# -*- coding: utf-8 -*-
# ------------------------------------------------------------------------------
# Name:         tempo.py
# Purpose:      Classes and tools relating to tempo
#
# Authors:      Christopher Ariza
#               Michael Scott Cuthbert
#
# Copyright:    Copyright © 2009-11, '15 Michael Scott Cuthbert and the music21 Project
# License:      BSD, see license.txt
# ------------------------------------------------------------------------------
'''
This module defines objects for describing tempo and changes in tempo.
'''
import copy
import unittest
from typing import Union, Optional

from music21 import base
from music21 import common
from music21 import duration
from music21 import exceptions21
from music21 import expressions
from music21 import note
from music21 import style

from music21 import environment
_MOD = 'tempo'
environLocal = environment.Environment(_MOD)


# all lowercase, even german, for string comparison
defaultTempoValues = {
    'larghissimo': 16,
    'largamente': 32,
    'grave': 40,
    'molto adagio': 40,
    'largo': 46,
    'lento': 52,
    'adagio': 56,
    'slow': 56,
    'langsam': 56,
    'larghetto': 60,
    'adagietto': 66,
    'andante': 72,
    'andantino': 80,
    'andante moderato': 83,  # need number
    'maestoso': 88,
    'moderato': 92,
    'moderate': 92,
    'allegretto': 108,
    'animato': 120,
    'allegro moderato': 128,  # need number
    'allegro': 132,
    'fast': 132,
    'schnell': 132,
    'allegrissimo': 140,  # need number
    'molto allegro': 144,
    'très vite': 144,
    'vivace': 160,
    'vivacissimo': 168,
    'presto': 184,
    'prestissimo': 208,
}


def convertTempoByReferent(
    numberSrc,
    quarterLengthBeatSrc,
    quarterLengthBeatDst=1.0
):
    '''
    Convert between equivalent tempi, where the speed stays the
    same but the beat referent and number change.


    60 bpm at quarter, going to half

    >>> tempo.convertTempoByReferent(60, 1, 2)
    30.0

    60 bpm at quarter, going to 16th

    >>> tempo.convertTempoByReferent(60, 1, 0.25)
    240.0

    60 at dotted quarter, get quarter

    >>> tempo.convertTempoByReferent(60, 1.5, 1)
    90.0

    60 at dotted quarter, get half

    >>> tempo.convertTempoByReferent(60, 1.5, 2)
    45.0

    60 at dotted quarter, get trip

    >>> tempo.convertTempoByReferent(60, 1.5, 1/3)
    270.0

    A Fraction instance can also be used:

    >>> tempo.convertTempoByReferent(60, 1.5, common.opFrac(1/3))
    270.0

    '''
    # find duration in seconds of of quarter length
    srcDurPerBeat = 60 / numberSrc
    # convert to dur for one quarter length
    dur = srcDurPerBeat / quarterLengthBeatSrc
    # multiply dur by dst quarter
    dstDurPerBeat = dur * float(quarterLengthBeatDst)
    # environLocal.printDebug(['dur', dur, 'dstDurPerBeat', dstDurPerBeat])
    # find tempo
    return float(60 / dstDurPerBeat)


# ------------------------------------------------------------------------------
class TempoException(exceptions21.Music21Exception):
    pass


# ------------------------------------------------------------------------------
class TempoIndication(base.Music21Object):
    '''
    A generic base class for all tempo indications to inherit.
    Can be used to filter out all types of tempo indications.
    '''
    classSortOrder = 1
    _styleClass = style.TextStyle

    # def __init__(self):
    #     super().__init__()
    #     # self.style.justify = 'left'  # creates a style object to share.

    def getSoundingMetronomeMark(self, found=None):
        '''Get the appropriate MetronomeMark from any sort of TempoIndication, regardless of class.
        '''
        if found is None:
            found = self

        if 'MetricModulation' in found.classes:
            return found.newMetronome
        elif 'MetronomeMark' in found.classes:
            return found
        elif 'TempoText' in found.classes:
            return found.getMetronomeMark()
        else:
            raise TempoException(
                f'cannot derive a MetronomeMark from this TempoIndication: {found}')

    def getPreviousMetronomeMark(self):
        '''
        Do activeSite and context searches to try to find the last relevant
        MetronomeMark or MetricModulation object. If a MetricModulation mark is found,
        return the new MetronomeMark, or the last relevant.

        >>> s = stream.Stream()
        >>> s.insert(0, tempo.MetronomeMark(number=120))
        >>> mm1 = tempo.MetronomeMark(number=90)
        >>> s.insert(20, mm1)
        >>> mm1.getPreviousMetronomeMark()
        <music21.tempo.MetronomeMark animato Quarter=120>
        '''
        # environLocal.printDebug(['getPreviousMetronomeMark'])
        # search for TempoIndication objects, not just MetronomeMark objects
        # must provide getElementBefore, as will otherwise return self
        obj = self.getContextByClass('TempoIndication',
                                     getElementMethod='getElementBeforeOffset')
        if obj is None:
            return None  # nothing to do
        return self.getSoundingMetronomeMark(obj)


# ------------------------------------------------------------------------------
class TempoText(TempoIndication):
    '''
    >>> import music21
    >>> tm = music21.tempo.TempoText('adagio')
    >>> tm
    <music21.tempo.TempoText 'adagio'>
    >>> print(tm.text)
    adagio
    '''

    def __init__(self, text=None):
        super().__init__()

        # store text in a TextExpression instance
        self._textExpression = None  # a stored object

        if text is not None:
            self.text = str(text)

    def _reprInternal(self):
        return repr(self.text)

    def _getText(self):
        '''
        Get the text used for this expression.
        '''
        return self._textExpression.content

    def _setText(self, value):
        '''
        Set the text of this repeat expression. This is also the primary way
        that the stored TextExpression object is created.
        '''
        if self._textExpression is None:
            self._textExpression = expressions.TextExpression(value)
            if self.hasStyleInformation:
                self._textExpression.style = self.style  # link styles
            else:
                self.style = self._textExpression.style
            self.applyTextFormatting()
        else:
            self._textExpression.content = value

    text = property(_getText, _setText, doc='''
        Get or set the text as a string.

        >>> import music21
        >>> tm = music21.tempo.TempoText('adagio')
        >>> tm.text
        'adagio'
        >>> tm.getTextExpression()
        <music21.expressions.TextExpression 'adagio'>
        ''')

    def getMetronomeMark(self):
        # noinspection PyShadowingNames
        '''
        Return a MetronomeMark object that is configured from this objects Text.

        >>> tt = tempo.TempoText('slow')
        >>> mm = tt.getMetronomeMark()
        >>> mm.number
        56
        '''
        mm = MetronomeMark(text=self.text)
        if self.hasStyleInformation:
            mm.style = self.style
        else:
            self.style = mm.style
        return mm

    def getTextExpression(self, numberImplicit=False):
        '''
        Return a TextExpression object for this text.

