Why chant 16 rounds?
Srila Prabhupada says, "The Krsna consciousness movement prescribes sixteen rounds daily because people in the Western countries cannot concentrate for long periods while chanting on beads. Therefore the minimum number of rounds is prescribed. However, Srila Bhaktisiddhanta Sarasvati used to say that unless one chants at least sixty-four rounds of japa (one hundred thousand names), he is considered fallen (patita). According to his calculation, practically every one of us is fallen, but because we are trying to serve the Supreme Lord with all seriousness and without duplicity, we can expect the mercy of Lord Sri Caitanya Mahaprabhu, who is famous as patita-pavana, the deliverer of the fallen."
So it is a concession made by Srila Prabhupada for the devotees who cannot concentrate for long periods while chanting on beads. That is why he always used to add the word 'minimum' before 16 rounds. So the devotees should know when they are chanting a minimum of 16 rounds everyday and should aspire to always chant extra rounds as and when they find any spare time from their practical devotional service. Not that I will relieve myself of the burden of the bead bag for the day as soon as I finish 16 rounds.
Srila Bhaktivinode Thakur explains that the prema-ruruksu devotees (those who earnestly strive for ascending up to the region of prema) chant 192 (3 x 64) rounds daily. If one were to chant each round in 7.5 minutes, these 192 rounds would completely fill up with his 24 hours leaving him no time to eat, sleep, earn a livelihood, or even go to the toilet. If one were to speed up his chanting and complete each round within 5 minutes, his chanting would still take 16 hours leaving him only 8 hours daily for sleeping, earning a livelihood, commuting, etc. The point is that for most people this much chanting is not possible. But still is it in described by Srinivasacarya "sankhya-purvaka-nama-gana" that one must maintain numerical strength while chanting the holy names. Therefore Srila Prabhupada has mercifully fixed up a number of at least 16 rounds of Hare Krishna chanting daily for us. This is a number which can be practically accomplished on a daily basis along with our other numerous material duties. He encouraged us to also to increase our chanting beyond 16 rounds as far as our daily schedule allows.
To become perfect in chanting we must obey the spiritual master's orders. Therefore at least 16 rounds daily of japa mala must be completed, if we are at all serious about attaining spiritual perfection. The disciples are always encouraged to chant more if possible, but not less.
Srila Prabhupada speaks about this in Bhagavad-gita class Nairobi Oct. 28, 1975
Indian man: Prabhupada, when we do our chanting, the chanting beads contain 108 beads. Why is this, and why do we chant sixteen rounds?
Srila Prabhupada: Not sixteen rounds. You can chant unlimitedly.
Indian man: No, minimum
Srila Prabhupada: Minimum because they cannot chant more than that, therefore minimum. Otherwise kirtaniyahsada harih[Cc. adi 17.31]. So you must have a fixed amount of kirtana. That is called tapasya, that “We must finish at least this much, if not more.” Sankhya-purvaka-nama-gana-natibhih. Sankhya-purvaka. By numerical strength one should chant. That is called vow. This is the idea. So these Europeans, Americans, they cannot imitate Haridasa Ṭhakura, who was chanting 300,000 times. So we do not advise to imitate. Really do something. One name is sufficient. If you can chant one name only, that is sufficient, but that is not possible. So to understand the value of name at least we must have some numerical strength. All the Gosvamis used to do that. We follow their footprints. Thank you. Now chant Hare Krsna.
Devotees: All glories to Srila Prabhupada.
