expenvelope.envelope.Envelope

class expenvelope.envelope.Envelope(levels: Sequence = (0,), durations: Sequence[float] = (), curve_shapes: Optional[Sequence[Union[float, str]]] = None, offset: float = 0)

Bases: SavesToJSON

Class representing a piece-wise exponential function. This class was designed with musical applications in mind, with the intention being to represent a continuously changing musical parameter over time. For instance, an Envelope might be used to represent the pitch curve of a glissando, or the volume curve of a forte-piano.

Parameters:

• levels – the levels of the curve. These can be anything that acts like a number. For instance, one could even use numpy arrays as levels.

• durations – the durations of the curve segments. (Should have length one less than levels.)

• curve_shapes – the curve shape values (optional, should have length one less than levels). Generally these will be floats, with the default of 0 representing linear change, > 0 representing late change, and < 0 representing early change. It is also possible to use the string “exp” to produce constant proportional change per unit time, so long as the segment does not touch zero. Finally, strings containing “exp”, such as “exp ** 2 / 5” will be evaluated with the curve shape required for exponential change being plugged in for the variable “exp”.

• offset – starts curve from somewhere other than zero

Variables:

segments – list of EnvelopeSegments representing the pieces of this envelope.

Methods

adsr(attack_length, attack_level, ...[, ...])	Construct a standard attack/decay/sustain/release envelope
append_envelope(envelope_to_append)	Extends this envelope by another one (shifted to start at the end of this one).
append_segment(level, duration[, ...])	Append a segment to the end of the curve ending at level and lasting for duration.
ar(attack_length, release_length[, ...])	Construct an attack/release envelope
asr(attack_length, sustain_level, ...[, ...])	Construct an attack/sustain/release envelope
average_level([t_range])	Returns the average value that the Envelope takes over the given range.
end_level()	Ending value of the Envelope
end_time()	End of the domain on which this Envelope is defined.
from_function(function[, domain_start, ...])	Constructs an Envelope that approximates an arbitrary function.
from_levels(levels[, length, offset])	Construct an envelope from levels alone, normalized to the given length.
from_levels_and_durations(levels, durations)	Construct an Envelope from levels, durations, and optionally curve shapes.
from_list(constructor_list)	Construct an envelope from a list that can take a number of formats
from_points(*points)	Construct an envelope from points
from_segments(segments)	Create a new envelope from a list of EnvelopeSegments.
get_upper_integration_bound(t1, desired_area)	Given a lower integration bound, find the upper bound that will result in the desired integral
insert(t, level[, curve_shape_in, ...])	Insert a curve point at time t, and set the shape of the curve into and out of it.
insert_interpolated(t[, min_difference])	Insert another curve point at the given time, without changing the shape of the curve.
integrate_interval(t1, t2)	Get the definite integral under this Envelope from t1 to t2
is_shifted_version_of(other[, tolerance])	Determines if this segment is simply a shifted version of another segment
length()	The length of the domain on which this Envelope is defined (end time minus start time).
local_extrema([include_saddle_points])	Returns a list of the times where the curve changes direction.
max_absolute_slope()	Returns the maximum absolute value of the slope over the entire Envelope.
max_level([t_range])	Returns the highest value that the Envelope takes over the given range.
min_level([t_range])	Returns the lowest value that the Envelope takes over the given range.
normalize_to_duration(desired_duration[, ...])	Stretch or squeeze the segments of this Envelope so that it has the desired total duration.
pop_segment()	Remove and return the last segment of this Envelope.
pop_segment_from_start()	Remove and return the first segment of this Envelope.
prepend_envelope(envelope_to_prepend)	Extends this envelope backwards by another one (shifted to end at the start of this one).
prepend_segment(level, duration[, ...])	Prepend a segment to the beginning of the curve, starting at level and lasting for duration.
release(duration[, start_level, curve_shape])	Construct an simple decaying envelope
remove_segments_after(t)	Removes all segments after the given time (including a partial segment if t lands in the middle of a segment).
remove_segments_before(t)	Removes all segments before the given time (including a partial segment if t lands in the middle of a segment).
scale_horizontal(amount)	Scales the domain of this Envelope by the specified amount.
scale_vertical(amount)	Scales the levels of this segment by the specified amount.
shift_horizontal(amount)	Shifts the domain of this Envelope by the specified amount.
shift_vertical(amount)	Shifts the levels of this Envelope the specified amount.
show_plot([title, resolution, ...])	Shows a plot of this Envelope using matplotlib.
split_at(t[, change_original, zero_out_offsets])	Splits the Envelope at one or several points and returns a tuple of the pieces
start_level()	Beginning value of the Envelope
start_time()	Beginning of the domain on which this Envelope is defined.
value_at(t[, from_left])	Get the value of this Envelope at the given time.

