Minimize gaps produced by quantization algorithm

music21/_version.py

@@ -47,8 +47,7 @@
 '''
 from __future__ import annotations
 
-__version__ = '9.0.0a11'
-
+__version__ = '9.0.0a12'
 
 def get_version_tuple(vv):
     v = vv.split('.')

music21/base.py

@@ -27,7 +27,7 @@
 <class 'music21.base.Music21Object'>
 
 >>> music21.VERSION_STR
-'9.0.0a11'
+'9.0.0a12'
 
 Alternatively, after doing a complete import, these classes are available
 under the module "base":

music21/midi/translate.py

@@ -2065,7 +2065,7 @@ def midiTrackToStream(
         singleN.editorial.midiTickStart = notes[0][0][0]
         s.coreInsert(o, singleN)
 
-    s.coreElementsChanged()
+    s.sort(force=True)  # will also run coreElementsChanged()
     # quantize to nearest 16th
     if quantizePost:
         s.quantize(quarterLengthDivisors=quarterLengthDivisors,

music21/stream/base.py

@@ -86,7 +86,7 @@
 
 BestQuantizationMatch = namedtuple(
     'BestQuantizationMatch',
-    ['error', 'tick', 'match', 'signedError', 'divisor']
+    ['remainingGap', 'error', 'tick', 'match', 'signedError', 'divisor']
 )
 
 class StreamDeprecationWarning(UserWarning):
@@ -9395,18 +9395,38 @@ def quantize(
         # this presently is not trying to avoid overlaps that
         # result from quantization; this may be necessary
 
-        def bestMatch(target, divisors):
+        def bestMatch(target, divisors, zeroAllowed=True, gapToFill=0.0):
             found = []
             for div in divisors:
-                match, error, signedErrorInner = common.nearestMultiple(target, (1 / div))
-                # Sort by unsigned error, then "tick" (divisor expressed as QL, e.g. 0.25)
-                found.append(BestQuantizationMatch(error, 1 / div, match, signedErrorInner, div))
+                tick = 1 / div  # divisor expressed as QL, e.g. 0.25
+                match, error, signedErrorInner = common.nearestMultiple(target, tick)
+                if not zeroAllowed and match == 0.0:
+                    match = tick
+                    signedErrorInner = round(target - match, 7)
+                    error = abs(signedErrorInner)
+                if gapToFill % tick == 0:
+                    remainingGap = 0.0
+                else:
+                    remainingGap = max(gapToFill - match, 0.0)
+                # Sort by remainingGap, then unsigned error, then tick
+                found.append(
+                    BestQuantizationMatch(
+                        remainingGap, error, tick, match, signedErrorInner, div))
             # get first, and leave out the error
             bestMatchTuple = sorted(found)[0]
             return bestMatchTuple
 
-        # if we have a min of 0.25 (sixteenth)
-        # quarterLengthMin = quarterLengthDivisors[0]
+        def findNextElementNotCoincident(
+            useStream: Stream,
+            startIndex: int,
+            startOffset: OffsetQL,
+        ) -> tuple[base.Music21Object | None, BestQuantizationMatch | None]:
+            for next_el in useStream._elements[startIndex:]:
+                next_offset = useStream.elementOffset(next_el)
+                look_ahead_result = bestMatch(float(next_offset), quarterLengthDivisors)
+                if look_ahead_result.match > startOffset:
+                    return next_el, look_ahead_result
+            return None, None
 
         if inPlace is False:
             returnStream = self.coreCopyAsDerivation('quantize')
@@ -9419,6 +9439,11 @@ def bestMatch(target, divisors):
 
