Is It Permissible to Call the Adhan in a Singing Tone ?
Question

Is it permissible to Call the Adhan in a Singing Tone?
Praise be to Allah.It is disliked to sing the Adhan in the sense of elongating the words excessively without changing the meaning. If the meaning is changed, then it becomes prohibited and the Adhan is not correct in this case.
Ibn Abi Shaybah (259) narrated that a Mu’adhdhin gave the Adhan and elongated the words in his Adhan and made it sound like singing. `Umar ibn `Abd Al-`Aziz (may Allah have mercy on him) said to him: Give a gentle Adhan otherwise keep away from us.
What is meant by a gentle Adhan is one without singing it. (End quote from Al-Maghrib fi Lughat Al-Fiqh by Abu Al-Makarim Al-Matrazi Al-Hanafi, p 234)
It says in Al-Mudawwanah (1/159):
Malik regarded it as disliked to sing the Adhan and disliked that intensely.
Imam Ash-Shafi`i said in Al-Umm (1/107):
I like the Adhan to be recited clearly without elongating any words or rushing it.
It says in Al-Mawsu`ah Al-Fiqhiyyah:
The jurists agreed that elongating the words of the Adhan and singing it and adding any elongation or letter at the beginning or the end is disliked, because it is contrary to proper focus and dignity. But if the singing and elongation changes the meaning then it is prohibited and there is no scholarly dispute on this point, because it was narrated that a man said to Ibn `Umar: “I love you for the sake of Allah.” He said: “I hate you for the sake of Allah, for you sing the Adhan.”
Shaykh Ibn `Uthaymin (may Allah have mercy on him) said, concerning the Adhan that is sung, this means giving the Adhan with a tune as if singing a song. It is valid but it is disliked.
And he said: But making grammatical mistakes in the Adhan falls into two categories, one which renders the Adhan invalid, which is when the meaning is changed, and one in which the Adhan is valid but is disliked, which is when the meaning is not changed. For example, if the Mu’adhdhin says “Allahu akbar” (elongating the `a’ sound), this is not valid because it changes the meaning, because Akbar is the plural of Kabar, which is a type of drum. (End quote from Ash-Sharh Al-Mumti`, 2/62)
Shaykh Muhammad ibn Ibrahim (may Allah have mercy on him) said: Excessive elongation is not appropriate, and if the vowels are elongated to such an extent that the meaning is changed, this is not valid, otherwise it is disliked. (End quote from Fatawa Ash-Shaykh, 1/125)
The point is that singing the Adhan is disliked, and may render the Adhan invalid if it changes the meaning.
For more details, please see the following answers:
Modulation and elongation of vowels in the Adhan
Meaning of taghanni in Quran recitation
Is exaggerating in beautifying the voice when leading people in prayer regarded as showing off?
Ruling on using auto-tune and vocal effects for the Quran
And Allah knows best.