Inherited Methods

duplicate()	Returns a copy of this object by serializing to and from JSON.
json_dumps()	Dump this object as a JSON string.
json_loads(s)	Load this object from a JSON string.
load_from_json(file_path)	Load this object from a JSON file with the given path.
save_to_json(file_path)	Save this object to a JSON file using the given path.

Attributes

curve_shapes	Tuple of all the segment curve shapes.
durations	Tuple of all the segment lengths.
levels	Tuple of levels at all segment boundary points.
offset	Alias for Envelope.start_time().
times	Tuple of all the segment start times.

classmethod from_segments(segments: Sequence[EnvelopeSegment]) → T

Create a new envelope from a list of EnvelopeSegments.

Parameters:

segments – list of segments

classmethod from_levels_and_durations(levels: Sequence, durations: Sequence[float], curve_shapes: Optional[Sequence[Union[float, str]]] = None, offset: float = 0) → T

Construct an Envelope from levels, durations, and optionally curve shapes.

Parameters:

• levels – the levels of the curve. These can be anything that acts like a number. For instance, one could even use numpy arrays as levels.

• durations – the durations of the curve segments. (Should have length one less than levels.)

• curve_shapes – the curve shape values (optional, should have length one less than levels). Generally these will be floats, with the default of 0 representing linear change, > 0 representing late change, and < 0 representing early change. It is also possible to use the string “exp” to produce constant proportional change per unit time, so long as the segment does not touch zero. Finally, strings containing “exp”, such as “exp ** 2 / 5” will be evaluated with the curve shape required for exponential change being plugged in for the variable “exp”.

• offset – starts curve from somewhere other than zero

Returns:

an Envelope constructed accordingly

classmethod from_levels(levels: Sequence, length: float = 1.0, offset: float = 0) → T

Construct an envelope from levels alone, normalized to the given length.

Parameters:

• levels – the levels of the curve. These can be anything that acts like a number. For instance, one could even use numpy arrays as levels.

• length – the total length of the curve, divided evenly amongst the levels

• offset – starts curve from somewhere other than zero

Returns:

an Envelope constructed accordingly

classmethod from_list(constructor_list: Sequence) → T

Construct an envelope from a list that can take a number of formats

Parameters:

constructor_list – Either a flat list that just contains levels, or a list of lists either of the form [levels_list, total_duration], [levels_list, durations_list] or [levels_list, durations_list, curve_shape_list] for example: - an input of [1, 0.5, 0.3] is interpreted as evenly spaced levels with a total duration of 1 - an input of [[1, 0.5, 0.3], 3.0] is interpreted as levels and durations with a total duration of e.g. 3.0 - an input of [[1, 0.5, 0.3], [0.2, 0.8]] is interpreted as levels and durations - an input of [[1, 0.5, 0.3], [0.2, 0.8], [2, 0.5]] is interpreted as levels, durations, and curvatures

Returns:

an Envelope constructed accordingly

classmethod from_points(*points: Sequence) → T

Construct an envelope from points

Parameters:

points – list of points, each of which is of the form (time, value) or (time, value, curve_shape)

Returns:

an Envelope constructed accordingly

classmethod release(duration: float, start_level=1, curve_shape: Optional[Union[float, str]] = None) → T

Construct an simple decaying envelope

Parameters:

