# An audio glance at algebra

(The sound recordings in the examples on these pages have been recorded to high and low qualities. The high quality ones sound better - but will take longer to arrive. You can choose which quality you want to hear by selecting either 'High' or 'Low'.)

In order to choose how to read a mathematical expression by browsing the user needs to know about the structure of the expression. A sighted reader of print algebra can have a glance or overview of an expression to judge its length, complexity and the types of structure present. The listening reader cannot get a glance and would have to get this information by listening to the whole expression.

Mathtalk provides an audio glance using algebra earcons. A glance must convey the order of the types of structure in an expression. In speech prosody can indicate the structure and the words indicate the types of objects. A glance should rapidly show the structure, but not the detail, in this case prosody without the words. Earcons allow us to do this because they have been designed such that they share the parameters of rhythm, pitch, tempo and amplitude (loudness) with the prosodic component of speech. An algebra earcon is the prosodic form of an expression presented as a structured sound (earcon). The objects within an expression are represented by musical sounds; one type of sound for each type of object, as follows.
Object Sound
Simple letter or number Piano
Binary operator Silence
Relational operator Drum
Subexpression Strings
Fraction Trombone
Superscript Beep

Each object in an expression is represented by a musical note, the length of note being propostional to the size of the object and the 'shape' of the algebra earcon being dictated by a set of rules based on those for algebraic prosody.

The sound recordings in the examples on these pages have been recorded to high and low qualities. The high quality ones sound better - but will take longer to arrive. You can choose which quality you want to hear by selecting either 'High' or 'Low' quality.

Compare the spoken forms of the following expressions.

In the expression a + b the letters are represented by piano sounds and the '+' by silence. Notice how the overall shape of the speech and audio glance are similar.

The expression a = b introduces the drum sound which represents relational operators - in this case the '='.

The expression ab uses a short high-pitched note to indicate a superscript.

The audio glance can rapidly show the difference between two lexcially similar expressions, such as

3x + 4 = 7 and 3(x + 4) = 7.

A long, flat strings sound is used to indicate the subexpression in 3(x + 4) = 7.

3x + 4 = 7

3(x + 4) = 7

The following two long expressions show how algebra earcons give a rapid overview of an expression's structure. The first easily shows the repetitions within the expression. The second, using a trombone sound to indicate the two parts of a fraction, easily shows that the right-hand side of the expression is one large fraction.

4x4 + 3x3 + 2x2 + 1 = 0

The association of musical sounds to different types of object can be exploited to aid orientation during browsing. Simple earcons are used to indicate the beginning and end of objects. The same structure of earcon was used for each object but the use of different musical sounds enables the reader to discriminate which object is being browsed.