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scales

JustScale

This class implements arbitrary just intonation scales.

Source code in /opt/hostedtoolcache/Python/3.11.3/x64/lib/python3.11/site-packages/jintonic/scales.py 
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class JustScale:
    """This class implements arbitrary just intonation scales."""

    def __init__(self, tones: List[JustInterval]):
        """Initializes a JustScale.

        Parameters:
            tones: A list of intervals or an object containing a list of
                intervals (that implements the attribute intervals)

        Examples:
            >>> scale = JustScale([JustInterval(1, 1)])
            >>> scale.append(JustInterval(3, 2))
            >>> scale.append(JustInterval(2, 1))
            >>> scale
            JustScale([1/1, 3/2, 2/1])
        """
        self._tones = tones

    def append(self, tone: JustInterval):
        """Appends tones to the scale.

        Parameters:
            tone: A new tone

        Examples:
            >>> scale = JustScale([JustInterval(3, 2)])
            >>> scale.append(JustInterval(4, 3))
            >>> scale.tones
            [JustInterval(4, 3), JustInterval(3, 2)]
        """
        if not isinstance(tone, JustInterval):
            msg = "cannot append type {}. ".format(type(tone))
            msg += 'Expecting type "JustInterval"'
            raise ValueError(msg)
        self._tones.append(tone)

    def hertz(self, fundamental: float) -> List[float]:
        """Translates scale intervals to pitches in Hertz over a fundamental

        Note:
            Here, the fundamental is always 1/1 and is not to be mistaken with
            the first tone of the scale. If 1/1 is not part of the scale's
            tones, the fundamental will not be part of the scale.

        Parameters:
            fundamental: The scale's 0 degree (fundamental) pitch in Hertz.

        Returns:
            Scale pitches as Hertz
        """
        return [fundamental * tone for tone in self.tones]

    @property
    def tones(self) -> List[JustInterval]:
        """JustScale tones.

        Returns:
            Scale tones
        """
        return sorted(self._tones)

    @tones.setter
    def tones(self, values: List[JustInterval]):
        """Sets JustScale tones.

        Parameters:
            values: A list of tones
        """
        for tone in values:
            if not isinstance(tone, JustInterval):
                msg = "tones must be a list of JustIntervals. "
                msg += "Got '{}'".format(values)
                raise ValueError(msg)
        self._tones = values

    @property
    def intervals(self) -> List[JustInterval]:
        """JustScale intervals.

        Returns:
            Scale intervals

        Examples:
            >>> scale = JustScale([JustInterval(1, 1)])
            >>> scale.append(JustInterval(3, 2))
            >>> scale.append(JustInterval(2, 1))
            >>> scale.intervals
            [JustInterval(3, 2), JustInterval(4, 3)]
        """
        return [tone - self.tones[i - 1] for i, tone in enumerate(self.tones)][1:]

    @property
    def complement(self) -> JustScale:
        """JustScale complement

        Returns:
            The complement scale

        Examples:
            >>> scale = JustScale([JustInterval(1, 1)])
            >>> scale.append(JustInterval(3, 2))
            >>> scale.append(JustInterval(2, 1))
            >>> scale.complement
            JustScale([1/1, 4/3, 2/1])
        """
        tones = [tone.complement for tone in self.tones]
        return JustScale(tones)

    @property
    def prime_limit(self) -> int:
        """JustScale prime limit"""
        return max([tone.prime_limit for tone in self.tones])

    def __repr__(self):
        """repr(self)"""
        pitches = ", ".join(
            [
                "/".join([str(tone.numerator), str(tone.denominator)])
                for tone in self.tones
            ]
        )
        return "{}([{}])".format(self.__class__.__name__, pitches)

tones: List[JustInterval] writable property

JustScale tones.

Returns:

Type Description
List[JustInterval]

Scale tones

intervals: List[JustInterval] property

JustScale intervals.