• duration – total decay length

• start_level – level decayed from

• curve_shape – shape of the curve (see documentation for Envelope.from_levels_and_durations())

Returns:

an Envelope constructed accordingly

classmethod ar(attack_length: float, release_length: float, peak_level=1, attack_shape: Optional[Union[float, str]] = None, release_shape: Optional[Union[float, str]] = None) → T

Construct an attack/release envelope

Parameters:

• attack_length – rise time

• release_length – release time

• peak_level – level reached after attack and before release (see documentation for Envelope.from_levels_and_durations())

• attack_shape – sets curve shape for attack portion of the curve (see documentation for Envelope.from_levels_and_durations())

• release_shape – sets curve shape for release portion of the curve (see documentation for Envelope.from_levels_and_durations())

Returns:

an Envelope constructed accordingly

classmethod asr(attack_length: float, sustain_level, sustain_length: float, release_length: float, attack_shape: Optional[Union[float, str]] = None, release_shape: Optional[Union[float, str]] = None) → T

Construct an attack/sustain/release envelope

Parameters:

• attack_length – rise time

• sustain_level – sustain level reached after attack and before release

• sustain_length – length of sustain portion of curve

• release_length – release time

• attack_shape – sets curve shape for attack portion of the curve (see documentation for Envelope.from_levels_and_durations())

• release_shape – sets curve shape for release portion of the curve (see documentation for Envelope.from_levels_and_durations())

Returns:

an Envelope constructed accordingly

classmethod adsr(attack_length: float, attack_level, decay_length: float, sustain_level, sustain_length: float, release_length: float, attack_shape: Optional[Union[float, str]] = None, decay_shape: Optional[Union[float, str]] = None, release_shape: Optional[Union[float, str]] = None) → T

Construct a standard attack/decay/sustain/release envelope

Parameters:

• attack_length – rise time

• attack_level – level reached after attack before decay

• decay_length – length of decay portion of the curve

• sustain_level – sustain level reached after decay and before release

• sustain_length – length of sustain portion of curve

• release_length – release time

• attack_shape – sets curve shape for attack portion of the curve (see documentation for Envelope.from_levels_and_durations())

• decay_shape – sets curve shape for decay portion of the curve (see documentation for Envelope.from_levels_and_durations())

• release_shape – sets curve shape for release portion of the curve (see documentation for Envelope.from_levels_and_durations())

Returns:

an Envelope constructed accordingly

classmethod from_function(function: Callable[[float], float], domain_start: float = 0, domain_end: float = 1, scanning_step_size: float = 0.05, key_point_resolution_multiple: int = 2, iterations: int = 6, min_key_point_distance: float = 1e-07, start_from_zero=True) → T

Constructs an Envelope that approximates an arbitrary function. By default, the function is split at local extrema and inflection points found through a pretty unsophisticated numerical process.

Parameters:

• function – a function from time to level (often a lambda function)

• domain_start – the beginning of the function domain range to capture

• domain_end – the end of the function domain range to capture

• scanning_step_size – when analyzing the function for discontinuities, maxima and minima, inflection points, etc., use this step size for the initial pass.

• key_point_resolution_multiple – factor by which we add extra key points between the extrema and inflection points to improve the curve fit.

• iterations – when a potential key point is found, we zoom in and scan again in the viscinity of the point. This determines how many iterations of zooming we do.

• min_key_point_distance – after scanning for key points, any that are closer than this distance are merged.

• start_from_zero – if true, the envelope is shifted so that it starts at time zero. Otherwise, it will have an offset equal to domain_start

Returns:

an Envelope constructed accordingly

length() → float

The length of the domain on which this Envelope is defined (end time minus start time).

start_time() → float

Beginning of the domain on which this Envelope is defined.

end_time() → float

End of the domain on which this Envelope is defined.

start_level()

Beginning value of the Envelope

end_level()

Ending value of the Envelope

max_level(t_range: Optional[tuple[float, float]] = None)

Returns the highest value that the Envelope takes over the given range.

