r/musictheory

Via Alexandra Smith on Facebook

Hi everyone,

I created this experimental website, which I called Z-Tonnetz, to test a new idea following my work on circleofthirds.com. This time I applied the same principle to the Neo-Riemann Tonnetz: I stripped the accidentals and made them change dynamically relative to context, leaving only 7 possible notes, each with their own letter name. This made new triad types appear that aren't on the regular Tonnetz: mainly diminished and augmented triads.

Working on this I realized that I was modeling a third dimension, several layers of the same Tonnetz but shifted so that each letter name were on the same column with a different accidental, like this: F𝄫, F♭, F, F♯, F𝄪...

This opened up a lot of possibilities. In this model, B and F aren't far apart anymore. They are neighbors, only on a different level. F is right below F#, and this made it possible to "close" the loop of tonal scales and have a visual model for these types of altered triads: they're represented by a tilted triangle.

This makes several musical concepts easy to grasp visually. The diminished fifth that is always present in the diatonic scale as the tritone can now be viewed as a geometric inevitability. Another example is the augmented 5th (C-G♯). This is a dissonant chord that happens to be enharmonic with the consonant minor sixth (C-A♭), and both intervals can be played using the same keys on a piano, which could make one wonder, how can the same interval be both consonant and dissonant? On the Z-Tonnetz, you can see that the C-G♯ augmented 5th crosses a layer to reach the note above the perfect fifth, and the C E G♯ triangle is tilted, while both C F A♭ (F minor) and C E♭ A♭ (A♭ major), which are perfect triads, are flat.

Functions of scale degrees can also be mapped out by the position of their triad relative to the "bend" of the tritone. The stable tonic, C E G (in C major) is the furthest away from it, and so is Am. In fact, all other triads in the diatonic scale touch the bend, which explains why in tonal music, degrees 1 and 6 are favored as stable centers.

Another geometric consequence of this model is the fully diminished 7th chord: it appears as two joined diminished triads, which create an oblique plane that cuts through two layers. If you toggle the "enharmonic" mode in the 3D view, you can see how it can reach several different layers, pointing to its versatile role in modulation. It also explains why we use a diminished 7th for this chord, rather than a sixth, which can be confusing to learners (why use B𝄫 when you can use A?...). This visualization provides a geometrical explanation to the rules of harmony and voice leading.

One application of this model is the enharmonic disambiguation algorithm I created: from a MIDI file that only encode 12 chromatic pitch classes, I worked out a way to score each possible spelling using their positions on the Tonnetz, and figure out which key a piece is in. As a proof of concept it actually works, though a lot more work is needed (for instance I don't differentiate yet between the actual key and a temporary tonicization). I added several demo files you can try out, or you can import your own. You can also test it out with the computer keys, or use a MIDI keyboard (you'll need to refresh the page after plugin it in).

I could say a lot more but this post is long enough. Not sure when I'll have more time to work on this, so I thought I'd share what I have now and hope that some people will find this niche project interesting. It has its limits, it doesn't explain everything (no theory or visualization ever could), but it's a novel way to look at some old concepts. I'll try to fix any bugs that remain in the near future, and hope to be able to work on this system some more when I can.

Link to the website: ztonnetz.com

Cheers,

Alex

acknowledgements:

Library (Meantonal) used for Pitch Class and Interval modeling by u/HexMusicTheory.

Theoretical foundation for this project by Andrew Milne can be found here: http://www.tonalcentre.org/

I am really struggling to identify the chord progression from a piece.

First: Yes, I can read sheet music. Yes, I know my chords, honestly quite well. If you ask me to name the notes of any major or minor triad, any major/minor/dominant 7th, and in any inversion, I can do it easily/play them easily on the piano AND the guitar pretty much instantly. I also know about other chords like diminished, augmented, sus, add, 9, 11, 13. Now I'm not going to say I can instantly recall these but I can easily derive them.