Returns:

Type Description
List[JustInterval]

Scale intervals

Examples:

>>> scale = JustScale([JustInterval(1, 1)])
>>> scale.append(JustInterval(3, 2))
>>> scale.append(JustInterval(2, 1))
>>> scale.intervals
[JustInterval(3, 2), JustInterval(4, 3)]

complement: JustScale property

JustScale complement

Returns:

Type Description
JustScale

The complement scale

Examples:

>>> scale = JustScale([JustInterval(1, 1)])
>>> scale.append(JustInterval(3, 2))
>>> scale.append(JustInterval(2, 1))
>>> scale.complement
JustScale([1/1, 4/3, 2/1])

prime_limit: int property

JustScale prime limit

__init__(tones)

Initializes a JustScale.

Parameters:

Name Type Description Default
tones List[JustInterval]

A list of intervals or an object containing a list of intervals (that implements the attribute intervals)

 required

Examples:

>>> scale = JustScale([JustInterval(1, 1)])
>>> scale.append(JustInterval(3, 2))
>>> scale.append(JustInterval(2, 1))
>>> scale
JustScale([1/1, 3/2, 2/1])
Source code in /opt/hostedtoolcache/Python/3.11.3/x64/lib/python3.11/site-packages/jintonic/scales.py 
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def __init__(self, tones: List[JustInterval]):
    """Initializes a JustScale.

    Parameters:
        tones: A list of intervals or an object containing a list of
            intervals (that implements the attribute intervals)

    Examples:
        >>> scale = JustScale([JustInterval(1, 1)])
        >>> scale.append(JustInterval(3, 2))
        >>> scale.append(JustInterval(2, 1))
        >>> scale
        JustScale([1/1, 3/2, 2/1])
    """
    self._tones = tones

append(tone)

Appends tones to the scale.

Parameters:

Name Type Description Default
tone JustInterval

A new tone

 required

Examples:

>>> scale = JustScale([JustInterval(3, 2)])
>>> scale.append(JustInterval(4, 3))
>>> scale.tones
[JustInterval(4, 3), JustInterval(3, 2)]
Source code in /opt/hostedtoolcache/Python/3.11.3/x64/lib/python3.11/site-packages/jintonic/scales.py 
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def append(self, tone: JustInterval):
    """Appends tones to the scale.

    Parameters:
        tone: A new tone

    Examples:
        >>> scale = JustScale([JustInterval(3, 2)])
        >>> scale.append(JustInterval(4, 3))
        >>> scale.tones
        [JustInterval(4, 3), JustInterval(3, 2)]
    """
    if not isinstance(tone, JustInterval):
        msg = "cannot append type {}. ".format(type(tone))
        msg += 'Expecting type "JustInterval"'
        raise ValueError(msg)
    self._tones.append(tone)

hertz(fundamental)

Translates scale intervals to pitches in Hertz over a fundamental

Note

Here, the fundamental is always 1/1 and is not to be mistaken with the first tone of the scale. If 1/1 is not part of the scale's tones, the fundamental will not be part of the scale.

Parameters:

Name Type Description Default
fundamental float

The scale's 0 degree (fundamental) pitch in Hertz.

 required

Returns:

Type Description
List[float]

Scale pitches as Hertz
Source code in /opt/hostedtoolcache/Python/3.11.3/x64/lib/python3.11/site-packages/jintonic/scales.py 
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def hertz(self, fundamental: float) -> List[float]:
    """Translates scale intervals to pitches in Hertz over a fundamental

    Note:
        Here, the fundamental is always 1/1 and is not to be mistaken with
        the first tone of the scale. If 1/1 is not part of the scale's
        tones, the fundamental will not be part of the scale.

    Parameters:
        fundamental: The scale's 0 degree (fundamental) pitch in Hertz.

    Returns:
        Scale pitches as Hertz
    """
    return [fundamental * tone for tone in self.tones]

JustTetrachord

This class implements disjunct just intonation tetrachords.

Source code in /opt/hostedtoolcache/Python/3.11.3/x64/lib/python3.11/site-packages/jintonic/scales.py 
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class JustTetrachord:
    """This class implements disjunct just intonation tetrachords."""

    def __init__(
        self,
        intervals: Optional[List[JustInterval]] = None,
        genus: Optional[str] = None,
        prime_limit: int = 7,
    ):
        """Initializes a JustTetrachord.