        What is this a deepcopy and not the actual one?
        '''
        if self._textExpression is None:
            return None
        else:
            self.applyTextFormatting(numberImplicit=numberImplicit)
            return copy.deepcopy(self._textExpression)

    def setTextExpression(self, value):
        '''
        Given a TextExpression, set it in this object.
        '''
        self._textExpression = value
        self.applyTextFormatting()

    def applyTextFormatting(self, te=None, numberImplicit=False):
        '''
        Apply the default text formatting to the text expression version of of this tempo mark
        '''
        if te is None:  # use the stored version if possible
            te = self._textExpression
        te.style.fontStyle = 'bold'
        if numberImplicit:
            te.style.absoluteY = 20  # if not showing number
        else:
            te.style.absoluteY = 45  # 4.5 staff lines above
        return te

    def isCommonTempoText(self, value=None):
        '''
        Return True or False if the supplied text seems like a
        plausible Tempo indications be used for this TempoText.


        >>> tt = tempo.TempoText('adagio')
        >>> tt.isCommonTempoText()
        True

        >>> tt = tempo.TempoText('Largo e piano')
        >>> tt.isCommonTempoText()
        True

        >>> tt = tempo.TempoText('undulating')
        >>> tt.isCommonTempoText()
        False
        '''
        def stripText(s):
            # remove all spaces, punctuation, and make lower
            s = s.strip()
            s = s.replace(' ', '')
            s = s.replace('.', '')
            s = s.lower()
            return s
        # if not provided, use stored text
        if value is None:
            value = self._textExpression.content

        for candidate in defaultTempoValues:
            candidate = stripText(candidate)
            value = stripText(value)
            # simply look for membership, not a complete match
            if value in candidate or candidate in value:
                return True
        return False


# ------------------------------------------------------------------------------
class MetronomeMarkException(TempoException):
    pass


# TODO: define if tempo applies only to part
# ------------------------------------------------------------------------------
class MetronomeMark(TempoIndication):
    '''
    A way of specifying a particular tempo with a text string,
    a referent (a duration) and a number.

    The `referent` attribute is a Duration object, or a string duration type or
    a floating-point quarter-length value used to create a Duration.

    MetronomeMarks, as Music21Object subclasses, also have .duration object
    property independent of the `referent`.

    >>> a = tempo.MetronomeMark('slow', 40, note.Note(type='half'))
    >>> a.number
    40
    >>> a.referent
    <music21.duration.Duration 2.0>
    >>> a.referent.type
    'half'
    >>> print(a.text)
    slow


    Some text marks will automatically suggest a number.


    >>> mm = tempo.MetronomeMark('adagio')
    >>> mm.number
    56
    >>> mm.numberImplicit
    True


    For certain numbers, a text value can be set implicitly


    >>> tm2 = tempo.MetronomeMark(number=208)
    >>> print(tm2.text)
    prestissimo
    >>> tm2.referent
    <music21.duration.Duration 1.0>

    Unicode values work fine thanks to Python 3:

    >>> marking = 'très vite'
    >>> marking
    'très vite'
    >>> print(tempo.defaultTempoValues[marking])
    144
    >>> tm2 = tempo.MetronomeMark(marking)
    >>> tm2.text.endswith('vite')
    True
    >>> tm2.number
    144
    '''

    def __init__(self, text=None, number=None, referent=None, parentheses=False):
        super().__init__()

        if number is None and isinstance(text, int):
            number = text
            text = None

        self._number = number  # may be None
        self.numberImplicit = None
        if self._number is not None:
            self.numberImplicit = False

        self._tempoText = None  # set with property text
        self.textImplicit = None
        if text is not None:  # use property to create object if necessary
            self.text = text

        # TODO: style??
        self.parentheses = parentheses

        self._referent = None  # set with property
        if referent is None:
            # if referent is None, set a default quarter note duration
            referent = duration.Duration(type='quarter')
        self.referent = referent  # use property

        # set implicit values if necessary
        self._updateNumberFromText()
        self._updateTextFromNumber()

        # need to store a sounding value for the case where where
        # a sounding different is different than the number given in the MM
        self._numberSounding = None

    def _reprInternal(self):
        if self.text is None:
            return f'{self.referent.fullName}={self.number}'
        else:
            return f'{self.text} {self.referent.fullName}={self.number}'

    def _updateTextFromNumber(self):
        '''Update text if number is given and text is not defined
        '''
        if self._tempoText is None and self._number is not None:
            # PyCharm inspection does not like using attributes on functions that become properties
            # noinspection PyArgumentList
            self._setText(self._getDefaultText(self._number),
                          updateNumberFromText=False)
            if self.text is not None:
                self.textImplicit = True

    def _updateNumberFromText(self):
        '''Update number if text is given and number is not defined
        '''
        if self._number is None and self._tempoText is not None:
            self._number = self._getDefaultNumber(self._tempoText)
            if self._number is not None:  # only if set
                self.numberImplicit = True

    # -------------------------------------------------------------------------
    def _getReferent(self):
        return self._referent

    def _setReferent(self, value):
        if value is None:  # this may be better not here
            # if referent is None, set a default quarter note duration
            self._referent = duration.Duration(type='quarter')
        # assume ql value or a type string
        elif common.isNum(value) or isinstance(value, str):
            self._referent = duration.Duration(value)
        elif 'Duration' not in value.classes:
            # try get duration object, like from Note
            self._referent = value.duration
        elif 'Duration' in value.classes:
            self._referent = value
            # should be a music21.duration.Duration object or a
            # Music21Object with a duration or None
        else:
            raise TempoException(f'Cannot get a Duration from the supplied object: {value}')

    referent = property(_getReferent, _setReferent, doc='''
        Get or set the referent, or the Duration object that is the
        reference for the tempo value in BPM.
        ''')

    # properties and conversions
    def _getText(self):
        if self._tempoText is None:
            return None
        return self._tempoText.text

    def _setText(self, value, updateNumberFromText=True):
        if value is None:
            self._tempoText = None
        elif isinstance(value, TempoText):
            self._tempoText = value
            self.textImplicit = False  # must set here
        else:
            self._tempoText = TempoText(value)
            if self.hasStyleInformation:
                self._tempoText.style = self.style  # link style information
            else:
                self.style = self._tempoText.style
            self.textImplicit = False  # must set here

        if updateNumberFromText:
            self._updateNumberFromText()

    text = property(_getText, _setText, doc='''
        Get or set a text string for this MetronomeMark. Internally implemented as a
        :class:`~music21.tempo.TempoText` object, which stores the text in
        a :class:`~music21.expression.TextExpression` object.

        >>> mm = tempo.MetronomeMark(number=123)
        >>> mm.text == None
        True
        >>> mm.text = 'medium fast'
        >>> print(mm.text)
        medium fast
        ''')

    def _getNumber(self):
        return self._number  # may be None

    def _setNumber(self, value, updateTextFromNumber=True):
        if not common.isNum(value):
            raise TempoException('cannot set number to a string')
        self._number = value
        self.numberImplicit = False
        if updateTextFromNumber:
            self._updateTextFromNumber()

    number = property(_getNumber, _setNumber, doc='''
        Get and set the number, or the numerical value of the Metronome.

