# NumberedPitch¶

class `abjad.pitch.NumberedPitch.``NumberedPitch`(number=0, *, arrow=None, octave=None)

Numbered pitch.

Initializes from number:

```>>> numbered_pitch = abjad.NumberedPitch(13)
``` Initializes from other numbered pitch

```>>> numbered_pitch = abjad.NumberedPitch(abjad.NumberedPitch(13))
``` Initializes from pitch-class / octave pair:

```>>> numbered_pitch = abjad.NumberedPitch((1, 5))
``` Attributes Summary

 `__add__` Adds argument to numbered pitch. `__lt__` Is true when argument can be coerced to a numbered pitch and when this numbered pitch is less than argument. `__neg__` Negates numbered pitch. `__radd__` Adds numbered pitch to argument. `__str__` Gets string representation of numbered pitch. `__sub__` Subtracts argument from numbered pitch. `accidental` Gets accidental of numbered pitch. `arrow` Gets arrow of numbered pitch. `from_hertz` Makes numbered pitch from hertz. `get_name` Gets name of numbered pitch name according to locale. `hertz` Gets frequency of numbered pitch in Hertz. `interpolate` Interpolates between numbered pitch and stop_pitch by fraction. `invert` Inverts numbered pitch around axis. `multiply` Multiplies numbered pitch by index n. `name` Gets name of numbered pitch. `number` Gets number of numbered pitch. `octave` Gets octave of numbered pitch. `pitch_class` Gets pitch-class of numbered pitch. `transpose` Tranposes numbered pitch by n semitones.

Special methods

`__add__`(argument)

Adds argument to numbered pitch.

```>>> abjad.NumberedPitch(12) + abjad.NumberedPitch(13)
NumberedPitch(25)
```
```>>> abjad.NumberedPitch(13) + abjad.NumberedPitch(12)
NumberedPitch(25)
```

Returns new numbered pitch.

`(AbjadValueObject).``__copy__`(*arguments)

Copies Abjad value object.

Returns new Abjad value object.

`(AbjadValueObject).``__eq__`(argument)

Is true when all initialization values of Abjad value object equal the initialization values of `argument`.

Returns true or false.

`(Pitch).``__float__`()

Coerce to float.

Returns float.

`(Pitch).``__format__`(format_specification='')

Formats pitch.

Set format_specification to ‘’, ‘lilypond’ or ‘storage’.

Returns string.

`(Pitch).``__ge__`(other, NotImplemented=NotImplemented)

Return a >= b. Computed by @total_ordering from (not a < b).

`(Pitch).``__gt__`(other, NotImplemented=NotImplemented)

Return a > b. Computed by @total_ordering from (not a < b) and (a != b).

`(AbjadValueObject).``__hash__`()

Hashes Abjad value object.

Returns integer.

`(Pitch).``__illustrate__`()

Illustrates pitch.

Returns LilyPond file.

`(Pitch).``__le__`(other, NotImplemented=NotImplemented)

Return a <= b. Computed by @total_ordering from (a < b) or (a == b).

`__lt__`(argument)

Is true when argument can be coerced to a numbered pitch and when this numbered pitch is less than argument.

```>>> pitch_1 = abjad.NumberedPitch(12)
>>> pitch_2 = abjad.NumberedPitch(12)
>>> pitch_3 = abjad.NumberedPitch(13)
```
```>>> pitch_1 < pitch_1
False
```
```>>> pitch_1 < pitch_2
False
```
```>>> pitch_1 < pitch_3
True
```
```>>> pitch_2 < pitch_1
False
```
```>>> pitch_2 < pitch_2
False
```
```>>> pitch_2 < pitch_3
True
```
```>>> pitch_3 < pitch_1
False
```
```>>> pitch_3 < pitch_2
False
```
```>>> pitch_3 < pitch_3
False
```

Returns true or false.

`__neg__`()

Negates numbered pitch.

```>>> -abjad.NumberedPitch(13.5)
NumberedPitch(-13.5)
```
```>>> -abjad.NumberedPitch(-13.5)
NumberedPitch(13.5)
```

Returns new numbered pitch.

`__radd__`(argument)

Adds numbered pitch to argument.

```>>> pitch = abjad.NumberedPitch(13)
NumberedPitch(25)
```
```>>> pitch = abjad.NumberedPitch(12)
NumberedPitch(25)
```

Returns new numbered pitch.

`(AbjadObject).``__repr__`()

Gets interpreter representation of Abjad object.

Returns string.

`__str__`()

Gets string representation of numbered pitch.

Returns string.

`__sub__`(argument)

Subtracts argument from numbered pitch.

```>>> abjad.NumberedPitch(12) - abjad.NumberedPitch(12)
NumberedInterval(0)
```
```>>> abjad.NumberedPitch(12) - abjad.NumberedPitch(13)
NumberedInterval(1)
```
```>>> abjad.NumberedPitch(13) - abjad.NumberedPitch(12)
NumberedInterval(-1)
```

Returns numbered interval.