        A JustTetrachord can be constructed in one of two ways :

            - from a genus name (with naive division)
            - from a list of intervals between each successive tone

        Parameters:
            intervals: A list of intervals
            genus: One of 'enharmonic', 'chromatic', or 'diatonic'
            prime_limit: The prime limit to respect

        Examples:
            >>> JustTetrachord(genus='chromatic')
            JustTetrachord('chromatic' [27:28, 14:15, 5:6])

            >>> JustTetrachord(genus='enharmonic')
            JustTetrachord('enharmonic' [45:46, 23:24, 4:5])
            >>> JustTetrachord(genus='enharmonic').prime_limit
            23

            >>> intervals = []
            >>> intervals.append(JustInterval(32, 31))
            >>> intervals.append(JustInterval(31, 30))
            >>> intervals.append(JustInterval(5, 4))
            >>> JustTetrachord(intervals)
            JustTetrachord('enharmonic' [31:32, 30:31, 4:5])
            >>> JustTetrachord(intervals).prime_limit
            31
        """
        if not is_prime(prime_limit):
            msg = "The prime limit must be a prime number. "
            msg += "Got: '{}'".format(prime_limit)
            raise ValueError(msg)
        self._prime_limit = prime_limit

        if intervals is not None:
            self.intervals = intervals
        elif genus is not None:
            self.genus = genus.strip().lower()
        else:
            self._intervals: List[JustInterval] = []

    @classmethod
    def validate_tetrachord(cls, tetrachord: Union[JustTetrachord, List[JustInterval]]):
        """Validates a tetrachord.

        Parameters:
            tetrachord: The tetrachord to validate

        Raises:
            ValueError: If the given tetrachord is invalid
        """
        if len(tetrachord) != 3:
            msg = "Tetrachords must be formed of exactly three intervals. "
            msg += 'Got: "{}"'.format(tetrachord)
            raise ValueError(msg)
        # TODO implement __add__ and __radd__ to avoid needing these sum loops
        total_interval = JustInterval(1, 1)
        if isinstance(tetrachord, JustTetrachord):
            for interval in tetrachord.intervals:
                total_interval += interval
        else:
            for interval in tetrachord:
                total_interval += interval
        if total_interval != JustInterval(4, 3):
            msg = "Tetrachord intervals must sum to JustInterval(4, 3). "
            msg += 'Got: "{}"'.format(total_interval)
            raise ValueError(msg)

    @property
    def intervals(self) -> List[JustInterval]:
        """JustTetrachord intervals.
        Returns:
            The tetrachord's intervals

        Examples:
            >>> JustTetrachord(genus='enharmonic').intervals
            [JustInterval(46, 45), JustInterval(24, 23), JustInterval(5, 4)]
        """
        return self._intervals

    @intervals.setter
    def intervals(self, values):
        """Set JustTetrachord intervals.

        Parameters:
            value: A list of exactly three intervals which sum to 4:3
        """
        self.validate_tetrachord(values)
        self._prime_limit = max(
            values[0].prime_limit, values[1].prime_limit, values[2].prime_limit
        )
        self._intervals = values

    @property
    def genus(self) -> str:
        """JustTetrachord genus."""
        if not self.intervals:
            raise ValueError("Undefined intervals")
        end_intervals = [JustInterval(5, 4), JustInterval(6, 5), JustInterval(10, 9)]
        genera = ["enharmonic", "chromatic", "diatonic"]
        try:
            return genera[end_intervals.index(self.intervals[-1])]
        except ValueError:
            return "non-classical"

    @genus.setter
    def genus(self, value: str):
        """Set JustTetrachord genus.

        Note:
            When setting the genus, the movable tone is set to its most basic
            position by dividing by two the interval remaining after taking the
            characteristic interval.

