# ------------------------------------------------------------------------------
# Name: harmonicFunction.py
# Purpose: Mapping between Roman numeral figures and harmonic function labels
#
# Authors: Mark Gotham
#
# Copyright: Copyright © 2022-2023 Michael Scott Asato Cuthbert
# License: BSD, see license.txt
# ------------------------------------------------------------------------------
from __future__ import annotations
import unittest
from music21 import common
from music21 import key
from music21 import roman
from music21 import scale
[docs]
class HarmonicFunction(common.enums.StrEnum):
TONIC_MAJOR = 'T'
TONIC_MAJOR_PARALLELKLANG_MINOR = 'Tp'
TONIC_MAJOR_GEGENKLANG_MINOR = 'Tg'
TONIC_MINOR = 't'
TONIC_MINOR_PARALLELKLANG_MAJOR = 'tP'
TONIC_MINOR_GEGENKLANG_MAJOR = 'tG'
SUBDOMINANT_MAJOR = 'S'
SUBDOMINANT_MAJOR_PARALLELKLANG_MINOR = 'Sp'
SUBDOMINANT_MAJOR_GEGENKLANG_MINOR = 'Sg'
SUBDOMINANT_MINOR = 's'
SUBDOMINANT_MINOR_PARALLELKLANG_MAJOR = 'sP'
SUBDOMINANT_MINOR_GEGENKLANG_MAJOR = 'sG'
DOMINANT_MAJOR = 'D'
DOMINANT_MAJOR_PARALLELKLANG_MINOR = 'Dp'
DOMINANT_MAJOR_GEGENKLANG_MINOR = 'Dg'
DOMINANT_MINOR = 'd'
DOMINANT_MINOR_PARALLELKLANG_MAJOR = 'dP'
DOMINANT_MINOR_GEGENKLANG_MAJOR = 'dG'
_functionFigureTuplesKeyNeutral = {
HarmonicFunction.TONIC_MAJOR: 'I', # 'T'
HarmonicFunction.TONIC_MINOR: 'i', # 't'
HarmonicFunction.SUBDOMINANT_MINOR_GEGENKLANG_MAJOR: 'bII', # 'sG'
HarmonicFunction.SUBDOMINANT_MAJOR_PARALLELKLANG_MINOR: 'ii', # 'Sp'
HarmonicFunction.SUBDOMINANT_MAJOR: 'IV', # 'S'
HarmonicFunction.SUBDOMINANT_MINOR: 'iv', # 's'
HarmonicFunction.DOMINANT_MAJOR: 'V', # 'D'
HarmonicFunction.DOMINANT_MINOR: 'v', # 'd'
HarmonicFunction.TONIC_MAJOR_PARALLELKLANG_MINOR: 'vi', # 'Tp'
HarmonicFunction.SUBDOMINANT_MAJOR_GEGENKLANG_MINOR: 'vi', # 'Sg'
HarmonicFunction.DOMINANT_MAJOR_GEGENKLANG_MINOR: 'bvii', # 'Dg'
}
functionFigureTuplesMajor = {
HarmonicFunction.TONIC_MINOR_PARALLELKLANG_MAJOR: 'bIII', # 'tP', note first
HarmonicFunction.DOMINANT_MINOR_GEGENKLANG_MAJOR: 'bIII', # 'dG'
HarmonicFunction.DOMINANT_MAJOR_PARALLELKLANG_MINOR: 'iii', # 'Dp', note first
HarmonicFunction.TONIC_MAJOR_GEGENKLANG_MINOR: 'iii', # 'Tg'
HarmonicFunction.SUBDOMINANT_MINOR_PARALLELKLANG_MAJOR: 'bVI', # 'sP', note first
HarmonicFunction.TONIC_MINOR_GEGENKLANG_MAJOR: 'bVI', # 'tG'
HarmonicFunction.DOMINANT_MINOR_PARALLELKLANG_MAJOR: 'bVII', # 'dP'
}
functionFigureTuplesMajor = {
**functionFigureTuplesMajor,
**_functionFigureTuplesKeyNeutral,
}
functionFigureTuplesMinor = {
HarmonicFunction.TONIC_MINOR_PARALLELKLANG_MAJOR: 'III', # 'tP', note first
HarmonicFunction.DOMINANT_MINOR_GEGENKLANG_MAJOR: 'III', # 'dG'
HarmonicFunction.DOMINANT_MAJOR_PARALLELKLANG_MINOR: '#iii', # 'Dp', note first
HarmonicFunction.TONIC_MAJOR_GEGENKLANG_MINOR: '#iii', # 'Tg'
HarmonicFunction.SUBDOMINANT_MINOR_PARALLELKLANG_MAJOR: 'VI', # 'sP', note first
