Chris:
...
> \score {
>  \new Voice {  \set Staff.midiInstrument = #"trumpet"
>      \relative c'''{
>        \tempo 2 = 100
>    \relative e'' { e4 \tuplet 5/4 { e16 f fis g gis }  }
>       }
>   } \layout{}  \midi{}  }

Compiling this with 2.19.16 and inspecting with
http://aspodata.se/git/musik/bin/midi.pl I get

$ midi.pl a.midi 
MIDI::Opus->new({
  'format' => 1,
  'ticks'  => 384,
  'tracks' => [   # 2 tracks...

    # Track #0 ...
    MIDI::Track->new({
      'type' => 'MTrk',
      'events' => [  # 6 events.
        ['track_name', 0, 'control track'],
        ['text_event', 0, 'creator: '],
        ['text_event', 0, 'GNU LilyPond 2.19.16          '],
        ['time_signature', 0, 4, 2, 18, 8],
        ['set_tempo', 0, 300000],
        ['end_track', 0],
      ]
    }),
    
    # Track #1 ...
    MIDI::Track->new({
      'type' => 'MTrk',
      'events' => [  # 18 events.
        ['track_name', 0, "\x5cnew:"],
        ['patch_change', 0, 0, 56],
        ['patch_change', 0, 0, 56],
        ['instrument_name', 0, 'trumpet'],
        ['control_change', 0, 0, 7, 100],
        ['note_on', 0, 0, 76, 75],
        ['note_on', 384, 0, 76, 0],
        ['note_on', 0, 0, 76, 75],
        ['note_on', 76, 0, 76, 0],
        ['note_on', 0, 0, 77, 75],
        ['note_on', 76, 0, 77, 0],
        ['note_on', 1, 0, 78, 75],
        ['note_on', 76, 0, 78, 0],
        ['note_on', 1, 0, 79, 75],
        ['note_on', 76, 0, 79, 0],
        ['note_on', 1, 0, 80, 75],
        ['note_on', 76, 0, 80, 0],
        ['end_track', 0],
      ]
    }),
    
  ]
});

(the presented format is ['note_on', dtime, channel, note, velocity])
which is mostly correct, the quintuplet doesn't add upp to a quarter 
note, a 1/384 is missing. Better would be to have ticks = 5*76 = 380.

Regards,
/Karl Hammar

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Lilla Aspö 148
S-742 94 Östhammar
Sweden
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