# NonreducedRatio¶

class `abjad.mathtools.NonreducedRatio.``NonreducedRatio`(numbers=(1, 1))

Nonreduced ratio.

Nonreduced ratio of two numbers:

```>>> abjad.NonreducedRatio((2, 4))
NonreducedRatio((2, 4))
```

Nonreduced ratio of three numbers:

```>>> abjad.NonreducedRatio((2, 4, 2))
NonreducedRatio((2, 4, 2))
```

Attributes Summary

 `__contains__` Is true when ratio contains `argument`. `__eq__` Is true when `argument` is a nonreduced ratio with numerator and denominator equal to those of this nonreduced ratio. `__format__` Formats duration. `__getitem__` Gets item or slice identified by `argument`. `__hash__` Hashes non-reduced ratio. `__iter__` Iterates ratio. `__len__` Gets length of ratio. `__rdiv__` Divides `number` by ratio. `__reversed__` Iterates ratio in reverse. `__rtruediv__` Divides `number` by ratio. `count` Gets count of `argument` in ratio. `index` Gets index of `argument` in ratio. `multipliers` Gets multipliers of nonreduced ratio. `numbers` Gets numbers of nonreduced ratio.

Special methods

`__contains__`(argument)

Is true when ratio contains `argument`.

Returns true or false.

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

Copies Abjad value object.

Returns new Abjad value object.

`__eq__`(argument)

Is true when `argument` is a nonreduced ratio with numerator and denominator equal to those of this nonreduced ratio.

Returns true or false.

`__format__`(format_specification='')

Formats duration.

```>>> ratio = abjad.NonreducedRatio((2, 4, 2))
>>> print(format(ratio))
abjad.NonreducedRatio((2, 4, 2))
```

Returns string.

`__getitem__`(argument)

Gets item or slice identified by `argument`.

```>>> ratio = abjad.NonreducedRatio((2, 4, 2))
>>> ratio
4
```

Returns integer or tuple.

`__hash__`()

Hashes non-reduced ratio.

Required to be explicitly redefined on Python 3 if __eq__ changes.

Returns integer.

`__iter__`()

Iterates ratio.

Returns generator.

`__len__`()

Gets length of ratio.

```>>> ratio = abjad.NonreducedRatio((2, 4, 2))
>>> len(ratio)
3
```

Returns integer.

`__rdiv__`(number)

Divides `number` by ratio.

```>>> 1 / abjad.Ratio((1, 1, 3))
[Fraction(1, 5), Fraction(1, 5), Fraction(3, 5)]
```
```>>> abjad.Fraction(1) / abjad.Ratio((1, 1, 3))
[Fraction(1, 5), Fraction(1, 5), Fraction(3, 5)]
```
```>>> 1.0 / abjad.Ratio((1, 1, 3))
[0.2, 0.2, 0.6]
```

Returns list of fractions or list of floats.

`(AbjadObject).``__repr__`()

Gets interpreter representation of Abjad object.

Returns string.

`__reversed__`()

Iterates ratio in reverse.

Returns generator.

`__rtruediv__`(number)

Divides `number` by ratio.

```>>> 1 / abjad.Ratio((1, 1, 3))
[Fraction(1, 5), Fraction(1, 5), Fraction(3, 5)]
```
```>>> abjad.Fraction(1) / abjad.Ratio((1, 1, 3))
[Fraction(1, 5), Fraction(1, 5), Fraction(3, 5)]
```
```>>> 1.0 / abjad.Ratio((1, 1, 3))
[0.2, 0.2, 0.6]
```

Returns list of fractions or list of floats.

Methods

`count`(argument)

Gets count of `argument` in ratio.

Returns integer.

`index`(argument)

Gets index of `argument` in ratio.

Returns integer.

Read-only properties

`multipliers`

Gets multipliers of nonreduced ratio.

Nonreduced ratio of two numbers:

```>>> ratio = abjad.NonreducedRatio((2, 4))
>>> ratio.multipliers
(Multiplier(1, 3), Multiplier(2, 3))
```

Nonreduced ratio of three numbers:

```>>> ratio = abjad.NonreducedRatio((2, 4, 2))
>>> ratio.multipliers
(Multiplier(1, 4), Multiplier(1, 2), Multiplier(1, 4))
```

Returns tuple of multipliers.

`numbers`

Gets numbers of nonreduced ratio.

Nonreduced ratio of two numbers:

```>>> ratio = abjad.NonreducedRatio((2, 4))
>>> ratio.numbers
(2, 4)
```

Nonreduced ratio of three numbers:

```>>> ratio = abjad.NonreducedRatio((2, 4, 2))
>>> ratio.numbers
(2, 4, 2)
```

Set to tuple of two or more numbers.

Returns tuple of two or more numbers.