Kratzke: February 2023

I went down a YouTube rabbit hole when I found WIRED magazine's YouTube channel. Specifically, I was trying to understand "Mathematician Explains Infinity in 5 Levels of Difficulty" and failing. I do tend to believe people when they say they can prove that some infinities are bigger than others, and that there are, in fact, an infinite number of different infinities, and they understand all of this stuff because they know how to create the right mappings between sets. Because why would they lie?

Then there was a link to "Musician Explains Harmony in 5 Levels of Difficulty," and that's how I discovered Jacob Collier like 5 years later than everyone else, and then I started watching other Jacob Collier videos, and that made me want to organize what I wrote at the end of my jazz theory post into a second post on chord and scale relationships. Here we are.

Instead of writing out a blues scale like: 1-♭3-4-♭5-5-♭7, which is what I did last time, there are some advantages to notating it like this: S m3 W H H m3 W, where

   S - starting pitch
   H - half step
   W - whole step
   m3 - minor 3rd

My students never like that I teach with this "S" to mean starting pitch. They always want to do what the books say, and the books say "a major scale is W W H W W W H." So then they try to build a C major scale, and they play a C and say "whole!" At this point in the lesson, I could either review the fact that "a whole step measures the distance between two notes, as does any interval," which means I would be repeating myself, boring them, and even worse, getting nowhere; or I could launch into a lecture on the fencepost problem, which would be even worse. So I insist on the “S.”

Here are some of the advantages I promised.
   S H H H H H H H H H H H H

S W W W W W W

S H W H W H W H W

S W H W H W H W H

Did you like them? This notation can make pattern recognition and scale comparisons a little easier, and it comes with the handy avoidance of choosing between enharmonic spellings. Also, if you didn't already know there were 12 half steps in an octave, I just told you four times. So we have a built-in double-checker; if the H's and W's don't add up to 12, then I made a mistake.

For my charts, I'll begin with the pattern, name the scale, and describe the resulting chord built from thirds. I don't tend to think past 7th chords, so the idea of a scale as a chord (specifically a 13th chord) is new to me. I imagine the jazz pianists to respond, “That’s not what we do either. Not everything is a 13th chord, and there are lots of rules about omitting notes.” To which I would say, “But Jacob Collier says that every note goes with every chord, and I imagined him to be the person telling me to write this post.” This is totally wrong because in reality, Jacob Collier would advise me to play and listen and maybe "be present," and definitely not make charts at all. But Lan Kratzke likes making charts.

So anyway, my own rule will be to limit chords to at most 7 notes, and otherwise enjoy the fact that I don’t even know the rules, which will therefore be exceedingly easy to ignore.

First let’s take a look at some chords we can build from some scales that don’t have 7 notes.

S H H H H H H H H H H H H	chromatic	pick something
S W W W W W W	whole tone	+ triad, 7(#5)
S H W H W H W H W	octatonic half whole	o7
S W H W H W H W H	octatonic whole half	o7
S W W H W W H H H	bebop dominant	13, M13
S W W H W H H W H	bebop major	M13, M11(♭13)
S W W m3 W m3	pentatonic	6/9
S m3 W W m3 W	minor pentatonic (mode 5)	m7(add 11)
S m3 W H H m3 W	blues	m7(♭5)(add 11)

The source for my last post, Puget Sound, provided a way of finding a scale from a chord:

1. Arrange the pitches in the chord so that they fit within an octave.
2. Fill in the gaps, avoiding consecutive half steps and augmented seconds.
To find a chord from a scale, then, we’ll construct scales, making sure to avoid consecutive half steps and augmented seconds, and then stack the thirds into 13ths.

But first, see how the minor pentatonic above is the same as a pentatonic scale starting on the 5th scale degree? (There are still some fencepost issues here, but it works out.) That’s why I wrote “(mode 5)” in the chart. Well, it turns out that every time there are 4 whole steps in a row in our 7-note scales, which happens exactly half the time, there is only one way to rearrange the remaining intervals so that there are no consecutive half steps. And it just so happens that the resulting scale is some mode of ascending melodic minor! So the third column of this chart will list the ascending melodic minor mode, should it apply. I'll notate this as "m mode" and notate the church modes, based on the major scale, as "M mode."

Here are all the scales that have exactly 7 notes with no consecutive half steps or augmented seconds.

S H W H W W W W	locrian ♭4, altered	m mode 7	m11(♭5♭9♭11♭13)
S H W W H W W W	locrian	M mode 7	m11(♭5♭9♭13)
S H W W W H W W	phrygian	M mode 3	m11(♭9♭13)
S H W W W W H W	phrygian dorian	m mode 2	mM13(♭9)
S W H W H W W W	locrian #2	m mode 6	m11(♭5♭13)
S W H W W H W W	aeolian, natural minor	M mode 6	m11(♭13)
S W H W W W H W	dorian	M mode 2	m13
S W H W W W W H	melodic minor	m mode 1	mM13
S W W H W H W W	mixolydian ♭6	m mode 5	(♭13)
S W W H W W H W	mixolydian	M mode 5	13
S W W H W W W H	ionian, major	M mode 1	M13
S W W W H W H W	lydian dominant	m mode 4	13(#11)
S W W W H W W H	lydian	M mode 4	M13(#11)
S W W W W H W H	lydian augmented	m mode 3	M13(#5 #11)

That was fun.

