Āyādi Ṣaḍvarga Modular Formulations
The dimensional arithmetic of Sthāpatya Veda: a building’s measures, counted in hastas, are multiplied and divided to leave a remainder, and each remainder is read against a list. The texts do this in more than one way, so this chapter sets the four traditions side by side, each with its locus, and then says what the engine’s default reading does differently.
1. The unit: the hasta
Eight yava make one aṅgula, twenty-four aṅgulas one kiṣku hasta, and four hastas one daṇḍa (Mayamata 5.3–12). The engine takes the aṅgula as 19.05 mm and the kiṣku as 0.4572 m (18 inches); no text gives the aṅgula in metres. The texts name other hastas too, and a reading states which one it used — see Hastas & the aṅgula.
2. The tests, tradition by tradition
Each row was read in the edition named. They differ in what they measure, in what they multiply by, and in what they divide by; none of them is the formula set below the table.
| Tradition | Measured on | Formulas | Read in |
|---|---|---|---|
| Mānasāra9.63–73 | Length L, breadth B and circumference C, measured with the dhanurgraha rod | Āya: L×8 mod 12 · Nakṣatra: L×8 mod 27 · Vyaya: B×9 mod 10 · Yoni: B×3 mod 8 · Vāra: C×9 mod 7 · Tithi: C×9 mod 30 · Aṃśa: C×4 mod 9 | Acharya's translation and Dictionary |
| Mayamata9.18–24 | Breadth plus length (the half-perimeter) | Āya: ×8 mod 12 · Vyaya: ×9 mod 10 · Yoni: ×3 mod 8 · Nakṣatra and age: ×8 ÷ 27, the remainder the nakṣatra and the quotient the age. The tithi and vāra are located in 9.22b–23 but not settled: the divisor “yamīśa” has no fixed value, and one manuscript reads ÷15. | Pandey's edition and Dagens' translation |
| Kerala: Tantrasamuccaya 2.3, by Manuṣyālaya Candrikā 3.253.25 | The sum of length and breadth, read as the perimeter in the worked example (in kōl) | Yoni: ×3 mod 8 · Vyaya: ×3 mod 14 or ×9 mod 10 · Āya: ×8 mod 12 · Nakṣatra and age: ×8 ÷ 27 · Tithi: ×8 mod 30 · Vāra: ×8 mod 7. A perimeter of 63 kōl gives 189, and 189 mod 8 = 5: Vṛṣa. | the Sanskrit with a Hindi commentary, and the Kannada translation |
| Viśvakarma Prakāśa2.49–72 | The area A = L×B in hastas | Āya: A mod 8, named Dhvaja to Vāyasa · multiplier and divisor pairs: āya 9/8, vāra 9/7, aṃśaka 6/9, dravya 8/12, ṛṇa 3/8, nakṣatra 8/27, tithi 8/15, yoga 4/27, āyu 8/120 · Vyaya: the house nakṣatra mod 8 | the Hindi edition with the Sanskrit |
Where to measure: inner dimensions for vessels, ponds, wells, courtyards and sanctums; the middle line for a four-sided house; outer dimensions elsewhere (Manuṣyālaya Candrikā 3.24). The same eight names are “yonis” in the southern texts and “āyas” in the Viśvakarma Prakāśa.
3. The eight yonis
The odd yonis — Dhvaja, Siṃha, Vṛṣa and Gaja — are the good ones and the even ones are the bad; a remainder of zero is the eighth, Kāka, which is weak. (Mayamata 9.21–22, Manuṣyālaya Candrikā 3.26, Viśvakarma Prakāśa 2.50–52, and the Mānasāra.)
| Remainder | Yoni | Direction | Counted as |
|---|---|---|---|
| 1 | Dhvaja (flag) | East | Good (odd) |
| 2 | Dhūma (smoke) | South-east | Not good (even) |
| 3 | Siṃha (lion) | South | Good (odd) |
| 4 | Śvan or Kukkura (dog) | South-west | Not good (even) |
| 5 | Vṛṣa (bull) | West | Good (odd) |
| 6 | Khara (donkey) | North-west | Not good (even) |
| 7 | Gaja (elephant) | North | Good (odd) |
| 0 (the eighth) | Kāka or Vāyasa (crow) | North-east | Not good (even) |
4. Āya should exceed Vyaya
The one rule the traditions share is that the āya (inflow) should exceed the vyaya (outflow): Mayamata 9.24 and Mānasāra 9.75–77. The Mānasāra (chapter 64) allows that equal is no fault. The other tests carry their own counsel — the Mānasāra counts Friday, Thursday, Monday and Wednesday good as the vāra and asks that the new moon, the eighth and the ninth be avoided as the tithi; the Viśvakarma Prakāśa (2.78) reads Sunday and Tuesday as a risk of fire, and counts the third, fifth and seventh stars from the owner’s own (2.80–82) as ones to avoid. These are what the texts say. The reference does not turn them into a prediction about any house.
5. What the engine’s default reading does differently
The default reading is a single convention applied to the plot’s area in hastas, with the yoni taken from the breadth. It is equal to none of the four traditions above, and its Āyu test (area × 27, mod 100, with 60 or more counted desirable) has no located verse behind it. It is a modern convention.
The default reading
Area in hastas; the engine's own convention
Parameters & variables
A- Area: Length times breadth, each in hastas(hastas²)
W_hasta- Breadth: The shorter side in hastas(hastas)
Āyādi Ṣaḍvarga sandbox
Illustration, not the engineChange a dimension and watch the modular arithmetic move. The residues here are computed in the page so the steps are visible; the authoritative values come from the Vaasthu engine.
Area = (L ÷ 1.5) × (W ÷ 1.5) ft/hasta = 533.4 hasta²
- Āya (×8 mod 12)
- 4
- Vyaya (×9 mod 10)
- 7
- Yoni (breadth ×3 mod 8)
- 4 · Śvan (Dog)
- Vāra (×9 mod 7)
- Soma (Moon)
- Nakṣatra (×8 mod 27)
- 25
- Āyu (×27 mod 100, no located verse)
- 91
Āya does not exceed Vyaya — the one condition the traditions share.
Yoni 4 (South-West) is an even yoni, not counted good — the texts' list gives no more than that.