Question

Assalaamu alaikum wa rahmatu Allah.

May Allah bless and help all the students and readers of Qur'an who read seeking His Pleasure and most especially our teachers.

It is said in the poem about tajweed called Al-Jazariyyah (by Imam Al-Jazaree) that the articulation points are 17;  are there any differences of opinion about this among the scholars?  Jazakumu Allahu khair.

Answer

Wa alaikum assalaam wa rahmatu Allahi wa barakatuh.  Ameen to your dua', may Allah reward all who have taught us even one letter of the Qur'an with the greatest of rewards.

Yes, there are differences of opinion among the old scholars about the number of articulation points for the Arabic letters.  Imam Al-Jazaree referred to this in the same poem you mentioned:
 "Manthoomah: Al-Muqaddimah feemaa yajibu 'alaa qaari'i –l-qur'aan an ya'lamah" when he said (may Allah be merciful to him):

 

Meaning: The articulation points of the letters are seventeen/ as is chosen by he who is of mastery in experiment.

The phrase "chosen by he…" indicates that there are others who did not choose this number for articulation points. The scholar who chose seventeen articulation points is Al-Khaleel bin Ahmed, one of the greatest of imams of all time in the Arabic language; he died 170 Al-Hijara.  Imaam Al-Khaleel was the sheikh of the famous scholar of the Arabic language, Sibawayh.   

Imaam Al-Khaleel's student, Sibawayh said there was sixteen different articulation points of the Arabic letters, dropping the empty space of the mouth and throat for the three medd letters, and giving them each an articulation point already assigned to other letters.  The alif, he said comes from the same articulation point as the hamzah, the lengthened wow from the same point as the unlengthened wow (the two lips) and the lengthened ya' from the same point as the unlengthened ya' (the middle of the tongue and that which lies opposite to it from the roof of the mouth). 

Another scholar, Al-Furra' [Abu Zakariyyaa Yahya bin Zayaad, died 207 Al-Hijara] stated that there was fourteen different articulation points for the Arabic letters, dropping the empty space in the mouth and throat, just as Sibawayh did, plus stating that the lam, ra', and noon all shared the same articulation point.  The truth is that the articulation points of these three letters are very close, but each has its own articulation point.  

In reality, there is truth in each of these theories.  The three lengthened letters (medd letters) rely on both a vibration of the vocal cords plus a portion of the articulation point of the unlengthened letter.  The lengthened wow relies on vibration of the vocal cords plus a circling of the two lips.  The lengthened wow cannot be produced without this circling of the lips.  What is said about the wow, can be said about the ya'.  And Allah knows best.