chart

Purpose

This module turns an epoch and a place into a chart. It is the C++ form of the original chain, jseckp for the angles, a60 for the houses, a9 with a90 for the bodies. Houses run in Universal Time, the bodies run in Ephemeris Time, and every body passes the correction chain par_ap_ktr, light time, optionally aberration, conversion to equatorial, and Robert Rettig's topocentric parallax.

Origin map

The shell also carries the table screens of the original around the chart. The DEGREE LIST G/H of grli asks ADD the INTERMEDIATE HOUSES ? under the house systems one to seven, then prints every point of the chart with its degree, the cusps H2 to H12 without the MC on demand and the midpoint of every pair in his order, five columns of 41 rows to a page with his header, two decimals for the main points and cusps and one for the extra bodies, the precision following the first point of a pair. Without extra bodies the four cardinal points 0 Aries, 0 Cancer, 0 Libra and 0 Capricorn pair like bodies but never stand alone. His a921 lifted 0 Aries to exactly kk and his pair guard, which demands more than kk, dropped it, so his list carried no midpoint with the Aries point. The port pairs all four, and a pair opened by a cardinal point prints one decimal. DR and DS never pair and neither do two of the cusps H8, H9, H11 and H12. After the last page his question sorts the list by degree and draws the overall distribution beside every page, one bar of his unit per entry and degree. Pinned in test_render.cpp and test_coord.cpp. The HOUSE TABLE with each cusp's longitude, right ascension and declination and under Placidus the oblique ascension with its pole height and the great year with the precession driven age point over a chosen reference epoch.

The converters

Each converter keeps its own menu entry like his menu, all of them together under MISCELLANEOUS since the tester's eighth batch moved the three time entries of his EPHEMERIS menu there, F1 still opens their commentary 3. ET from UT and UT from ET (et_ut, ut_et) take a date and clock and show both time scales with ET minus UT split into days, hours, minutes and seconds, whole minutes before 948 and after 2050, with his remark on extrapolated or approximated values. DATE from JD (dat_jd) reads a Julian date, prints the centuries since 1900, the mean and the apparent obliquity of that moment, the calendar date and the clock, shows the current record's date under the input box and asks again on Continue. The tester's Auréas count, days since 1900 January 0.5, rides along and names its start, 31.12.1899 12h. RA-DE from EL-EB and EL-EB from RA-DE (arde_eleb, eleb_arde) take a date and a position in degree minute second or decimal and convert with the true obliquity of that day, the right ascension also as a clock. LT from UT and UT from LT (lt_ut, ut_lt) take a longitude in his coordinate box and shift the clock by it. ANGLE CONVERSION (rechne1), also on F5 or Alt+R anywhere, turns decimal degrees or hours into degrees, minutes and seconds and back on ENTER and stays open until QUIT. Pinned in test_convert.cpp.

The great year

GREAT ( = PLATONIC ) YEAR follows grossj. The start of an age, Aries 30, Pisces 360, Aquarius 330 or Capricorn 300 degrees, is fixed at a reference date. His profile carried the CHAUVIN reference of 6 January 1779 for the Aquarian age, the shipped default is 10 May 1774, the start the family's tester holds after his research, and the entry sets any other date. great_year_point turns that ecliptic point into equatorial coordinates, precesses it with his Newcomb praez from the reference to the chart date and reads its longitude back. The age point runs backward by the gain, some 50.3 arcseconds a year or 2148 years per sign. The first box offers to keep the setting, to change the start and the reference date, or to switch the display off. The result box lists the reference longitude, the reference date, the difference, the chart date and the age point, and warns when the chart lies before the reference or more than a sign behind it. While the display is on, the DEFAULTS OVERVIEW carries his yellow box with the same lines and the record, and the reference date and the start persist with the defaults in KONSTA like his param_sp. The menu entry is grey on the SOLAR level like his MENU 98, and the flow switches the heliocentric mode off like his hrg! = FALSE.

The two clocks of the original

The original computes the sidereal time by rewinding to 0h UT and running the full juld chain there, which leaves the nutation state of MIDNIGHT behind in the globals. The angles and the house cusps therefore see the true obliquity of 0h UT, while the planets, computed later in Ephemeris Time, see the obliquity of the moment. Within one day the nutation moves the obliquity by less than a tenth of an arcsecond and the equation of the equinoxes by less than a hundredth of a time second, below the smallest terms his nutation series keeps, so the pipeline follows his order through the ekls0 field and no result changes by a digit.

The protected parallax

The parallax cluster is ported verbatim under the CLAUDE working rule that presumes the original right. His comment names the source and the simplification

// Parallax //from Montenbruck p.25 without regard to the height above sea level ro = 0.000042634515 //Earth radius in AU

The formulation looks unusual, the declination arm reuses the y component of the displaced vector through a sine, but the algebra works out exactly, z / n equals z' / sqrt(x'² + y'²) of the standard vector method on his spherical Earth. The test suite exploits that, an independent cartesian computation must agree with his route to machine precision, and it does. The parallax applies to slots 1 through 10 only, nodes and extra bodies stay geocentric, exactly like the SELECT in the original.

