This is a complicated and messy subject. I will try to be as objective as I can at my answer, in summary I will mention three different opinions along with their proofs:

Music is Haram

Music is Halal

Music is Halal in accordance to Denatology

My final opinion on the matter

Music is Haram

From Quran

Allah says:

And of the people is he who buys the amusement of speech to mislead [others] from the way of Allah without knowledge and who takes it in ridicule. Those will have a humiliating punishment. [31:6]

amusement of speech has been referenced as the following by the following people:

Ibn Abbas PBUH: Singing

Mogahed: Drums

Alhassan Albasri: Singing and Flutes

Ibn Masood: Singing

Abi Omar PBUH: Singing

Allah also says:

And incite [to senselessness] whoever you can among them with your voice and assault them with your horses and foot soldiers and become a partner in their wealth and their children and promise them." But Satan does not promise them except delusion. [17:64]

Same source as above, Moghaed claims that your voice references Singing and falsehood.

From Sunnah

The prophet says:

وَقَالَ هِشَامُ بْنُ عَمَّارٍ حَدَّثَنَا صَدَقَةُ بْنُ خَالِدٍ، حَدَّثَنَا عَبْدُ الرَّحْمَنِ بْنُ يَزِيدَ بْنِ جَابِرٍ، حَدَّثَنَا عَطِيَّةُ بْنُ قَيْسٍ الْكِلاَبِيُّ، حَدَّثَنَا عَبْدُ الرَّحْمَنِ بْنُ غَنْمٍ الأَشْعَرِيُّ، قَالَ حَدَّثَنِي أَبُو عَامِرٍ ـ أَوْ أَبُو مَالِكٍ ـ الأَشْعَرِيُّ وَاللَّهِ مَا كَذَبَنِي سَمِعَ النَّبِيَّ صلى الله عليه وسلم يَقُولُ ‏ "‏ لَيَكُونَنَّ مِنْ أُمَّتِي أَقْوَامٌ يَسْتَحِلُّونَ الْحِرَ وَالْحَرِيرَ وَالْخَمْرَ وَالْمَعَازِفَ، وَلَيَنْزِلَنَّ أَقْوَامٌ إِلَى جَنْبِ عَلَمٍ يَرُوحُ عَلَيْهِمْ بِسَارِحَةٍ لَهُمْ، يَأْتِيهِمْ ـ يَعْنِي الْفَقِيرَ ـ لِحَاجَةٍ فَيَقُولُوا ارْجِعْ إِلَيْنَا غَدًا‏.‏ فَيُبَيِّتُهُمُ اللَّهُ وَيَضَعُ الْعَلَمَ، وَيَمْسَخُ آخَرِينَ قِرَدَةً وَخَنَازِيرَ إِلَى يَوْمِ الْقِيَامَةِ ‏"‏‏.‏ that he heard the Prophet (ﷺ) saying, "From among my followers there will be some people who will consider illegal sexual intercourse, the wearing of silk, the drinking of alcoholic drinks and the use of musical instruments, as lawful. And there will be some people who will stay near the side of a mountain and in the evening their shepherd will come to them with their sheep and ask them for something, but they will say to him, 'Return to us tomorrow.' Allah will destroy them during the night and will let the mountain fall on them, and He will transform the rest of them into monkeys and pigs and they will remain so till the Day of Resurrection."

A small mention that the hadith was also narrated from another source missing the Musical instrument part.

The prophet also mentions that the selling of singers in 2 hadiths, both are weak:

