Notes from the Staff uTheory

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 SystemsGreg 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 ChoirsDiscussion on how choirs tend to move towards just intervals in their performances.
0:02:43.2 - Historical Context of Tuning SystemsWe 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 WavesExploration 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 TuningDemonstration of how close frequencies can create a beating effect in sound, relevant to tuning and intonation.
0:11:25.7 - Constructing Scales with Tuning SystemsExamining 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 notesA practical approach to assigning frequencies to piano notes, highlighting the challenges in tuning.
0:24:00.8 - The Pythagorean Tuning System and the Wolf FifthUnderstanding the Pythagorean tuning system, its implications, and the infamous 'wolf fifth.'
0:27:24.5 - Equal Temperament Tuning SystemDiscussion on equal temperament tuning, its compromises, and comparison with just intonation.
0:28:27.3 - Comparison of Major and Minor Thirds in Different Tuning SystemsExploring how major and minor thirds differ in various tuning systems, including just intonation and equal temperament.
0:31:04.3 - Just Intonation and Chord TuningDemonstration of how chords are tuned in just intonation, contrasting with equal temperament.
0:35:56.5 - Field Trip to Oberlin's Brombaugh OrganGreg 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 OrganExploration of the organ's split black keys and how they impact tuning and playability.
0:47:08.4 - Musical Composition and Tuning SystemsDiscussion on how composers historically wrote music with specific tuning systems in mind, affecting the musical expression.
0:49:00.3 - Wrapping UpWe 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 notes@uTheory.com. 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 thi

In this episode, Greg Ristow and David Newman talk about the value and role of intervallic ear training, why it's time to move beyond Here comes the bride, and ways of teaching intervallic hearing that build fundamental skills for sight singing and dictation.
Links:
Karpinski, Gary. "A Cognitive Basis for Choosing a Solmization System," Music Theory Online, Vol. 27, No. 2. June 2021. https://mtosmt.org/issues/mto.21.27.2/mto.21.27.2.karpinski.html
 
Transcript
[music]
0:00:21.2 Gregory 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.
0:00:35.5 David Newman: Hi, I'm David Newman, and I teach voice and music theory at James Madison University. And I write code and create content for uTheory.
0:00:43.4 GR: Hi, I'm Greg Ristow. I conduct the choirs at the Oberlin Conservatory of Music, and I'm the founder of uTheory.
0:00:49.9 DN: Thank you listeners for your comments and episode suggestions. We love to read them, send them our way by email at notes@uTheory.com, and remember to like us and subscribe wherever you get your podcasts.
0:01:01.7 GR: So today we'll be talking about interval ear training. And interval ear training is central to many teachers' and textbooks' approaches to sight singing and dictation. But the title of this episode is maybe a little bit misleading because research in music cognition suggests that for most common aural skills, ear training tasks we process notes by their relationship to a tonic or by their position in a scale rather than by actually hearing adjacent note to note intervallic relationships. So in our conversation today, we'll look at this research on how we hear and the role that intervals play in that hearing. We'll talk about why classic techniques we're teaching intervals can actually undermine students' reading skills. And we'll look at ways of teaching intervals that instead compliment and strengthen students' aural skills. It's a lot to get through in the course of an hour. [chuckle]
0:02:03.2 DN: It is.
0:02:04.5 GR: But David and I have agreed to play particular roles on this. So I'm going to, I'm gonna be sort of the the playback, keep us on track role and David's gonna be the the color commentary, [chuckle] role.
0:02:14.0 DN: Playing to our strengths.
0:02:15.4 GR: Playing to our strengths for sure, for sure. It is hard to talk about or even to think about how we hear, so much of how we hear music is really innate, that we don't, especially for someone with a well-developed ear, "how do I know how I know what I'm hearing?" is a hard question to answer.
0:02:40.1 DN: Yeah.
0:02:40.8 GR: And fortunately we have scientists and researchers who've been looking at exactly this question for a little, I don't know little over 40 years now. And what they have pretty consistently found is that when someone who is experienced in a particular musical culture, and so let's say broadly Western music, music that exists within the notes on a Western piano.
0:03:17.7 DN: An equal tempered scale.
0:03:19.2 GR: Yeah. A tempered major-y minor-y or rotation of its scale as opposed to for instance, some of the Turkish collections that have more notes in the scale than we have and notes that don't exist on our piano. So when someone is encultured in a musical system, when first they start hearing notes, the primary thing that their brain does is seek to determine a central pitch, what we would call a tonic and that's known in music cognition as the primacy hypothesis. The idea being that David, if I throw a few notes at you, before you're going to do anything with those notes, your mind is going to say, "what could potentially be tonic given these notes?" And we're gonna hold onto them.
0:04:20.8 DN: We contextualize it.
0:04:22.5 GR: Exactly. We seek to find the context in which that's o