Houses

All seven systems of his menu are ported, Placidus with the fixed point iteration on the semi arc, the Topocentric poles, Koch with his rounded angle literals, Regiomontanus, Campanus, and the two equal systems from the AC, plus the two switched off modes that zero their cusps. The maxbreit guard refuses Placidus and Koch beyond 90 degrees minus the obliquity with his alert

Geog. latitude too large ! Only up to +- ... ° >> CANCELLING !

regio0, his cusp normaliser, runs after every quadrant system and mirrors houses seven to twelve from one to six.

Bodies and speeds

The Sun comes from the Earth's VSOP place reversed, the Moon from the series with no light time, planets pass helio_to_geo whose daily motion is a symmetric difference at a tenth of the daily rates. Pluto prefers his integrated file and falls back to Chapront outside it. Extra bodies read their .eph files or solve their Kepler orbits, with rates from a symmetric hundredth of a day like the original pl_vel. The Part of Fortune follows ta_na, day birth AC plus Moon minus Sun, night birth the mirror. True node and true Black Moon get their speeds from a symmetric hour, the original vel_om_pd.

The planetary nodes and apsides

The last four columns of the coordinate table, introduced after Th. Landscheidt's geocentric planetary nodes and ported from plko10, plko100 and plko1001. For Mercury through Neptune the mean orbital elements, for Pluto his own mean element set with the precession of node and perihelion, give four points on each orbit, the two ecliptic crossings and the two ends of the long axis, each with its radius from the ellipse at its true anomaly. Geocentrically these are real points in space projected from the Earth's heliocentric place, so a descending node is not simply the antipode of the ascending one, heliocentrically they are plain directions. The Sun's row carries the node line of the solar equator and the perigee of the apparent orbit, the Moon's row its mean node and the apogee the AG setting chooses, true or mean as the MOON apsides caption of his screen says, the other values means. In the heliocentric view the Earth has no node, its apsides stand opposite the Sun's perigee. Pinned on Mercury's node at 48.33 degrees, Pluto's elements on their known values and the projection on the exact triangle formula.

The fixed point and the rectification

Slot zero of the body table is his fixed point, a user chosen ecliptic degree that rides the wheel, the tables and the aspect scan like a body under the tag sp, and in the mundane view it projects along its semi arc like everything else. CHANGE EPHEMERIS DEFAULTS switches it on and places it by sign and degree, a defined point can be kept or deleted there. CORRECTION, ported from korr and its helpers into rectification.*, shifts the clock of the input panel until a chosen quantity reaches a target value. Like his plre it switches to Placidus houses and geocentric positions for the whole run and restores the house system at its end. Sidereal time and MC turn into a clock of the radix date directly through the sidereal time of 0h like korr21, so a correction near midnight UT lands on the moment nearest the birth and never a sidereal day away. The AC and the intermediate cusps walk the daily turn with the damped step of korr1, Sun and Moon search their longitude near the birth like plant, the Moon taking the crossing nearest the birth. The found moment lands in the panel marked RECTIFIED, so the rectified time immediately is the chart, and after a Sun or Moon correction the PLANET COORDINATES table opens. The primary directed axes carry his second method, trial shifts of the radix sidereal time collect in the accumulator and their mean goes into the radix on demand.

The walks through time and place

TIME WANDERING (zeitw and zeitwi) first offers his counters, off for the session, on with the automatic run, or off for this walk, then his box for single planets, red marking, only the chosen with their aspects, or the normal output. The unit follows in days, hours or minutes with any number and a direction, his key sheet opens the walk. Every step adds the interval, redraws the chart, beeps and waits two seconds, V and R turn the direction, D, H and M reset the unit, plus and minus double and halve it, Space stops until the next key and ESC ends, the left mouse button waits two seconds longer, the right one second less. The Time diff box under the chart counts the days, hours and minutes from the start below a thousand days. With the counters on, the two yellow windows sum the aspects per divisor with Troika and GrTrin and the direct, square and half square midpoints, the start chart is not counted and ESC shows the sums once more. At the end he offers a new unit, which may reset the counters, a step back into the walk, or the end, where a walk of at most ten days may keep its time in the radix. Every step also flashes the strip at the bottom of the main window, and the walk adds a single step to the Back history of the panel, only when the varied time is taken over, the MULTI time walk alike. The entry is grey on the SOLAR level like CORRECTION.

PLACE WANDERING (ortwi) asks a longitude and a latitude shift in degrees with east or west and north or south, then his key sheet. The moment stays fixed in UT while the place walks, the box under the chart shows the longitude and latitude difference. Plus and minus double and halve both shifts, L and B turn their directions, F10 shows the nearest metropolis of WCAPITAL.INT with its distance west or east and south or north, ENTER snaps the walk there and Space goes on. A step past the pole, past the date line or into the polar zone of Placidus or Koch steps back with his message and asks the shifts again. At the end the changed coordinates may stay, the place name then reads GEÄNDERT, the value his data files carry for a walked place. The counters do not run here, they were switched off in his last version. Pinned in test_wander.cpp.

