LUNI-SOLAR PHASE (1) - Felipe III Rex Hispania

 LUNISOLAR PHASE (1)

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Felipe III
06 Sep 1581 JUL    CAL
wednesday JUL
 | lat 40° 23' 59" | N 3°41' W
0
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natal (bt) 13 h 30 min
raas-rams :0h 5' 14"
reckoned bt Lat --> lmt 1 h 50 min
tu 2h 4' 44"
tsn 1h 27' 9"
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timezone  : 0
DST : 0 (-)
Equation of time 0h 5' 14"
ΔT 0h 2' 10"
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source : Andrea Argoli, De diebus criticis et aegrorum Decubitu, p. 166, Patavii, MDCLII (Padua, Pauli Frambotti, 1653)

Placidus writes in his Primum mobile that Philip III died on March 31, 1621, aged 42 years and 11 months [in fact he died at the age of 40, exactly 39.56, born 1581.68, died 1621.25]. We note - as is quite common with Placidus - a discrepancy between the times he gives and those of his colleagues: in Placidus, the time of birth is 14:47 PM; in Argoli 14:21 PM.

Here is the "modern" horoscope of Felipe III. I remind you that the aspects between planets and ASC are indicated directly in OA and those between planets and MC are indicated directly in AR. The aspects between planets are indicated in mundo (Regiomontanus).

LUNI-SOLAR PHASE            
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This is a method that we find outlined in Vettius Valens [book VI 9] as indicated by Anthony Louis in his blog :              
 'Vettius Valens had a different notion of annual returns. He felt that the return of the Sun each year was insufficient for forecasting for the year ahead because it omitted the influence of the the Sun’s partner, the Moon. As a result, Valens used a hybrid chart for the annual return which consisted of the positions of the planets when the Sun returned to its natal position each year but these positions were placed in a chart whose Ascendant and houses were determined by the moment the Moon returned to its natal degree during the zodiacal month when the Sun was in its birth sign.' [The Tithi Pravesh and its Monthly and Daily Iterations, November 5, 2022]              
Placidus uses it in his Primum mobile (Tabulae primi mobilis cum thesibus et canonibus 1657) and gives the procedure to follow in the XL canon (De Progressionibus, p. 53). A complete example appears in the analysis of the theme of Charles V (Exemplum Primum Caroli V. Austriaci Imperatoris, pp. 59-62).              
There is only one site on the internet that does this calculation:  https://horoscopes.astro-seek.com/calculate-planet-revolutions-returns/            
            
but it only gives the soli-lunar return at D0; Placidus continues the progression until end of process (i.e. the even). For example in the case of Felipe III, if we take the date of 31 Mar 1621, we must first translate this date into 'life-year equivalent': we find :            
---------------------------------------            
EVEN    42,9605353483002    42    Y
                11,5264241796021    11    M
                15,7927253880635    15    D
                19,0254093135241    19    H
                                                   1,52    M
---------------------------------------            
The method of “embolismic lunations” as a predictive technique :  
See : Tabulae Primi Mobilis,,, Placido De Titis, Patavii, MDCLVII  
            
