text: #-----------------------------------------------------------------------------
  # Name:        MidiFile.py
  # Purpose:     MIDI file manipulation utilities
  #
  # Author:      Mark Conway Wirt <emergentmusics) at (gmail . com>
  #
  # Created:     2008/04/17
  # Copyright:   (c) 2009 Mark Conway Wirt
  # License:     Please see License.txt for the terms under which this
  #              software is distributed.
  #-----------------------------------------------------------------------------
  
  import struct,  sys,  math
  
  # TICKSPERBEAT is the number of "ticks" (time measurement in the MIDI file) that
  # corresponds to one beat. This number is somewhat arbitrary, but should be chosen
  # to provide adequate temporal resolution.
  
  TICKSPERBEAT_CONFIG = 960
  TICKSPERBEAT = 1
  
  controllerEventTypes = {
                          'pan' : 0x0a
                          }
  class MIDIEvent:
      '''
      The class to contain the MIDI Event (placed on MIDIEventList.
      '''
      def __init__(self):
          self.type='unknown'
          self.time=0
          self.ord = 0
     
      def __cmp__(self, other):
          ''' Sorting function for events.'''
          if self.time < other.time:
              return -1
          elif self.time > other.time:
              return 1
          else:
              if self.ord < other.ord:
                  return -1
              elif self.ord > other.ord:
                  return 1
              else:
                  return 0
  
  class GenericEvent():
      '''The event class from which specific events are derived
      '''
      def __init__(self,time):
          self.time = time
          self.type = 'Unknown'
  
  
     
      def __eq__(self, other):
          '''
          Equality operator for Generic Events and derived classes.
     
          In the processing of the event list, we have need to remove duplicates. To do this
          we rely on the fact that the classes are hashable, and must therefore have an
          equality operator (__hash__() and __eq__() must both be defined).
     
          This is the most embarrassing portion of the code, and anyone who knows about OO
          programming would find this almost unbelievable. Here we have a base class that
          knows specifics about derived classes, thus breaking the very spirit of
          OO programming.
     
          I suppose I should go back and restructure the code, perhaps removing the derived
          classes altogether. At some point perhaps I will.
          '''
          if self.time != other.time or self.type != other.type:
              return False
         
          # What follows is code that encodes the concept of equality for each derived
          # class. Believe it f you dare.
     
          if self.type == 'note':
              if self.pitch != other.pitch or self.channel != other.channel:
                  return False
          if self.type == 'tempo':
              if self.tempo != other.tempo:
                  return False
          if self.type == 'programChange':
              if self.programNumber != other.programNumber or self.channel != other.channel:
                  return False
          if self.type == 'trackName':
              if self.trackName != other.trackName:
                  return False
          if self.type == 'controllerEvent':
              if self.parameter1 != other.parameter1 or \
                  self.channel != other.channel or \
                  self.eventType != other.eventType:
                  return False
             
          if self.type == 'SysEx':
              if self.manID != other.manID:
                  return False
             
          if self.type == 'UniversalSysEx':
              if self.code != other.code or\
                  self.subcode != other.subcode or \
                  self.sysExChannel != other.sysExChannel:
                  return False
             
          return True
     
      def __hash__(self):
          '''
          Return a hash code for the object.
     
          This is needed for the removal of duplicate objects from the event list. The only
          real requirement for the algorithm is that the hash of equal objects must be equal.
          There is probably great opportunity for improvements in the hashing function.
          '''
          # Robert Jenkin's 32 bit hash.
          a = int(self.time)
          a = (a+0x7ed55d16) + (a<<12)
          a = (a^0xc761c23c) ^ (a>>19)
          a = (a+0x165667b1) + (a<<5)
          a = (a+0xd3a2646c) ^ (a<<9)
          a = (a+0xfd7046c5) + (a<<3)
          a = (a^0xb55a4f09) ^ (a>>16)
          return a
  
  class MIDITrack:
      '''A class that encapsulates a MIDI track
      '''
      # Nested class definitions.
  
      class note(GenericEvent):
          '''A class that encapsulates a note
          '''
          def __init__(self,channel, pitch,time,duration,volume):
         
              GenericEvent.__init__(self,time)
              self.pitch = pitch
              self.duration = duration
              self.volume = volume
              self.type = 'note'
              self.channel = channel
         
          def compare(self, other):
              '''Compare two notes for equality.
              '''
              if self.pitch == other.pitch and \
                  self.time == other.time and \
                  self.duration == other.duration and \
                  self.volume == other.volume and \
                  self.type == other.type and \
                  self.channel == other.channel:
                      return True
              else:
                      return False
                 
         
      class tempo(GenericEvent):
          '''A class that encapsulates a tempo meta-event
          '''
          def __init__(self,time,tempo):
         
