षोडश-वर्ग · D1 → D60 · BPHS CH. 7
वर्ग-चक्रम् Varga-Cakram
Pāraśara’s sixteen divisional charts. Each varga is a fixed arithmetic slice of the sidereal longitude — part = ⌊d·n/30⌋ — mapped to a sign by the chapter-7 tables. Same input, sixteen magnifications. SOURCE LONGITUDES · SUN p95 ~0.1′ · MOON WITHIN ~1′ OF NASA/JPL HORIZONS
16vargas · Pāraśara’s canon
4extended vargas · D5 D8 D11 D108
20vimśopaka points · Daśavarga scale
30′finest part · D60 ṣaṣṭyāṃśa
P7 · P32 · परम्परा-पूर्वकम् · tradition anchor
The per-Dn division arithmetic is Tier-S — residue-class computation under ring axioms (P7) with the D9 period structure Pisano-locked at 9·12 = 108 segments (P32). The choice of exactly these sixteen slices is Pāraśara’s witnessed taxonomy — Tier-W provenance, honoured with explicit boundary via P137 · Ṣoḍaśa-varga-maṇḍalam, never asserted as algebraic derivation.
TIER-S · TAGS (i)(iv) · RING-AXIOMATIC — TIER-W · TAG (vii) · PROVENANCE HONOURED
षोडश-वर्ग-घन-चक्रम्· the 16 divisional charts as Pāraśara’s cube of vargas
01
पाराशर-षोडश-वर्गाः · The sixteen
lord · domain · reading · śāstraएकं रूपम् · षोडशधा विभक्तम् — one form, divided sixteen ways; each with its adhipati, its domain, and its chapter anchor.
| Dn | Part | वर्ग · Varga | अधिपति · Lord | Domain | Reading | Śāstra |
|---|---|---|---|---|---|---|
| D1 | 30°/1 | राशि Rāśi | सूर्य Sūrya | Physical self · overall life | Master canvas — read first, always; every other varga magnifies one of its themes. | BPHS Ch. 6 · Rāśy-adhyāya |
| D2 | 30°/2 | होरा Horā | सूर्य-चन्द्र Sūrya & Candra | Money · resources | Wealth-stream check — luminary-horā separates income via authority (Sūrya-horā) from income via public sustenance (Candra-horā). | BPHS Ch. 7.5–7.6 |
| D3 | 30°/3 | द्रेक्काण Drekkāṇa | मङ्गल Maṅgala | Brothers · courage · short journeys | Co-born axis — siblings, courage, short journeys, near-circle alliances. | BPHS Ch. 7.7–7.10 · Phaladīpikā 4.3 |
| D4 | 30°/4 | चतुर्थांश Caturthāṃśa | चन्द्र Candra | Property · residence · fixed assets | Fortune & foundations — property, residence, ancestral land; each 7°30′ tranche maps to a kendra-sign from itself. | BPHS Ch. 7.9–7.10 |
| D7 | 30°/7 | सप्तांश Saptāṃśa | गुरु Guru | Children · grandchildren | Progeny axis — fertility, children's grahas, lineage; consulted in santāna analysis. | BPHS Ch. 7.11–7.14 · Hora-Sāra Ch. 3 |
| D9 | 30°/9 | नवांश Navāṃśa | गुरु-शुक्र Guru & Śukra | Marriage · planetary strength · dharma | The decider — marriage compatibility, dharma direction, and the strength-verdict on every graha; the vargottama check lives here. | BPHS Ch. 7.15–7.30 · Jaimini 1.2.20 |
| D10 | 30°/10 | दशांश Daśāṃśa | सूर्य Sūrya | Career · status · accomplishments | Career chart — profession, status, achievements; the daśāṃśa lord reads as the effective vocational graha. | BPHS Ch. 7.31–7.34 |
| D12 | 30°/12 | द्वादशांश Dvādaśāṃśa | गुरु Guru | Mother and father | Parents' karma — mother (4th of D12), father (9th of D12); genetic and emotional inheritance. | BPHS Ch. 7.35–7.38 · Phaladīpikā 4.7 |
| D16 | 30°/16 | षोडशांश Ṣoḍaśāṃśa | शुक्र Śukra | Conveyances · luxury · pleasures | Vehicles and comforts — consulted around major asset decisions; affliction here is read against the running daśā. | BPHS Ch. 7.39–7.42 |
| D20 | 30°/20 | विंशांश Viṃśāṃśa | गुरु Guru | Sādhanā · upāsanā · mantra | Spiritual current — mantra-aptitude, iṣṭa-devatā, depth of sādhanā. | BPHS Ch. 7.43–7.46 · Sarvārtha-cintāmaṇi |