An embolismic lunation, correctly termed an embolismic month, is an intercalary month, inserted in some calendars, such as the Jewish, when the 11-days' annual excess over twelve lunar months adds up to 30. An arbitrary application of this was used by Placidus, who applied the term Embolismic Lunation, to a Figure cast for the moment of the Moon's return to the same relation to the Sun that it occupied at birth. It was made the basis for judgement concerning the affairs and conditions of the ensuing year of life.' [https://astrologysoftware.com/community/learn/dictionary/lunation.html]               
The solar year does not have a whole number of lunar months (it is about 365/29.5 = 12.37 lunations), so a luni-solar calendar must have a variable number of months in a year. Regular years have 12 months, but embolismic years insert a 13th "intercalary" or "leap" month or "embolismic" month every second or third year [...]. Whether to insert an intercalary month in a given year may be determined using regular cycles such as the 19-year Metonic cycle [...] or using calculations of lunar phases [...]. [wikipedia]               
The whole difficulty therefore comes from the fact that there is no overlap between the solar month (30 D) and the lunar month (synodic month 29.53), consequently between the solar year (365.242) and the lunar year (354.367).             
 'In Vedic timekeeping, a tithi is a "duration of two faces of moon that is observed from earth", known as milа̄lyа̄ [...] in Nepal Bhasa, or the time it takes for the longitudinal angle between the Moon and the Sun to increase by 12°. In other words, a tithi is a time duration between the consecutive epochs that correspond to when the longitudinal angle between the Sun and the Moon is an integer multiple of 12°. Tithis begin at varying times of day and vary in duration approximately from 19 to 26 hours. Every day of a lunar month is called tithi.' [wikipedia]              
We see that the interest of Placidus' method (outlined by Vettius Valens) comes from the fact that the individualisation structure of the progression system is no longer represented by a single point (solar return or lunar return) but by a distance ( in this case the distance between SU radix and MO radix).            
We find in the literature another method which is similar to that of the soli-lunar phase: it is the tertiary directions. We find a critique of it in “Les Moyens de pronostic en Astrologie” by Max DUVAL [ed Traditionnelles, 1986, pp. 67-71] and a complete analysis in "A close look at tertiary progressions" by Elva Howson & Jack Nichols, [Considerations, vol XI-4, 1996; pp 3-12]- https://archive.org/details/considerations-21-1/considerations-11-4/page/n1/mode/2up        
In the case of Felipe III, we observe:            
            
SU radix = 172° 56' 25" (172,94° VIR)            
            
MO radix = 262° 05' 2"° (262,08° SAG)            
            
∆ = |89° 8' 36"| (89,14° ) [ 7 tithi = ROUNDUP (∆/12)]            
            
Here is now the way in which Placidus would have proceeded: for 36 full years, 33 embolismic lunations are accomplished in 6 years after birth but with 33 days less, that is to say 11*3 since the moon covers 12 lunations in 11 days less than a whole year, as indicated in canon XL            
... if you wish to have a ready calculation of the progressions for several years, note that the moon does not complete twelve lunations in one whole year -i.e. a solar year - but in eleven days less. Having therefore the distance from the moon to the sun in the sky of birth, search for this eleventh day before the end of the first year of life and having found it, then know that the progression of twelve years of life is completed. Likewise 22 days before the end of the second year after birth gives the progressions accomplished for 24 years and so on' [De Progressionibus, op. cit., p. 54]            
Therefore on 14 APR 1581, by removing 33 days, we arrive at 13 March 1581 [,,,] and then, the process is completed for 33 full years. Then, for the 6 other years elapsed during the twelve embolismic lunations, I arrive at 3 September 1581, for the remaining 5 months and 24 days. I compute the tithi (exact distance between SU and MO radix) for the last time : the date of Embolismic Progression J0 is : 6 September 1581 at 2h 5min tu. Thereafter, i add to this date 28,37 d corresponding to 11,526M [see EVEN] :            
            
JD Pr Emb = 11,53 x 30 / (365.24 /29.53) = 28,37 D            
            
where 365.24 is the number of tropical days in a year and 29.53 is the average period for the synodic month of MO            
            
 trop days 365,242215585481 (1)            
            
syn month = 29,530587934914 (2)            
            
where T = (JD-2451545)/36525            
            
In the present case JD = 2298766,5            
            
so, T = -4,21679671457906 (see formula 1 and 2)            
            
Finally, we find : date for J28,37D = 4 October 1581 at 10h 36min  local (10h 51min  TU).

(1) exact value for number of tropical days is : 365,2421896698-0,00000615359*T-0,000000000729*T^2+0,000000000264*T³
(2) exact value for synodic month is : 29,5305888531+0,00000021621*T-0,000000000364*T^2

The outer circle (in red) represents the arrangement of the planets and houses during the luni-solar cycle; the inner circle (in gray) represents the natal horoscope.
There is a discrepancy between MO given by Placidus (27°29' ♐) and 6°72 ♑ taking into account the difference in years of Felipe's death (moreover he does not indicate the reason why he removes 24° from MO which he first calculates at 21° ♑...).

Anyway, we find the following aspects (R = radix):
- ♀ ◻ ♂R
- ♂ ☍ ♀R
- ♄ # ☉R

We give below the table of Placidus' positions (Primum mobile, op cit, p. 67, exemplum III) :

(for MO, we must read 27 19♐   and no 17 19♐).