              GenericEvent.__init__(self,time)
              self.type = 'tempo'
              self.tempo = int(60000000 / tempo)
         
      class programChange(GenericEvent):
          '''A class that encapsulates a program change event.
          '''
     
          def __init__(self,  channel,  time,  programNumber):
              GenericEvent.__init__(self, time,)
              self.type = 'programChange'
              self.programNumber = programNumber
              self.channel = channel
         
      class SysExEvent(GenericEvent):
          '''A class that encapsulates a System Exclusive  event.
          '''
     
          def __init__(self,  time,  manID,  payload):
              GenericEvent.__init__(self, time,)
              self.type = 'SysEx'
              self.manID = manID
              self.payload = payload
         
      class UniversalSysExEvent(GenericEvent):
          '''A class that encapsulates a Universal System Exclusive  event.
          '''
     
          def __init__(self,  time,  realTime,  sysExChannel,  code,  subcode,  payload):
              GenericEvent.__init__(self, time,)
              self.type = 'UniversalSysEx'
              self.realTime = realTime
              self.sysExChannel = sysExChannel
              self.code = code
              self.subcode = subcode
              self.payload = payload
         
      class ControllerEvent(GenericEvent):
          '''A class that encapsulates a program change event.
          '''
     
          def __init__(self,  channel,  time,  eventType,  parameter1,):
              GenericEvent.__init__(self, time,)
              self.type = 'controllerEvent'
              self.parameter1 = parameter1
              self.channel = channel
              self.eventType = eventType
  
      class trackName(GenericEvent):
          '''A class that encapsulates a program change event.
          '''
     
          def __init__(self,  time,  trackName):
              GenericEvent.__init__(self, time,)
              self.type = 'trackName'
              self.trackName = trackName
  
         
      def __init__(self, removeDuplicates,  deinterleave):
          '''Initialize the MIDITrack object.
          '''
          self.headerString = struct.pack('cccc','M','T','r','k')
          self.dataLength = 0 # Is calculated after the data is in place
          self.MIDIdata = ""
          self.closed = False
          self.eventList = []
          self.MIDIEventList = []
          self.remdep = removeDuplicates
          self.deinterleave = deinterleave
     
      def addNoteByNumber(self,channel, pitch,time,duration,volume):
          '''Add a note by chromatic MIDI number
          '''
          self.eventList.append(MIDITrack.note(channel, pitch,time,duration,volume))
     
      def addControllerEvent(self,channel,time,eventType, paramerter1):
          '''
          Add a controller event.
          '''
     
          self.eventList.append(MIDITrack.ControllerEvent(channel,time,eventType, \
                                               paramerter1))
     
      def addTempo(self,time,tempo):
          '''
          Add a tempo change (or set) event.
          '''
          self.eventList.append(MIDITrack.tempo(time,tempo))
     
      def addSysEx(self,time,manID, payload):
          '''
          Add a SysEx event.
          '''
          self.eventList.append(MIDITrack.SysExEvent(time, manID,  payload))
     
      def addUniversalSysEx(self,time,code, subcode, payload,  sysExChannel=0x7F,  \
          realTime=False):
          '''
          Add a Universal SysEx event.
          '''
          self.eventList.append(MIDITrack.UniversalSysExEvent(time, realTime,  \
              sysExChannel,  code,  subcode, payload))
     
      def addProgramChange(self,channel, time, program):
          '''
          Add a program change event.
          '''
          self.eventList.append(MIDITrack.programChange(channel, time, program))
     
      def addTrackName(self,time,trackName):
          '''
          Add a track name event.
          '''
          self.eventList.append(MIDITrack.trackName(time,trackName))
     
      def changeNoteTuning(self,  tunings,   sysExChannel=0x7F,  realTime=False,  \
          tuningProgam=0):
          '''Change the tuning of MIDI notes
          '''
          payload = struct.pack('>B',  tuningProgam)
          payload = payload + struct.pack('>B',  len(tunings))
          for (noteNumber,  frequency) in tunings:
              payload = payload + struct.pack('>B',  noteNumber)
              MIDIFreqency = frequencyTransform(frequency)
              for byte in MIDIFreqency:
                  payload = payload + struct.pack('>B',  byte)
             
          self.eventList.append(MIDITrack.UniversalSysExEvent(0, realTime,  sysExChannel,\
              8,  2, payload))
  
      def processEventList(self):
          '''
          Process the event list, creating a MIDIEventList
     