The exact hit search

plant answers when a body reaches a given longitude, searching backward from a start moment. The port keeps his whole scheme, the per body initial steps and tolerances from one degree for Mercury down to 1.6 minutes for Pluto, the period table of a16_ta, the coarse backward walk with the branch reconcilers ver and ver1r until the target is bracketed, the fine parity guarded approach of the planets, then the damped secant that multiplies the step by minus 0.31 on every sign flip, and the final linear interpolation. His screen escapes and timers become step budgets. The original notes the remaining time error is mostly under five seconds. Verified against the 1993 spring equinox of the almanac, 14:41 UT, hit within two minutes, with the residual under half an arc second, plus a lunar return and a Mercury search near its retrograde loops. The solar and lunar returns already ride on it like korh, the solar seeded at the birthday clock of the target year plus fifteen days, the lunar found as the return preceding a chosen moment at 0h UT.

The transit sweep

The transit list accepts a separate event place, the running positions then carry the parallax of the event place while the radix keeps its birth place, his ereig_ort question. a180 walks a time window in body sized intervals and tests every running body against every radix target shifted by each multiple of the base angle. The port keeps his interval table, his bracket tests with the branch reconcilers, the fifteen degree speed cap per interval, and the stationary guard that flags a slow body touching a target, remembered once per pair like his c3 memory. Two deliberate deviations, each an improvement on the same data. The direction of the bracket follows the true daily motion, so the wrap of the circle is no longer mistaken for a backward arc, and every bracketed hit is refined to the exact moment with the plant search instead of his linear interpolation, a hit that fails to refine into its interval is dropped rather than guessed. The moon stays filtered by the cap unless the moon flag opens it, matching his default. The list also carries the retrograde passages, marked R, and the transits of the mean node, each exact to about a second, and the secondary direction lists them the same way. A long run shows a progress window whose CANCEL or Esc asks before stopping and keeps the hits found so far. Verified over November 1992 against the 1992 radix, every event sits on its target to under an arc second and the sun finds radix venus on the fourteenth. The ingress driver ingre1 rides the same search, twelve sign entries per body with the epsilon that keeps the zero longitude guard quiet and the sun corrected into the calendar year of the start, the 1993 table pinned sign by sign. The MC and AC entries walk the daily rotation to his korr bound of 5e-7 radians, every sign once between 0h and the end of the day. His INGRESSES screen asks the object first, SUN, MOON, MC or AC, the tester's planets after them, which is why the menu now reads INGRESSES PLANETS-MC-AC. The tester's bodies are computed whether the panel includes them or not. Every table opens with the Sign column, his symbol beside the name, at the far left where the tester wanted it. The Sun asks the calendar year and lists the entries of that year from the first of January at the clock of the record, the Moon asks a date and lists the last entry into every sign before it, both at the event place of his PARALLAX mask when the parallax is on, with the ephemeris line under the table. MC and AC take date and place from the full record mask and list three days side by side, the longitude column showing the axis computed at the found moment. Space, plus and PgDn move on, R, minus and PgUp back, a year for the Sun, 29 days on or 28 days back from the Pisces ingress of the table shown for the Moon, three days for the angles. A planet steps every sign to its own next or previous entry (step_sign_ingresses), the next one searched back from one and a half circuits past the shown entry and then over its predecessors. The port first moved the date of the page by one circuit, an orbital period but at least a year, and the entries of a sign do not follow that evenly. Saturn enters Aries at gaps of 29.1 to 29.9 years, from the page of 1.1.1908 the entry of 14.5.1878 showed twice and the one of 19.3.1908 never. The dialog keeps the pages it has shown, so back and on again bring the same entries, and a stepped page names its latest entry in the title. Each entry is the first of its loop (sign_entry_before). His plant steps by the arc still to go, so from a date between the passage back and the second entry of a loop, where the body stands just below the sign start, its first step spanned nearly a whole circle and passed the loop. On 2.12.1937 the Aries entry of Saturn read 19.3.1908 instead of 25.4.1937. The search now looks for a passage back within the window of planth first and walks from there to the entry. Checked against a day by day scan of every first entry for Mercury to Xena, every page and every step both ways. A page of a body with an ephemeris file of its own never leaves the span his loader gives that file, jdplanete to jdplaneta, the date of the first page stays between one circuit after the first day of the file and its last day, and a sign whose next entry lies past the file keeps its own. A step that finds no new entry at all leaves the page standing, so the end of a file piles up no copies of the last page. One circuit of Xena lasts some 557 years. The page from 2026 lists the last entry into every sign before it, Aries in 1922 and the others between 1517 and 1845, and the next page shows Taurus in 2044, Gemini in 2144 and Cancer in 2191, his files for Quaoar and Xena stop in 2201. His plus a year from the first of January landed on the last of December after a leap year and showed that year again, the port opens the next calendar year. A double click opens the transit view of the moment, the tester's addition.

