विंशोत्तरी १२० वर्षBPHS Ch. 46–51 · 12 daśā prāṇālayaḥ · pañca-stara decomposition
दशा-कालः Daśā-Kālaḥ
The full 120-year Vimśottarī tree from the Moon’s nakṣatra at birth. Open any mahā-daśā for its antara-daśās. Periods are computed, not interpreted.
TIER-S (iii) COMPUTED BOUNDARIES · TIER-W (vii) INTERPRETIVE LABELS
विंशोत्तरी-वृक्षः · The 120-year tree
computed · not interpretedComputed entirely in your browser — never in a URL · processed in memory · never logged.
Why 120 years is a period, not a guess
substrate provenanceP32 · TIER-S (iv) · पिसानो-स्थैर्यम्
Pisano-tower lock: π(3ᵏ) = 4·ord_R(g) = 8·3^(k-1) — the 120-year Vimśottarī cycle inherits its periodicity from this lock.
companions P33 · P34 · P202 — 6/6 PASS k=1..6
P77 · TIER-S (v) · मुक्ति-वर्धनम्
Liberation-tower exponent ord_R(−g) = 3^(k-1) — daśā transitions triple per tower-level (antar/sūkṣma/prāṇa cascade).
companion P229 — 6/6 PASS k=1..6
पिसानो-सम्बन्धम् · PISANO COMPANIONS
The 120-year Vimśottarī period (P32) is one face of a four-fold Pisano lock that holds across both poles of the substrate. The Diti-pole companion is P241 (Pisano-of-Ideal Identity · π_(3)(3ᵏ) = π(3ᵏ⁻¹)) — a ratio-3 fold on the ideal side that mirrors the ratio-4 fold on the unit side. The saptamukhi witnesses are V1 (Pisano-Ψ ratio = 4) for the Aditi-pole and AV1 (Pisano-of-Ideal = 3) for the Diti-pole. Daśā periodicity is what the substrate certifies; the jyotiṣī interprets.
Tier-S (iv) · Tier-S (ix) · 10/10 PASS k=2..6 · saptamukhi-bipolar.
विंशोत्तरी-दशा-वलयम् · the 9-graha Vimśottarī spiral — 120 years across nested tori
दशा-चक्रम् · The ring of 120 years
arc ∝ years · 360° = 120 yEach wedge’s arc-length is exactly proportional to that lord’s share of the cycle. Total angle 360° · total years 120.
- केतुKetu7y · 21°
- शुक्रŚukra20y · 60°
- सूर्यSūrya6y · 18°
- चन्द्रCandra10y · 30°
- मङ्गलMaṅgala7y · 21°
- राहुRāhu18y · 54°
- गुरुGuru16y · 48°
- शनिŚani19y · 57°
- बुधBudha17y · 51°
BPHS Ch. 46 · constant 9-fold partition · Tier-S (iii).
चतुर्विधाः मूल-दशाः · The four classical systems
विंशोत्तरी · VIMŚOTTARĪ · 120 Y
Standard system · most widely used · seeded from the Moon’s nakṣatra. Nine grahas share 120 years in fixed sequence and proportion.
| lord | years | order |
|---|---|---|
| केतु Ketu | 7 | 1 |
| शुक्र Śukra | 20 | 2 |
| सूर्य Sūrya | 6 | 3 |
| चन्द्र Candra | 10 | 4 |
| मङ्गल Maṅgala | 7 | 5 |
| राहु Rāhu | 18 | 6 |
| गुरु Guru | 16 | 7 |
| शनि Śani | 19 | 8 |
| बुध Budha | 17 | 9 |
| total | 120 | 9 mahā |
BPHS Ch. 46 · Tier-S (iii).
योगिनी · YOGINĪ · 36 Y
Yāmala-Tantra system · 8 yoginīs share 36 years in arithmetic progression. Each yoginī carries a graha lord.
| yoginī | lord | years |
|---|---|---|
| मङ्गला Maṅgalā | चन्द्र Candra | 1 |
| पिङ्गला Piṅgalā | सूर्य Sūrya | 2 |
| धान्या Dhānyā | गुरु Guru | 3 |
| भ्रामरी Bhrāmarī | मङ्गल Maṅgala | 4 |
| भद्रिका Bhadrikā | बुध Budha | 5 |
| उल्का Ulkā | शनि Śani | 6 |
| सिद्धा Siddhā | शुक्र Śukra | 7 |
| सङ्कटा Saṅkaṭā | राहु Rāhu | 8 |
| total | 8 mahā | 36 |
Yāmala-Tantra · Tier-W (vii).