          For each item in the event list, one or more events in the MIDIEvent
          list are created.
          '''
     
          # Loop over all items in the eventList
     
          for thing in self.eventList:
              if thing.type == 'note':
                  event = MIDIEvent()
                  event.type = "NoteOn"
                  event.time = thing.time * TICKSPERBEAT
                  event.pitch = thing.pitch
                  event.volume = thing.volume
                  event.channel = thing.channel
                  event.ord = 3
                  self.MIDIEventList.append(event)
  
                  event = MIDIEvent()
                  event.type = "NoteOff"
                  event.time = (thing.time + thing.duration) * TICKSPERBEAT
                  event.pitch = thing.pitch
                  event.volume = thing.volume
                  event.channel = thing.channel
                  event.ord = 2
                  self.MIDIEventList.append(event)
  
              elif thing.type == 'tempo':
                  event = MIDIEvent()
                  event.type = "Tempo"
                  event.time = thing.time * TICKSPERBEAT
                  event.tempo = thing.tempo
                  event.ord = 3
                  self.MIDIEventList.append(event)
  
              elif thing.type == 'programChange':
                  event = MIDIEvent()
                  event.type = "ProgramChange"
                  event.time = thing.time * TICKSPERBEAT
                  event.programNumber = thing.programNumber
                  event.channel = thing.channel
                  event.ord = 1
                  self.MIDIEventList.append(event)
  
              elif thing.type == 'trackName':
                  event = MIDIEvent()
                  event.type = "TrackName"
                  event.time = thing.time * TICKSPERBEAT
                  event.trackName = thing.trackName
                  event.ord = 0
                  self.MIDIEventList.append(event)
  
              elif thing.type == 'controllerEvent':
                  event = MIDIEvent()
                  event.type = "ControllerEvent"
                  event.time = thing.time * TICKSPERBEAT
                  event.eventType = thing.eventType
                  event.channel = thing.channel
                  event.paramerter1 = thing.parameter1
                  event.ord = 1
                  self.MIDIEventList.append(event)
  
              elif thing.type == 'SysEx':
                  event = MIDIEvent()
                  event.type = "SysEx"
                  event.time = thing.time * TICKSPERBEAT
                  event.manID = thing.manID
                  event.payload = thing.payload
                  event.ord = 1
                  self.MIDIEventList.append(event)
  
              elif thing.type == 'UniversalSysEx':
                  event = MIDIEvent()
                  event.type = "UniversalSysEx"
                  event.realTime = thing.realTime
                  event.sysExChannel = thing.sysExChannel
                  event.time = thing.time * TICKSPERBEAT
                  event.code = thing.code
                  event.subcode = thing.subcode
                  event.payload = thing.payload
                  event.ord = 1
                  self.MIDIEventList.append(event)
  
              else:
                  print "Error in MIDITrack: Unknown event type"
                  sys.exit(2)
         
          # Assumptions in the code expect the list to be time-sorted.
          # self.MIDIEventList.sort(lambda x, y: x.time - y.time)
  
          self.MIDIEventList.sort(lambda x, y: int( 1000 * (x.time - y.time)))
  
          if self.deinterleave:
              self.deInterleaveNotes()
  
      def removeDuplicates(self):
          '''
          Remove duplicates from the eventList.
     
          This function will remove duplicates from the eventList. This is necessary
          because we the MIDI event stream can become confused otherwise.
          '''
     
          # For this algorithm to work, the events in the eventList must be hashable
          # (that is, they must have a __hash__() and __eq__() function defined).
     
          tempDict = {}
          for item in self.eventList:
              tempDict[item] = 1
         
          self.eventList = tempDict.keys()
     
          # Sort on type, them on time. Necessary because keys() has no requirement to return
          # things in any order.
     
          self.eventList.sort(lambda x, y: cmp(x.type ,  y.type))
          self.eventList.sort(lambda x, y: int( 1000 * (x.time - y.time))) #A bit of a hack.
  
      def closeTrack(self):
          '''Called to close a track before writing
     
          This function should be called to "close a track," that is to
          prepare the actual data stream for writing. Duplicate events are
          removed from the eventList, and the MIDIEventList is created.
     