| D24 | 30°/24 | चतुर्विंशांश Caturviṃśāṃśa | बुध Budha | Education · skills · siddhi-vidyā | Learning and vidyā — academic capacity, professional study, mastery of arts. | BPHS Ch. 7.47–7.50 |
| D27 | 30°/27 | सप्तविंशांश Saptaviṃśāṃśa | मङ्गल Maṅgala | Physical · mental · spiritual resilience | Nakṣatrāṃśa — physical, mental, and spiritual stamina; resilience under stress. | BPHS Ch. 7.51–7.54 |
| D30 | 30°/30 | त्रिंशांश Triṃśāṃśa | शनि Śani | Difficulties · curses · enemies | Mishap chart — chronic ailments, accidents, adversarial karma; benefics here mitigate, malefics intensify. | BPHS Ch. 7.55–7.62 · Hora-Sāra 3.10 |
| D40 | 30°/40 | खवेदांश Khavedāṃśa | चन्द्र Candra | Mother's lineage · matriarchal karma | Matriline — effects descending through the mother's family; genealogical patterning. | BPHS Ch. 7.63–7.66 |
| D45 | 30°/45 | अक्षवेदांश Akṣavedāṃśa | सूर्य Sūrya | Father's lineage · patriarchal karma | Patriline — effects descending through the father's family; clan-karma. | BPHS Ch. 7.67–7.70 |
| D60 | 30°/60 | षष्ट्यंश Ṣaṣṭyāṃśa | शनि Śani | Pūrva-janma karma · root causes | Pūrva-janma — past-life imprint; the named ṣaṣṭyāṃśa + its lord read the root of present-life themes. Pāraśara held this as the most subtle varga. | BPHS Ch. 7.71–7.108 (entire ṣaṣṭyāṃśa adhyāya) |
02
विंशोपक-बलम् · Vimśopaka — the 20-point scale
Daśavarga partition of 20A graha’s full strength is not its D1 position alone. Pāraśara’s Daśavarga scheme partitions a 20-point scale across ten vargas; the graha’s dignity in each varga decides what fraction of that weight it earns. The sum is its vimśopaka-bala.
| वर्ग · Varga | विंशोपकम् · Weight | अंशः · Share | कारणम् · Reason |
|---|---|---|---|
| D1 | 6 | 21% | Root canvas — half the weight by itself |
| D2 | 2 | 7% | Wealth axis — material baseline |
| D3 | 4 | 14% | Co-born courage — strong daily-life signal |
| D7 | 2 | 7% | Progeny axis — generational |
| D9 | 5 | 17% | Dharma and strength verdict — second only to D1 |
| D10 | 1 | 3% | Profession lens — focused but narrow |
| D12 | 2 | 7% | Parental inheritance — formational |
| D16 | 1 | 3% | Comforts — secondary indicator |
| D30 | 1 | 3% | Mishap filter — corrective only |
| D60 | 5 | 17% | Pūrva-janma root — Pāraśara's heaviest subtle varga |
| Total | 29 | 100% | Sum of ten weighted vargas |
उत्तमम् · High≥ 15 / 20Pārijāta — unambiguously empowered
मध्यमम् · Mid10 – 15 / 20Uttama — capable, conditionally fruitful
अधमम् · Low< 10 / 20Adhama — partial or obstructed expression
Variants4 systemsṢaḍvarga · Saptavarga · Daśavarga (preferred) · Ṣoḍaśavarga — each ÷ 20
BPHS Ch. 7 · vimśopaka-bala adhyāya. A score, not a verdict — read against daśā and gocara, never alone.
03
वर्गोत्तम-स्थानम् · Vargottama — the amplifier position
same rāśi in D1 and D9A graha is vargottamawhen it occupies the same rāśi in the rāśi chart (D1) and the navāṃśa (D9) simultaneously. Pāraśara reads the coincidence as a graha rooted in its own seat across two scales, and treats it as equivalent to own-sign strength even when the rāśi is not the graha’s own.
- 01
Read the graha’s rāśi in D1 (lagna chart).
- 02
Read the graha’s rāśi in D9 (navāṃśa chart).
- 03
Same sign in both → vargottama.
worked example
गुरु Guru at 6°14′ Mithuna in D1. Mithuna is mutable → D9 counts from the 5th from itself = Tulā. Part within sign = ⌊6.233 × 9 / 30⌋ = 1 (the 2nd navāṃśa). Tulā + 1 = Vṛścika. D1 = Mithuna, D9 = Vṛścika — not vargottama. At 23°45′ Mithuna instead, D9 = Mithuna → vargottama.