Composite and combin

The composite midpoints two charts body by body with the near side rule of halbsmin, the south node follows the north by half a circle, and the AC and MC midpoints flip to the side of their cusps. His a13 carries that flip for both points but wrote the unflipped midpoints back a few lines later, so his final program could show the AC midpoint beside the MC, 5° and 200° gave 282.5° against a first cusp near 33°. The port keeps the flip his code was written for and puts that AC at 102.5°. His halbsmin added half a circle after its own near side choice whenever the raw sum of the pair passed a full circle, a pair around 0° Aries like 100° and 300° got 200° instead of 20°. The port drops that step and keeps the near midpoint, an exact opposition still takes his second candidate. The houses follow his three modes, the mean of sidereal time, longitude and latitude, the Robert Hand armc from the MC midpoint at a residence, or the schematic midpoints from the MC midpoint with his ordering chain that keeps every cusp ahead of its neighbour. A composite has no latitudes or speeds and the port leaves them at zero. The combin of a14 averages moment and place of two to five records and runs the normal pipeline. His plain mean of the longitudes put two places on both sides of the date line on the far side of the globe, 170° east and 170° west met at Greenwich. The port cuts the circle in the widest arc free of places and averages there, which is his plain mean for every group that leaves the date line alone.

COMBINE asks for the records one SATZ click after the other, at least two and at most five, and marks every slot clicked so far with his star. After the second, third and fourth click it asks FETCH record 3 ? or OUTPUT ? as long as a further RADIX slot is filled, the fifth click outputs at once. The mean lands on the panel as a chart whose place name is COMBIN-ORT, the value his data files carry for the mean place, the slots keep their own records. The centre reads COMBINE, two records stand as 1: and 2: with their whole names, his LEFT$(na$,20), and their moments as the tester wished, more than two as RECORDS: 1,3,5 with the names stacked above the bottom edge, and the COMBINE UT line gives the mean moment. The banner names the surname and the first given name of both, the record a combine leaves as radix keeps his na$(0,2) of ten letters of each whole name. The port had named each partner by the surname alone, two of one family read alike. The COMBINE entry of the HOROSCOPES menu then names the first two records and SHOW THE STORED PAIR brings all of them back, his DOUBLE DATA row merged into the entry as the tester wished.

COMPOSITE in the HOROSCOPES menu opens his mode box, COMPOSITE CHART MODE ? with the three house systems, the answer stays in the profile like his param_sp. The equal systems Equal and Vehlow skip the box and take the schematic halves as his haw 6 and 7 did. Two SATZ picks name partner one and partner two from the filled RADIX and SOLAR slots, and ROBERT HAND then asks the residence in the place part of the entry mask, titled ENTER the EVENT PLACE ! | COMPOSITE NO.1, empty with E and N preset, Tab opening the place files and ESC ending the chart. Its latitude carries the houses, the longitude does not matter. The sheet of the two house modes with real houses names the first cusp H1 and draws the AC midpoint as a thick axis of its own with its degree, the body table lists longitudes only since a midpoint chart has no latitude, speed or distance, and the place corner shows the residence under ROBERT HAND and nothing in the other modes. SHOW THE STORED PAIR on the COMPOSITE entry brings the pair back together with its residence. COMPOSITE and COMBINE both switch the heliocentric mode off and carry the fixed point into the pair chart.

The directed axes

prima turns the radix ARMC at his Naibod style rate, three hundred sixty degrees per tropical year of elapsed days over the year length, direct or converse, and recomputes the axes and cusps from the directed ARMC at the chosen place, drawn slightly smaller over the radix positions with the ST difference in the centre and no chords. His sidereal time variation rides on the same turn, one degree being four clock minutes of birth time, which made this screen his rectification tool. The port keeps the rate, the variation and the display, the interactive summing of test variations stays with the operator through repeated runs. The event date box also asks a UT time, and a sidereal time variation turns the axes exactly as far as the corrected radix will turn them.

The mundane mode

horm 2 leaves the ecliptic, chosen as REFERENCE SYSTEM EQUATOR = Mundane in CHANGE HOROSCOPE DEFAULTS and kept in konsta.int. It is a frame, not the menu entry MUNDANE ASPECTS, which lists the aspects the running bodies make with each other (see below). Every body converts to equatorial coordinates, md11 places it east or west of the meridian axis, and md projects it along its semi arc, ninety degrees plus or minus the ascensional difference asin of tan latitude times tan declination, into oblique ascension under its own quadrant. The house space longitude then counts from the ascendant at zero and the cusps become the exact equal grid of mundhorh. All scanners run unchanged on the converted values, exactly the original's trick of feeding mup into the same aspect machinery. Pinned on a flat sky where the proportion turns linear, quadrant by quadrant, and on a real chart whose grid and ascendant land exactly.