          Called by the parent MIDIFile object.
          '''
  
          if self.closed == True:
              return
          self.closed = True
     
          if self.remdep:
              self.removeDuplicates()
         
  
          self.processEventList()
     
      def writeMIDIStream(self):
          '''
          Write the meta data and note data to the packed MIDI stream.
          '''
  
          #Process the events in the eventList
  
          self.writeEventsToStream()
  
          # Write MIDI close event.
  
          self.MIDIdata = self.MIDIdata + struct.pack('BBBB',0x00,0xFF, \
              0x2F,0x00)
     
          # Calculate the entire length of the data and write to the header
     
          self.dataLength = struct.pack('>L',len(self.MIDIdata))
  
      def writeEventsToStream(self):
          '''
          Write the events in MIDIEvents to the MIDI stream.
          '''
          preciseTime = 0.0                   # Actual time of event, ignoring round-off
          actualTime = 0.0                    # Time as written to midi stream, include round-off
          for event in self.MIDIEventList:
  
              preciseTime = preciseTime + event.time
  
              # Convert the time to variable length and back, to see how much
              # error is introduced
  
              testBuffer = ""
              varTime = writeVarLength(event.time)
              for timeByte in varTime:
                  testBuffer = testBuffer + struct.pack('>B',timeByte)
              (roundedVal,discard) = readVarLength(0,testBuffer)
              roundedTime = actualTime + roundedVal
              # print "Rounded, Precise: %15.10f %15.10f" % (roundedTime, preciseTime)
  
              # Calculate the delta between the two and apply it to the event time.
  
              delta = preciseTime - roundedTime
              event.time = event.time + delta
  
              # Now update the actualTime value, using the updated event time.
  
              testBuffer = ""
              varTime = writeVarLength(event.time)
              for timeByte in varTime:
                  testBuffer = testBuffer + struct.pack('>B',timeByte)
              (roundedVal,discard) = readVarLength(0,testBuffer)
              actualTime = actualTime + roundedVal
     
          for event in self.MIDIEventList:
              if event.type == "NoteOn":
                  code = 0x9 << 4 | event.channel
                  varTime = writeVarLength(event.time)
                  for timeByte in varTime:
                      self.MIDIdata = self.MIDIdata + struct.pack('>B',timeByte)
                  self.MIDIdata = self.MIDIdata + struct.pack('>B',code)
                  self.MIDIdata = self.MIDIdata + struct.pack('>B',event.pitch)
                  self.MIDIdata = self.MIDIdata + struct.pack('>B',event.volume)
              elif event.type == "NoteOff":
                  code = 0x8 << 4 | event.channel
                  varTime = writeVarLength(event.time)
                  for timeByte in varTime:
                      self.MIDIdata = self.MIDIdata + struct.pack('>B',timeByte)
                  self.MIDIdata = self.MIDIdata + struct.pack('>B',code)
                  self.MIDIdata = self.MIDIdata + struct.pack('>B',event.pitch)
                  self.MIDIdata = self.MIDIdata + struct.pack('>B',event.volume)
              elif event.type == "Tempo":
                  code = 0xFF
                  subcode = 0x51
                  fourbite = struct.pack('>L', event.tempo)
                  threebite = fourbite[1:4]       # Just discard the MSB
                  varTime = writeVarLength(event.time)
                  for timeByte in varTime:
                      self.MIDIdata = self.MIDIdata + struct.pack('>B',timeByte)
                  self.MIDIdata = self.MIDIdata + struct.pack('>B',code)
                  self.MIDIdata = self.MIDIdata + struct.pack('>B',subcode)
                  self.MIDIdata = self.MIDIdata + struct.pack('>B', 0x03) # Data length: 3
                  self.MIDIdata = self.MIDIdata + threebite
              elif event.type == 'ProgramChange':
                  code = 0xC << 4 | event.channel
                  varTime = writeVarLength(event.time)
                  for timeByte in varTime:
                      self.MIDIdata = self.MIDIdata + struct.pack('>B',timeByte)
                  self.MIDIdata = self.MIDIdata + struct.pack('>B',code)
                  self.MIDIdata = self.MIDIdata + struct.pack('>B',event.programNumber)
              elif event.type == 'TrackName':
                  varTime = writeVarLength(event.time)
                  for timeByte in varTime:
                      self.MIDIdata = self.MIDIdata + struct.pack('>B',timeByte)
                  self.MIDIdata = self.MIDIdata + struct.pack('B',0xFF) # Meta-event
                  self.MIDIdata = self.MIDIdata + struct.pack('B',0X03) # Event Type
                  dataLength = len(event.trackName)
                  dataLenghtVar = writeVarLength(dataLength)
                  for i in range(0,len(dataLenghtVar)):
                      self.MIDIdata = self.MIDIdata + struct.pack("b",dataLenghtVar[i])
                  self.MIDIdata = self.MIDIdata + event.trackName
              elif event.type == "ControllerEvent":
                  code = 0xB << 4 | event.channel
                  varTime = writeVarLength(event.time)
                  for timeByte in varTime:
                      self.MIDIdata = self.MIDIdata + struct.pack('>B',timeByte)
                  self.MIDIdata = self.MIDIdata + struct.pack('>B',code)
                  self.MIDIdata = self.MIDIdata + struct.pack('>B',event.eventType)
                  self.MIDIdata = self.MIDIdata + struct.pack('>B',event.paramerter1)
              elif event.type == "SysEx":
                  code = 0xF0
                  varTime = writeVarLength(event.time)
                  for timeByte in varTime:
                      self.MIDIdata = self.MIDIdata + struct.pack('>B',timeByte)
                  self.MIDIdata = self.MIDIdata + struct.pack('>B', code)
             