        Parameters:
            value: A valid classical genus from ['enharmonic', 'chromatic', 'diatonic']
        """
        characteristic_intervals = {
            "enharmonic": JustInterval(5, 4),
            "chromatic": JustInterval(6, 5),
            "diatonic": JustInterval(10, 9),
        }
        characteristic = characteristic_intervals[value]
        remainder = JustInterval(4, 3) - characteristic
        intervals = remainder.divisions(2, self.prime_limit)
        intervals.append(characteristic)
        self.intervals = intervals

    @property
    def prime_limit(self) -> int:
        """JustTetrachord prime limit."""
        return self._prime_limit

    @property
    def permutations(self) -> List[JustTetrachord]:
        """All (there are six) possible permutations of the JustTetrachord.

        Returns:
            The permutations of the JustTetrachord
        """
        return [
            JustTetrachord(intervals=list(permutation))
            for permutation in permutations(self.intervals)
        ]

    def __repr__(self):
        """repr(self)"""
        return "{}('{}' [{}:{}, {}:{}, {}:{}])".format(
            self.__class__.__name__,
            self.genus,
            self.intervals[0].denominator,
            self.intervals[0].numerator,
            self.intervals[1].denominator,
            self.intervals[1].numerator,
            self.intervals[2].denominator,
            self.intervals[2].numerator,
        )

    def __eq__(self, other):
        """self == other"""
        return self.intervals == other.intervals

    def __len__(self):
        """len(self)"""
        return len(self.intervals)

intervals: List[JustInterval] writable property

JustTetrachord intervals.

Returns:

Type Description
List[JustInterval]

The tetrachord's intervals

Examples:

>>> JustTetrachord(genus='enharmonic').intervals
[JustInterval(46, 45), JustInterval(24, 23), JustInterval(5, 4)]

genus: str writable property

JustTetrachord genus.

prime_limit: int property

JustTetrachord prime limit.

permutations: List[JustTetrachord] property

All (there are six) possible permutations of the JustTetrachord.

Returns:

Type Description
List[JustTetrachord]

The permutations of the JustTetrachord

__init__(intervals=None, genus=None, prime_limit=7)

Initializes a JustTetrachord.

A JustTetrachord can be constructed in one of two ways
  • from a genus name (with naive division)
  • from a list of intervals between each successive tone

Parameters:

Name Type Description Default
intervals Optional[List[JustInterval]]

A list of intervals

 None
genus Optional[str]

One of 'enharmonic', 'chromatic', or 'diatonic'

 None
prime_limit int

The prime limit to respect

 7

Examples:

>>> JustTetrachord(genus='chromatic')
JustTetrachord('chromatic' [27:28, 14:15, 5:6])

>>> JustTetrachord(genus='enharmonic')
JustTetrachord('enharmonic' [45:46, 23:24, 4:5])
>>> JustTetrachord(genus='enharmonic').prime_limit
23

>>> intervals = []
>>> intervals.append(JustInterval(32, 31))
>>> intervals.append(JustInterval(31, 30))
>>> intervals.append(JustInterval(5, 4))
>>> JustTetrachord(intervals)
JustTetrachord('enharmonic' [31:32, 30:31, 4:5])
>>> JustTetrachord(intervals).prime_limit
31
Source code in /opt/hostedtoolcache/Python/3.11.3/x64/lib/python3.11/site-packages/jintonic/scales.py 
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def __init__(
    self,
    intervals: Optional[List[JustInterval]] = None,
    genus: Optional[str] = None,
    prime_limit: int = 7,
):
    """Initializes a JustTetrachord.

    A JustTetrachord can be constructed in one of two ways :

        - from a genus name (with naive division)
        - from a list of intervals between each successive tone

    Parameters:
        intervals: A list of intervals
        genus: One of 'enharmonic', 'chromatic', or 'diatonic'
        prime_limit: The prime limit to respect

    Examples:
        >>> JustTetrachord(genus='chromatic')
        JustTetrachord('chromatic' [27:28, 14:15, 5:6])

        >>> JustTetrachord(genus='enharmonic')
        JustTetrachord('enharmonic' [45:46, 23:24, 4:5])
        >>> JustTetrachord(genus='enharmonic').prime_limit
        23