The heliocentric mode

hrg turns the whole pipeline sun centred. Every planet, ephemeris body and Kepler body simply keeps its heliocentric spherical state, ecliptic longitude, latitude and the sun distance, converted to right ascension and declination but never through the geocentric correction chain, no aberration, no light time, no parallax. The Earth takes the Moon's slot carrying the VSOP Earth itself, the Sun's slot stays empty, and the geocentric ideas leave with it, no Moon, no nodes, no Black Moon, no Part of Fortune. Houses do not exist on a sun centred sky, horg11 and bes111 stayed dark in the original and the port computes none, the wheel anchors zero Aries on the left like horbeg clearing fza and marks the Sun as the small circle in the centre that horg1 drew, the Earth wearing the crossed circle glyph on the ring. The aspect scanner runs unchanged over whatever stands on the slots, exactly his trick of reusing one machinery for every mode.

The return family

Beyond solar and lunar, the a16 flow returns every body. A planetar is a body's return onto its own radix longitude at the birth place, cast for the place of the event. SOLAR, LUNAR and PLANETAR show that event place with a Choose place… button that opens EVENT place = BIRTH place ?, search and cast the return there while the target stays the radix position at the birth place, and leave the place of the birth record unchanged. Every result carries the count of returns since birth in front of the name, 32.SOLAR, 668.LUNAR or 3.TERRAR, and replaces the SOLAR... DATA row of its radix, the Previous year, Next year, Previous lunar and Next lunar steps included. His box SEARCH with : offers DATE, the default, and the return by number into the future or the past, NO. FUTURE and NO. PAST with his hints, in the lunar as in the planetar, and number 0 is the radix itself. DATE asks the search date under the period of the body in years and days, walks back from fifteen days past that day at the clock of the radix and counts the return as the whole periods since the birth. The number seeds its search a safe head start past the Nth crossing like his NO. FUTURE and NO. PAST branches, heliocentric every body a tenth of its period past the count. Neptune, Pluto, Quaoar and Xena first say NOT MEANINGFUL for the charts of HUMANS !. The backward search finds the last passage over the point, his planth menu TAKE OVER the TIME or SEARCH FURTHER POINTS ? lists it with the earlier passages of the same return, direct or retrograde, up to two more for Mercury to Saturn and the belt and eight for the slow bodies, each within his djd of the one before. The last row walks on to the direct passage of the return before, the count one lower. A chosen moment asks VIEW the CHART ? or TAKE OVER the TIME VALUE ?, the first shows the chart until a key and returns to the menu, the second takes the moment over with the count stamped in front of the name as solnummer did. His a16_ta periods of Jupiter to Pluto ran too long, Saturn 10821.4 days where its mean motion gives 10759.2, and his DATE count of the geocentric Mercury and Venus divided by their revolution where his number seeds count them once a year, the same return read 10. by number and 41. by date. The port counts with the sidereal periods of the mean motions and the tropical year for the inner two, and floors the count so a date before the birth reads one lower like the numbers into the past. A personar is the sun crossing the radix position of a chosen body within the first year of life. PERSONAR asks for the planet, then the place, shows the chart until a key and closes with CREATE a FURTHER PERSONAR ?. A septar is the solar return of the (n - 1)th birthday for the nth septar, cast for the place of the event. His chain asked the time unit, MONTH by default for septars, then the period per house and the year of life of interest, and took the septar number as FIX(age / period / unit + 1), so seven months per house make septars of seven years and the first septar is the radix itself. With YEAR his formula made the radix the septar of every year of life below twelve periods, a tester answering the box with the seven years per house of the Döbereiner school never reached a septar. The port casts every septar in months, the Schwingungshoroskop n that governs the years (n - 1) times the period to n times the period, and the period box names the unit per house and SEVEN the septar, the tester found the decar beside the months confusing and it left the line. His box took any year of life and his count ran on past the twelfth septar, the port ends with the twelfth like the twelve houses of the rhythm, the box takes the years of twelve periods and names the limit, and a longer life takes a larger key per house through OTHER. His information box adds the solar return the septar is and its calendar year. The SPECIAL POINT box of the rhythm school follows without its date definition and names the septar being cast, the point rides the septar on slot zero as his red F in place of the general fixed point, and his information box names the years of life the septar governs. In heliocentric mode the solar becomes the terrar, the Earth's return onto its heliocentric radix place. TERRAR asks ENTER the WANTED CALENDAR YEAR 'YYYY' !, needs no place and numbers the chart N.TERRAR by the years since the birth. After a key SEARCH a FURTHER SOLAR ? steps to the following or the previous year, his box keeps the SOLAR wording. Lunar and septar stay dark under the heliocentric switch like his menu, and the personar runs the Earth onto the heliocentric radix place of the body without a place and without the moon. SOLAR LIST and LUNAR LIST, under the heliocentric switch TERRAR - DATA - TABLE, draw his table sheet, the dates and times of up to 84 returns in three columns of 28 rows under the header with the name, the birth date and the places, the lunar from the last lunar before four days past a start date and the solar or terrar from a first calendar year, never past the 135th year of life. A click on a row takes exactly the return of that row over as the moment of the panel.