                  payloadLength = writeVarLength(len(event.payload)+2)
                  for lenByte in payloadLength:
                      self.MIDIdata = self.MIDIdata + struct.pack('>B',lenByte)
                 
                  self.MIDIdata = self.MIDIdata + struct.pack('>B', event.manID)
                  self.MIDIdata = self.MIDIdata + event.payload
                  self.MIDIdata = self.MIDIdata + struct.pack('>B',0xF7)
              elif event.type == "UniversalSysEx":
                  code = 0xF0
                  varTime = writeVarLength(event.time)
                  for timeByte in varTime:
                      self.MIDIdata = self.MIDIdata + struct.pack('>B',timeByte)
                  self.MIDIdata = self.MIDIdata + struct.pack('>B', code)
             
                  # Do we need to add a length?
                  payloadLength = writeVarLength(len(event.payload)+5)
                  for lenByte in payloadLength:
                      self.MIDIdata = self.MIDIdata + struct.pack('>B',lenByte)
             
                  if event.realTime :
                      self.MIDIdata = self.MIDIdata + struct.pack('>B', 0x7F)
                  else:
                      self.MIDIdata = self.MIDIdata + struct.pack('>B', 0x7E)
                 
                  self.MIDIdata = self.MIDIdata + struct.pack('>B', event.sysExChannel)
                  self.MIDIdata = self.MIDIdata + struct.pack('>B', event.code)
                  self.MIDIdata = self.MIDIdata + struct.pack('>B', event.subcode)
                  self.MIDIdata = self.MIDIdata + event.payload
                  self.MIDIdata = self.MIDIdata + struct.pack('>B',0xF7)
     
      def deInterleaveNotes(self):
          '''Correct Interleaved notes.
     
          Because we are writing multiple notes in no particular order, we
          can have notes which are interleaved with respect to their start
          and stop times. This method will correct that. It expects that the
          MIDIEventList has been time-ordered.
          '''
     
          tempEventList = []
          stack = {}
     
          for event in self.MIDIEventList:
         
              if event.type == 'NoteOn':
                  if stack.has_key(str(event.pitch)+str(event.channel)):
                      stack[str(event.pitch)+str(event.channel)].append(event.time)
                  else:
                      stack[str(event.pitch)+str(event.channel)] = [event.time]
                  tempEventList.append(event)
              elif event.type == 'NoteOff':
                  if len(stack[str(event.pitch)+str(event.channel)]) > 1:
                      event.time = stack[str(event.pitch)+str(event.channel)].pop()
                      tempEventList.append(event)
                  else:
                      stack[str(event.pitch)+str(event.channel)].pop()
                      tempEventList.append(event)
              else:
                  tempEventList.append(event)
                 
          self.MIDIEventList = tempEventList
     
          # A little trickery here. We want to make sure that NoteOff events appear
          # before NoteOn events, so we'll do two sorts -- on on type, one on time.
          # This may have to be revisited, as it makes assumptions about how
          # the internal sort works, and is in essence creating a sort on a primary
          # and secondary key.
     
          self.MIDIEventList.sort(lambda x, y: cmp(x.type ,  y.type))
          self.MIDIEventList.sort(lambda x, y: int( 1000 * (x.time - y.time)))
  
      def adjustTime(self,origin):
          '''
          Adjust Times to be relative, and zero-origined
          '''
     
          if len(self.MIDIEventList) == 0:
              return
          tempEventList = []
  
          runningTime = 0
     
          for event in self.MIDIEventList:
              adjustedTime = event.time - origin
              event.time = adjustedTime - runningTime
              runningTime = adjustedTime
              tempEventList.append(event)
         
          self.MIDIEventList = tempEventList
     
      def writeTrack(self,fileHandle):
          '''
          Write track to disk.
          '''
     
          if not self.closed:
              self.closeTrack()
         
          fileHandle.write(self.headerString)
          fileHandle.write(self.dataLength)
          fileHandle.write(self.MIDIdata)
  
  
  class MIDIHeader:
      '''
      Class to encapsulate the MIDI header structure.
  