حَدَّثَنَا قُتَيْبَةُ، حَدَّثَنَا بَكْرُ بْنُ مُضَرَ، عَنْ عُبَيْدِ اللَّهِ بْنِ زَحْرٍ، عَنْ عَلِيِّ بْنِ يَزِيدَ، عَنِ الْقَاسِمِ بْنِ عَبْدِ الرَّحْمَنِ، وَهُوَ عَبْدُ الرَّحْمَنِ مَوْلَى عَبْدِ الرَّحْمَنِ عَنْ أَبِي أُمَامَةَ عَنْ رَسُولِ اللَّهِ صلى الله عليه وسلم قَالَ ‏"‏ لاَ تَبِيعُوا الْقَيْنَاتِ وَلاَ تَشْتَرُوهُنَّ وَلاَ تُعَلِّمُوهُنَّ وَلاَ خَيْرَ فِي تِجَارَةٍ فِيهِنَّ وَثَمَنُهُنَّ حَرَامٌ ‏"‏ ‏.‏ فِي مِثْلِ ذَلِكَ أُنْزِلَتْ عَلَيْهِ هَذِهِ الآيَةُ ‏:‏ ‏(‏ومِنَ النَّاسِ مَنْ يَشْتَرِي لَهْوَ الْحَدِيثِ لِيُضِلَّ عَنْ سَبِيلِ اللَّهِ ‏)‏ إِلَى آخِرِ الآيَةِ ‏.‏ قَالَ أَبُو عِيسَى هَذَا حَدِيثٌ غَرِيبٌ إِنَّمَا يُرْوَى مِنْ حَدِيثِ الْقَاسِمِ عَنْ أَبِي أُمَامَةَ ‏.‏ وَالْقَاسِمُ ثِقَةٌ وَعَلِيُّ بْنُ يَزِيدَ يُضَعَّفُ فِي الْحَدِيثِ قَالَ سَمِعْتُ مُحَمَّدَ بْنَ إِسْمَاعِيلَ يَقُولُ الْقَاسِمُ ثِقَةٌ وَعَلِيُّ بْنُ يَزِيدَ يُضَعَّفُ ‏.‏ Narrated Abu Umamah: that the Messenger of Allah (ﷺ) said: "Do not sell the female singers, nor purchase them, nor teach them (to sing). And there is no good in trade in them, and their prices are unlawful. It was about the likes of this that this Ayah was revealed: 'And among mankind is he who purchases idle talk to divert from the way of Allah (31:6).'"

Another Munkar hadith, that was made Sahih by Alabani:

حَدَّثَنَا أَحْمَدُ بْنُ عُبَيْدِ اللَّهِ الْغُدَانِيُّ، حَدَّثَنَا الْوَلِيدُ بْنُ مُسْلِمٍ، حَدَّثَنَا سَعِيدُ بْنُ عَبْدِ الْعَزِيزِ، عَنْ سُلَيْمَانَ بْنِ مُوسَى، عَنْ نَافِعٍ، قَالَ سَمِعَ ابْنُ عُمَرَ، مِزْمَارًا - قَالَ - فَوَضَعَ أُصْبُعَيْهِ عَلَى أُذُنَيْهِ وَنَأَى عَنِ الطَّرِيقِ وَقَالَ لِي يَا نَافِعُ هَلْ تَسْمَعُ شَيْئًا قَالَ فَقُلْتُ لاَ ‏.‏ قَالَ فَرَفَعَ أُصْبُعَيْهِ مِنْ أُذُنَيْهِ وَقَالَ كُنْتُ مَعَ النَّبِيِّ صلى الله عليه وسلم فَسَمِعَ مِثْلَ هَذَا فَصَنَعَ مِثْلَ هَذَا ‏.‏ قَالَ أَبُو عَلِيٍّ اللُّؤْلُؤِيُّ سَمِعْتُ أَبَا دَاوُدَ يَقُولُ هَذَا حَدِيثٌ مُنْكَرٌ ‏.‏ Nafi' said: Ibn Umar heard a pipe, put his fingers in his ears and went away from the road. He said to me: Are you hearing anything? I said: No. He said: He then took his fingers out of his ears and said: I was with the Prophet (ﷺ), and he heard like this and he did like this. AbuAli al-Lu'lu said: I heard AbuDawud say: This is a rejected hadith.

Music is Halal

From the Quran

Unfortunately, there is no proof from the explicitly allows Music. However, those are claim it is Halal do not go to extreme interruption of amusement of speech and your voice that was claimed above. If that was meant as Music, the Prophet PBUH would have made it crisp clear and not for his companions to interrupt it.