Parameters:

t_range – tuple defining the start and end time of the interval to check. If None, return the max level reached over the entire Envelope.

min_level(t_range: Optional[tuple[float, float]] = None)

Returns the lowest value that the Envelope takes over the given range.

Parameters:

t_range – tuple defining the start and end time of the interval to check. If None, return the max level reached over the entire Envelope.

average_level(t_range: Optional[tuple[float, float]] = None)

Returns the average value that the Envelope takes over the given range.

Parameters:

t_range – tuple defining the start and end time of the interval to check. If None, return the average level reached over the entire Envelope.

max_absolute_slope()

Returns the maximum absolute value of the slope over the entire Envelope.

property levels: Sequence

Tuple of levels at all segment boundary points.

property durations: Sequence[float]

Tuple of all the segment lengths.

property times: Sequence[float]

Tuple of all the segment start times.

property curve_shapes: Sequence[Union[float, str]]

Tuple of all the segment curve shapes.

property offset: float

Alias for Envelope.start_time().

insert(t, level, curve_shape_in=0, curve_shape_out=0) → None

Insert a curve point at time t, and set the shape of the curve into and out of it. This essentially divides the segment at that point in two.

Parameters:

• t – The time at which to add a point

• level – The level of the new point we are adding

• curve_shape_in – the curve shape of the new segment going into the point we are adding

• curve_shape_out – the curve shape of the new segment going out of the point we are adding

insert_interpolated(t: float, min_difference: float = 1e-07) → float

Insert another curve point at the given time, without changing the shape of the curve. A point only gets added if it’s at least min_difference from all existing control points.

Parameters:

• t – the point at which to insert the point

• min_difference – the minimum difference that this point has to be from an existing point on the curve in order for a new point to be added.

Returns:

the t value at which we interpolated. If we try to insert within min_difference of an existing control point, then no new point is added, and we return the t of the nearest control point.

append_segment(level, duration: float, curve_shape: Optional[float] = None, tolerance: float = 0, halfway_level=None) → None

Append a segment to the end of the curve ending at level and lasting for duration. If we’re adding a linear segment to a linear segment, then we extend the last linear segment instead of adding a new one if the level is within tolerance of where the last one was headed

Parameters:

• level – the level we’re going to

• duration – the duration of the new segment

• curve_shape – defaults to 0 (linear)

• tolerance – tolerance for extending a linear segment rather than adding a new one

• halfway_level – alternate way of defining the curve shape. If this is set and the curve shape is not then we use this to determine the curve shape.

prepend_segment(level, duration: float, curve_shape: Optional[float] = None, tolerance: float = 0, halfway_level=None) → None

Prepend a segment to the beginning of the curve, starting at level and lasting for duration. If we’re adding a linear segment to a linear segment, then we extend the last linear segment instead of adding a new one if the level is within tolerance of where the last one was headed

Parameters:

• level – the level that the prepended segment starts at

• duration – the duration of the new segment

• curve_shape – defaults to 0 (linear)

• tolerance – tolerance for extending a linear segment rather than adding a new one

• halfway_level – alternate way of defining the curve shape. If this is set and the curve shape is not then we use this to determine the curve shape.

pop_segment() → EnvelopeSegment | None

Remove and return the last segment of this Envelope. If there is only one segment, reduce it to length zero and return None.

pop_segment_from_start() → EnvelopeSegment | None

Remove and return the first segment of this Envelope. If there is only one segment, reduce it to length zero and return None.

remove_segments_after(t: float) → None

Removes all segments after the given time (including a partial segment if t lands in the middle of a segment).

Parameters:

t – the point at which this Envelope is to be truncated.

remove_segments_before(t: float) → None

Removes all segments before the given time (including a partial segment if t lands in the middle of a segment).

Parameters:

t – the point at which this Envelope is to be truncated.

append_envelope(envelope_to_append: T) → T

Extends this envelope by another one (shifted to start at the end of this one).

prepend_envelope(envelope_to_prepend: T) → T

Extends this envelope backwards by another one (shifted to end at the start of this one).

value_at(t: float, from_left: bool = False)

Get the value of this Envelope at the given time.

