Beginner's guide to scales and tunings

Welcome to the world of xenharmonic music! Here you will find a wealth of information regarding the research and experimentation along with various ideas and theories for different tunings and scales. However, although the information is available to you, it doesn't help you much if you don't understand what the heck you're doing. That's why I've written this nice, little guide here to guide you along your journey in the world of alt-tuned music! The biggest problem people have when they go online to learn about microtonal music is either:

• A. They see a bunch of confusing math which is a bit higher than high school algebra, or
• B. They see a bunch of theory ideas about ratios and chords that makes no sense.

While I can't educate you in the mathematics as I suck at math myself even though I find higher maths interesting, it's not my thing. What is my thing, is music theory; I believe I'm good at seeing the connections, patterns, and can simplify those for others who have more trouble. This guide hopefully will tell you everything you need to know about tunings and scales that involves as little maths as necessary. Some maths will be needed to understand certain principles, but this guide mainly focuses on scales and how they are constructed.

What you can learn from this guide

• How scales are constructed by the use of various step sizes
• Understand generators and periods and how they can be used to build scales
• Learn how just intonation ratios are approximated in a scale
• Understand how different Equal Temperaments work for different purposes
• Learn how to construct chords from scales
• Much much more! :)

Basic terminology

Scale

A finite row of tones ordered by pitch.

Tuning

A finite superset of scales (scales exist within tunings). Tunings also are considered to be scales because they are a row of tones as well.

Chord

A set of notes acting as one unit taken from an existing scale/tuning.

Equal temperament

A tuning/scale made of notes that are all equally spaced apart.

MOS

Moment of symmetry—A scale in which every interval comes in two sizes.

Step

The distance from one note to another.

Interval

A name of a particular distance of one note to another.

"What is a scale?", you might ask? Put simply, it's just some notes which are arranged from low to high. While the word "scale" is generic and changes meaning slightly depending on context, the word "tuning" more specifically refers to the maximum number of possible unique pitches in a piece of music or instrument. What I mean is, a tuning refers to the set of notes in which we say are "allowed" or "possible", on a real instrument, this is easy to demonstrate but we first must understand octaves and cents.

Cent notation and octaves

In music theory, the way we measure the distance from one pitch to another is through a unit called the cent. One cent is exactly 1200^th of an octave. A standard semitone, the smallest interval in 12-tone equal temperament, is exactly 100 cents (by definition), and this is what we base interval measurements on. If we know that 100 cents is the distance from one key on a piano to one higher or lower by a half step, then we know that the distance between two keys is 200 cents. If we keep going we eventually arrive at 1200 cents. At this point the two notes 0 cents and 1200 cents from the same note sound identical but one is higher and one is lower. This is what we call the "octave". You might have heard of the term in basic music theory, and the name octave comes from the eighth note in a major scale.

Looking at music in this way is cool. We know that we can break down a piano into cents in increments of 100 cents.