HarmonicFunction.TONIC_MINOR_GEGENKLANG_MAJOR: 'VI', # 'tG'
HarmonicFunction.DOMINANT_MINOR_PARALLELKLANG_MAJOR: 'VII', # 'dP'
}
functionFigureTuplesMinor = {
**functionFigureTuplesMinor,
**_functionFigureTuplesKeyNeutral,
}
[docs]
def functionToRoman(thisHarmonicFunction: HarmonicFunction,
keyOrScale: key.Key|scale.ConcreteScale|str = 'C'
) -> roman.RomanNumeral|None:
'''
Takes harmonic function labels (such as 'T' for major tonic)
with a key (keyOrScale, default = 'C') and
returns the corresponding :class:`~music21.roman.RomanNumeral` object.
>>> analysis.harmonicFunction.functionToRoman('T')
<music21.roman.RomanNumeral I in C major>
The harmonicFunction argument can be a string (as shown),
though strictly speaking, it's handled through a special HarmonicFunction enum object.
>>> fn = analysis.harmonicFunction.HarmonicFunction.TONIC_MAJOR
>>> str(fn)
'T'
>>> analysis.harmonicFunction.functionToRoman(fn).figure
'I'
As with Roman numerals, this is case sensitive.
For instance, 't' indicates a minor tonic
as distinct from the major tonic, 'T'.
>>> analysis.harmonicFunction.functionToRoman('t').figure
'i'
There are 18 main functional labels supported in all, for
the three functional categories
(T for tonic, S for subdominant, and D for dominant) and
three relevant transformation types (none, P, and G)
all in upper and lower case (for major/minor):
T, Tp, Tg, t, tP, tG,
S, Sp, Sg, s, sP, sG,
D, Dp, Dg, d, dP, dG.
Note that this module uses terminology from modern German music theory
where Functional notation ('HarmonicFunctionstheorie') is typically used
throughout the curriculum in preference over Roman numerals ('Stufentheorie').
First, note the false friend: here 'P' for 'Parallel'
connects a major triad with the minor triad a minor third below (e.g. C-a).
(in English-speaking traditions this would usually be 'relative').
Second, note that this module uses
'G' (and 'g'), standing for
'Gegenklänge' or 'Gegenparallelen'.
'L' (and 'l') for Leittonwechselklänge is equivalent to this.
(Again, 'G' is more common in modern German-language music theory).
Use the keyOrScale argement to specify a key.
This makes a difference where 6th and 7th degrees of minor are involved.
>>> analysis.harmonicFunction.functionToRoman('sP', keyOrScale='C').figure
'bVI'
>>> analysis.harmonicFunction.functionToRoman('sP', keyOrScale='a').figure
'VI'
Some of the 18 main functions overlap, with two functional labels
referring to the same Roman numeral figure.
For instance both 'Tg' and 'Dp' simply map to 'iii':
>>> analysis.harmonicFunction.functionToRoman('Tp').figure
'vi'
>>> analysis.harmonicFunction.functionToRoman('Sg').figure
'vi'
The reverse operation is handled by the complementary
:func:`~music21.analysis.harmonicFunction.romanToFunction`.
In this case, :func:`~music21.analysis.harmonicFunction.romanToFunction`
follows the convention of preferring the P-version over alternatives.