David Newman and Greg Ristow chat about four ways to teach intervals in music theory, as well as how to overcome some of the challenges of teaching intervals.
 
Transcript
[music]
0:00:20.8 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.
0:00:33.4 David Newman: Hi, I'm David Newman, and I teach voice and music theory at James Madison University and I create content and code for uTheory.
0:00:42.0 Greg Ristow: Hi, I'm Greg Ristow, founder of uTheory and Associate Professor of conducting at the Oberlin Conservatory.
0:00:47.8 DN: Thank you listeners for your comments and episode suggestions. We love to read them, send them our way by email at notes@utheory.com and remember to like us and subscribe wherever you get your podcasts.
0:01:00.1 GR: Today we'll be talking about teaching intervals, teaching reading and writing intervals more so than teaching the oral side of intervals, which we'll save for another episode and this David, I find to be one of the most challenging things to teach in fundamentals of theory.
0:01:17.0 DN: There's certainly a lot of approaches to use and picking one is hard.
0:01:22.5 GR: Yeah.
0:01:23.1 DN: And doing them all is also hard.
[chuckle]
0:01:24.8 GR: Yeah, for sure. For sure. And there's just a lot involved too, right? I mean, it's like you've got the generic interval size. You've got the specific size or quality, you've got the inversions, you have the compound intervals, consonance and dissonance. It just adds up and it's one of those concepts that it seems like, I often forget to budget enough time for because there's almost always a next step.
0:01:56.0 DN: And it's one of those foundational concepts that if you are struggling with it, you're gonna struggle with everything else.
0:02:02.7 GR: Yeah, for sure. For sure. And I find it's also one that can be hard to motivate students to learn, because if you're not careful, it feels really like a terrible set of math problems.
0:02:13.2 DN: Yeah. Also, it's really easy to do if you have plenty of time but it's, you need to know it better than that. You need to know it so well that it doesn't take you time.
0:02:26.2 GR: Yeah and I think for a lot of us who are teaching it there's also that challenge that both Leigh VanHandel and Melissa Hoag talked about of we already know it so well, it's really hard to conceive of what it's like not to know it.
0:02:40.2 DN: Yeah. And there's all these extra concepts involved, the letter names and...
0:02:46.2 GR: So I guess one of the things that I think about a lot is this challenge of how do we keep the teaching of intervals musical, right? 
[laughter]
0:02:55.6 GR: I think I'm gonna be really honest here and say, I think the first 15 times I taught intervals it was the dullest thing. I remember saying to classes, I'm sorry, this is gonna seem really boring, but it's really critical. As like a motivator, and I guess it's an okay motivator but there may be better ways the more I've taught it recently I've focused a lot on ways to keep it musical and make it musically relevant.
0:03:25.3 DN: Yeah. Yeah. And of course we've also had... We've talked to people this just recently about other ways of making it fun, but making it fun is not necessarily the same thing as making it musical. And making it musical is certainly more compelling.
0:03:40.4 GR: Yeah. Yeah. And if you can do both, all the better, right? Yeah.
0:03:44.5 DN: Right.
0:03:45.2 GR: Yeah. So I guess I don't know. I'd be curious your take on this. For me, I spend a lot more time teaching when I teach intervals now than I used to talking about consonance and dissonance really early on and talking about intervals as a way to get into how notes work together or work against each other.
0:04:06.3 DN: Ooh. I think that's fabulous

Dr. Paula Telesco walks us through some of the "gotchas" that come up when teaching accidentals, and shares some great musical examples for explaining concepts like enharmonic spelling, double accidentals, and cautionary accidentals.
 