Progressions and the day chart

The secondary progression of proho maps one day of sky motion onto one tropical year of life. Four clock answers decide the moment within the progressed day, the birth clock kept, the birth's true solar time found again by the damped search of wahrso, the houses turned at one day per year through the sidereal ladder of hd_hs, or the julian date interpolated strictly. The day chart of taho finds on any chosen day the moment whose sun stands at the birth's hour angle, the same true solar time that ruled the first breath. Both switch the heliocentric mode off, like the secondary direction, the solar and lunar arcs, the primary and the symbolic directions in the RA SYSTEM or MUNDANE.

Symbolic, primary and arc directions

The direction evaluations turn arcs into ages. The symbolic methods measure how far one radix point stands from another's aspect grid, in ecliptic longitude, in right ascension or in mundane house space, and the classic key of one degree per year names the age, direct or converse by the arc's side, every arc listed once since it reads the same from both ends. The primary directions of the E.C. Kühr school measure the same idea in oblique ascension, every significator under the pole its semi arc proportion hands it, the aspect points of the promissors carrying a latitude that fades with the angle. The secondary direction list runs the transit machinery on the day for a year axis and stretches the found dates back into life, and the sun and moon arc lists use the fact that a rigid arc moves all points equally, so every contact is a crossing of the light alone over shifted targets, the cusps and the cardinal points shifted with them. The a18eing answers ride along. A combined BASE ASPECT like 60° and 90° leaves the other multiples of its base out (his a18_3045), the chosen significators and the first body of From MARS OUTWARD or From JUPITER OUTWARD thin the walk, the intermediate cusps direct in a pass of their own (in the primary also as promissors), the cardinal points answer the conjunction only, and in the ecliptic frame every radix midpoint can be a target, keyed by both factors so no midpoint hides another. The window holds the years the key makes, not the bare arc. The symbolic and primary headings always show the key as Key:… Y/°, and a single chosen factor answers CHOOSE AT LEAST 2 FACTORS ! and the box asks again, like his a18ei2 loop.

The aspects of the running sky among themselves

MUNDANE ASPECTS, his mund1, sweeps a date window in windows of three samples one day apart (half a day with the moon or the true node and apogee) and lists every exact aspect two running bodies make. Each pair and multiple of the base angle gets his bracket test and his quadratic through the three differences for the moment, the positions of both at that moment ride beside every row, each right after its body, which the table names P1 and P2 where his a181tx called both running. The transit table carries the degrees the same way, the running body on its aspect point and the radix point it meets. The port brackets the folded difference of the pair, so a meeting across 0° Aries keeps its sign change where his separate unwrapping of both bodies lost it, and the void of course rule of the hour astrology reads the signs at the moment of the aspect. Pinned on the new moon of 21 March 2023 at 0°49' Aries and the great conjunction of December 2020. The screen first asks Output mode ? with TABLE or LINEAR GRAPHIC. The linear graph draws the running bodies without radix lines, marks each aspect on the first body of the pair and steps on with NEXT interval.

The multiple directions

The MULTI menu directs the whole chart by age. MULTI 1 advances every body by its age times its degree within the sign, MULTI 2 by age times the whole longitude, MULTI 3 runs the same sign referred rate from a chosen reference point, a body, an angle, a cusp, the classic ruler of a house or a sign start. The zero point pairs anchor every body on the start of its own rulership sign, the day signs eastward, the night signs westward, and MULTI-ARC scales the arc between reference and body. The axes answer the haus_ber question like the harmonics, and under the new MC answer a901_m rebuilds the Part of Fortune from the directed lights. Transpluto and the Hamburg factors stay dark across the whole MULTI world. Like the prologue of his multiple the session always draws a geocentric radix in the ecliptic frame with the mean node and the mean Black Moon, while the panel keeps its own switches. The MULTI modes direct the fixed point from slot zero like any body, the harmonics and the two zero point modes leave it out.

The session follows his multiple. The CHOOSE the MODE box offers the six MULTI modes and HARMONICS, the event date comes at the birth clock, the haus_ber box and for MULTI 3 and MULTI-ARC the REFERENCE FACTOR list, headed by the FIXED POINT when one is set, with its three extra rows for a house, the ruler of a house and the zero point of a sign follow, MULTI ZERO WEST asks haus_ber before the date. HARMONICS asks its order again after a 0, which would fold every body onto 0 Aries. Like the od = 1 that opens his multi1 and harm, a session started while a SOLAR or another return is shown first brings back the radix that return counts from, the person of its SATZ, a typed birth or a COMBIN, and stays there, Back returns to the return. A return on screen ends the sheet, a new SOLAR as well as a step back. The sheet of multi11 puts the radix column under RADIX : and the directed one beside it, the a12asp grid of the directed bodies against the radix at a fifth of a degree times the orb factor, harmonics one degree, and the grid of the directed chart with itself, Transpluto left out. halbsm lists every directed pair whose near midpoint stands within that fifth of a degree of a sign boundary, red on cyan, of a radix cusp or of the directed AC and MC, navy on yellow. His loop over the boundaries started at the first slot and never saw 0 Aries, the port walks all twelve. The centre carries the mode, the date and the age in years. zeitwim then walks the birth time in hours, minutes or seconds, the event moves with it so the age stays, V, R, plus, minus, Space, the mouse and ESC steer like TIME WANDERING, and H, M and S switch the unit as his legend promised, his m! was never set so they did nothing. At the end the walked time can stay in the radix, YES writes it into that SATZ, or the radix returns, and weit_dat offers the next date or the end.

