The gAnaM rules are thus constructed. First we define elements corresponding to the padas of the R^ik, here a,b,c,d : 4*11 in the triShTubh example we are considering.

a=brahma jaGYAnaM prathamaM purastAd

b=vi sImataH surucho vena AvaH

c=sa budhniyA upamA asya viShThAH

d=satash cha yoniM asatash cha vivaH

Then the musical stobhAs are defined:

A= huve hA yi

B= heShAyA

C= au ho vA

D= e R^itaM amR^itaM

W=A+A+B

Then the gAnaM is specified as :

W+a b c d+W+C D+D+D

1 2 3 4 5

The parts of the gAnaM labeled 1-5 are refered to in the brAhmaNas of the sAma veda by the technical terms:

1 prastAva

2 udgItha

3 pratihAra

4 upadrava

5 nidhana

This is one of the simplest gAnaM constructs.

This general rule may be construct other traiShTubha gAnaMs, though different stobhas may be defined.

The satyaM class of chants- the song of the inviolable satya upheld by deva mitra is defined thus:

a=satya

E= ho yi

F= hA A vu vA

G= e suvar jyotiH

p=the praNava, oM

Ganam:

a.p a+E+a+E+a+F G

a.p represent the insertion of the praNava into satya to give satyoM.

satya may be replaced by puruSha, agna, vAya, sUrya, chandra, nAkA, shukra, to give rise through the same above formula to the 8 “space filling chants”. These represent the equivalence between the elements of space and the sacrificial altar. The adhvaryu lays the bricks with the yajur brick chants. Even as he does so the udgAtA establishes with these sAmans the equivalence with the inviolable satya, the puruSha that pervades, heat (agna), atmosphere (vAya), the sun (sUrya), moon (chandra), nAkA (the night sky) , shukra (Venus). Thus, completing the identification of the sacrificial platform with these elements of space.

The sAman adopts the operator notation to represent cases where the nidhana element may differ in the space filling charms.

Thus, exactly like the Hamiltonian of mechanics, the ‘space filling chant operator’, H is defined as :

H(x)=x.oM x + ho yi+ x + ho yi+x+hA A vu vA e

Then the new sAmans are indicated as:

H(satya)+C1

H(puruSha)+C1

H(agna)+C2

H(vAya)+C3

H(sUryA)+C4

H(chandra)+C5

H(nAka)+C6

H(shukra)+C7

C1=suvar jyotiH; C2= jyotiH; C3=rAjA; C4=bhrAjA; C5=A bhrAjA; C6= pR^iShThaM; C7= bhrALA bhrAjA