From the Sunnah

It was mentioned in several hadiths that:

حَدَّثَنِي مُحَمَّدُ بْنُ الْمُثَنَّى، حَدَّثَنَا غُنْدَرٌ، حَدَّثَنَا شُعْبَةُ، عَنْ هِشَامٍ، عَنْ أَبِيهِ، عَنْ عَائِشَةَ، أَنَّ أَبَا بَكْرٍ، دَخَلَ عَلَيْهَا وَالنَّبِيُّ صلى الله عليه وسلم عِنْدَهَا يَوْمَ فِطْرٍ أَوْ أَضْحًى، وَعِنْدَهَا قَيْنَتَانِ ‏{‏تُغَنِّيَانِ‏}‏ بِمَا تَقَاذَفَتِ الأَنْصَارُ يَوْمَ بُعَاثَ‏.‏ فَقَالَ أَبُو بَكْرٍ مِزْمَارُ الشَّيْطَانِ مَرَّتَيْنِ‏.‏ فَقَالَ النَّبِيُّ صلى الله عليه وسلم ‏ "‏ دَعْهُمَا يَا أَبَا بَكْرٍ، إِنَّ لِكُلِّ قَوْمٍ عِيدًا، وَإِنَّ عِيدَنَا هَذَا الْيَوْمُ ‏"‏‏.‏ That once Abu Bakr came to her on the day of Id-ul-Fitr or Id ul Adha while the Prophet (ﷺ) was with her and there were two girl singers with her, singing songs of the Ansar about the day of Buath. Abu Bakr said twice. "Musical instrument of Satan!" But the Prophet (ﷺ) said, "Leave them Abu Bakr, for every nation has an Id (i.e. festival) and this day is our Id."

As you can clearly see the prophet PBUH allowed Musical instruments, if that haram he wouldn't allow it at times.

In another set of hadiths, the prophet says:

حَدَّثَنَا عَبْدُ الْعَزِيزِ بْنُ عَبْدِ اللَّهِ، قَالَ حَدَّثَنَا إِبْرَاهِيمُ بْنُ سَعْدٍ، عَنْ صَالِحٍ، عَنِ ابْنِ شِهَابٍ، قَالَ أَخْبَرَنِي عُرْوَةُ بْنُ الزُّبَيْرِ، أَنَّ عَائِشَةَ، قَالَتْ لَقَدْ رَأَيْتُ رَسُولَ اللَّهِ صلى الله عليه وسلم يَوْمًا عَلَى باب حُجْرَتِي، وَالْحَبَشَةُ يَلْعَبُونَ فِي الْمَسْجِدِ وَرَسُولُ اللَّهِ صلى الله عليه وسلم يَسْتُرُنِي بِرِدَائِهِ، أَنْظُرُ إِلَى لَعِبِهِمْ‏.‏ زَادَ إِبْرَاهِيمُ بْنُ الْمُنْذِرِ حَدَّثَنَا ابْنُ وَهْبٍ، أَخْبَرَنِي يُونُسُ، عَنِ ابْنِ شِهَابٍ، عَنْ عُرْوَةَ، عَنْ عَائِشَةَ، قَالَتْ رَأَيْتُ النَّبِيَّ صلى الله عليه وسلم وَالْحَبَشَةُ يَلْعَبُونَ بِحِرَابِهِمْ‏.‏ Once I saw Allah's Messenger (ﷺ) at the door of my house while some Ethiopians were playing in the mosque (displaying their skill with spears). Allah's Messenger (ﷺ) was screening me with his Rida' so as to enable me to see their display. ( Urwa said that Aisha said, "I saw the Prophet (ﷺ) and the Ethiopians were playing with their spears.")

Anyone who have watched ancient Ethopian dance songs, like most African dances, knows that it not included Musical instrument, but barely clothed warriors dancing with spears.

Music is Halal in accordance to Denatology

This opinion, many would not like, but basically it is an overall modernization of Islamic logic of where it says that Allah claims in the Quran that it is complete, with all the rules and regulations:

This day those who disbelieve have despaired of [defeating] your religion; so fear them not, but fear Me. This day I have perfected for you your religion and completed My favor upon you and have approved for you Islam as religion. But whoever is forced by severe hunger with no inclination to sin - then indeed, Allah is Forgiving and Merciful. [5:3]

Many claim that the Hadith is the same level as the word of God citing, which is incorrect. The Quran was meant as a complete Halal/Haram template. The Sunnah was meant to explain and interrupt the Quran and no more. The prophet PBUH will never make something Haram from a whim of his own, and if it was a revelation it would be in the Quran, as that is what the Quran is, a revelation of Allah's orders.

On such basis, the Music is not Haram since Allah did not forbid it explicitly in the Quran.

My final opinion on the matter

Music itself is not Haram. However, the wording of the Music - which is not what the question asks can make it Haram or Halal. The same way as Knife is Halal but it's usage can make it Halal or Haram.