        >>> mm = tempo.MetronomeMark('slow')
        >>> mm.number
        56
        >>> mm.numberImplicit
        True
        >>> mm.number = 52.5
        >>> mm.number
        52.5
        >>> mm.numberImplicit
        False
        ''')

    def _getNumberSounding(self):
        return self._numberSounding  # may be None

    def _setNumberSounding(self, value):
        if not common.isNum(value):
            raise TempoException('cannot set numberSounding to a string')
        self._numberSounding = value

    numberSounding = property(_getNumberSounding, _setNumberSounding, doc='''
        Get and set the numberSounding, or the numerical value of the Metronome that
        is used for playback independent of display. If numberSounding is None, number is
        assumed to be numberSounding.


        >>> mm = tempo.MetronomeMark('slow')
        >>> mm.number
        56
        >>> mm.numberImplicit
        True
        >>> mm.numberSounding == None
        True
        >>> mm.numberSounding = 120
        >>> mm.numberSounding
        120
        ''')

    # -------------------------------------------------------------------------
    def getQuarterBPM(self, useNumberSounding=True):
        '''
        Get a BPM value where the beat is a quarter; must convert from the
        defined beat to a quarter beat. Will return None if no beat number is defined.

        This mostly used for generating MusicXML <sound> tags when necessary.


        >>> mm = tempo.MetronomeMark(number=60, referent='half')
        >>> mm.getQuarterBPM()
        120.0
        >>> mm.referent = 'quarter'
        >>> mm.getQuarterBPM()
        60.0
        '''
        if useNumberSounding and self.numberSounding is not None:
            return convertTempoByReferent(self.numberSounding,
                                          self.referent.quarterLength,
                                          1.0)
        if self.number is not None:
            # target quarter length is always 1.0
            return convertTempoByReferent(self.number,
                                          self.referent.quarterLength,
                                          1.0)
        return None

    def setQuarterBPM(self, value, setNumber=True):
        '''
        Given a value in BPM, use it to set the value of this MetronomeMark.
        BPM values are assumed to be refer only to quarter notes; different beat values,
        if defined here, will be scaled


        >>> mm = tempo.MetronomeMark(number=60, referent='half')
        >>> mm.setQuarterBPM(240)  # set to 240 for a quarter
        >>> mm.number  # a half is half as fast
        120.0
        '''
        # assuming a quarter value coming in, what is with our current beat
        value = convertTempoByReferent(value, 1.0, self.referent.quarterLength)
        if not setNumber:
            # convert this to a quarter bpm
            self._numberSounding = value
        else:  # go through property so as to set implicit status
            self.number = value

    def _getDefaultNumber(self, tempoText):
        '''
        Given a tempo text expression or an TempoText, get the default number.

        >>> mm = tempo.MetronomeMark()
        >>> mm._getDefaultNumber('schnell')
        132
        >>> mm._getDefaultNumber('adagio')
        56
        >>> mm._getDefaultNumber('Largo e piano')
        46
        '''
        if isinstance(tempoText, TempoText):
            tempoStr = tempoText.text
        else:
            tempoStr = tempoText
        post = None  # returned if no match
        if tempoStr.lower() in defaultTempoValues:
            post = defaultTempoValues[tempoStr.lower()]
        # an exact match
        elif tempoStr in defaultTempoValues:
            post = defaultTempoValues[tempoStr]
        # look for partial matches
        if post is None:
            for word in tempoStr.split(' '):
                for key in defaultTempoValues:
                    if key == word.lower():
                        post = defaultTempoValues[key]
        return post

    def _getDefaultText(self, number, spread=2):
        '''
        Given a tempo number try to get a text expression;
        presently only looks for approximate matches

        The `spread` value is a +/- shift around the default tempo
        indications defined in defaultTempoValues


        >>> mm = tempo.MetronomeMark()
        >>> mm._getDefaultText(92)
        'moderate'
        >>> mm._getDefaultText(208)
        'prestissimo'
        '''
        if common.isNum(number):
            tempoNumber = number
        else:  # try to convert
            tempoNumber = float(number)
        # get a items and sort
        matches = []
        for tempoStr, tempoValue in defaultTempoValues.items():
            matches.append([tempoValue, tempoStr])
        matches.sort()
        # environLocal.printDebug(['matches', matches])
        post = None
        for tempoValue, tempoStr in matches:
            if (tempoValue - spread) <= tempoNumber <= (tempoValue + spread):
                # found a match
                post = tempoStr
                break
        return post

    def getTextExpression(self, returnImplicit=False):
        '''
        If there is a TextExpression available that is not implicit, return it;
        otherwise, return None.

        >>> mm = tempo.MetronomeMark('presto')
        >>> mm.number
        184
        >>> mm.numberImplicit
        True
        >>> mm.getTextExpression()
        <music21.expressions.TextExpression 'presto'>
        >>> mm.textImplicit
        False

        >>> mm = tempo.MetronomeMark(number=90)
        >>> mm.numberImplicit
        False
        >>> mm.textImplicit
        True
        >>> mm.getTextExpression() is None
        True
        >>> mm.getTextExpression(returnImplicit=True)
        <music21.expressions.TextExpression 'maestoso'>
        '''
        if self._tempoText is None:
            return None
        # if explicit, always return; if implicit, return if returnImplicit true
        if not self.textImplicit or (self.textImplicit and returnImplicit):
            # adjust position if number is implicit; pass number implicit
            return self._tempoText.getTextExpression(
                numberImplicit=self.numberImplicit)

    # -------------------------------------------------------------------------
    def getEquivalentByReferent(self, referent):
        '''
        Return a new MetronomeMark object that has an equivalent speed but
        different number and referent values based on a supplied referent
        (given as a Duration type, quarterLength, or Duration object).


        >>> mm1 = tempo.MetronomeMark(number=60, referent=1.0)
        >>> mm1.getEquivalentByReferent(0.5)
        <music21.tempo.MetronomeMark larghetto Eighth=120.0>
        >>> mm1.getEquivalentByReferent(duration.Duration('half'))
        <music21.tempo.MetronomeMark larghetto Half=30.0>

        >>> mm1.getEquivalentByReferent('longa')
        <music21.tempo.MetronomeMark larghetto Imperfect Longa=3.75>

        '''
        if common.isNum(referent):  # assume quarter length
            quarterLength = referent
        elif isinstance(referent, str):  # try to get quarter len
            d = duration.Duration(referent)
            quarterLength = d.quarterLength
        else:  # TODO: test if a Duration
            quarterLength = referent.quarterLength

        if self.number is not None:
            newNumber = convertTempoByReferent(self.number,
                                               self.referent.quarterLength,
                                               quarterLength)
        else:
            newNumber = None

        return MetronomeMark(text=self.text, number=newNumber,
                             referent=duration.Duration(quarterLength))

#     def getEquivalentByNumber(self, number):
#         '''
#         Return a new MetronomeMark object that has an equivalent speed but different number and
#         referent values based on a supplied tempo number.
#         '''
#         pass

    def getMaintainedNumberWithReferent(self, referent):
        '''
        Return a new MetronomeMark object that has an equivalent number but a new referent.
        '''
        return MetronomeMark(text=self.text, number=self.number,
                             referent=referent)

    # --------------------------------------------------------------------------
    # real-time realization
    def secondsPerQuarter(self):
        '''
        Return the duration in seconds for each quarter length
        (not necessarily the referent) of this MetronomeMark.