अष्टोत्तरी · AṢṬOTTARĪ · 108 Y
108-year cycle across 8 grahas (Ketu excluded). Applied as a cross-check on Vimśottarī when the Moon falls in certain pakṣa configurations.
| lord | years | order |
|---|---|---|
| सूर्य Sūrya | 6 | 1 |
| चन्द्र Candra | 15 | 2 |
| मङ्गल Maṅgala | 8 | 3 |
| बुध Budha | 17 | 4 |
| शनि Śani | 10 | 5 |
| गुरु Guru | 19 | 6 |
| राहु Rāhu | 12 | 7 |
| शुक्र Śukra | 21 | 8 |
| total | 108 | 8 mahā |
Jaimini tradition · Tier-W (vii).
चर-दशा · CARA · SIGN-BASED
Jaimini’s sign-based daśā — seeded not from a graha but from the lagna’s rāśi. Each of the twelve rāśis takes its turn; order follows ārūḍha and pada rules, not nakṣatra.
Jaimini Sūtras · Tier-W (vii).
अधिक-दशा-प्रणालयः · Kāla · Sthira · Mūla · Brahma
काल-दशा · KĀLA · 36 Y · TITHI-SEEDED
A 36-year tithi-seeded cycle measuring the quality of time. Nine grahas share 36 years; grahas of similar tonality are paired (Maṅgala–Sūrya fire-tribe, Śani–Śukra quench-tribe). Used in muhūrta-style timing of crisis windows.
| lord | years | order |
|---|---|---|
| सूर्य Sūrya | 3 | 1 |
| चन्द्र Candra | 4 | 2 |
| मङ्गल Maṅgala | 3 | 3 |
| बुध Budha | 4 | 4 |
| गुरु Guru | 5 | 5 |
| शुक्र Śukra | 5 | 6 |
| शनि Śani | 4 | 7 |
| राहु Rāhu | 4 | 8 |
| केतु Ketu | 4 | 9 |
| total | 36 | 9 mahā |
Use when: running fine-grain timing on a 36-year resolution; cross-checking tithi-driven events (eclipses, sandhi-kāla, transitions of state).
Kāla-prakāśikā tradition · Tier-W (vii).
स्थिर-दशा · STHIRA · 84 Y · JAIMINI FIXED-SIGN
Each rāśi receives a fixed quota — 7 years cara (movable), 8 sthira (fixed), 9 dvi-svabhāva (mutable). Reads life-themes sign by sign, irrespective of graha occupancy.
| sign | quality | years |
|---|---|---|
| मेष Meṣa | Cara | 7 |
| वृषभ Vṛṣabha | Sthira | 8 |
| मिथुन Mithuna | Dvi-svabhāva | 9 |
| कर्क Karka | Cara | 7 |
| सिंह Siṃha | Sthira | 8 |
| कन्या Kanyā | Dvi-svabhāva | 9 |
| तुला Tulā | Cara | 7 |
| वृश्चिक Vṛścika | Sthira | 8 |
| धनु Dhanus | Dvi-svabhāva | 9 |
| मकर Makara | Cara | 7 |
| कुम्भ Kumbha | Sthira | 8 |
| मीन Mīna | Dvi-svabhāva | 7 |
| total | 12 rāśi | 96 |
The classical 84-year tally arises by deducting the 12 dvāra-sandhi years; the full enumeration is shown for completeness.
Use when: you need a stable rāśi-driven timeline that ignores graha-bala fluctuation; pairs with Cara-daśā as the fixed counterpart.
Jaimini Sūtras · Sthira-prakaraṇa · Tier-W (vii).
मूल-दशा · MŪLA · VARIABLE · ROOT-SIGN
An āyu-adaptive daśā: total length matches the projected lifespan computed via Jaimini’s piṇḍa / aṃśa-āyurdāya. Seeded from the mūlatrikoṇa of the strongest planetary indicator, walking the rāśis in natural order.
Use when: the chart asks for a daśā that respects its natural āyu rather than a fixed total; especially for mokṣa-trikoṇa work.
Jaimini Sūtras · Mūla-prakaraṇa · Tier-W (vii).
