (or one revolution is cancelled).
I think a much better idea is the move the pegs annually and
after each peg cycle make the sun wheel slip a tooth against the moon wheel.
Since making the wheels slip could damage them, one could
instead turn the moon wheel forward 99 revolutions (1881 teeth), then the sun
wheel would turn 8 revolutions (1880 teeth) and one tooth, so achieving the
same effect as slipping the sun wheel. This makes it evident that this
correction truncates a Metonic cycle by 8 years to 11 years.
Karl
10(08(25
Scanned by iCritical.
|
|
Re: Accurate Lunisolar Calendar
Nice. I forgot to mention one important feature of my scheme. Days are never mentioned. That was by design in order to make it immune to any delta-t issues. Victor On Wed, May 20, 2009 at 1:20 AM, Sepp Rothwangl <calendersign@...> wrote:
Hi Vic, I have designed already the moon gear and my wife wears it golden on her ears.
servus sepp
Am 20.05.2009 um 00:06 schrieb Victor Engel:
Dear Calendar People,
The following would be a device useful for an observational lunisolar calendar.
The device consists of two gears that intermesh with each other or with a common gear.
The moon gear has 19 teeth.
The sun gear has 235 teeth.
One tooth on the moon gear is specially marked.
One tooth on the sun gear is specially marked.
Both gears are moved together each time there is a new moon. If this results in the specially marked teeth of both gears lining up, then a new year is started. So far, the Metonic cycle has been duplicated.
The Metonic cycle is a good approximation, but the year length is too long for the month length. So the following amends the above procedures:
The moon gear has two pegs that travel around the gear. The pegs at epoch start out together, and one is taller than the other. At epoch, the shorter one sits in the cog with the mark that's used to align with the sun gear. Each time the marks on the moon and sun gears line up, the tall peg is moved one cog. The cogs have only one hole used by both pegs, so when the tall peg catches up to the short peg, they trade places (the short peg is moved to where the tall peg was when the tall peg is moved).
If this last leap-frog operation results in the short peg landing in the marked cog, then the sun gear is advanced one cog.
This operation effectively introduces a leap month every 342 Metonic cycles. This gives a month:year ratio of:
19*342 : 235*342-1
One need not wait several thousand years for this device to be useful. The distance between the small peg and the mark is a measure of how far the year and month are drifting with respect to each other. You can extend that precision by using the long peg. Perhaps short and long hands, clock style, should be used instead, since we're familiar with that.
Victor
|
|
Re: Accurate Lunisolar Calendar
Some parts of this message have been removed.
Learn more about Nabble's security policy.
Dear Victor and Calendar People
The moon wheel can be driven by any lunar calendar and any
delta-T issue would apply to the lunar calendar.
Karl
From: East Carolina University Calendar
discussion List [mailto:CALNDR-L@...] On Behalf Of Victor
Engel
Sent: 20 May 2009 16:30
To: CALNDR-L@...
Subject: Re: Accurate Lunisolar Calendar
Nice.
I forgot to mention one important feature of my scheme. Days are never
mentioned. That was by design in order to make it immune to any delta-t issues.
Victor
On Wed, May 20, 2009 at 1:20 AM, Sepp Rothwangl <calendersign@...> wrote:
Hi Vic,
I have designed already the moon gear and my wife wears it
golden on her ears.
Am 20.05.2009 um 00:06 schrieb Victor Engel:
Dear Calendar People,
The following would be a device useful for an observational lunisolar calendar.
The device consists of two gears that intermesh with each other or with a
common gear.
The moon gear has 19 teeth.
The sun gear has 235 teeth.
One tooth on the moon gear is specially marked.
One tooth on the sun gear is specially marked.
Both gears are moved together each time there is a new moon. If this results in
the specially marked teeth of both gears lining up, then a new year is started.
So far, the Metonic cycle has been duplicated.
The Metonic cycle is a good approximation, but the year length is too long for
the month length. So the following amends the above procedures:
The moon gear has two pegs that travel around the gear. The pegs at epoch start
out together, and one is taller than the other. At epoch, the shorter one sits
in the cog with the mark that's used to align with the sun gear. Each time the
marks on the moon and sun gears line up, the tall peg is moved one cog. The
cogs have only one hole used by both pegs, so when the tall peg catches up to
the short peg, they trade places (the short peg is moved to where the tall peg
was when the tall peg is moved).
