Tuning Systems

In this episode we explore the difference between just intonation and equal temperament, and take a field trip to learn about an organ with 15 keys per octave (instead of the usual 12), that makes it possible to play purely tuned chords in almost all of the keys.

Links:

Tuning systems synthesizer: https://utheory.com/experiments/tuning-systems

Organ demo field trip video: https://youtu.be/A9Enpt8hREg

Chrome Music Lab: https://musiclab.chromeexperiments.com/

Intonation/Tuning System "Puzzle Pieces": https://casfaculty.case.edu/ross-duffin/just-intonation-in-renaissance-theory-practice/benedettis-puzzles/

 

Show Notes:

0:00:20.9 - Introduction

0:01:03.5 - Topic Introduction: Tuning Systems Greg Ristow explains the complexity of tuning systems and opens the discussion on various aspects related to them.

0:01:58.4 - Just Intervals and Singing in Choirs Discussion on how choirs tend to move towards just intervals in their performances.

0:02:43.2 - Historical Context of Tuning Systems We delve into the historical variations of the A note’s frequency and introduces the concept of just intonation tuning.

0:03:22.2 - The Law of Superposition and Sound Waves Exploration of how sound waves interact and affect what we hear, using sine waves as an example.

0:07:00.8 - Beating in Sound Waves and Tuning Demonstration of how close frequencies can create a beating effect in sound, relevant to tuning and intonation.

0:11:25.7 - Constructing Scales with Tuning Systems Examining how scales can be formed using different intervals, like perfect fifths, and the issues that arise in tuning systems like Pythagorean tuning.

0:21:16.4 - Assigning frequencies to notes A practical approach to assigning frequencies to piano notes, highlighting the challenges in tuning.

0:24:00.8 - The Pythagorean Tuning System and the Wolf Fifth Understanding the Pythagorean tuning system, its implications, and the infamous 'wolf fifth.'

0:27:24.5 - Equal Temperament Tuning System Discussion on equal temperament tuning, its compromises, and comparison with just intonation.

0:28:27.3 - Comparison of Major and Minor Thirds in Different Tuning Systems Exploring how major and minor thirds differ in various tuning systems, including just intonation and equal temperament.

0:31:04.3 - Just Intonation and Chord Tuning Demonstration of how chords are tuned in just intonation, contrasting with equal temperament.

0:35:56.5 - Field Trip to Oberlin's Brombaugh Organ Greg Ristow and David Kazimir discuss the unique features of the Brombaugh Organ at Oberlin, demonstrating quarter-comma meantone tuning.

0:41:12.1 - Split Black Keys and Specialized Tuning on the Brombaugh Organ Exploration of the organ's split black keys and how they impact tuning and playability.

0:47:08.4 - Musical Composition and Tuning Systems Discussion on how composers historically wrote music with specific tuning systems in mind, affecting the musical expression.

0:49:00.3 - Wrapping Up We preview the next episode's topic, focusing on teaching intonation, and Leah Sheldon's experience in this area.

Transcript:

[music]

0:00:20.9 Greg Ristow: Welcome to Notes From the Staff, a podcast from the creators of uTheory, where we dive into conversations about music theory, ear training, and music technology with members of the uTheory staff and thought leaders from the world of music education.

0:00:35.4 David Newman: Hi, I'm David Newman. I teach voice and music theory at James Madison University, and I write code and create content for uTheory.

0:00:42.4 Leah Sheldon: I'm Leah Sheldon. I'm head of teacher engagement for uTheory.

0:00:45.7 GR: And I'm Greg Ristow. I'm the founder of uTheory, and I direct the choirs at the Oberlin Conservatory of Music.

0:00:51.9 DN: Thank you listeners for your comments and episode suggestions. We love to read them. Send them our way by email at [e-mail]. And remember to like us and subscribe wherever you get your podcasts.

0:01:03.5 GR: So, today our topic is tuning systems, and this one has taken us a while to put together, partly because we wanted to build some tools to show them off. It's a concept that I think a lot of us have heard little bits about, but maybe one that not all of us know mathematically and musically in a really deep way. So, I'm excited to talk about this one. Maybe to kick it off, what kinds of things come to mind when you think of tuning systems, Leah and David? 

0:01:32.2 DN: Oh, man. I let the harpsichordists decide what tuning system we're using. [laughter]<