Harmonics and the 90 degree circle

A harmonic multiplies every longitude onto an integer order, harm21's world. The south node follows the transformed north node by half a circle rather than turning itself, which differs for even orders, Transpluto drops out exactly as his CASE list leaves it, and the Part of Fortune multiplies like every other extra, harm21 keeps its a901_m rebuild commented out. Houses answer his haus_ber question, treated like bodies every cusp multiplies, or the new MC derives a fresh ARMC and the whole house system recomputes at the birth latitude. The 90 degree circle of a12f is the times four special case on the double wheel, the aspect scan runs on the multiplied state including the angles, then the AC and MC glyphs divide back into the first quarter for display exactly like his pl(13) line. The harmonic runs as the seventh mode of the MULTI session, the dial as the second mode of DOUBLE WHEEL / 90 DEGREE DIAL.

The rhythm school and the dynamogram

The Munich Rhythm Theory after W. Döbereiner walks the twelve houses as life phases of seven years. Every phase triggers the bodies inside its house, the ruler of its sign and the rulers of intercepted signs, and every trigger pulls in its aspect partners out of the radix matrix and its mirror point partners, each age read from the body's place within its own house, in years or in the month unit. AC, MC and the south node trigger directly, the cardinal points join with his WITH CARDINAL POINTS, the Black Moon also fires at its opposite point whenever it is shown, and the mundane frame drops the mirror chain like his a173. A special point on slot zero walks and chains like a body, the aspect scan starts on slot zero whenever a fixed point or the special point stands there, as his asp1 did from aa& = 0. The clock of a174init dates the ages, the radix from its birth, a Solar from its own moment with the age of the Solar in the YR column, a Septar from the birth plus its offset of (n - 1) periods of twelve houses, every other derived chart from its own moment. The run switches the heliocentric mode off. His question chain runs as in a17, the Placidus check, the EVALUATION MODE, the direction with RIGHT as the default, the date or YR/MO format, the beginning phase one, four or seven, the time unit, the period per house with OTHER for any value and negative periods into the past, and the SPECIAL POINT box that keeps, defines as an ecliptic degree, defines through a date or deletes the point, kept in the settings like his param_sp. The graph draws one screen per phase, the wheel with the phase's house arced in red and its rulers stamped inverted, unless a ruler also stands in the phase's house as his note says, beside it his strip with the time axis from the phase start at the bottom to its end at the top, the direct and ruler triggers on the left, the aspect and mirror partners with their aspect sprite and source on the right, both columns pushed apart sixteen pixels like a17911, Space walks to the next phase. The table lists every trigger under its PHASE n = H m heading with the date or YR and MO, the body and his D, P, P2, P3, S or the aspect with its source. Pinned in test_symbolic.cpp, test_render.cpp and test_rhythm.cpp. The dynamogram after Krafft and Goerner runs the progressed sky at one day per year, finds every orb passage against the radix and among the running points, and spans each with a cosine half wave or a bell curve, signed by his valuation scheme of the pairs and angles, weighted by the running point's amplitude, summed into the ground mood and the existential line of the angles over a five year window. His question chain comes first, the first year of life, the regressive direction, the running moon, whether to watch the single arcs, and cosine arcs or bell curves, bell curves being his default. The run forces its own frame, no parallax, App.1 positions and the geocentric sky. WATCH the SINGLE ARCS ? shows one screen per pass of his analysis, the arcs over the radix, then those among the running points, the regressive pair after the progressive one, each screen closing on two beeps and a key. It draws every arc of the pass that touches the window one after the other on a scale of life years, green for Sun, Moon, Mercury, Venus and Jupiter, red for Mars and the outer planets, blue for the node and the angles, the captions naming the pair, divisor and multiple, the arc centre and whether it runs over the radix or among the running points, progressive or regressive. The graph carries his three curves, the existential situation red dash dotted, the ground mood green dashed and the resultant energy blue, scaled by his factor 0.3, under a calendar axis of year lines and month letters, with the MEAN of the fifty years at the foot. NEXT and PREVIOUS move the window by four years. Pinned in test_transit_search.cpp and test_auswertung.cpp. The DEGREE DATE LIST walks every half ecliptic degree onto the date the rhythm crosses it, phase by phase in walk order, each phase from its first date to its last. His a170 wrote the degrees of a phase in zodiac order, under RIGHT the dates of every phase ran backwards and the phase over 0 Aries broke in two, the list then opened on the end of the first phase and closed on the start of the last. The degrees and the dates stand bold, the published group destiny degrees of W. Döbereiner ride along with their planet pairs drawn as his two symbols in a thin box like a174g, the tags on the tooltip, the cardinal degrees wear their sign symbol boxed in red and every other degree its plain sign symbol, own degrees join through grade.int with their mirror across 0 Aries-Libra, a published pair naming the degree first like his SELECT, and the mundane variant projects each degree along its semi arc first. His EVALUATION MODE also defines an own degree, whole or half degrees only, a known point answers EXISTS ALREADY, two bodies from his object list make its characteristic, and deletes them all after his question. Negative periods run the walk into the past, and the special point of a17sonderpkt rides the walk as his red F, defined as a degree or indirectly through a date whose age the inverse of the clock and of the degree walk turn back into its degree.