        >>> from music21 import tempo
        >>> mm1 = tempo.MetronomeMark(referent=1.0, number=60.0)
        >>> mm1.secondsPerQuarter()
        1.0
        >>> mm1 = tempo.MetronomeMark(referent=2.0, number=60.0)
        >>> mm1.secondsPerQuarter()
        0.5
        >>> mm1 = tempo.MetronomeMark(referent=2.0, number=30.0)
        >>> mm1.secondsPerQuarter()
        1.0
        '''
        qbpm = self.getQuarterBPM()
        if qbpm is not None:
            return 60.0 / self.getQuarterBPM()
        else:
            raise MetronomeMarkException('cannot derive seconds as getQuarterBPM() returns None')

    def durationToSeconds(self, durationOrQuarterLength):
        '''Given a duration specified as a :class:`~music21.duration.Duration` object or a
        quarter length, return the resultant time in seconds at the tempo specified by
        this MetronomeMark.

        >>> from music21 import tempo
        >>> mm1 = tempo.MetronomeMark(referent=1.0, number=60.0)
        >>> mm1.durationToSeconds(60)
        60.0
        >>> mm1.durationToSeconds(duration.Duration('16th'))
        0.25
        '''
        if common.isNum(durationOrQuarterLength):
            ql = durationOrQuarterLength
        else:  # assume a duration object
            ql = durationOrQuarterLength.quarterLength
        # get time per quarter
        return self.secondsPerQuarter() * ql

    def secondsToDuration(self, seconds):
        '''
        Given a duration in seconds,
        return a :class:`~music21.duration.Duration` object equal to that time.

        >>> from music21 import tempo
        >>> mm1 = tempo.MetronomeMark(referent=1.0, number=60.0)
        >>> mm1.secondsToDuration(0.25)
        <music21.duration.Duration 0.25>
        >>> mm1.secondsToDuration(0.5).type
        'eighth'
        >>> mm1.secondsToDuration(1)
        <music21.duration.Duration 1.0>
        '''
        if not common.isNum(seconds) or seconds <= 0.0:
            raise MetronomeMarkException('seconds must be a number greater than zero')
        ql = seconds / self.secondsPerQuarter()
        return duration.Duration(quarterLength=ql)


# ------------------------------------------------------------------------------
class MetricModulationException(TempoException):
    pass


# ------------------------------------------------------------------------------
class MetricModulation(TempoIndication):
    '''
    A class for representing the relationship between two MetronomeMarks.
    Generally this relationship is one of equality, where the number is maintained but
    the referent that number is applied to changes.

    The basic definition of a MetricModulation is given by supplying two MetronomeMarks,
    one for the oldMetronome, the other for the newMetronome. High level properties,
    oldReferent and newReferent, and convenience methods permit only setting the referent.

    The `classicalStyle` attribute determines of the first MetronomeMark describes the
    new tempo, not the old (the reverse of expected usage).

    The `maintainBeat` attribute determines if, after an equality statement,
    the beat is maintained. This is relevant for moving from 3/4 to 6/8, for example.

    >>> s = stream.Stream()
    >>> mm1 = tempo.MetronomeMark(number=60)
    >>> s.append(mm1)
    >>> s.repeatAppend(note.Note(quarterLength=1), 2)
    >>> s.repeatAppend(note.Note(quarterLength=0.5), 4)

    >>> mmod1 = tempo.MetricModulation()
    >>> mmod1.oldReferent = 0.5  # can use Duration objects
    >>> mmod1.newReferent = 'quarter'  # can use Duration objects
    >>> s.append(mmod1)
    >>> mmod1.updateByContext()  # get number from last MetronomeMark on Stream
    >>> mmod1.newMetronome
    <music21.tempo.MetronomeMark animato Quarter=120.0>

    >>> s.append(note.Note())
    >>> s.repeatAppend(note.Note(quarterLength=1.5), 2)

    >>> mmod2 = tempo.MetricModulation()
    >>> s.append(mmod2)  # if the obj is added to Stream, can set referents
    >>> mmod2.oldReferent = 1.5  # will get number from previous MetronomeMark
    >>> mmod2.newReferent = 'quarter'
    >>> mmod2.newMetronome
    <music21.tempo.MetronomeMark animato Quarter=80.0>

    Note that an initial metric modulation can set old and new referents and get None as
    tempo numbers:

    >>> mmod3 = tempo.MetricModulation()
    >>> mmod3.oldReferent = 'half'
    >>> mmod3.newReferent = '16th'
    >>> mmod3
    <music21.tempo.MetricModulation
        <music21.tempo.MetronomeMark
            Half=None>=<music21.tempo.MetronomeMark 16th=None>>

    test w/ more sane referents that either the old or the new can change without a tempo number

    >>> mmod3.oldReferent = 'quarter'
    >>> mmod3.newReferent = 'eighth'
    >>> mmod3
    <music21.tempo.MetricModulation
        <music21.tempo.MetronomeMark
            Quarter=None>=<music21.tempo.MetronomeMark Eighth=None>>
    >>> mmod3.oldMetronome
    <music21.tempo.MetronomeMark Quarter=None>
    >>> mmod3.oldMetronome.number = 60

    New number automatically updates:

    >>> mmod3
    <music21.tempo.MetricModulation
        <music21.tempo.MetronomeMark larghetto
            Quarter=60>=<music21.tempo.MetronomeMark larghetto Eighth=60>>
    '''

    def __init__(self):
        super().__init__()

        self.classicalStyle = False
        self.maintainBeat = False
        self.transitionSymbol = '='  # accept different symbols
        # some old formats use arrows
        self.arrowDirection = None  # can be left, right, or None

        # showing parens or not
        self.parentheses = False

        # store two MetronomeMark objects
        self._oldMetronome = None
        self._newMetronome = None

    def _reprInternal(self):
        return f'{self.oldMetronome}={self.newMetronome}'

    # --------------------------------------------------------------------------
    # core properties
    def _setOldMetronome(self, value):
        if value is None:
            pass  # allow setting as None
        elif not hasattr(value, 'classes') or 'MetronomeMark' not in value.classes:
            raise MetricModulationException(
                'oldMetronome property must be set with a MetronomeMark instance')
        self._oldMetronome = value

    def _getOldMetronome(self):
        if self._oldMetronome is not None:
            if self._oldMetronome.number is None:
                self.updateByContext()
        return self._oldMetronome

    oldMetronome = property(_getOldMetronome, _setOldMetronome, doc='''
        Get or set the left :class:`~music21.tempo.MetronomeMark` object
        for the old, or previous value.