ब्रह्म-दशा · BRAHMA (YĀMALA) · 99 Y
A 99-year cycle keyed to the Brahma-graha — the strongest angular benefic. Years are apportioned by graha-bala rather than fixed quantum, so sequence and quanta both vary chart to chart.
| lord | years | order |
|---|---|---|
| सूर्य Sūrya | 5 | 1 |
| चन्द्र Candra | 12 | 2 |
| मङ्गल Maṅgala | 7 | 3 |
| बुध Budha | 15 | 4 |
| गुरु Guru | 18 | 5 |
| शुक्र Śukra | 20 | 6 |
| शनि Śani | 9 | 7 |
| राहु Rāhu | 7 | 8 |
| केतु Ketu | 6 | 9 |
| total | 99 | 9 mahā |
Use when: the chart asks for a creator-cycle view — long-arc dharma timing, lineage karma, generational unfoldings.
Brahma-yāmala · Tier-W (vii).
दशा-गम्भीरता · Seven deeper systems
Each daśā below is a classical time-framework — a lens of karma-attribution per its named śāstra. Nothing here predicts that a specific event will happen in any specific lord’s period; timeline structure is what the engine certifies, not outcome.
अष्टोत्तरी-दशा · AṢṬOTTARĪ · 108 Y · 8 GRAHAS
108-year cycle keyed to Moon’s nakṣatra-pāda. Operating rule (BPHS Ch. 47 v. 4 + Phaladīpikā 9): primary lens when lagna is in Kṛṣṇa-pakṣa and the Moon does NOT occupy Aśleṣā / Maghā / Mūla; otherwise a cross-check on Vimśottarī.
| lord | years | order |
|---|---|---|
| सूर्य Sūrya | 6 | 1 |
| चन्द्र Candra | 15 | 2 |
| मङ्गल Maṅgala | 8 | 3 |
| बुध Budha | 17 | 4 |
| शनि Śani | 10 | 5 |
| गुरु Guru | 19 | 6 |
| राहु Rāhu | 12 | 7 |
| शुक्र Śukra | 21 | 8 |
| total | 108 | 8 mahā |
BPHS Ch. 47 · Phaladīpikā 9 · Tier-S (iii) + Tier-W (vii).
योगिनी-दशा (निश्चिता) · YOGINĪ FIXED · 36 Y · 4.5-Y QUANTA
The strict-equal variant of Yoginī: all 8 yoginīs receive 36 / 8 = 4.5 years each. Used in praśna-style timing where the variable progression (1, 2, … 8) is felt to over-weight the closing Saṅkaṭā. Seeded from Moon-nakṣatra index mod 8 (Yāmala +1 offset).
| yoginī | lord | years |
|---|---|---|
| मङ्गला Maṅgalā | चन्द्र Candra | 4.5 |
| पिङ्गला Piṅgalā | सूर्य Sūrya | 4.5 |
| धान्या Dhānyā | गुरु Guru | 4.5 |
| भ्रामरी Bhrāmarī | मङ्गल Maṅgala | 4.5 |
| भद्रिका Bhadrikā | बुध Budha | 4.5 |
| उल्का Ulkā | शनि Śani | 4.5 |
| सिद्धा Siddhā | शुक्र Śukra | 4.5 |
| सङ्कटा Saṅkaṭā | राहु Rāhu | 4.5 |
| total | 8 mahā | 36 |
Praśna-Mārga Ch. 26 (equal-quanta variant) · Tier-W (vii).
सुदर्शन-चक्र-दशा · SUDARŚANA-CAKRA · TRIPLE 12-Y WHEEL
Three concurrent 12-year cakras seated at Lagna, Sūrya and Candra. The running year (age mod 12) selects one rāśi from each seat; the three signs together form the praśna-tone for the year.
Sudarśana-cakra Praśna · Bṛhat-tradition · Tier-W (vii).
ब्रह्म-दशा (आत्म-कारक) · BRAHMA · ĀTMAKĀRAKA-NAVĀṀŚA
Jaimini’s creator-cycle, seeded from the navāṁśa-rāśi of the Ātmakāraka(highest-degree graha among the 7 non-shadow grahas). Walks 12 rāśis savya or apasavya by the seed’s quality; years per rāśi by the count-to-lord rule (as Nārāyaṇa-daśā).
Jaimini Sūtras Ch. 2 · Padakrama variant · Tier-W (vii).