The harmonic minor scale neither belongs in the first chart because it has 7 notes, nor in the second chart because it has an augmented second (enharmonically a minor third). But I don’t think that means we leave it out in the cold to fend for itself.

S W H W W H A2 H

harmonic minor

N/A

mM11(♭13)

Well that nearly concludes this post. I'll mention a few things Jacob Collier said in his presentation at USC: Music & Mindset. We can all choose individually whether or not to agree with them.

Regarding the circle of fifths,

1. "The useful thing about this circle is that it's just a nice shape."

Ha ha ha, I loved that.

2. Major chords are based on 5ths, and minor chords are based on 4ths.

For example, fifths yield C G D A E B F#, which is a CM13(#11) chord.

From our chart, we know this means the fifths create a lydian scale.

Fourths yield: C F B♭ E♭ A♭ D♭ G♭, which is a Cm11(♭5♭9♭13) chord.

From our chart, we know this means the fourths create a locrian scale.

3. Moving clockwise on the circle of fifths creates brighter triads.

For example, skip over one and listen: C major triad - D major triad.

4. Moving counterclockwise on the circle of fifths creates darker triads.

Skip over one and listen again: C major triad - B♭ major tirad.

5. Root position triads are home.

First inversions are unsettled.

Second inversions are half settled.

6. "Of course you can change key. It's one of my hobbies. I do it as much as I can every day."

Cute.

Perhaps a favorite line from the presentation:

"Embrace the nonsense. Sense is massively overrated."

Although I only needed to reference "Music & Mindset" to write this post, I'll leave you with links to my favorite Jacob Collier discovery - an interview that touches on just tuning, microtonal voice leading, and negative harmony. Have fun!

Jacob Collier Interview with June Lee Part I

Jacob Collier Interview with June Lee Part II

Jacob Collier Interview with June Lee Part III

Back in June, I published a musical analysis of Sweeney Todd because Austin Opera was going to put on a production in over half a year, and I had to prepare my family for what was to come. And come it did - that day was today! We were at the Long Center, with a party of eight right in the middle of orchestra row C, in a sold out show. Sweeney Todd sold more tickets than any show in Austin Opera's history. Needless to say, we were ever so close to all the make-up and spit and glory, and I had a marvelous time. Marvelous!!! I'm not sure if you can tell, but I'm fairly giddy as I type this. Johanna's voice was lush and rich - not shrill as usual. Pirelli's accents were so perfectly over the top, Beadle was hilarious in both Parlour Songs, and not to undermine his vocals, but Tobias was an absolute cutie pie. Sweeney Todd and Mrs. Lovett were excellent too, of course. I've been in love with this show for over 20 years, and today was the first time that all the lines in "A Little Priest" were truly funny. Some lines like "shepherd's pie" and "with is extra" are always funny, but this time it was all of them.

Fifteen years from now I don't want to wonder who played what, so I'll jot that down real quick.

Austin Opera Orchestra Conductor - Timothy Myers

Director - Doug Scholz-Carlson

Sweeney Todd - Kevin Burdette

Mrs. Lovett - Mela Dailey

Anthony - Mark Diamond

Johanna - Raven McMillon

Toby - Christian Sanders

Judge Turpin - Ron Raines

Beggar Woman - Zoie Reams

Pirelli - Angel Romero

Beadle Bamford - Bille Bruley

24 piece chorus

This week, we also watched:

Sweeney Todd: North American National Tour, Angela Lansbury, George Hearn 1982

Sweeney Todd in Concert: San Francisco Symphony, Patti LuPone, George Hearn 2001

Sweeney Todd in Concert: New York Philharmonic, Emma Thompson, Bryn Terfel 2014

Apparently, these other productions have also been filmed, but I haven't been able to get my grubby little hands on them:

Royal National Theater BBC 1994

Barcelona Cast 1995

Opera North BBC 1998

Opera House BBC 2003

That's okay, though, because now I know what to ask Liên for my birthday for the next four years. And if you don't think I'm crazy already, I'll be seeing Annaleigh Ashford and Josh Groban in Sweeney Todd on Broadway this April. George and I are flying out to New York.

The point of this post, though, was to post pictures from our Sweeney Todd lunch party!!! Malinda and Ripley came over to join the rest of us, and we ate a bunch of people. When I remember this fondly, like in 30 years or maybe tomorrow, I hope I'll be thinking, "God, that's good that is de have you Licious ever tasted smell such Oh my God what perfect more that's Pies such flavor God, that's good!!"