>>> rn = roman.RomanNumeral('vi')
>>> str(analysis.harmonicFunction.romanToFunction(rn))
'Tp'
'''
if isinstance(keyOrScale, str):
keyOrScale = key.Key(keyOrScale)
referenceTuples = functionFigureTuplesMajor
if isinstance(keyOrScale, key.Key) and keyOrScale.mode == 'minor':
referenceTuples = functionFigureTuplesMinor
try:
figure = referenceTuples[thisHarmonicFunction]
except KeyError:
return None
return roman.RomanNumeral(figure, keyOrScale)
[docs]
def romanToFunction(rn: roman.RomanNumeral,
onlyHauptHarmonicFunction: bool = False
) -> HarmonicFunction|None:
'''
Takes a Roman numeral and returns a corresponding harmonic function label.
>>> rn1 = roman.RomanNumeral('VI', 'a')
>>> fn1 = analysis.harmonicFunction.romanToFunction(rn1)
>>> fn1
<HarmonicFunction.SUBDOMINANT_MINOR_PARALLELKLANG_MAJOR>
This can be converted into a string:
>>> str(fn1)
'sP'
Optionally, set onlyHauptHarmonicFunction to True to return
a simplified version with only the HauptHarmonicFunction
(one of t, T, s, S, d, D: major and minor forms of the tonic, subdominant and dominant).
>>> fn1 = analysis.harmonicFunction.romanToFunction(rn1, onlyHauptHarmonicFunction=True)
>>> fn1
<HarmonicFunction.SUBDOMINANT_MINOR>
>>> str(fn1)
's'
Inversions are not currently considered (they may be in a future version of this).
This function simply uses the romanNumeral attribute of the roman.RomanNumeral object.
This excludes inversions, but
includes, where applicable, the frontAlterationAccidental.modifier.
>>> rn2 = roman.RomanNumeral('bII6', 'g')
>>> fn2 = analysis.harmonicFunction.romanToFunction(rn2)
>>> fn2
<HarmonicFunction.SUBDOMINANT_MINOR_GEGENKLANG_MAJOR>
>>> str(fn2)
'sG'
See further notes on the complementary
:func:`~music21.analysis.harmonicFunction.functionToRoman`.
'''
referenceTuples = functionFigureTuplesMajor
if rn.key: # RomanNumeral object can be created without one.
if rn.key.mode == 'minor':
referenceTuples = functionFigureTuplesMinor
for thisKey, thisValue in referenceTuples.items():
if rn.romanNumeral == thisValue:
if onlyHauptHarmonicFunction:
return HarmonicFunction(str(thisKey)[0])
else:
return thisKey
return None
# ------------------------------------------------------------------------------
class Test(unittest.TestCase):
def testAllFunctionLabelsInEnum(self):
'''
Test that all the entries in the functionFigureTuples
(both major and minor) are represented in the HarmonicFunction enum.
Also tests one fake (invalid) function label.
'''
# All and only valid
for thisHarmonicFunction in functionFigureTuplesMajor:
HarmonicFunction(thisHarmonicFunction)
for thisHarmonicFunction in functionFigureTuplesMinor:
HarmonicFunction(thisHarmonicFunction)
# Invalid
fakeExample = 'TPG'
self.assertRaises(ValueError, HarmonicFunction, fakeExample)
def testFunctionToRoman(self):
self.assertEqual(functionToRoman(HarmonicFunction.TONIC_MAJOR).figure, 'I')
def testSimplified(self):
rn = roman.RomanNumeral('III', 'f')
fn1 = romanToFunction(rn)
self.assertIs(fn1, HarmonicFunction.TONIC_MINOR_PARALLELKLANG_MAJOR)
self.assertEqual(str(fn1), 'tP')
fn2 = romanToFunction(rn, onlyHauptHarmonicFunction=True)
self.assertIs(fn2, HarmonicFunction.TONIC_MINOR)
self.assertEqual(str(fn2), 't')
def testIgnoresInversion(self):
self.assertEqual(romanToFunction(roman.RomanNumeral('i6')), 't')
# -----------------------------------------------------------------------------
if __name__ == '__main__':
import music21
music21.mainTest(Test)