      This class encapsulates a MIDI header structure. It isn't used for much,
      but it will create the appropriately packed identifier string that all
      MIDI files should contain. It is used by the MIDIFile class to create a
      complete and well formed MIDI pattern.
  
      '''
      def __init__(self,numTracks):
          ''' Initialize the data structures
          '''
          self.headerString = struct.pack('cccc','M','T','h','d')
          self.headerSize = struct.pack('>L',6)
          # Format 1 = multi-track file
          self.format = struct.pack('>H',1)
          self.numTracks = struct.pack('>H',numTracks)
          self.ticksPerBeat = struct.pack('>H',TICKSPERBEAT_CONFIG)
  
  
      def writeFile(self,fileHandle):
          fileHandle.write(self.headerString)
          fileHandle.write(self.headerSize)
          fileHandle.write(self.format)
          fileHandle.write(self.numTracks)
          fileHandle.write(self.ticksPerBeat)
  
  class MIDIFile:
      '''Class that represents a full, well-formed MIDI pattern.
  
      This is a container object that contains a header, one or more tracks,
      and the data associated with a proper and well-formed MIDI pattern.
  
      Calling:
  
          MyMIDI = MidiFile(tracks, removeDuplicates=True,  deinterleave=True)
     
          normally
     
          MyMIDI = MidiFile(tracks)
     
      Arguments:
  
          tracks: The number of tracks this object contains
         
          removeDuplicates: If true (the default), the software will remove duplicate
          events which have been added. For example, two notes at the same channel,
          time, pitch, and duration would be considered duplicate.
     
          deinterleave: If True (the default), overlapping notes (same pitch, same
          channel) will be modified so that they do not overlap. Otherwise the sequencing
          software will need to figure out how to interpret NoteOff events upon playback.
      '''
  
      def __init__(self, numTracks, removeDuplicates=True,  deinterleave=True):
          '''
          Initialize the class
          '''
          self.header = MIDIHeader(numTracks)
     
          self.tracks = list()
          self.numTracks = numTracks
          self.closed = False
     
          for i in range(0,numTracks):
              self.tracks.append(MIDITrack(removeDuplicates,  deinterleave))
         
         
      # Public Functions. These (for the most part) wrap the MIDITrack functions, where most
      # Processing takes place.
  
      def addNote(self,track, channel, pitch,time,duration,volume):
          """
          Add notes to the MIDIFile object
     
          Use:
              MyMIDI.addNotes(track,channel,pitch,time, duration, volume)
         
          Arguments:
              track: The track to which the note is added.
              channel: the MIDI channel to assign to the note. [Integer, 0-15]
              pitch: the MIDI pitch number [Integer, 0-127].
              time: the time (in beats) at which the note sounds [Float].
              duration: the duration of the note (in beats) [Float].
              volume: the volume (velocity) of the note. [Integer, 0-127].
          """
          self.tracks[track].addNoteByNumber(channel, pitch, time, duration, volume)
  
      def addTrackName(self,track, time,trackName):
          """
          Add a track name to a MIDI track.
     
          Use:
              MyMIDI.addTrackName(track,time,trackName)
         
          Argument:
              track: The track to which the name is added. [Integer, 0-127].
              time: The time at which the track name is added, in beats [Float].
              trackName: The track name. [String].
          """
          self.tracks[track].addTrackName(time,trackName)
     
      def addTempo(self,track, time,tempo):
          """
          Add a tempo event.
     
          Use:
              MyMIDI.addTempo(track, time, tempo)
         
          Arguments:
              track: The track to which the event is added. [Integer, 0-127].
              time: The time at which the event is added, in beats. [Float].
              tempo: The tempo, in Beats per Minute. [Integer]
          """
          self.tracks[track].addTempo(time,tempo)
     
      def addProgramChange(self,track, channel, time, program):
          """
          Add a MIDI program change event.
     
          Use:
              MyMIDI.addProgramChange(track,channel, time, program)
         
          Arguments:
              track: The track to which the event is added. [Integer, 0-127].
              channel: The channel the event is assigned to. [Integer, 0-15].
              time: The time at which the event is added, in beats. [Float].
              program: the program number. [Integer, 0-127].
          """
          self.tracks[track].addProgramChange(channel, time, program)
  
      def addControllerEvent(self,track, channel,time,eventType, paramerter1):
          """
          Add a MIDI controller event.
     
