This summer I’ve been playing more of the glass etudes for piano, which are sort of a study of modern minimalist piano techniques. Etudes in a literal sense.
Anyway just yesterday I was playing etude 5 which has a Cb/Ab chord and then 3 measures later a B/G# chord (with a Db/Ab chord over it), but in the context of the particular piece its the right way to notate it. That B/G# is a real dissonance. (Although I would also be fine if it was notated Cb/Fb/Ab)
aha, I love it when people give me theory puzzles! I would call that first chord you’ve put in a square Db7, the one following it (as well as preceding it) is Fm/C, and then the second chord highlighted is probably best described as E6/B or E13b7/B, but this is where lead sheet notation is stretched beyond usefulness in my opinion. I think you might have mixed up some of the lead sheet notation symbols, I don’t see any Cb/Ab chords, although if there was a chord that looked like that it would probably be more accurate to say Ab7. The slash notation is meant to show the chord first, and then the bass note the chord is over, so a voicing of Cm7 in third inversion could be written as Cm/Bb.
Anyhow, all of my previous writings is to say that keys/scales are conventionally written a particular way to avoid mixing accidentals. Real written music need not do so! Lot’s of contemporary music has modulations to different keys, and chords borrowed from other keys. Looks like that is what is going on here. It looks like the left hand is “planing” (possibly a colloquial theory term?) the F minor chord down a half step. F minor and E major are distantly related chords (see the circle of fifths) and therefore to maintain “tertian harmonic order” (stacking chords in thirds, as opposed to seconds, fourths and their inversions) it made more sense to keep the left hand playing the same visual pattern of a chord in second inversion, but switch the accidentals temporarily. All the while the right hand need not make any such drastic changes, since its voice leading is smooth enough without switching the accidentals (A C# in measure 11 would only cause confusion, since we go right back to C natural in the next measure. Its better to show the movement than to temporarily “modulate” to the key the left hand is playing)
A final thought: the most dissonant notes here are likely tritone between the Db and A. This particular chord isn’t stacked in thirds the way most chords are, it would be a conventional 13 chord if not for the flat 7th cord member. Pretty neat! I’ll have to try this out on my piano when I get home.
Sorry I wasn’t using lead sheet notation. Was just being sloppy about the pairs.
The first chord in red is {Cb, Ab} over {Db F Gb} which I agree is some Db7 type thing.
The main point I was making is the second chord is notated as E/B in the right hand (this time in lead sheet notation) and a Db and Ab in the top. But it could also be Fb/Cb in the right hand. Or C# G# in the top but then it couldn’t tie to the voice led F before.
The really important thing as you point out (and if you play it as you see right away!) is you move from F minor sense to the major sense a half step below. That’s the musical idea communicated. And I thought the notation choice was an interesting one.
Ah, I’m so used to the lead sheet notation I didn’t even clock that that wasn’t what you were saying! Also you made me realize I missed that the Ab in m.11 is tied from the previous measure, disregard all that about E13b7, this is simply an E6 chord in second inversion. But yes, I actually like Glass’s choice in notation here. Even if theoretically we are changing an F minor chord to a “neigboring” Fb major chord, that would be pretty hard to read! (or at least, far more musically taxing than the E chord). Musicians don’t like to read Fbs and Cbs if they don’t have to. If we need to move far across the circle of fifths anyway like this chord is doing, its better to just write the simpler chord. Lot’s of hard decisions to make when engraving music like this.
I personally would rather see mixed accidentals with a chord I can quickly recognize (which is almost negligible to read at speed) than have to figure out that Cb, Fb and Cb form a major triad in first inversion, when it’s the exact same hand shape as before!
I agree. But also the cb two measures before makes sense too oddly.
I think his choices are good ones. But I also shared it to remind us they are choices and notation communicates music, it isn’t music itself. And the b to me when playing it communicated a dissonance and the earlier cb more of a consonance. Oddly.
Absolutely, we’re on the same page. I understand what you were saying with your original comment now. That alto voice moves chromatically in each direction, once staying on a written C, and the other reaching up to Db when we all of a sudden have sharps in the left hand. It definitely does seem like an odd choice without any context, but given what we’ve discussed I think its a sensible engraving choice. Thanks for the puzzle and thoughts!
I just read thru a lesson Messiaen gave on poly chords in pieces by Ravel and Debussy and Stravinsky and the texture of a minor chord a half step above a major is of considerable interest to all these composers and apparently Glass teased at the sonority hear as well though less overlap. Great passage to study.
Ok, time for my contribution to Pauls predicted 827 lol.