Transcript 
[music]
0:00:21.0 Gregory 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 Leah Sheldon: Hi, I'm Leah Sheldon, head of teacher engagement for uTheory.
0:00:39.7 GR: And I'm Gregory Ristow, founder of uTheory and Associate Professor of conducting at the Oberlin Conservatory.
0:00:46.5 LS: Thank you listeners for your comments and your episode suggestions, we'd love to read them, so please send them our way by email at notes@uTheory.com. And remember to like us and subscribe wherever you get your podcasts.
0:01:00.5 GR: We'll be taking a deep dive into the topic of teaching accidentals today, and we're delighted to have Dr. Paula Telesco with us for this. Dr. Telesco is a professor of music theory at the University of Massachusetts, Lowell. Her research interests include music theory and oral skills, pedagogy, analysis of classical and romantic era music, the omnibus progression and her monism and musical cognition. Her writing has appeared in The Journal of music theory pedagogy, the Journal of musicology and music theory spectrum, among others. Most recently, her chapter on the pedagogy of accidental was released in the Routledge Companion to Music Theory Pedagogy, edited by Leigh VanHandel, who we just spoke with in December. Paula, thanks for joining us.
0:01:44.4 Paula Telesco: Well, thank you, it's great to be here. Thank you for inviting me.
0:01:48.8 GR: Yeah, we're delighted to have you. Tell us a little bit about yourself. You've been teaching at UMass Lowell for some time now. What all do you teach there? 
0:01:58.8 PT: Well, I've taught many things. Currently, I'm teaching a basic music theory. I also teach the non-major music history course. The basic theory I'm teaching right now is for non-majors. Well, they're non-majors, they're also music miners or people who want to get into the Music program, but they're not quite ready.
0:02:29.1 GR: Yeah. So, what we often call Fundamentals of Music, sorts of things? 
0:02:32.8 PT: Exactly. Yes.
0:02:33.9 GR: Yeah. Excellent, excellent. And I've to say, I really enjoyed your chapter in Leigh VanHandel Routledge Companion on teaching accidental. It reminded me of some things about accidents that frankly, I myself had forgotten.
0:02:47.8 PT: Well, thank you. Yeah, there's a lot more to know, certainly than students are aware of. The students who come into my class have mostly some background, and so they already think they kinda know accidental, but they don't. They know the basic things about them, but there are all these other things, the niceties of them that they're not aware of, so I wanted to make sure that they... I tell them, "This is the best theory deal in town." And I'm trying to give them as much information as I can.
[laughter]
0:03:27.2 GR: That's great. I think, one of the things I have experienced, I'm sure you've experienced as well, and Leah certainly in your teaching with the elementary, middle and high school students, I know we've talked about this, is that accidentals can be a really hard topic for students to first grasp. What are some of the things that students struggle with when learning accidental? 
0:03:50.7 PT: Well, for my students, the basic concept is not that difficult, it immediately starts getting difficult when you add an E sharp or E flat, something like that. And I tell them throughout the semester, we're gonna see why those kinds of notes are necessary. We're not just doing it just for the sake of putting a sharp next to the note E. So the black notes are always the e

Dr. Leigh VanHandel joins us to talk about the science of memory and learning, and how it can help us better structure our teaching. We also chat about her new book, the Routledge Companion to Music Theory Pedagogy, which recently received an Outstanding Multi-Authored Collection award from the Society for Music Theory, and about the Workshops in Music Theory Pedagogy series she coordinates.

Dr. Stefanie Dickinson joins us to share some of the music fundamentals games that she uses in her music theory classroom.