        >>> intervals = []
        >>> intervals.append(JustInterval(32, 31))
        >>> intervals.append(JustInterval(31, 30))
        >>> intervals.append(JustInterval(5, 4))
        >>> JustTetrachord(intervals)
        JustTetrachord('enharmonic' [31:32, 30:31, 4:5])
        >>> JustTetrachord(intervals).prime_limit
        31
    """
    if not is_prime(prime_limit):
        msg = "The prime limit must be a prime number. "
        msg += "Got: '{}'".format(prime_limit)
        raise ValueError(msg)
    self._prime_limit = prime_limit

    if intervals is not None:
        self.intervals = intervals
    elif genus is not None:
        self.genus = genus.strip().lower()
    else:
        self._intervals: List[JustInterval] = []

validate_tetrachord(tetrachord) classmethod

Validates a tetrachord.

Parameters:

Name Type Description Default
tetrachord Union[JustTetrachord, List[JustInterval]]

The tetrachord to validate

 required

Raises:

Type Description
ValueError

If the given tetrachord is invalid
Source code in /opt/hostedtoolcache/Python/3.11.3/x64/lib/python3.11/site-packages/jintonic/scales.py 
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@classmethod
def validate_tetrachord(cls, tetrachord: Union[JustTetrachord, List[JustInterval]]):
    """Validates a tetrachord.

    Parameters:
        tetrachord: The tetrachord to validate

    Raises:
        ValueError: If the given tetrachord is invalid
    """
    if len(tetrachord) != 3:
        msg = "Tetrachords must be formed of exactly three intervals. "
        msg += 'Got: "{}"'.format(tetrachord)
        raise ValueError(msg)
    # TODO implement __add__ and __radd__ to avoid needing these sum loops
    total_interval = JustInterval(1, 1)
    if isinstance(tetrachord, JustTetrachord):
        for interval in tetrachord.intervals:
            total_interval += interval
    else:
        for interval in tetrachord:
            total_interval += interval
    if total_interval != JustInterval(4, 3):
        msg = "Tetrachord intervals must sum to JustInterval(4, 3). "
        msg += 'Got: "{}"'.format(total_interval)
        raise ValueError(msg)

JustTetrachordalScale

This class implements disjunct just intonation tetrachordal scales.

Source code in /opt/hostedtoolcache/Python/3.11.3/x64/lib/python3.11/site-packages/jintonic/scales.py 
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class JustTetrachordalScale:
    """This class implements disjunct just intonation tetrachordal scales."""

    def __init__(
        self,
        lower: JustTetrachord,
        upper: Optional[JustTetrachord] = None,
    ):
        """Initializes a JustTetrachordalScale.

        Parameters:
            lower: The lower tetrachord
            upper: The upper tetrachord. If None is passed, the lower tetrachord
                is also used for the upper, creating an 'equal' tetrachordal scale.

        Examples:
            >>> JustTetrachordalScale(JustTetrachord(genus='enharmonic'))
            JustTetrachordalScale([46/45, 24/23, 5/4, 9/8, 46/45, 24/23, 5/4])
        """

        self._lower = lower
        if upper is None:
            self._upper = lower
        else:
            self._upper = upper

    @property
    def lower(self) -> JustTetrachord:
        """Lower JustTetrachord."""
        return self._lower

    @lower.setter
    def lower(self, value: JustTetrachord):
        """Set lower JustTetrachord."""
        JustTetrachord.validate_tetrachord(value)
        self._lower = value

    @property
    def upper(self) -> JustTetrachord:
        """Upper JustTetrachord."""
        return self._upper

    @upper.setter
    def upper(self, value: JustTetrachord):
        """Set upper JustTetrachord."""
        JustTetrachord.validate_tetrachord(value)
        self._upper = value

    @property
    def intervals(self) -> List[JustInterval]:
        """JustTetrachordalScale intervals.