Parameters:

• t – the time

• from_left – if true, get the limit as we approach t from the left. In the case of a zero-length segment, which suddenly changes the value, this tells us what the value was right before the jump instead of right after the jump.

integrate_interval(t1: float, t2: float)

Get the definite integral under this Envelope from t1 to t2

Parameters:

• t1 – lower bound of integration

• t2 – upper bound of integration

get_upper_integration_bound(t1: float, desired_area: float, max_error: float = 1e-10) → float

Given a lower integration bound, find the upper bound that will result in the desired integral

Parameters:

• t1 – lower bound of integration

• desired_area – desired value of the integral.

• max_error – the upper bound is found through a process of successive approximation; once we get within this error, the approximation is considered good enough.

normalize_to_duration(desired_duration: float, in_place: bool = True) → T

Stretch or squeeze the segments of this Envelope so that it has the desired total duration.

Parameters:

• desired_duration – the desired new duration of the Envelope

• in_place – if True, modifies this Envelope in place; if False, makes a copy first

local_extrema(include_saddle_points: bool = False) → Sequence[float]

Returns a list of the times where the curve changes direction.

Parameters:

include_saddle_points – if True, also include points where the curve starts to plateau

split_at(t: Union[float, Sequence[float]], change_original: bool = False, zero_out_offsets: bool = True) → Sequence[T]

Splits the Envelope at one or several points and returns a tuple of the pieces

Parameters:

• t – either the time t or a tuple/list of times t at which to split the curve

• change_original – if true, the original Envelope gets turned into the first of the returned tuple

• zero_out_offsets – if true, each new piece is shifted to start at zero

Returns:

tuple of Envelopes representing the pieces this has been split into

is_shifted_version_of(other: T, tolerance: float = 1e-10) → bool

Determines if this segment is simply a shifted version of another segment

Parameters:

• other – another EnvelopeSegment

• tolerance – how close it needs to be to count as the same

shift_vertical(amount) → T

Shifts the levels of this Envelope the specified amount.

Parameters:

amount – the amount to shift up and down by

Returns:

self, for chaining purposes

scale_vertical(amount) → T

Scales the levels of this segment by the specified amount.

Parameters:

amount – amount to scale output by

Returns:

self, for chaining purposes

shift_horizontal(amount: float) → T

Shifts the domain of this Envelope by the specified amount.

Parameters:

amount – the amount to shift the domain by

Returns:

self, for chaining purposes

scale_horizontal(amount: float) → T

Scales the domain of this Envelope by the specified amount.

Parameters:

amount – amount to scale domain by

Returns:

self, for chaining purposes

show_plot(title: Optional[str] = None, resolution: int = 25, show_segment_divisions: bool = True, x_range: Optional[tuple[float, float]] = None, y_range: Optional[tuple[float, float]] = None) → None

Shows a plot of this Envelope using matplotlib.

Parameters:

• title – A title to give the plot.

• resolution – number of points to use per envelope segment

• show_segment_divisions – Whether or not to place dots at the division points between envelope segments

• x_range – min and max value shown on the x-axis

• y_range – min and max value shown on the y-axis

duplicate() → T

Returns a copy of this object by serializing to and from JSON.

json_dumps() → str

Dump this object as a JSON string. This uses a custom encoder that recognizes and appropriately converts any attributes that are object inheriting from SavesToJSON.

classmethod json_loads(s: str) → T

Load this object from a JSON string. This uses a custom decoder that looks for a “_type” key in any object/dictionary being parsed and converts it to the class specified (assuming it a subclass of SavesToJSON).

Parameters:

s – a string representing this object in JSON format

classmethod load_from_json(file_path: str) → T

Load this object from a JSON file with the given path. This uses a custom decoder that looks for a “_type” key in any object/dictionary being parsed and converts it to the class specified (assuming it a subclass of SavesToJSON).

Parameters:

file_path – path for loading the file

save_to_json(file_path: str) → None

Save this object to a JSON file using the given path. This uses a custom encoder that recognizes and appropriately converts any attributes that are object inheriting from SavesToJSON.

Parameters:

file_path – path for saving the file