        >>> mm1 = tempo.MetronomeMark(number=60, referent=1)
        >>> mm1
        <music21.tempo.MetronomeMark larghetto Quarter=60>
        >>> mmod1 = tempo.MetricModulation()
        >>> mmod1.oldMetronome = mm1

        Note that we do need to have a proper MetronomeMark instance to figure this out:

        >>> mmod1.oldMetronome = 'junk'
        Traceback (most recent call last):
        music21.tempo.MetricModulationException: oldMetronome property
            must be set with a MetronomeMark instance
        ''')

    def _setOldReferent(self, value):
        if value is None:
            raise MetricModulationException('cannot set old referent to None')
        # try to get and reassign equivalent
        if self._oldMetronome is not None:
            mm = self._oldMetronome.getEquivalentByReferent(value)
        else:
            # try to do a context search and get the last MetronomeMark
            mm = self.getPreviousMetronomeMark()
            if mm is not None:
                # replace with an equivalent based on a provided value
                mm = mm.getEquivalentByReferent(value)
        if mm is not None:
            self._oldMetronome = mm
        else:
            # create a new metronome mark with a referent, but not w/ a value
            self._oldMetronome = MetronomeMark(referent=value)
            # raise MetricModulationException('cannot set old MetronomeMark from provided value.')

    def _getOldReferent(self):
        if self._oldMetronome is not None:
            return self._oldMetronome.referent

    oldReferent = property(_getOldReferent, _setOldReferent, doc='''
        Get or set the referent of the old MetronomeMark.

        >>> mm1 = tempo.MetronomeMark(number=60, referent=1)
        >>> mmod1 = tempo.MetricModulation()
        >>> mmod1.oldMetronome = mm1
        >>> mmod1.oldMetronome
        <music21.tempo.MetronomeMark larghetto Quarter=60>
        >>> mmod1.oldReferent = 0.25
        >>> mmod1.oldMetronome
        <music21.tempo.MetronomeMark larghetto 16th=240.0>

        ''')

    def _setNewMetronome(self, value):
        if value is None:
            pass  # allow setting as None
        elif not hasattr(value, 'classes') or 'MetronomeMark' not in value.classes:
            raise MetricModulationException(
                'newMetronome property must be set with a MetronomeMark instance')
        self._newMetronome = value

    def _getNewMetronome(self):
        # before returning the referent, see if we can update the number
        if self._newMetronome is not None:
            if self._newMetronome.number is None:
                self.updateByContext()
        return self._newMetronome

    newMetronome = property(_getNewMetronome, _setNewMetronome, doc='''
        Get or set the right :class:`~music21.tempo.MetronomeMark`
        object for the new, or following value.

        >>> mm1 = tempo.MetronomeMark(number=60, referent=1)
        >>> mm1
        <music21.tempo.MetronomeMark larghetto Quarter=60>
        >>> mmod1 = tempo.MetricModulation()
        >>> mmod1.newMetronome = mm1
        >>> mmod1.newMetronome = 'junk'
        Traceback (most recent call last):
        music21.tempo.MetricModulationException: newMetronome property must be
            set with a MetronomeMark instance
        ''')

    def _setNewReferent(self, value):
        if value is None:
            raise MetricModulationException('cannot set new referent to None')
        # of oldMetronome is defined, get new metronome from old
        mm = None
        if self._newMetronome is not None:
            # if metro defined, get based on new referent
            mm = self._newMetronome.getEquivalentByReferent(value)
        elif self._oldMetronome is not None:
            # get a new mm with the same number but a new referent
            mm = self._oldMetronome.getMaintainedNumberWithReferent(value)
        else:
            # create a new metronome mark with a referent, but not w/ a value
            mm = MetronomeMark(referent=value)
            # raise MetricModulationException('cannot set old MetronomeMark from provided value.')
        self._newMetronome = mm

    def _getNewReferent(self):
        if self._newMetronome is not None:
            return self._newMetronome.referent

    newReferent = property(_getNewReferent, _setNewReferent, doc='''
        Get or set the referent of the new MetronomeMark.

        >>> mm1 = tempo.MetronomeMark(number=60, referent=1)
        >>> mmod1 = tempo.MetricModulation()
        >>> mmod1.newMetronome = mm1
        >>> mmod1.newMetronome
        <music21.tempo.MetronomeMark larghetto Quarter=60>
        >>> mmod1.newReferent = 0.25
        >>> mmod1.newMetronome
        <music21.tempo.MetronomeMark larghetto 16th=240.0>
        ''')

    @property
    def number(self):
        '''
        Get and the number of the MetricModulation, or the number
        assigned to the new MetronomeMark.

        >>> s = stream.Stream()
        >>> mm1 = tempo.MetronomeMark(number=60)
        >>> s.append(mm1)
        >>> s.repeatAppend(note.Note(quarterLength=1), 2)
        >>> s.repeatAppend(note.Note(quarterLength=0.5), 4)

        >>> mmod1 = tempo.MetricModulation()
        >>> mmod1.oldReferent = 0.5  # can use Duration objects
        >>> mmod1.newReferent = 'quarter'
        >>> s.append(mmod1)
        >>> mmod1.updateByContext()
        >>> mmod1.newMetronome
        <music21.tempo.MetronomeMark animato Quarter=120.0>
        >>> mmod1.number
        120.0
        '''
        if self._newMetronome is not None:
            return self._newMetronome.number

#     def _setNumber(self, value, updateTextFromNumber=True):
#         if not common.isNum(value):
#             raise MetricModulationException('cannot set number to a string')
#         self._newMetronome.number = value
#         self._oldMetronome.number = value

    # --------------------------------------------------------------------------
    # high-level configuration methods
    def updateByContext(self):
        '''Update this metric modulation based on the context,
        or the surrounding MetronomeMarks or MetricModulations.
        The object needs to reside in a Stream for this to be effective.
        '''
        # try to set old number from last; there must be a partially
        # defined metronome mark already assigned; or create one at quarter?
        mmLast = self.getPreviousMetronomeMark()
        mmOld = None
        if mmLast is not None:
            # replace with an equivalent based on a provided value
            if (self._oldMetronome is not None
                    and self._oldMetronome.referent is not None):
                mmOld = mmLast.getEquivalentByReferent(
                    self._oldMetronome.referent)
            else:
                mmOld = MetronomeMark(referent=mmLast.referent,
                                      number=mmLast.number)
        if mmOld is not None:
            self._oldMetronome = mmOld
        # if we have an a new referent, then update number
        if (self._newMetronome is not None
                and self._newMetronome.referent is not None
                and self._oldMetronome.number is not None):
            self._newMetronome.number = self._oldMetronome.number

    def setEqualityByReferent(self, side=None, referent=1.0):
        '''Set the other side of the metric modulation to
        an equality; side can be specified, or if one side
        is None, that side will be set.


