# Tuning and interval

## Overview

A tuning system determines which notes you can use to write melody, how many there are, and how they relate to each other.

Choosing a tuning system is a fundamental feature of writing music. However, you may not have a free hand in the choice because there is one, significant, constraint: many instruments have a fixed tuning.

Fixed tuning is a real limitation on live performance. Music intended for live performance by instruments with fixed tuning must use the tuning system for which these instruments were designed. Writing music for live performance by such instruments means using their tuning system. In effect, the tuning system is decided in advance.

The constraint of fixed tuning applies to most musical instruments. Reed instruments such as the recorder and saxophone have fixed tuning for example. Other instruments have variable tuning, such as the piano, but take so long to retune that, for practical performance purposes, their tuning is fixed. Even a guitar takes a while to be retuned. The only instrument that has instant variable tuning is that most versatile instrument of all, the human voice.

There are at least 32 different tuning systems in existence. We look at three of them in this section: Pythagorean tuning, just intonation and the most widely used tuning in contemporary music, equal temperament. Tuning systems can and do evolve over time and new tuning systems continue to emerge. There is plenty of scope for you to invent your own tuning system if you so wish.

An interval is the starting point in tuning systems. Interval is a shorthand term for the frequency ratio between two notes. The most important intervals are unison and octave and intervals always come in pairs, the interval and its inversion.

Pythagorean tuning uses a frequency ratio of 3:2 to construct the intervals of fourth and fifth, second and seventh and third and sixth. Some of these intervals are further divided into major and minor intervals. The tritone is a problematic interval to construct.

Just intonation and equal temperament are two tuning systems that attempt to improve on Pythagorean tuning. They both produce the same named intervals as Pythagorean tuning but use different frequency ratios to do so.

A tuning comparison demonstrates the difference in the sound of a melody in Pythagorean tuning, just intonation and equal temperament.