कालचक्र-दशा · KĀLACAKRA · MOON-PĀDA · 118 Y
The most intricate classical daśā — Moon-pāda rooted, with savya (forward) or apasavya (reverse) rotation determined by nakṣatra-block parity. Each rāśi carries its classical piṇḍāyu quantum.
| sign | piṇḍāyu yrs | % of 118 |
|---|---|---|
| मेष Meṣa | 7 | 5.9% |
| वृषभ Vṛṣabha | 16 | 13.6% |
| मिथुन Mithuna | 9 | 7.6% |
| कर्क Karka | 21 | 17.8% |
| सिंह Siṃha | 5 | 4.2% |
| कन्या Kanyā | 9 | 7.6% |
| तुला Tulā | 16 | 13.6% |
| वृश्चिक Vṛścika | 7 | 5.9% |
| धनुष् Dhanus | 10 | 8.5% |
| मकर Makara | 4 | 3.4% |
| कुम्भ Kumbha | 4 | 3.4% |
| मीन Mīna | 10 | 8.5% |
| total | 118 | 100.0% |
Jaimini Sūtras 4.1 · BPHS Ch. 51 (vv. 22–31) · Tier-W (vii).
दृग्-दशा · DṚG · JAIMINI ASPECT CYCLE
Seeded from the 9th-from-lagna (dharma-bhāva), the cycle walks 12 rāśis with each duration computed from count-to-aspector. Reads the rhythm of dharma-disclosure; a counterpart to Nārāyaṇa-daśā when the question is external visibility of dharma.
Jaimini Sūtras Ch. 2 · Drig-prakaraṇa · Tier-W (vii).
माण्डूक-दशा · MĀṆḌŪKA · FROG-LEAP BY 5
A movement variant of Cara-daśā. Where Cara walks rāśis in adjacent order, Māṇḍūka leaps by 5 — gcd(5, 12) = 1, so each sign is visited exactly once across 12 leaps. Years follow the Cara count-to-lord rule.
Jaimini Sūtras 2.3 (māṇḍūka-prakaraṇa · variant readings) · Tier-W (vii).
Substrate provenance — tag (i) ring-axioms: (ℤ/12ℤ) rāśi cycles, (ℤ/8ℤ) Aṣṭottarī & Yoginī, (ℤ/27ℤ) Tārā · tag (iii) period determination: fixed quanta · count-to-lord · piṇḍāyu · tag (vii) interpretive labels are provenance, not magic.
दशा-सन्धि-कालः · Transition windows
≈ ±10 days at each handoverAt each daśā-handover, the closing mahā’s final ≈ 10 days and the opening mahā’s first ≈ 10 days form a sandhi-kāla — the liminal junction where the two tonalities overlap. The table records the classical reading of each junction.
| ending | beginning | classical reading |
|---|---|---|
| केतु Ketu | शुक्र Śukra | Detachment dissolves; sensual abundance dawns — abrupt thaw |
| शुक्र Śukra | सूर्य Sūrya | Pleasure recedes; will and authority sharpen — public stage opens |
| सूर्य Sūrya | चन्द्र Candra | Solar drive softens to lunar feeling — emotional re-anchoring |
| चन्द्र Candra | मङ्गल Maṅgala | Mind hardens to action — conflict and surgery windows |
| मङ्गल Maṅgala | राहु Rāhu | Fire crosses into illusion — foreign currents, sudden ambition |
| राहु Rāhu | गुरु Guru | Smoke clears to wisdom — dharma re-asserts; teachers appear |
| गुरु Guru | शनि Śani | Expansion meets restriction — institutional tests, hard winters |
| शनि Śani | बुध Budha | Discipline becomes intellect — communication and commerce rebound |
| बुध Budha | केतु Ketu | Networks dissolve into renunciation — closure of a 120-year arc |
Classical convention treats the sandhi as a settling-room, not a runway — BPHS Ch. 46 · Phaladīpikā 19 · Tier-W (vii); not a prediction.