If this last leap-frog operation results in the short peg landing in the marked
cog, then the sun gear is advanced one cog.
This operation effectively introduces a leap month every 342 Metonic cycles.
This gives a month:year ratio of:
19*342 : 235*342-1
One need not wait several thousand years for this device to be useful. The
distance between the small peg and the mark is a measure of how far the year
and month are drifting with respect to each other. You can extend that
precision by using the long peg. Perhaps short and long hands, clock style,
should be used instead, since we're familiar with that.
Victor
Scanned by iCritical.
|
|
Re: Accurate Lunisolar Calendar
Dear Karl, Irv, Sepp, and Calendar People, On Wed, May 20, 2009 at 10:27 AM, Palmen, KEV (Karl) <karl.palmen@...> wrote:
Dear Victor, Irv and Calendar People
From: East Carolina University Calendar
discussion List [mailto:CALNDR-L@...] On Behalf Of Victor
Engel
Sent: 19 May 2009 23:07
To: CALNDR-L@...
Subject: Accurate Lunisolar Calendar
Dear Calendar People,
The following would be a device useful for an observational lunisolar calendar.
The device consists of two gears that intermesh with each other or with a
common gear.
The moon gear has 19 teeth.
The sun gear has 235 teeth.
One tooth on the moon gear is specially marked.
One tooth on the sun gear is specially marked.
Both gears are moved together each time there is a new moon. If this results in
the specially marked teeth of both gears lining up, then a new year is started.
So far, the Metonic cycle has been duplicated.
I’ve had difficulty understanding this. If moved
together means moved together by one tooth, then it’d would take
235*19=4465 new moons, which is about 361 years to the two marked teeth to come
together. I am aware that if the moon gear wheel were turned one revolution per
lunation, the sun gear would turn about once per year and its marked tooth reaching
the moon gear wheel would mark the new year.
I now think what Victor meant by moved together was that
the moon gear wheel was turned one complete revolution each new moon. By together, I simply meant that the 19 cog gear and the 235 cog gear were either interlocked to each other or interlocked to a common gear. My original idea was for them to be interlocked to each other, but if that were the case, one gears yin, would be the other's yang, and vice versa, making the peg holes out of phase with respect to each other. So I left it purposely undefined how they would be lined up. One possibility would be for both bears to be cotangent to a common gear that is twice as wide. Another idea would be for the peg holes to be at the cogs on one gear and between the cogs on the other. Then the two gears would simply need to abut each other. The main point, though, is that both gears move at the same speed as measured in cogs per unit time.
Karl is also right that one revolution of the 19 cog gear would correspond to one lunation. One revolution of the 235 cog gear, similarly, would correspond to one year.
An alternative (to one complete revolution on the new moon) is
to move it one tooth every 2nd, 3rd , 5th, 6th,
8th, 9th, 11th, 12th, 14th
day after a new moon and likewise for the following 14 days, then one more
tooth on the new moon to complete one revolution of the moon gear wheel. I was trying to stay away from days, which would eliminate this idea.
Another alternative is to move the wheels one tooth according
the same 14-day cycle till 26 cycles have passed then for a common year move
one tooth the next (and 365th) day to complete a year and in a leap
year move one tooth the next but one (and 366th) day to complete a
year. The moon gear wheel would turn close to once per lunation. Same comment here.
However the lining up of the marked teeth on both the moon and
sun gear wheels would occur just once every 19 years.
The Metonic cycle is a good approximation, but the year length is too long for
the month length. So the following amends the above procedures:
It can be corrected by making the sun gear wheel slip one tooth against
the moon gear wheel , so the sun wheel turns one tooth, the moon gear
wheel does not turn. Instead of slipping gears, I used pegged cogs. The marks can be moved with respect to the gear without altering the interlocking of the gears. Slipping the gears accomplishes the same thing.
I think a much better idea is the move the pegs annually and
after each peg cycle make the sun wheel slip a tooth against the moon wheel.
Why is that better?
Victor
|