        >>> mm1 = tempo.MetronomeMark(number=60, referent=1)
        >>> mmod1 = tempo.MetricModulation()
        >>> mmod1.newMetronome = mm1
        >>> mmod1.setEqualityByReferent(None, 2)
        >>> mmod1
        <music21.tempo.MetricModulation
             <music21.tempo.MetronomeMark larghetto
                   Half=30.0>=<music21.tempo.MetronomeMark larghetto Quarter=60>>

        '''
        if side is None:
            if self._oldMetronome is None:
                side = 'left'
            elif self._newMetronome is None:
                side = 'right'
        if side not in ['left', 'right']:
            raise TempoException(f'cannot set equality for a side of {side}')

        if side == 'right':
            self._newMetronome = self._oldMetronome.getEquivalentByReferent(
                referent)
        elif side == 'left':
            self._oldMetronome = self._newMetronome.getEquivalentByReferent(
                referent)

    def setOtherByReferent(
        self,
        side: Optional[str] = None,
        referent: Union[str, int, float] = 1.0
    ):
        '''
        Set the other side of the metric modulation not based on equality,
        but on a direct translation of the tempo value.

        referent can be a string type or a int/float quarter length
        '''
        if side is None:
            if self._oldMetronome is None:
                side = 'left'
            elif self._newMetronome is None:
                side = 'right'
        if side not in ['left', 'right']:
            raise TempoException(f'cannot set equality for a side of {side}')
        if side == 'right':
            self._newMetronome = self._oldMetronome.getMaintainedNumberWithReferent(referent)
        elif side == 'left':
            self._oldMetronome = self._newMetronome.getMaintainedNumberWithReferent(referent)


# ------------------------------------------------------------------------------
def interpolateElements(element1, element2, sourceStream,
                        destinationStream, autoAdd=True):
    # noinspection PyShadowingNames
    '''
    Assume that element1 and element2 are two elements in sourceStream
    and destinationStream with other elements (say eA, eB, eC) between
    them.  For instance, element1 could be the downbeat at offset 10
    in sourceStream (a Stream representing a score) and offset 20.5
    in destinationStream (which might be a Stream representing the
    timing of notes in particular recording at approximately but not
    exactly qtr = 30). Element2 could be the following downbeat in 4/4,
    at offset 14 in source but offset 25.0 in the recording:

    >>> sourceStream = stream.Stream()
    >>> destinationStream = stream.Stream()
    >>> element1 = note.Note('C4', type='quarter')
    >>> element2 = note.Note('G4', type='quarter')
    >>> sourceStream.insert(10, element1)
    >>> destinationStream.insert(20.5, element1)
    >>> sourceStream.insert(14, element2)
    >>> destinationStream.insert(25.0, element2)

    Suppose eA, eB, and eC are three quarter notes that lie
    between element1 and element2 in sourceStream
    and destinationStream, as in:

    >>> eA = note.Note('D4', type='quarter')
    >>> eB = note.Note('E4', type='quarter')
    >>> eC = note.Note('F4', type='quarter')
    >>> sourceStream.insert(11, eA)
    >>> sourceStream.insert(12, eB)
    >>> sourceStream.insert(13, eC)
    >>> destinationStream.append([eA, eB, eC])  # not needed if autoAdd were true

    then running this function will cause eA, eB, and eC
    to have offsets 21.625, 22.75, and 23.875 respectively
    in destinationStream:

    >>> tempo.interpolateElements(element1, element2,
    ...         sourceStream, destinationStream, autoAdd=False)
    >>> for el in [eA, eB, eC]:
    ...    print(el.getOffsetBySite(destinationStream))
    21.625
    22.75
    23.875

    if the elements between element1 and element2 do not yet
    appear in destinationStream, they are automatically added
    unless autoAdd is False.

    (with the default autoAdd, elements are automatically added to new streams):

    >>> destStream2 = stream.Stream()
    >>> destStream2.insert(10.1, element1)
    >>> destStream2.insert(50.5, element2)
    >>> tempo.interpolateElements(element1, element2, sourceStream, destStream2)
    >>> for el in [eA, eB, eC]:
    ...    print('%.1f' % (el.getOffsetBySite(destStream2),))
    20.2
    30.3
    40.4

    (unless autoAdd is set to False, in which case a Tempo Exception arises:)

    >>> destStream3 = stream.Stream()
    >>> destStream3.insert(100, element1)
    >>> destStream3.insert(500, element2)
    >>> eA.id = 'blah'
    >>> tempo.interpolateElements(element1, element2, sourceStream, destStream3, autoAdd=False)
    Traceback (most recent call last):
    music21.tempo.TempoException: Could not find element <music21.note.Note D> with id ...
    '''
    try:
        startOffsetSrc = element1.getOffsetBySite(sourceStream)
    except exceptions21.Music21Exception as e:
        raise TempoException('could not find element1 in sourceStream') from e
    try:
        startOffsetDest = element1.getOffsetBySite(destinationStream)
    except exceptions21.Music21Exception as e:
        raise TempoException('could not find element1 in destinationStream') from e

    try:
        endOffsetSrc = element2.getOffsetBySite(sourceStream)
    except exceptions21.Music21Exception as e:
        raise TempoException('could not find element2 in sourceStream') from e
    try:
        endOffsetDest = element2.getOffsetBySite(destinationStream)
    except exceptions21.Music21Exception as e:
        raise TempoException('could not find element2 in destinationStream') from e

    scaleAmount = ((endOffsetDest - startOffsetDest) / (endOffsetSrc - startOffsetSrc))

    interpolatedElements = sourceStream.iter.getElementsByOffset(
        offsetStart=startOffsetSrc,
        offsetEnd=endOffsetSrc
    )
    for el in interpolatedElements:
        elOffsetSrc = el.getOffsetBySite(sourceStream)
        try:
            el.getOffsetBySite(destinationStream)  # dummy
        except base.SitesException as e:
            if autoAdd is True:
                destinationOffset = (scaleAmount * (elOffsetSrc - startOffsetSrc)) + startOffsetDest
                destinationStream.insert(destinationOffset, el)
            else:
                raise TempoException(
                    'Could not find element '
                    + f'{el!r} with id {el.id!r} '
                    + 'in destinationStream and autoAdd is false') from e
        else:
            destinationOffset = (scaleAmount * (elOffsetSrc - startOffsetSrc)) + startOffsetDest
            el.setOffsetBySite(destinationStream, destinationOffset)


# ------------------------------------------------------------------------------
class Test(unittest.TestCase):

    def testCopyAndDeepcopy(self):
        '''Test copying all objects defined in this module
        '''
        import sys
        import types
        for part in sys.modules[self.__module__].__dict__:
            match = False
            for skip in ['_', '__', 'Test', 'Exception']:
                if part.startswith(skip) or part.endswith(skip):
                    match = True
            if match:
                continue
            obj = getattr(sys.modules[self.__module__], part)
            # noinspection PyTypeChecker
            if callable(obj) and not isinstance(obj, types.FunctionType):
                copy.copy(obj)
                copy.deepcopy(obj)

    def testSetup(self):
        mm1 = MetronomeMark(number=60, referent=note.Note(type='quarter'))
        self.assertEqual(mm1.number, 60)

        tm1 = TempoText('Lebhaft')
        self.assertEqual(tm1.text, 'Lebhaft')

    def testUnicode(self):
        # test with no arguments
        TempoText()
        # test with arguments
        TempoText('adagio')

