Understanding Temperament in Music

Introduction to Temperament

• Temperament refers to the tuning system used for musical instruments.
• Focus on equal temperament tuning between F3 and F4.
• Priority is given to the interval of the fifth.

Importance of the Fifth Interval

• The fifth is the first and strongest harmonic interval in the harmonic series.
• When tuning, the fifth is made as clean and quiet as possible but kept narrow.
• Only the fifth and minor third are tuned narrow of perfect.
• Other intervals (third, sixth, tenth) are tuned wide of perfect.

Tuning Process

1. Starting Point:
   • Used A4 with an aural pitch source, set to 440 Hz.
2. Dropping Down a Tenth:
   • Tuned to have 7 beats or slightly faster per second.
3. Tuning Intervals from F3:
   • A3 tuned to be slightly slower than the tenth.
   • A flat 3 tuned as a minor third (narrow of perfect).

Comparison of Intervals

• Major third and minor third comparison show distinct differences.
• From A flat, tune C to have the major third slightly slower than the minor third.
• Objective is to have a close-to-perfect fifth.

Utilizing Fourths and Fifths

• Tune up a fourth from the bottom of the fifth and down a fourth from the top.
• These form a minor third, useful for creating minor third sequences.
• Equal progression is achieved when fourths beat similarly and minor thirds fit evenly.

Tuning Remaining Notes

• Tune F sharp and B using minor and major thirds to achieve an even progression of thirds.
• Chromatic force results have tempered intervals.

Completing the Temperament

• Continue by tuning upwards using fifths and checking major/minor thirds.
• Note the comparison between outside sixths and inside thirds.
• When priority is given to the fifth, the sixth beats faster than the third due to an expanded fourth.

Final Observations

• Chords like dominant seventh and major chords should sound clean, quiet, and settled.
• The temperament should have a gravitational pull, contributing to a balanced sound.