        Examples:
            >>> JustTetrachordalScale(JustTetrachord(genus='diatonic')).intervals
            [JustInterval(16, 15), JustInterval(9, 8), JustInterval(10, 9),
            JustInterval(9, 8), JustInterval(16, 15), JustInterval(9, 8),
            JustInterval(10, 9)]
        """
        return self.lower.intervals + [JustInterval(9, 8)] + self.upper.intervals

    @property
    def complement(self) -> JustScale:
        """JustTetrachordalScale complement

        Note:
            Returns a JustScale! The result will not be Tetrachordal.

        Returns:
            The JustScale that is the complement

        Examples:
            >>> JustTetrachordalScale(JustTetrachord(genus='chromatic')).complement
            JustScale([1/1, 6/5, 9/7, 4/3, 3/2, 9/5, 27/14, 2/1])
        """
        tones = [tone.complement for tone in self.tones]
        return JustScale(tones)

    @property
    def tones(self) -> List[JustInterval]:
        """JustTetrachordalScale tones.

        Examples:
            >>> JustTetrachordalScale(JustTetrachord(genus='diatonic')).tones
            [JustInterval(1, 1), JustInterval(16, 15), JustInterval(6, 5),
            JustInterval(4, 3), JustInterval(3, 2), JustInterval(8, 5),
            JustInterval(9, 5), JustInterval(2, 1)]
        """
        tones = [JustInterval(1, 1)]
        tones += [
            sum(self.intervals[:i], start=JustInterval(1, 1))
            for i in range(1, len(self.intervals))
        ]
        tones += [JustInterval(2, 1)]
        return tones

    def hertz(self, fundamental: float) -> List[float]:
        """Translates scale intervals to pitches in Hertz over a fundamental

        Parameters:
            fundamental: The scale's 0 degree (fundamental) pitch in Hertz.

        Returns:
            The scale's pitches as Hertz

        Examples:
            >>> JustTetrachordalScale(JustTetrachord(genus='diatonic')).hertz(60.)
            [60.0, 64.0, 72.0, 80.0, 90.0, 96.0, 108.0, 120.0]
        """
        return [fundamental * tone for tone in self.tones]

    @property
    def genera(self) -> Tuple[str, ...]:
        """JustTetrachordalScale genera for each constituent tetrachord.

        Examples:
            >>> intervals = []
            >>> intervals.append(JustInterval(32, 31))
            >>> intervals.append(JustInterval(31, 30))
            >>> intervals.append(JustInterval(5, 4))
            >>> scale = JustTetrachordalScale(JustTetrachord(intervals))
            >>> scale.upper = JustTetrachord(genus='diatonic')
            >>> scale.genera
            ('enharmonic', 'diatonic')
        """
        return (self.lower.genus, self.upper.genus)

    @property
    def is_equal(self) -> bool:
        """Evaluates whether the JustTetrachordalScale is equal or mixed."""
        return self.lower == self.upper

    @property
    def prime_limit(self) -> int:
        """JustTetrachordalScale prime limit."""
        return max(self.lower.prime_limit, self.upper.prime_limit)

    @property
    def permutations(self) -> List[JustTetrachordalScale]:
        """All (thirty-six) possible permutations of the JustTetrachordalScale."""
        return [
            JustTetrachordalScale(pair[0], pair[1])
            for pair in product(self.lower.permutations, self.upper.permutations)
        ]

    def __repr__(self):
        """repr(self)"""
        pitches = ", ".join(
            [
                "/".join([str(interval.numerator), str(interval.denominator)])
                for interval in self.intervals
            ]
        )
        return "{}([{}])".format(self.__class__.__name__, pitches)

lower: JustTetrachord writable property

Lower JustTetrachord.

upper: JustTetrachord writable property

Upper JustTetrachord.

intervals: List[JustInterval] property

JustTetrachordalScale intervals.

Examples:

>>> JustTetrachordalScale(JustTetrachord(genus='diatonic')).intervals
[JustInterval(16, 15), JustInterval(9, 8), JustInterval(10, 9),
JustInterval(9, 8), JustInterval(16, 15), JustInterval(9, 8),
JustInterval(10, 9)]

complement: JustScale property

JustTetrachordalScale complement

Note

Returns a JustScale! The result will not be Tetrachordal.