        # environLocal.printDebug(['testing tempo instantiation', tm])
        mm = MetronomeMark('adagio')
        self.assertEqual(mm.number, 56)
        self.assertTrue(mm.numberImplicit)

        self.assertEqual(mm.number, 56)
        tm2 = TempoText('très vite')

        self.assertEqual(tm2.text, 'très vite')
        mm = tm2.getMetronomeMark()
        self.assertEqual(mm.number, 144)

    def testMetronomeMarkA(self):
        from music21 import tempo
        mm = tempo.MetronomeMark()
        mm.number = 56  # should implicitly set text
        self.assertEqual(mm.text, 'adagio')
        self.assertTrue(mm.textImplicit)
        mm.text = 'slowish'
        self.assertEqual(mm.text, 'slowish')
        self.assertFalse(mm.textImplicit)
        # default
        self.assertEqual(mm.referent.quarterLength, 1.0)

        # setting the text first
        mm = tempo.MetronomeMark()
        mm.text = 'presto'
        mm.referent = duration.Duration(3.0)
        self.assertEqual(mm.text, 'presto')
        self.assertEqual(mm.number, 184)
        self.assertTrue(mm.numberImplicit)
        mm.number = 200
        self.assertEqual(mm.number, 200)
        self.assertFalse(mm.numberImplicit)
        # still have default
        self.assertEqual(mm.referent.quarterLength, 3.0)
        self.assertEqual(repr(mm), '<music21.tempo.MetronomeMark presto Dotted Half=200>')

    def testMetronomeMarkB(self):
        mm = MetronomeMark()
        # with no args these are set to None
        self.assertEqual(mm.numberImplicit, None)
        self.assertEqual(mm.textImplicit, None)

        mm = MetronomeMark(number=100)
        self.assertEqual(mm.number, 100)
        self.assertFalse(mm.numberImplicit)
        self.assertEqual(mm.text, None)
        # not set
        self.assertEqual(mm.textImplicit, None)

        mm = MetronomeMark(number=101, text='rapido')
        self.assertEqual(mm.number, 101)
        self.assertFalse(mm.numberImplicit)
        self.assertEqual(mm.text, 'rapido')
        self.assertFalse(mm.textImplicit)

    def testMetronomeModulationA(self):
        from music21 import tempo
        # need to create a mm without a speed
        # want to say that an eighth is becoming the speed of a sixteenth
        mm1 = tempo.MetronomeMark(referent=0.5, number=120)
        mm2 = tempo.MetronomeMark(referent='16th')

        mmod1 = tempo.MetricModulation()
        mmod1.oldMetronome = mm1
        mmod1.newMetronome = mm2

        # this works, and new value is updated:
        self.assertEqual(str(mmod1),
                         '<music21.tempo.MetricModulation '
                         + '<music21.tempo.MetronomeMark animato Eighth=120>='
                         + '<music21.tempo.MetronomeMark animato 16th=120>>')

        # we can get the same result by using setEqualityByReferent()
        mm1 = tempo.MetronomeMark(referent=0.5, number=120)
        mmod1 = tempo.MetricModulation()
        mmod1.oldMetronome = mm1
        # will automatically set right mm, as presently is None
        mmod1.setOtherByReferent(referent='16th')
        # should get the same result as above, but with defined value
        self.assertEqual(str(mmod1),
                         '<music21.tempo.MetricModulation '
                         + '<music21.tempo.MetronomeMark animato Eighth=120>='
                         + '<music21.tempo.MetronomeMark animato 16th=120>>')
        # the effective speed as been slowed by this modulation
        self.assertEqual(mmod1.oldMetronome.getQuarterBPM(), 60.0)
        self.assertEqual(mmod1.newMetronome.getQuarterBPM(), 30.0)

    def testGetPreviousMetronomeMarkA(self):
        from music21 import tempo
        from music21 import stream

        # test getting basic metronome marks
        p = stream.Part()
        m1 = stream.Measure()
        m1.repeatAppend(note.Note(quarterLength=1), 4)
        m2 = copy.deepcopy(m1)
        mm1 = tempo.MetronomeMark(number=56, referent=0.25)
        m1.insert(0, mm1)
        mm2 = tempo.MetronomeMark(number=150, referent=0.5)
        m2.insert(0, mm2)
        p.append([m1, m2])
        self.assertEqual(str(mm2.getPreviousMetronomeMark()),
                         '<music21.tempo.MetronomeMark adagio 16th=56>')
        # p.show()

    def testGetPreviousMetronomeMarkB(self):
        from music21 import tempo
        from music21 import stream

        # test using a tempo text, will return a default metronome mark if possible
        p = stream.Part()
        m1 = stream.Measure()
        m1.repeatAppend(note.Note(quarterLength=1), 4)
        m2 = copy.deepcopy(m1)
        mm1 = tempo.TempoText('slow')
        m1.insert(0, mm1)
        mm2 = tempo.MetronomeMark(number=150, referent=0.5)
        m2.insert(0, mm2)
        p.append([m1, m2])
        self.assertEqual(str(mm2.getPreviousMetronomeMark()),
                         '<music21.tempo.MetronomeMark slow Quarter=56>')
        # p.show()

    def testGetPreviousMetronomeMarkC(self):
        from music21 import tempo
        from music21 import stream

        # test using a metric modulation
        p = stream.Part()
        m1 = stream.Measure()
        m1.repeatAppend(note.Note(quarterLength=1), 4)
        m2 = copy.deepcopy(m1)
        m3 = copy.deepcopy(m2)

        mm1 = tempo.MetronomeMark('slow')
        m1.insert(0, mm1)

        mm2 = tempo.MetricModulation()
        mm2.oldMetronome = tempo.MetronomeMark(referent=1, number=52)
        mm2.setOtherByReferent(referent='16th')
        m2.insert(0, mm2)

        mm3 = tempo.MetronomeMark(number=150, referent=0.5)
        m3.insert(0, mm3)

        p.append([m1, m2, m3])
        # p.show()

        self.assertEqual(str(mm3.getPreviousMetronomeMark()),
                         '<music21.tempo.MetronomeMark lento 16th=52>')

    def testSetReferentA(self):
        '''Test setting referents directly via context searches.
        '''
        from music21 import tempo
        from music21 import stream
        p = stream.Part()
        m1 = stream.Measure()
        m1.repeatAppend(note.Note(quarterLength=1), 4)
        m2 = copy.deepcopy(m1)
        m3 = copy.deepcopy(m2)

        mm1 = tempo.MetronomeMark(number=92)
        m1.insert(0, mm1)

        mm2 = tempo.MetricModulation()
        m2.insert(0, mm2)

        p.append([m1, m2, m3])

        mm2.oldReferent = 0.25
        self.assertEqual(str(mm2.oldMetronome),
                         '<music21.tempo.MetronomeMark moderate 16th=368.0>')
        mm2.setOtherByReferent(referent=2)
        self.assertEqual(str(mm2.newMetronome),
                         '<music21.tempo.MetronomeMark moderate Half=368.0>')
        # p.show()

