modes of recital of vedas (pāṭha:):

There are two main modes for veda - nirbhuja and pratṝṇa - nirbhuja (or samhitā pāṭha) means without arms; it is reciting the entire veda without any break, from start to end. pratṝṇa means pada pATha, each pada or word is pronounced clearly and separately.

eg., अग्निम् ईळे, पुरोहितम्, यज्ञस्य, देवम्, ऋत्विजम्....and so on.
(agnim īḷe, purohitam, yajñasya, devam, ṛtvijam....)
The ending 'm' is not pronounced as m but halfway between ma & mu.

By combining the above two modes, a third mode called "krama" or 'kramasamhita' has been created. It will be like:
अग्निम् ईळे, ईळे पुरोहितम्, पुरोहितमिति पुरः हितम्
agnim īḷe, īḷe purohitam, purohitamiti puraḥ hitam

vikṛtis:
(विकृति - विकृतयः - plural) :

The samhita is the natural form - prakṛti - of the veda. From this 8 main vikṛtis have been created. These vikṛtis (or deformations) help to prevent mistakes. The eight vikṛtis are:-

1. जटा - jaṭā
2. माला - mālā
3. शिखा - śikhā
4. लॆखा, रॆखा - lekhā, rekhā
5. ध्वज - dhvaja
6. दण्ड - daṇḍa
7. रथ - ratha
8. घन - ghana

The words of the ṛk or sometimes even a whole sūkta are committed to memory in different orders. For example if the words are 1,2,3,4,5,6, the arrangements for pañcasandhi ghanapāṭha (पञ्चसन्धि घनपाठ) will be:

1-2, 2-2, 2-1, 1-1, 1-2

1-2, 2-1, 1-2, 3; 3 –2-1, 1-2-3

2-3, 3-3, 3-2, 2-2, 2-3,

2-3, 3-2, 2-3- 4. 4-3-2, 2-3-4

3-4, 4-4, 4-3, 3-3, 3-4

3-4, 4-3 , 3-4 –5 , 5- 4-3, 3-4-5

4-5, 5-5, 5-4, 4 –4, 4-5

4-5, 5-4, 4-5 –6 ; 6-5-4, 4-5-6

This is the most difficult of all the vikṛtis. And one who has mastered this pāṭha for the veda is called ghanapāṭhi.

This apparently extra-ordinary obsession with the permutations & combinations in word-rendering reveals the analytical or scientific genius of our ancients which they put to use in ensuring the transmission of the vedas without any mistake in its word structure as well as intonation, to the future generations. An instance was the yajurveda mantra which goes as "natasya pratimā asti..." giving two derivations viz., na tasya pratimā asti... (His idol is not there.) or, "natasya pratimā asti..." (The idol of the one who bowed down is not there.) Both sides argued in favour of their interpretation till the arbitrator asked for the ghanapāṭha whence it became clear that the right rendering was "na + tasya" and not 'natasya'.

Note:
1. The mention of 'na tasya' brings to mind the way most people recite the verse containing these words in śivakavacam - phalaśruti, which goes as follows:

yaḥ sadā dhārayenmartyaḥ śaivam kavacam uttamam |
na tasya jāyate kāpi bhayam śambhoranugrahāt ||

Most people blissfully pronounce it as one word "natasya" because of ignorance. If there was some insight the two words would be pronounced with a very brief pause like 'na tasya'.

2. Despite all the precautions (described above), taken by our ancients, the horrible "satī" came to be practised, reportedly, on the basis of changing one word "agre" to "agne" in RV 10-18-08. It was probably done deliberately.