Formulating Pythagorean Tuning Using Fifths & Just Intonation Tuning Using the Harmonic Series

Описание: A recap of how to build a Pythagorean Tuned scale (which is itself a form of just intonation tuning) followed by a look at Just Intonation Tuning derived through octave reduction and expansion techniques of the Harmonic Series. Then, a critique of the 2 tuning systems and why another tuning temperament has been popularized in modern music.

TOC:

00:00 — Introduction
00:16 — Review of Pythagorean Tuning
03:26 — Discrepancies with Pythagorean Tuning
04:02 — Consonant vs. Dissonant Intervals
05:08 — The Fundamental Dilemma
06:21 — Tempering the Pythagorean Comma
06:40 — The Wolf Fifth
09:51 — The Case for Just Intonation Tuning
10:28 — The Harmonic Series in a Blacksmith’s Forge
11:24 — A Cosmic Sound, Part I
12:23 — A Cosmic Sound, Part II
12:40 — Harmonics Determine Timbre
13:01 — A Cosmic Sound, Part III
13:31 — The Diatonic Scale Through the Harmonic Series
14:22 — Building a Just Intonation Scale Using the Harmonic Series
16:54 — MicroTonal Complications
18:37 — Building a JIT Scale the Other Way
20:07 — Choosing Simplest Ratios for a JIT Scale
20:34 — Comparing Intervals of Just Intonation Tuning with Pythagorean Tuning
22:23 — Which Tuning System to Choose?
22:49 — The Case for Irrational Intervals’
23:05 — The Consistency of Equal Temperament