- In MIDI note off event velocity can be specified as well, why?
- Always when a Note On event's velocity is zero, it basically represents a Note Off event? and vice versa, always when there is a NoteOff event it represents Note Off regardless of its velocity?
- I noticed in some MIDI files, instead of using Note Off events, there is another Note On with velocity set to zero for the corresponding Note On, why not just use simple Note Off events?

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5 Answers
In MIDI note off event velocity can be specified as well, why?
I'm not sure of the intention behind its origins but the classic use-case for note off velocity is a harpsichord — the hammer falls differently depending on the speed of the release and changes the sound. Some sample libraries (usually 'complete'ish ones for specific instruments like piano or violin) include separate "key off" samples. Release velocity can be used to vary the level and length of those samples.
For general synthesis, key off velocity is often patched to an envelope's release time. Release quickly and get staccato notes. Release more slowly and the sound will ring out a bit. Of course, you could map it to any modulation destination your synthesizer supports. Increase the ring modulation on the tails? Why not.

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- see wwwar's answer - it's for after-touch
- yes, NoteOn with zero velocity is essentially NoteOff
- this is simply because that is what a lot of MIDI keyboards send out. You can do either according to the MIDI spec. The advantage of using note on with zero velocity is that it can be sent more efficiently if you use MIDI running status

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Could you please elaborate a bit more about no. 1? what is after-touch for note-off? – Shimmy Weitzhandler Jul 25 '10 at 14:16
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A feature brought in the late 1980s, whereby dynamics are added after the key is hit, allowing the sound to be modulated in some way (such as fade away or return), based upon the amount of pressure applied to the keyboard. From http://en.wikipedia.org/wiki/Electronic_keyboard – Khurram Aziz Oct 18 '10 at 19:44
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2"It's for after-touch" is a bit misleading, because [after-touch](http://home.roadrunner.com/~jgglatt/tech/midispec/aftert.htm) is a separate MIDI message from [note-off](http://home.roadrunner.com/~jgglatt/tech/midispec/noteoff.htm). – Craig McQueen Jun 02 '14 at 02:43
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@CraigMcQueen yes, I think you're right - it's not really after-touch. But I think some soft-synths can use it to affect release time. Ultimately, it's not really a particularly useful part of the MIDI spec. – Mark Heath Jun 02 '14 at 10:14
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1On my Yamaha Clavinova piano, it affects the decay time of the note release. E.g. slow lifting of the key results in slower decay. Somewhat useful I guess. – Craig McQueen Jun 03 '14 at 07:47
Note off velocity has ABSOLUTELY NOTHING to do with aftertouch!
Just like you can use (Attack/Note on) Velocity MIDI value to affect any parameter in your synth, you can use Release/Note off velocity value to affect any parameter in your synth.
Typical use would be for instance that depending how fast you let go of a key, it changes (modulates) the speed of the amp envelope release: let go of a key fast and the sound of the corresponding note fades out quickly; let go of the key slower and the corresponding note takes accordingly more time to fade out.

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Note Off with velocity makes sense for after-touch capable synths.

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2A paragraph on what after-touch is (and perhaps a link to more material) would be an excellent addition to this answer. – olafure Nov 09 '16 at 22:40
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downvote because: 1) it does not answer any of the questions 2) if gives a personal opinion which is quite questionable: note off velocity has nothing to do with aftertouch-capable synths. – oromoiluig Dec 01 '20 at 19:04
yeah... there is also an after touch message in the statusbyte list of a channel voice message as well, after touch is no logical explanation for the velocity data byte in a note off message.

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There's one global expression of aftertouch and then also there's per-note aftertouch which is rarely implemented. And as for velocity of note-off, there are all the dynamics of an instruments which only begin after the "touch" as in how rapidly the action of "stopping" a note can affect the decay. This doesn't apply at all to piano but consider any fretted instrument and variations on natural decay, holding the fret, vs other ways you can "stop" the note. – snakeoil Aug 04 '17 at 00:32