When it comes to naming the notes of diatonic scales and their modes (which if I understand right was @cosinekitty’s goal here) it is generally more directly helpful to think of a chain of fifths than a circle. The naming convention we use here has its roots in european music back in the medieval era and through the rennaissance and baroque. The underlying logic of it is based on stacking fifths. But, unlike equal temperament, the way the fifths were tuned back then, F# does not equal Gb.
So, it made no sense to wrap the line into a circle, rather the chain continues in both directions, adding progressively more sharps/flats. Like such:
And the trick is: any diatonic scale is made up of 7 contiguous notes on that chain.
Choose a note and go right (stacking fifths up) until you have 7 notes, and you have lydian.
If you go left (stacking fifths down) until you have 7 notes, you get locrian. The other modes are somewhere in between, but the 7 notes always neighbor each other on the chain. Dorian has the root note centered on the chain for example. You can work the rest out if you want I’m sure. The more notes come from the left side, the more minor degrees you get, from the right side major. Etc etc.
…which is also why, as was mentioned by @eanfran above, in diatonic scales you never mix sharps and flats. Any sharp and any flat are further away on the chain than 7 steps.
Anyway. That’s where the logic comes from. And writing things out with “correct” spellings is helpful also in equal temperament, because the scale ascends on the staff in the intuitive way, and each note of the scale has its own letter. And the chain of fifths helps with that more than the circle does because it doesn’t wrap around and confuse the note names.
…with complex harmony as discussed above, things are a little different indeed. 12-equal makes it easy to break out of the diatonic logic, and in some of those situations I agree it makes sense to go for something that makes reading easier.
Wow, I love this way of visualizing it! Man, I think some people would be less intimidated by the circle of fifths if it was laid out like this instead… something for the pedagogues to take a look at.
Yup! Equal temperament is good for many things. But the way we are taught about it sometimes obscures things a bit.
For anyone interested in more of the nerdery: In medieval times the most common tuning standard was so called Pythagorean tuning, which just means you tune your octaves and fifths as they are in the overtone series. The fifth is then a little sharper than in 12-equal (by a barely noticeable amount), so as you stack fifths, F# ends up being sharper than Gb.
In the rennaissance, people started to compromise the tuning of the fifths. They had discovered that the first major third in the overtone series sounds real nice, and is lower than the one you get in pythagorean. So they tuned the fifths a little flat so as you stack them you get a flatter major third/seventh/etc (and sharper minors). That’s called Meantone, and in it, F# is instead flatter than Gb.
If you mistune your fifths by exactly the right amount such that when you stack them, F# ends up equal to Gb, you have 12-tone equal temperament. That possibility was known a long time ago, but it didn’t become the standard it is today until the late 19th-early 20th century. By which time the common practice language was already deeply established, based on the earlier practices.
The major third is even worse than the fifth. The natural ratio is 5/4 = 1.25, but four half tones in 12-tone equal temperament are ~1.26. Every guitar player knows that from the down-the-neck G-chord, where the open B-string sounds a litte sharp when tuned with an electronic tuner.
Peterson tuners actually offer a “sweetened” tuning for dobro and banjo (tuned to open G), where the B string is halfway between 1.25 and 1.26.
Indeed. That’s the rennaissance thing I mentioned above. Stacking fifths (and octave-reducing), you get a sharper major third (81/64). The difference between that and 5/4 is called the syntonic comma. Flattening each fifth by a quarter of that comma means stacking fifths will land you on 5/4 exactly. It’s pretty cool! And guitar music can sound really great in such tuning. Though the fretboards end up looking like this: BaltimoreRecorders.org: Information about the Quarter Comma Meantone Guitar
But maybe that’s enough tuning spam in Dons patch thread.
We don’t need to do that… I’m enjoying the conversation, and this is educational for me. It would make sense to split the thread if someone posted the thread asking for help on a particular topic. In this thread I’m just hanging out, so no worries!
Tonight I used extreme feedback settings in Sapphire Echo, and several instances of Sapphire Zoo for complex modulation, to create a “One Button Symphony”.
The idea is that you only have to press a single button to add emphasis. Even if you never press the button, interesting background stuff happens.
My first time trying out the JW-Modules AbcdSeq. It is a lot of fun! I like controlling multiple voices and alternating between them in interesting ways. The integrated quantizer is good for keeping all voices in a consistent scale.
In this patch (available here) I was pleased with the cello-like voice and the “tinkly angel” voice going through Sapphire Echo.
Hi @cosinekitty hope it’s okay if I ask a basic question here.
First of all, I’ve been enjoying dipping my toes slowly into exploring your cool modules, and some of the videos and patches to go with them after discovering the Sapphire echo.
It appears to me that, rather than being completely random, Glee appears to produce interesting patterns. This is neat. I don’t claim to even begin to understand the math equasions involved; I was never good at basic algebra. What kind of changes do the different chaos modes produce? Thanks.