COMPOUND FORMS · PĀRIJĀTA = D1+D9+D10 SAME SIGN · UTTAMA = 6 OF 16 VARGAS · PĀRAŚARA = ALL 16 (RARE)
BPHS CH. 7.20 · PHALADĪPIKĀ 5
The caster computes both D1 and D9 — vargottama grahas show the same rāśi label in both grids. Structure, not prediction.
04
अधिक-वर्गाः · Beyond the sixteen
finer slicings · specialised workFour additional vargas outside Pāraśara’s sixteen — extended Pāraśarī tradition, Tier-W provenance.
D5 · 30°/5पञ्चांशPañcāṃśa · Power & influenceAuthority · willpower · capacity to direct. Each 6° part is allocated by the ojayugma (odd/even) rule from the same sign.
D8 · 30°/8अष्टांशAṣṭāṃśa · Unexpected eventsSudden gains, sudden losses, hidden adversaries, longevity nuance. Each 3°45′ part follows the maṅgala-aṣṭa pattern.
D11 · 30°/11रुद्रांशRudrāṃśa · Destruction & dissolutionCapacity to dismantle and transform; used in āyu-vivecana and pralaya-yoga analysis.
D108 · 30°/108अष्टोत्तर-शतांशAṣṭottara-śatāṃśa · 108-fold — finest classical vargaMantra-saṅkhyā varga. Each rāśi divided into 108 parts of 16′40″ — every nakṣatra-pāda receives four parts. Used in ultra-subtle iṣṭa-devatā work.
05
वर्ग-गणितम् · Computation rules
implemented in lib/varga.ts| वर्ग · Varga | अंशः · Part-size | नियम · Rule |
|---|---|---|
| साधारण-नियम General Dn | — | Let L = sidereal longitude; R = ⌊L/30⌋ (rāśi index 0–11); d = L − 30R (deg-in-sign 0–30); part = ⌊d·n/30⌋. Map part to sign via varga-specific table. |
| होरा D2 | 30°/2 | 0–15° in odd-sign → Siṃha (Sūrya-horā); 15–30° in odd-sign → Karka (Candra-horā). Even signs reversed. |
| द्रेक्काण D3 | 30°/3 | 0–10° = same sign; 10–20° = 5th from itself; 20–30° = 9th from itself (the trine cycle). |
| सप्तांश D7 | 30°/7 | Each part = 4°17′8.6″. Odd signs start from themselves; even signs start from the 7th from themselves. |
| नवांश D9 | 30°/9 | Each part = 3°20′. Movable signs start from themselves; fixed from the 9th; mutable from the 5th. The vargottama check sits here. |
| दशांश D10 | 30°/10 | Each part = 3°. Odd signs start from themselves; even signs start from the 9th from themselves. |
| द्वादशांश D12 | 30°/12 | Each part = 2°30′. Every sign starts its own dvādaśāṃśa from itself, then walks the zodiac sequentially. |
| षोडशांश D16 | 30°/16 | Each part = 1°52′30″. Movable → from Meṣa, fixed → from Siṃha, mutable → from Dhanus. |
| विंशांश D20 | 30°/20 | Each part = 1°30′. Movable → from Meṣa, fixed → from Dhanus, mutable → from Siṃha. |
| चतुर्विंशांश D24 | 30°/24 | Each part = 1°15′. Odd signs → from Siṃha (Sūrya); even signs → from Karka (Candra). |
| सप्तविंशांश D27 | 30°/27 | Each part = 1°06′40″ (one nakṣatra-pāda × 9/4). Fire signs → Meṣa, earth → Karka, air → Tulā, water → Makara. |
| त्रिंशांश D30 | 30°/30 | Uneven Pāraśarī tranches per malefic. Odd: Mars 0–5°, Saturn 5–10°, Jupiter 10–18°, Mercury 18–25°, Venus 25–30°. Even sign mapping reversed. |
| षष्ट्यंश D60 | 30°/60 | Each part = 30′. Each carries a named deity/asura (60 names per rāśi, BPHS Ch. 7.71+). Past-life imprint is read from this name. |
BPHS Ch. 7 · varga-cakra-niyamāḥ. Tier-S arithmetic · Tier-W table provenance.
स्व-कुण्डल्यां द्रष्टव्यम् · See these vargas in your own chart
The caster computes every divisional chart from your sidereal graha positions — each varga shows where the nine grahas land in its own zodiac.
16 VARGAS · 16 DIVISORS · BPHS CH. 7
Birth data: never in a URL · processed in memory · never logged.
Substrate
bharat-ephemeris-web · v∞.4 · (R,g,k)=(ℤ/3³³⁷ℤ,2,k=337) · published: 230 props · 83/83 (DOI 10.5281/zenodo.20024273 v3) · internal: 890 · 805/805 (pub. pending) · MK-Ayanāṃśa · sealed 2026-05-11
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JAI MAA KAMAKHYA