    def testSetReferentB(self):
        from music21 import tempo
        from music21 import stream
        s = stream.Stream()
        mm1 = tempo.MetronomeMark(number=60)
        s.append(mm1)
        s.repeatAppend(note.Note(quarterLength=1), 2)
        s.repeatAppend(note.Note(quarterLength=0.5), 4)

        mmod1 = tempo.MetricModulation()
        mmod1.oldReferent = 0.5  # can use Duration objects
        mmod1.newReferent = 'quarter'  # can use Duration objects
        s.append(mmod1)
        mmod1.updateByContext()

        self.assertEqual(str(mmod1.oldMetronome.referent), '<music21.duration.Duration 0.5>')
        self.assertEqual(mmod1.oldMetronome.number, 120)
        self.assertEqual(str(mmod1.newMetronome),
                         '<music21.tempo.MetronomeMark animato Quarter=120.0>')

        s.append(note.Note())
        s.repeatAppend(note.Note(quarterLength=1.5), 2)

        mmod2 = tempo.MetricModulation()
        mmod2.oldReferent = 1.5
        mmod2.newReferent = 'quarter'  # can use Duration objects
        s.append(mmod2)
        mmod2.updateByContext()
        self.assertEqual(str(mmod2.oldMetronome),
                         '<music21.tempo.MetronomeMark animato Dotted Quarter=80.0>')
        self.assertEqual(str(mmod2.newMetronome),
                         '<music21.tempo.MetronomeMark andantino Quarter=80.0>')

        # s.repeatAppend(note.Note(), 4)
        # s.show()

    def testSetReferentC(self):
        from music21 import tempo
        from music21 import stream
        s = stream.Stream()
        mm1 = tempo.MetronomeMark(number=60)
        s.append(mm1)
        s.repeatAppend(note.Note(quarterLength=1), 2)
        s.repeatAppend(note.Note(quarterLength=0.5), 4)

        mmod1 = tempo.MetricModulation()
        s.append(mmod1)
        mmod1.oldReferent = 0.5  # can use Duration objects
        mmod1.newReferent = 'quarter'  # can use Duration objects

        self.assertEqual(str(mmod1.oldMetronome.referent), '<music21.duration.Duration 0.5>')
        self.assertEqual(mmod1.oldMetronome.number, 120)
        self.assertEqual(str(mmod1.newMetronome),
                         '<music21.tempo.MetronomeMark larghetto Quarter=120.0>')

        s.append(note.Note())
        s.repeatAppend(note.Note(quarterLength=1.5), 2)

        mmod2 = tempo.MetricModulation()
        s.append(mmod2)
        mmod2.oldReferent = 1.5
        mmod2.newReferent = 'quarter'  # can use Duration objects

        self.assertEqual(str(mmod2.oldMetronome),
                         '<music21.tempo.MetronomeMark larghetto Dotted Quarter=80.0>')
        self.assertEqual(str(mmod2.newMetronome),
                         '<music21.tempo.MetronomeMark larghetto Quarter=80.0>')
        # s.repeatAppend(note.Note(), 4)
        # s.show()

    def testSetReferentD(self):
        from music21 import tempo
        from music21 import stream
        s = stream.Stream()
        mm1 = tempo.MetronomeMark(number=60)
        s.append(mm1)
        s.repeatAppend(note.Note(quarterLength=1), 2)
        s.repeatAppend(note.Note(quarterLength=0.5), 4)

        mmod1 = tempo.MetricModulation()
        s.append(mmod1)
        # even with we have no assigned metronome, update context will create
        mmod1.updateByContext()

        self.assertEqual(str(mmod1.oldMetronome.referent), '<music21.duration.Duration 1.0>')
        self.assertEqual(mmod1.oldMetronome.number, 60)  # value form last mm
        # still have not set new
        self.assertEqual(mmod1.newMetronome, None)

        mmod1.newReferent = 0.25
        self.assertEqual(str(mmod1.newMetronome), '<music21.tempo.MetronomeMark larghetto 16th=60>')
        # s.append(note.Note())
        # s.repeatAppend(note.Note(quarterLength=1.5), 2)

    def testSetReferentE(self):
        from music21 import stream

        s = stream.Stream()
        mm1 = MetronomeMark(number=70)
        s.append(mm1)
        s.repeatAppend(note.Note(quarterLength=1), 2)
        s.repeatAppend(note.Note(quarterLength=0.5), 4)

        mmod1 = MetricModulation()
        mmod1.oldReferent = 'eighth'
        mmod1.newReferent = 'half'
        s.append(mmod1)
        self.assertEqual(mmod1.oldMetronome.number, 140)
        self.assertEqual(mmod1.newMetronome.number, 140)

        s = stream.Stream()
        mm1 = MetronomeMark(number=70)
        s.append(mm1)
        s.repeatAppend(note.Note(quarterLength=1), 2)
        s.repeatAppend(note.Note(quarterLength=0.5), 4)

        # make sure it works in reverse too
        mmod1 = MetricModulation()
        mmod1.oldReferent = 'eighth'
        mmod1.newReferent = 'half'
        s.append(mmod1)
        self.assertEqual(mmod1.newMetronome.number, 140)
        self.assertEqual(mmod1.oldMetronome.number, 140)
        self.assertEqual(mmod1.number, 140)

    def testSecondsPerQuarterA(self):
        mm = MetronomeMark(referent=1.0, number=120.0)
        self.assertEqual(mm.secondsPerQuarter(), 0.5)
        self.assertEqual(mm.durationToSeconds(120), 60.0)
        self.assertEqual(mm.secondsToDuration(60.0).quarterLength, 120.0)

        mm = MetronomeMark(referent=0.5, number=120.0)
        self.assertEqual(mm.secondsPerQuarter(), 1.0)
        self.assertEqual(mm.durationToSeconds(60), 60.0)
        self.assertEqual(mm.secondsToDuration(60.0).quarterLength, 60.0)

        mm = MetronomeMark(referent=2.0, number=120.0)
        self.assertEqual(mm.secondsPerQuarter(), 0.25)
        self.assertEqual(mm.durationToSeconds(240), 60.0)
        self.assertEqual(mm.secondsToDuration(60.0).quarterLength, 240.0)

        mm = MetronomeMark(referent=1.5, number=120.0)
        self.assertAlmostEqual(mm.secondsPerQuarter(), 1 / 3)
        self.assertEqual(mm.durationToSeconds(180), 60.0)
        self.assertEqual(mm.secondsToDuration(60.0).quarterLength, 180.0)

    def testStylesAreShared(self):
        halfNote = note.Note(type='half')
        mm = MetronomeMark('slow', 40, halfNote)
        mm.style.justify = 'left'
        self.assertIs(mm._tempoText.style, mm.style)
        self.assertIs(mm._tempoText._textExpression.style, mm.style)


# ------------------------------------------------------------------------------
# define presented order in documentation
_DOC_ORDER = [MetronomeMark, TempoText, MetricModulation, interpolateElements]


if __name__ == '__main__':
    import music21
    music21.mainTest(Test)  # , runTest='testStylesAreShared')