          Use:
              MyMIDI.addControllerEvent(track, channel, time, eventType, parameter1)
         
          Arguments:
              track: The track to which the event is added. [Integer, 0-127].
              channel: The channel the event is assigned to. [Integer, 0-15].
              time: The time at which the event is added, in beats. [Float].
              eventType: the controller event type.
              parameter1: The event's parameter. The meaning of which varies by event type.
          """
          self.tracks[track].addControllerEvent(channel,time,eventType, paramerter1)
     
      def changeNoteTuning(self,  track,  tunings,   sysExChannel=0x7F,  \
                           realTime=False,  tuningProgam=0):
          """
          Change a note's tuning using SysEx change tuning program.
         
          Use:
              MyMIDI.changeNoteTuning(track,[tunings],realTime=False, tuningProgram=0)
         
          Arguments:
              track: The track to which the event is added. [Integer, 0-127].
              tunings: A list of tuples in the form (pitchNumber, frequency).
                       [[(Integer,Float]]
              realTime: Boolean which sets the real-time flag. Defaults to false.
              sysExChannel: do note use (see below).
              tuningProgram: Tuning program to assign. Defaults to zero. [Integer, 0-127]
         
          In general the sysExChannel should not be changed (parameter will be depreciated).
     
          Also note that many software packages and hardware packages do not implement
          this standard!
          """
          self.tracks[track].changeNoteTuning(tunings,   sysExChannel,  realTime,\
                                                tuningProgam)
  
      def writeFile(self,fileHandle):
          '''
          Write the MIDI File.
     
          Use:
              MyMIDI.writeFile(filehandle)
     
          Arguments:
              filehandle: a file handle that has been opened for binary writing.
          '''
     
          self.header.writeFile(fileHandle)
     
          #Close the tracks and have them create the MIDI event data structures.
          self.close()
     
          #Write the MIDI Events to file.
          for i in range(0,self.numTracks):
              self.tracks[i].writeTrack(fileHandle)
  
      def addSysEx(self,track, time, manID, payload):
          """
          Add a SysEx event
     
          Use:
              MyMIDI.addSysEx(track,time,ID,payload)
         
          Arguments:
              track: The track to which the event is added. [Integer, 0-127].
              time: The time at which the event is added, in beats. [Float].
              ID: The SysEx ID number
              payload: the event payload.
         
          Note: This is a low-level MIDI function, so care must be used in
          constructing the payload. It is recommended that higher-level helper
          functions be written to wrap this function and construct the payload if
          a developer finds him or herself using the function heavily.
          """
          self.tracks[track].addSysEx(time,manID, payload)
  
      def addUniversalSysEx(self,track,  time,code, subcode, payload,  \
                            sysExChannel=0x7F,  realTime=False):
          """
          Add a Universal SysEx event.
     
          Use:
              MyMIDI.addUniversalSysEx(track, time, code, subcode, payload,\
                                        sysExChannel=0x7f, realTime=False)
                 
          Arguments:
              track: The track to which the event is added. [Integer, 0-127].
              time: The time at which the event is added, in beats. [Float].
              code: The even code. [Integer]
              subcode The event sub-code [Integer]
              payload: The event payload. [Binary string]
              sysExChannel: The SysEx channel.
              realTime: Sets the real-time flag. Defaults to zero.
     
          Note: This is a low-level MIDI function, so care must be used in
          constructing the payload. It is recommended that higher-level helper
          functions be written to wrap this function and construct the payload if
          a developer finds him or herself using the function heavily. As an example
          of such a helper function, see the changeNoteTuning function, both here and
          in MIDITrack.
          """
     
          self.tracks[track].addUniversalSysEx(time,code, subcode, payload,  sysExChannel,\
                                                 realTime)
                                            
      def shiftTracks(self,  offset=0):
          """Shift tracks to be zero-origined, or origined at offset.
     
          Note that the shifting of the time in the tracks uses the MIDIEventList -- in other
          words it is assumed to be called in the stage where the MIDIEventList has been
          created. This function, however, it meant to operate on the eventList itself.
          """
          origin = 1000000 # A little silly, but we'll assume big enough
  
          for track in self.tracks:
                  if len(track.eventList) > 0:
                      for event in track.eventList:
                          if event.time < origin:
                              origin = event.time
     
          for track in self.tracks:
              tempEventList = []
              #runningTime = 0
     
              for event in track.eventList:
                  adjustedTime = event.time - origin
                  #event.time = adjustedTime - runningTime + offset
                  event.time = adjustedTime + offset
                  #runningTime = adjustedTime
                  tempEventList.append(event)
         
              track.eventList = tempEventList
  
      #End Public Functions ########################
  
      def close(self):
          '''Close the MIDIFile for further writing.
     