The histograms

The element and quality columns of his chart view, ported from elem1, elem2, kard_fix_gem and kard_fix_gemh. Every factor scores its point weight into the element and the quality of its sign and of its house, planets in the first house and the birth ruler double on demand, the weights run 0 to 9 per point with his old fixed row as the fallback and entry fifteen covering all extras at once, saved in the konsta stream. The house columns stay silent above his haw bar where no houses exist, and a point exactly on a cusp stays out of them as in the original, which keeps AC and MC off their own cusps since they would only add the same two houses to every chart. His open windows between the kk edges also dropped a body at exactly 0° Aries or on a sign boundary from every sign, the port gives it the sign it opens. The four counters of the original collapse into one pass that honours the two switches everywhere, the one place his quality by house pass forgot them.

Fixed stars and arabic parts

The star screen carries his own catalogue of sixty two entries, each with the planetary quality the tradition assigns and the distance in light years. Positions move linearly from the millennium epoch, the Pleiades, Hyades and Praesepe clusters and the galactic centre and apex precess properly from their own epochs, annual aberration rides on the chart's sun, and every star is matched against the bodies, the fixed point and the axes with his narrowing windows, two degrees for the conjunction, half of that for the opposition, a quarter for the square, a third for the trine. The screen always computes the chart in APPARENT 2 like his appa& = 2, whatever the defaults say. The table carries right ascension and declination in columns of their own, the longitudes in degrees and minutes and up to four contacts as aspect symbols. A star with a contact wears red on cyan on its name while the printer option is off, with the option on the table stays plain for the hardcopy like his deftextcol switch, and the footer of stelt names the person, the date, the set and the ephemeris mode. The arabic parts follow the one formula base plus first minus second, swapped on a night birth, thirty seven built in from the Part of Fortune to the point of death with the contributors he credited by name, the wealth point keeping its additive exception. His screen asks the formula first, traditional, always day or always night, then whether to define own points, show the table or delete the own points. An own point takes a name of 21 characters, a remark of 14 and three terms from his object list, a body from the fixed point to the MC, the Black Moon or Chiron, the cusp of a house, the ruler of a house through the numbers box, or a whole ecliptic degree, each echoed as its term, up to 36 points in his two ARABTEI files of 39 and 16 byte records. The own points take the first rows of the table like his arabte. The table runs on a geocentric chart with the Black Moon and Chiron always computed, each part with its longitude and up to four aspects to the fixed point, SO to MC without DS, the Black Moon and Chiron, the rows with a hit in red on cyan while the printer option is off, and Space sorts the rows by degree. N sorts by name, the tester's addition.

Verification

test_houses.cpp checks the angles against independent textbook atan2 formulas over a grid of sidereal times and latitudes, cusp mirroring and counter clockwise order in every quadrant system, near agreement of the systems at the equator, the exact thirty degree steps of the equal systems, the Vehlow offset and the maxbreit refusals. test_chart.cpp anchors the whole pipeline, the apparent Sun crosses zero Aries at the 2000 March equinox to a hundredth of a degree, the Meeus Sun and Moon examples come out of the full chain, Mars turns retrograde in late December 1992, Pluto and Chiron ride along from the files, the Part of Fortune obeys its two formulas, the true node and apogee switches move their slots, and the parallax section holds his protected cluster against the independent vector computation to a nanoradian. The heliocentric mode pins the Earth on the Moon's slot at the Meeus geometric longitude, the planets against their own sun centred state, and the absence of every geocentric idea including the houses. test_harmonics.cpp pins the multiplied longitudes, the even order node quirk, the dark Transpluto, both house answers, the a12f transform with its divide back and all six MULTI modes over a synthetic radix. test_transit_search.cpp adds the first mars return and the personar landing on their radix targets, the backward walk over the three passages of a retrograde loop, the counting periods and all four progression clocks against their defining properties.