Methods

`get_name`(locale=None)

Gets name of numbered pitch name according to locale.

```>>> abjad.NumberedPitch(13).get_name()
"cs''"
```
```>>> abjad.NumberedPitch(13).get_name(locale='us')
'C#5'
```

Set locale to ‘us’ or none.

Returns string.

`interpolate`(stop_pitch, fraction)

Interpolates between numbered pitch and stop_pitch by fraction.

Interpolates from C4 to C5:

```>>> start_pitch = abjad.NumberedPitch(0)
>>> stop_pitch = abjad.NumberedPitch(12)
```
```>>> start_pitch.interpolate(stop_pitch, abjad.Fraction(0))
NumberedPitch(0)
```
```>>> start_pitch.interpolate(stop_pitch, abjad.Fraction(1, 4))
NumberedPitch(3)
```
```>>> start_pitch.interpolate(stop_pitch, abjad.Fraction(1, 2))
NumberedPitch(6)
```
```>>> start_pitch.interpolate(stop_pitch, abjad.Fraction(3, 4))
NumberedPitch(9)
```
```>>> start_pitch.interpolate(stop_pitch, abjad.Fraction(1))
NumberedPitch(12)
```

Interpolates from C5 to C4:

```>>> start_pitch = abjad.NumberedPitch(12)
>>> stop_pitch = abjad.NumberedPitch(0)
```
```>>> start_pitch.interpolate(stop_pitch, abjad.Fraction(0))
NumberedPitch(12)
```
```>>> start_pitch.interpolate(stop_pitch, abjad.Fraction(1, 4))
NumberedPitch(9)
```
```>>> start_pitch.interpolate(stop_pitch, abjad.Fraction(1, 2))
NumberedPitch(6)
```
```>>> start_pitch.interpolate(stop_pitch, abjad.Fraction(3, 4))
NumberedPitch(3)
```
```>>> start_pitch.interpolate(stop_pitch, abjad.Fraction(1))
NumberedPitch(0)
```

Returns new numbered pitch.

`invert`(axis=None)

Inverts numbered pitch around axis.

Inverts pitch-class about pitch-class 0 explicitly:

```>>> abjad.NumberedPitch(2).invert(0)
NumberedPitch(-2)
```
```>>> abjad.NumberedPitch(-2).invert(0)
NumberedPitch(2)
```

Inverts pitch-class about pitch-class 0 implicitly:

```>>> abjad.NumberedPitch(2).invert()
NumberedPitch(-2)
```
```>>> abjad.NumberedPitch(-2).invert()
NumberedPitch(2)
```

Inverts pitch-class about pitch-class -3:

```>>> abjad.NumberedPitch(2).invert(-3)
NumberedPitch(-8)
```

Returns new numbered pitch.

`multiply`(n=1)

Multiplies numbered pitch by index n.

```>>> abjad.NumberedPitch(14).multiply(3)
NumberedPitch(42)
```

Returns new numbered pitch.

`transpose`(n=0)

Tranposes numbered pitch by n semitones.

```>>> abjad.NumberedPitch(13).transpose(1)
NumberedPitch(14)
```

Returns new numbered pitch.

Class & static methods

classmethod `from_hertz`(hertz)

Makes numbered pitch from hertz.

```>>> abjad.NumberedPitch.from_hertz(440)
NumberedPitch(9)
```

REGRESSION. Returns 12 (not 0):

```>>> abjad.NumberedPitch.from_hertz(519)
NumberedPitch(12)
```

Returns newly constructed numbered pitch.

`accidental`

Gets accidental of numbered pitch.

```>>> abjad.NumberedPitchClass(13).accidental
Accidental('sharp')
```

Returns accidental.

`arrow`

Gets arrow of numbered pitch.

Gets no arrow:

```>>> abjad.NumberedPitch(13).arrow is None
True
```

Gets up-arrow:

```>>> abjad.NumberedPitch(13, arrow=abjad.Up).arrow
Up
```

Gets down-arrow:

```>>> abjad.NumberedPitch(13, arrow=abjad.Down).arrow
Down
```

Returns up, down or none.

`hertz`

Gets frequency of numbered pitch in Hertz.

```>>> abjad.NumberedPitch(9).hertz
440.0
```
```>>> abjad.NumberedPitch(0).hertz
261.6255653005986
```
```>>> abjad.NumberedPitch(12).hertz
523.2511306011972
```

Returns float.

`name`

Gets name of numbered pitch.

```>>> abjad.NumberedPitch(13).name
"cs''"
```

Returns string

`number`

Gets number of numbered pitch.

```>>> abjad.NumberedPitch(13).number
13
```

Returns number.

`octave`

Gets octave of numbered pitch.

```>>> abjad.NumberedPitch(13).octave
Octave(5)
```

Returns octave.

`pitch_class`

Gets pitch-class of numbered pitch.

```>>> abjad.NumberedPitch(13).pitch_class
NumberedPitchClass(1)
```

Returns numbered pitch-class.