Returns:

Type Description
JustScale

The JustScale that is the complement

Examples:

>>> JustTetrachordalScale(JustTetrachord(genus='chromatic')).complement
JustScale([1/1, 6/5, 9/7, 4/3, 3/2, 9/5, 27/14, 2/1])

tones: List[JustInterval] property

JustTetrachordalScale tones.

Examples:

>>> JustTetrachordalScale(JustTetrachord(genus='diatonic')).tones
[JustInterval(1, 1), JustInterval(16, 15), JustInterval(6, 5),
JustInterval(4, 3), JustInterval(3, 2), JustInterval(8, 5),
JustInterval(9, 5), JustInterval(2, 1)]

genera: Tuple[str, ...] property

JustTetrachordalScale genera for each constituent tetrachord.

Examples:

>>> intervals = []
>>> intervals.append(JustInterval(32, 31))
>>> intervals.append(JustInterval(31, 30))
>>> intervals.append(JustInterval(5, 4))
>>> scale = JustTetrachordalScale(JustTetrachord(intervals))
>>> scale.upper = JustTetrachord(genus='diatonic')
>>> scale.genera
('enharmonic', 'diatonic')

is_equal: bool property

Evaluates whether the JustTetrachordalScale is equal or mixed.

prime_limit: int property

JustTetrachordalScale prime limit.

permutations: List[JustTetrachordalScale] property

All (thirty-six) possible permutations of the JustTetrachordalScale.

__init__(lower, upper=None)

Initializes a JustTetrachordalScale.

Parameters:

Name Type Description Default
lower JustTetrachord

The lower tetrachord

 required
upper Optional[JustTetrachord]

The upper tetrachord. If None is passed, the lower tetrachord is also used for the upper, creating an 'equal' tetrachordal scale.

 None

Examples:

>>> JustTetrachordalScale(JustTetrachord(genus='enharmonic'))
JustTetrachordalScale([46/45, 24/23, 5/4, 9/8, 46/45, 24/23, 5/4])
Source code in /opt/hostedtoolcache/Python/3.11.3/x64/lib/python3.11/site-packages/jintonic/scales.py 
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def __init__(
    self,
    lower: JustTetrachord,
    upper: Optional[JustTetrachord] = None,
):
    """Initializes a JustTetrachordalScale.

    Parameters:
        lower: The lower tetrachord
        upper: The upper tetrachord. If None is passed, the lower tetrachord
            is also used for the upper, creating an 'equal' tetrachordal scale.

    Examples:
        >>> JustTetrachordalScale(JustTetrachord(genus='enharmonic'))
        JustTetrachordalScale([46/45, 24/23, 5/4, 9/8, 46/45, 24/23, 5/4])
    """

    self._lower = lower
    if upper is None:
        self._upper = lower
    else:
        self._upper = upper

hertz(fundamental)

Translates scale intervals to pitches in Hertz over a fundamental

Parameters:

Name Type Description Default
fundamental float

The scale's 0 degree (fundamental) pitch in Hertz.

 required

Returns:

Type Description
List[float]

The scale's pitches as Hertz

Examples:

>>> JustTetrachordalScale(JustTetrachord(genus='diatonic')).hertz(60.)
[60.0, 64.0, 72.0, 80.0, 90.0, 96.0, 108.0, 120.0]
Source code in /opt/hostedtoolcache/Python/3.11.3/x64/lib/python3.11/site-packages/jintonic/scales.py 
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def hertz(self, fundamental: float) -> List[float]:
    """Translates scale intervals to pitches in Hertz over a fundamental

    Parameters:
        fundamental: The scale's 0 degree (fundamental) pitch in Hertz.

    Returns:
        The scale's pitches as Hertz

    Examples:
        >>> JustTetrachordalScale(JustTetrachord(genus='diatonic')).hertz(60.)
        [60.0, 64.0, 72.0, 80.0, 90.0, 96.0, 108.0, 120.0]
    """
    return [fundamental * tone for tone in self.tones]