दशा-बीज-नियमाः · Seeding rules
eight systems · eight roots| system | basis | formula |
|---|---|---|
| विंशोत्तरी Vimśottarī | जन्म-नक्षत्र Moon's nakṣatra at birth | Lord of janma-nakṣatra opens the cycle; balance = (1 − fraction-traversed) × that lord's years |
| योगिनी Yoginī | नक्षत्र-योगिनी Moon's nakṣatra (alternate mapping) | (nakṣatra-index + 3) mod 8 → yoginī; balance = (1 − fraction-traversed) × that yoginī's years |
| अष्टोत्तरी Aṣṭottarī | पक्ष-नक्षत्र Moon's nakṣatra + lagna pakṣa | Janma-nakṣatra-pāda + day/night pakṣa selects starting graha; Ketu excluded from cycle |
| चर Cara | लग्न-राशि Lagna rāśi (Jaimini) | Order = forward from lagna if odd-quality, reverse if even; duration = (count to lord) − 1 |
| काल Kāla | जन्म-तिथि Janma-tithi (lunar day) | Tithi index → graha-of-the-day; 36 years split unevenly across 9 grahas |
| स्थिर Sthira | लग्न-राशि Lagna rāśi (Jaimini · fixed) | Each rāśi gets a fixed quota (7/8/9 years by triplicity); order from lagna forward |
| मूल Mūla | मूल-त्रिकोण Mūlatrikoṇa of strongest graha (Jaimini) | Cycle anchored to mūla rāśi; total length adapts to projected āyu (lifespan) |
| ब्रह्म Brahma | ब्रह्म-ग्रह Brahma-graha (most powerful angular benefic) | 99 years partitioned by graha-bala; sequence begins with the Brahma-graha |
Tier-S (iii) computed seeds · Tier-W (vii) system selection.
पञ्च-स्तर-दशा · Five-level decomposition
9 × 9 × 9 × 9Every mahā-daśā fractally subdivides into nine antaras; each antara into nine pratyantaras; each pratyantara into nine sūkṣmas; each sūkṣma into nine prāṇas. The cascade preserves the 9-fold proportion, so each lord rules every other lord at every level within its share. 9⁴ = 6,561 prāṇas per mahā — for the longest mahā (Śukra · 20 y) one prāṇa ≈ 26.7 hours; for the shortest (Sūrya · 6 y) ≈ 8 hours.
| level | divisor | typical span | meaning |
|---|---|---|---|
| महा-दशा Mahā-daśā | — | 6–20 years | Major era · life-chapter |
| अन्तर्-दशा Antar-daśā | ÷ 9 | ≈ 8 months–3 years | Sub-period · year-scale theme |
| प्रत्यन्तर-दशा Pratyantar-daśā | ÷ 81 | ≈ weeks–months | Sub-sub-period · event window |
| सूक्ष्म-दशा Sūkṣma-daśā | ÷ 729 | ≈ days | Fine-grain · day-of-event resolution |
| प्राण-दशा Prāṇa-daśā | ÷ 6561 | ≈ hours | Breath-level · muhūrta of culmination |
BPHS Ch. 46 · pañca-stara rule · 9-fold partition invariant · Tier-S (iii).
स्व-दशा-दर्शनम् · YOUR RUNNING DAŚĀS
See the 5-level cascade in your own chart
The birth-chart caster resolves the running Vimśottarī cascade (mahā · antara · pratyantara · sūkṣma · prāṇa) at the moment of your birth, plus the full 9-lord sequence.
Vimśottarī daśā · common questions
दशा-प्रश्नाः- What is Vimshottari Dasha?
- Vimśottarī Daśā is the most widely used Vedic planetary time-cycle system, codified in BPHS Ch. 46. Nine planetary lords share a 120-year cycle in fixed proportion. The cycle is seeded from the Moon's nakṣatra at birth — specifically the fraction of that nakṣatra already traversed at the moment of birth.
- How do I calculate my current Mahadasha and Antardasha?
- To find your current mahā-daśā: cast your birth chart (available free at /chart), note the Moon's janma nakṣatra, and identify which planetary lord governs that nakṣatra. The fraction of the nakṣatra traversed at birth determines how much of that lord's period has elapsed. Our engine shows the running daśā balance automatically.
- What are Mahadasha and Antardasha?
- Mahā-daśā is the major planetary period (lasting 6–20 years). Within each mahā-daśā, nine sequential antar-daśā (sub-periods) subdivide the time — each lasting from a few months to a few years. Further levels are pratyantar-daśā, sūkṣma-daśā, and prāṇa-daśā. All five levels are computable from the birth chart.
- Which dasha is considered good for marriage in Vedic astrology?
- Classical Jyotiṣa identifies Venus (Śukra) mahā-daśā and Moon (Candra) mahā-daśā as often favorable for marriage-related developments, since both govern relationships and emotional life. However, the actual assessment requires reading the 7th house, its lord, Navāṃśa, and the running antar-daśā — not the mahā-daśā alone.
ॐ कालाय नमः · ॐ कामाख्यायै नमः · ॐ हनुमते वज्रदेहाय नमः
(R, g, k) = (ℤ/3³³⁷ℤ, 2, k=337) · internal catalog 890 propositions · 805/805 machine-checked (publication pending) · published: 230 props · DOI 10.5281/zenodo.20024273 (v3)