          To close the File for events, we must close the tracks, adjust the time to be
          zero-origined, and have the tracks write to their MIDI Stream data structure.
          '''
     
          if self.closed == True:
              return
             
          for i in range(0,self.numTracks):
              self.tracks[i].closeTrack()
              # We want things like program changes to come before notes when they are at the
              # same time, so we sort the MIDI events by their ordinality
              self.tracks[i].MIDIEventList.sort()
         
          origin = self.findOrigin()
  
          for i in range(0,self.numTracks):
              self.tracks[i].adjustTime(origin)
              self.tracks[i].writeMIDIStream()
         
          self.closed = True
  
  
      def findOrigin(self):
          '''Find the earliest time in the file's tracks.append.
          '''
          origin = 1000000 # A little silly, but we'll assume big enough
  
      # Note: This code assumes that the MIDIEventList has been sorted, so this should be insured
      # before it is called. It is probably a poor design to do this.
      # TODO: -- Consider making this less efficient but more robust by not assuming the list to be sorted.
  
          for track in self.tracks:
                  if len(track.MIDIEventList) > 0:
                      if track.MIDIEventList[0].time < origin:
                          origin = track.MIDIEventList[0].time
                     
     
          return origin
         
  def writeVarLength(i):
      '''Accept an input, and write a MIDI-compatible variable length stream
  
      The MIDI format is a little strange, and makes use of so-called variable
      length quantities. These quantities are a stream of bytes. If the most
      significant bit is 1, then more bytes follow. If it is zero, then the
      byte in question is the last in the stream
      '''
      input = int(i+0.5)
      output = [0,0,0,0]
      reversed = [0,0,0,0]
      count = 0
      result = input & 0x7F
      output[count] = result
      count = count + 1
      input = input >> 7
      while input > 0:
          result = input & 0x7F
          result = result | 0x80
          output[count] = result
          count = count + 1
          input = input >> 7
  
      reversed[0] = output[3]
      reversed[1] = output[2]
      reversed[2] = output[1]
      reversed[3] = output[0]
      return reversed[4-count:4]
  
  # readVarLength is taken from the MidiFile class.
  
  def readVarLength(offset, buffer):
      '''A function to read a MIDI variable length variable.
  
      It returns a tuple of the value read and the number of bytes processed. The
      input is an offset into the buffer, and the buffer itself.
      '''
      toffset = offset
      output = 0
      bytesRead = 0
      while True:
          output = output << 7
          byte = struct.unpack_from('>B',buffer,toffset)[0]
          toffset = toffset + 1
          bytesRead = bytesRead + 1
          output = output + (byte & 127)
          if (byte & 128) == 0:
              break
      return (output, bytesRead)
  
  def frequencyTransform(freq):
      '''Returns a three-byte transform of a frequencyTransform
      '''
      resolution = 16384
      freq = float(freq)
      dollars = 69 + 12 * math.log(freq/(float(440)), 2)
      firstByte = int(dollars)
      lowerFreq = 440 * pow(2.0, ((float(firstByte) - 69.0)/12.0))
      if freq != lowerFreq:
          centDif = 1200 * math.log( (freq/lowerFreq), 2)
      else:
          centDif = 0
      cents = round(centDif/100 * resolution) # round?
      secondByte = min([int(cents)>>7, 0x7F])
      thirdByte = cents - (secondByte << 7)
      thirdByte = min([thirdByte, 0x7f])
      if thirdByte == 0x7f and secondByte == 0x7F and firstByte == 0x7F:
          thirdByte = 0x7e
     
      thirdByte = int(thirdByte)
      return [firstByte,  secondByte,  thirdByte]
  
  def returnFrequency(freqBytes):
      '''The reverse of frequencyTransform. Given a byte stream, return a frequency.
      '''
      resolution = 16384.0
      baseFrequency = 440 * pow(2.0, (float(freqBytes[0]-69.0)/12.0))
      frac = (float((int(freqBytes[1]) << 7) + int(freqBytes[2])) * 100.0) / resolution
      frequency = baseFrequency * pow(2.0, frac/1200.0)
      return frequency
  
  