         rests_lacking_durations: list[note.Rest] = []
         for useStream in useStreams:
+            # coreSetElementOffset() will immediately set isSorted = False,
+            # but we need to know if the stream was originally sorted to know
+            # if it's worth "looking ahead" to the next offset. If a stream
+            # is unsorted originally, this "looking ahead" could become O(n^2).
+            originallySorted = useStream.isSorted
             for i, e in enumerate(useStream._elements):
                 if processOffsets:
                     o = useStream.elementOffset(e)
@@ -9427,35 +9452,27 @@ def bestMatch(target, divisors):
                         sign = -1
                         o = -1 * o
                     o_matchTuple = bestMatch(float(o), quarterLengthDivisors)
-                    useStream.coreSetElementOffset(e, o_matchTuple.match * sign)
+                    o = o_matchTuple.match * sign
+                    useStream.coreSetElementOffset(e, o)
                     if hasattr(e, 'editorial') and o_matchTuple.signedError != 0:
                         e.editorial.offsetQuantizationError = o_matchTuple.signedError * sign
                 if processDurations:
                     ql = e.duration.quarterLength
                     ql = max(ql, 0)  # negative ql possible in buggy MIDI files?
-                    d_matchTuple = bestMatch(float(ql), quarterLengthDivisors)
-                    # Check that any gaps from this quantized duration to the next onset
-                    # are at least as large as the smallest quantization unit (the largest divisor)
-                    # If not, then re-quantize this duration with the divisor
-                    # that will be used to quantize the next element's offset
-                    if processOffsets and i + 1 < len(useStream._elements):
-                        next_element = useStream._elements[i + 1]
-                        next_offset = useStream.elementOffset(next_element)
-                        look_ahead_result = bestMatch(float(next_offset), quarterLengthDivisors)
-                        next_offset = look_ahead_result.match
-                        next_divisor = look_ahead_result.divisor
-                        if (0 < next_offset - (e.offset + d_matchTuple.match)
-                                < 1 / max(quarterLengthDivisors)):
-                            # Overwrite the earlier matchTuple with a better result
-                            d_matchTuple = bestMatch(float(ql), (next_divisor,))
-                    # Enforce nonzero duration for non-grace notes
-                    if (d_matchTuple.match == 0
-                            and isinstance(e, note.NotRest)
-                            and not e.duration.isGrace):
-                        e.quarterLength = 1 / max(quarterLengthDivisors)
-                        if hasattr(e, 'editorial'):
-                            e.editorial.quarterLengthQuantizationError = ql - e.quarterLength
-                    elif d_matchTuple.match == 0 and isinstance(e, note.Rest):
+                    zeroAllowed = not isinstance(e, note.NotRest) or e.duration.isGrace
+                    if processOffsets and originallySorted:
+                        next_element, look_ahead_result = (
+                            findNextElementNotCoincident(
+                                useStream=useStream, startIndex=i + 1, startOffset=o))
+                        if next_element is not None and look_ahead_result is not None:
+                            gapToFill = opFrac(look_ahead_result.match - e.offset)
+                            d_matchTuple = bestMatch(
+                                float(ql), quarterLengthDivisors, zeroAllowed, gapToFill)
+                        else:
+                            d_matchTuple = bestMatch(float(ql), quarterLengthDivisors, zeroAllowed)
+                    else:
+                        d_matchTuple = bestMatch(float(ql), quarterLengthDivisors, zeroAllowed)
+                    if d_matchTuple.match == 0 and isinstance(e, note.Rest):
                         rests_lacking_durations.append(e)
                     else:
                         e.duration.quarterLength = d_matchTuple.match

music21/stream/tests.py

@@ -4027,6 +4027,8 @@ def procCompare(srcOffset, srcDur, dstOffset, dstDur, divList):
                 n = note.Note()
                 n.quarterLength = srcDur[i]
                 s.insert(srcOffset[i], n)
+            # Must be sorted for quantizing to work optimally.
+            s.sort()
 
             s.quantize(divList, processOffsets=True, processDurations=True, inPlace=True)
 
@@ -4071,6 +4073,18 @@ def procCompare(srcOffset, srcDur, dstOffset, dstDur, divList):
 
                     [8, 6])  # snap to 0.125 and 0.1666666
 
+        # User-reported example: contains overlap and tiny gaps
+        # Parsing with fewer gaps in v.9, as long as stream is sorted
+        # https://github.com/cuthbertLab/music21/issues/1536
+        procCompare([2.016, 2.026, 2.333, 2.646, 3.0, 3.323, 3.651],
+                    [0.123, 0.656, 0.104, 0.094, 0.146, 0.099, 0.141],
+
+                    [2, 2, F('7/3'), F('8/3'), 3.0, F('10/3'), F('11/3')],
+                    [F('1/3'), F('2/3'), F('1/3'), F('1/3'),
+                     F('1/3'), F('1/3'), 0.25],
+
+                    [4, 3])
+
     def testQuantizeMinimumDuration(self):
         '''
         Notes (not rests!) of nonzero duration should retain a nonzero