Tuning by Ratios

## Table of Contents

- Introduction
- A Close-up Look at Frequency

- Tuning Intervals by Ratios
- The A Major Scale Expressed
in Ratios

- Common chords
- Derivations of the Major and Minor Triads
- C Major Triad
- F Minor Triad

- The Simplified Schematic Diagram
- C Major Triad
- F Minor Triad
- Observations on Simplified Diagrams
- Conclusions

- Optimal Durations for Chords
- Overview
- Formula to Determine Smallest Optimized
Duration for a Chord
- Proof
- Application of Theory

- What is Csound?
- Orchestra and Score Files
- Standard Csound Format

- Tape Loop Program
- Running the Tapeloop Program
- Sample Run of Tapeloop.exe

- Bach Two Part Invention
- Traditionally Notated Score
- Csound Orchestra and Score

- Chord Progression
Example
- Traditionally Notated
Score
- Csound Orchestra
- Csound Score

- Bach Chorale Example
#1
- Traditionally Notated
Score
- Csound Orchestra and Score

- Bach Chorale Example
#2
- Traditionally Notated
Score
- Csound Orchestra and Score

- Conclusion