The third verse of "Hallelujah" by Leonard Cohen goes like this:
You say I took the name in vain I don't even know the name
But if I did well really what's it to you
There's a blaze of light in every word
It doesn't matter which you heard
The holy or the broken Hallelujah
What is meant by the 'holy' and 'broken' Hallelujahs? Is this a reference to something?
In one of the version of the songs, there is this part:
And remember when I moved in you
the holy dove was moving too
And every breath we drew was Hallelujah
So the singer was praising the Lord with every breath. Now if you look at the lyrics of the part in OP, you'll notice that the singer is being chided for "taking the name in vain".
You say I took the Name in vain
I don't even know the Name
This is of course against the commandment "Thou shalt not take the name of the Lord thy God in vain". So in another words, the singer apparently called God while not addressing him in prayer - judging by the rest of the song it was something akin to "Oh God, she is so beautiful!".
You saw her bathing on the roof
Her beauty and the moonlight overthrew you [...]
And from your lips she drew the hallelujah
This was of course a blasphemy, but then the singer argues:
It doesn't matter which you heard
The holy or the broken Hallelujah
Similarly, you can take another part of the song :
Maybe there's a God above
All I've ever learned from love
Was how to shoot somebody who outdrew you
And it's not a cry that you hear at night
It's not somebody who's seen the light
It's a cold and it's a broken Hallelujah
Or in different version
It's no complaint you hear tonight
It's not some pilgrim who's seen the light
it's a cold and it's a lonely(/broken )Hallelujah
Someone (who lost the loved one) is not wordlessly crying or praying (seeing the light) at night - they instead keep sobbing and calling God (as in "Oh God, Oh God, why?" ), in such a "broken", blasphemous hallelujah.
Addressing your question from a somewhat literal perspective, the "holy" Hallelujah is likely that of the first verse, "The baffled king composing hallelujah" where as the "broken" Hallelujah is that that the female of the song (Bathsheba based on the bathing reference) drew from him, "She broke your throne, and she cut your hair / And from your lips she drew the hallelujah". My reasoning is essentially that the first versus associates the Hallelujah with God, which fits the definition of "holy" whereas the second is paired up with imagery of broken thrones and cut hair.
Now, I've heard there was a secret chord
That David played, and it pleased the Lord
But you don't really care for music, do you?
It goes like this, the fourth, the fifth
The minor fall, the major lift
The baffled king composing hallelujah‹chorus›
Your faith was strong but you needed proof
You saw her bathing on the roof
Her beauty and the moonlight overthrew ya
She tied you to a kitchen chair
She broke your throne, and she cut your hair
And from your lips she drew the hallelujah
From that context, the third verse seems like it would be contrasting the sacred and the profane joys in life.
You say I took the name in vain
I don't even know the name
But if I did, well really, what's it to you?
There's a blaze of light in every word
It doesn't matter which you heard
The holy or the broken hallelujah
That said, I've yet to find a statement by Leonard Cohen on the subject, only what others have stated. Complicating matters, Leonard Cohen initially wrote 80 different verses according to Wikipedia, and changed them for different performances, only keeping the final verse the same.
I did my best, it wasn't much
I couldn't feel, so I tried to touch
I've told the truth, I didn't come to fool you
And even though it all went wrong
I'll stand before the lord of song
With nothing on my tongue but hallelujah
My understanding of this has always been that the "holy" Halleluy-ah is the Jewish (Old Testament/Old Covenant) one and the "broken" Halleluy-ah is the Christian one. Leonard Cohen had a lot of trouble figuring out which of these was truer to him, and changed his mind on the matter multiple times throughout his life. It seems that the various women in his orbit, including the one to whom this song is addressed, did not exactly make things clearer--but that at the point when he wrote this song, it seems he thought there was some "light" in both.
Sources:
These are less biographical than I'd like, but here are some sources which treat Leonard Cohen's religious dilemma (including the majority of articles on Leonard Cohen in The New Yorker):
This and this and this and this and this and this and this.
My position, and apparently The New Yorker's, is that one has first to understand Leonard Cohen as a seriously religious man. Religion is his Berlinian hedgehog and his bête grise; it is his obsession. Most of all (for us), it is his paintbox, and to understand his songs correctly, you have to understand that they are made of religion and of Scripture. There are some exceptions - "Seems So Long Ago, Nancy," which I think is the saddest song I've ever heard, is apparently one - but, in general, religiously was how Leonard Cohen wrote -- as it was how Nikolai Gogol wrote and how Fra Angelico painted and how many, many artists now and before have done their work.
Leonard Cohen has admitted as much. But you don't need to read biographies nor interviews to pick this up. You just have to read the holy sources, then read his work.
'Hallelujah' means 'praise the lord'. I always assumed that the "Holy and The Broken hallelujah" referred to the praise offered up to Yahweh, the Holy/Whole, in the synagogues and churches and mosques, and the profanities we scream invoking the divine while rapt in the throes of sexual ecstasy or in moments of extreme distress/physical pain (eg- "God yes!!! yes!", "Jesus f*cking Christ!" etc.)
"And from your lips she drew the hallelujah" .. I think he might have been thinking of something a little stronger than "oh god, she is so beautiful" as a previous contributor suggested - but that's along the right lines ;)
Cohen's vision of the divine is immanent, ie- all-pervading, present everywhere. One eternal G-d knowable only through his Many manifestations. Thus sexual union for him is always a sacrament, a form of communion with G-d, which is why his songs slip so effortlessly between the mystical and the intimate, the microcosm and the macrocosm.
