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TES: The largest network of teachers in the world

Portions not contributed by visitors are Copyright 2018 Tangient LLC

TES: The largest network of teachers in the world

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Here are some links to some of the key ideas underlying tuning:

## Basics

RatiosCents

Chords

Scales

Notation

## Core Concepts

JIRegular Temperaments

Equal Temperaments

Periods and Generators

EDO

EDT

MOS Scales

Periodic scale

EDL (Equal divisions of length)

Arithmetic irrational divisions

ADO (Arithmetic rational divisions)

Comma pump

## How it Works

MonzosVals

Mappings

Patent val

Tempering Out

Rank and codimension

## Personal Explanations

Mike's Lectures On Regular Temperament TheoryKeenan's explanation of vals

## Javascript tools

Interval calculator--a nice online interval calculator tool, shows linear fraction and EDO fraction expansions, tooAn animated Javascript Moment of Symmetry (MOS) ring demo, another untwelve.org creation

An excellent Firefox browser tuning demo synthesizer, 'Wicksynth'

## Additional Stuff

Benedetti heightKees height

Tenney Height

ABC, High Quality Commas, and Epimericity

Graham complexity

Generator complexity

Lumma stability

chord of nature

Modal UDP Notation

Cluster temperament

Consonant Class Scale

Maximum variety

Distributional Evenness

Essential tempering commas

## Advanced Theory

Mathematical Theory