Despite this, if you hand me a piece and ask me to tell you the chord progression from the sheet music, I never can do it. It seems like absolutely no song, no matter how basic, uses chord progressions with "obvious" chords. It seems like there is always some omissions, always some strange tone added, etc.

My process for attempting it is this:

1. Identify key of song to help determine context (I use the key signature and then play a bit of it to see if it resolves to the major or minor of that key signature)

2. For each measure, identify all the notes being played (and I do this across both the bass and treble clef)

3. see if the notes played belong to any of the diatonic chords. If not, consider the chords within the parallel or relative minor. if not, consider things like secondary dominants.

4. So often it seems like the chords played omit certain tones, and so I consider if perhaps the chord is omitting the 5th say in a 7th chord, etc.

I literally get nowhere with this method. I am clearly doing something wrong. I also don't know when a tone should be considered a "non-chord" tone and thus ignored from this "analysis".

Let me do an example from a pretty basic piece, which to me seems to be in G major:
https://www.youtube.com/watch?v=4liWweR89uo

The first four measures are playing CFG and CDF. The key is G major, and since these are natural, I would think maybe these chords come from G minor. In G minor, C F, G is what I would call Csus4. Also in G minor, we have C D F which would seems to remind me of a Dminor7 with the fifth omitted. SO would I be write to say this piece, which is in G major, begins in G minor with a Csus4 leading to a Dmin7 (omit 5)?

Continuing on to measure 5, we have C and E in the treble and C, G, A in the bass. In the context of G major, especially with the ii7 being A minor, I can't imagine this being anything else besides Am7, which from my knowledge consists of A, C, E, G.

IN measure 6, B, A, G in the bass, D in the treble. To me, G, B, D, is obviously a G major chord which is diatonic, but what the heck is that A doing in there? How would I interpret that. My best guess here is that this is a Gadd9.

I mean we can continue here, but I want to know the following:

1. Did I do this right?

2. Is my method a good one?

3. How do you know when to ignore a tone as a non-chord tone and thus omit from this analysis? If a tone is intentionally selected by the composer to not be a chord tone, then this would lead me to a faulty conclusion about the progression.

4. Is it possible for there to be multiple "answers" where two people derive the chord progression, are effectively saying the same thing but doing it differently?

PS: I have a teacher, she just wants to focus on learning piano technique/mechanics for now AND studying theory independently, and she says we will apply it to songs starting in 6 or so months... but I'm an engineer by trade so not understanding this stuff drives me crazy because i always need to know what i'm doing/playing.

Which one must go?

I'm having trouble figuring out how this is counted.

I think a bar of 5 is involved, alternating with 4? or 6?

But... this is beyond me at the moment:

Orchéstre Baka Gbiné playing Kopolo

Song link

I’m struggling to tell if it’s in F# major or C# major. I first heard it in F#, but then I started doubting myself the more I thought about it.

Some arguments for F#:

• The chord progression in the verse(?) seems to follow a fairly typical I—vi—V—V in the key of F# major, also putting F# in the metrically strong position of the chord loop
• Vocal melody outlines the fifths of these chords in the verse

Some arguments for C#:

• Each verse ends on 8 bars of G#7, which would be a fairly unlikely unless it’s a secondary dominant
• The melody resolves to a C# in this section ”…for the Bentswood boys” (but the chords still resolve to F#?)
• The section from 1:47 has a melody which quite clearly says C# to me, especially the ”Don’t take me down, don’t take me down, don’t take me down south” mostly walking down the C# major scale and landing on chord tones of C# major

My theory on why it’s hard to tell is because Brett Anderson never sings a B (4th degree in F#) or C (technically B#, 7th degree in C#) so we don’t get a clear indication from the vocal melody. The harmony and one melody plays a C over the G#7 but nowhere else.

So I ask r/musictheory; what key is this song in? Let me know your thoughts in the comments!

bro ANALYZES yet another JAZZ SONG. you WON'T believe it.

Suppose I know the notes of a particular sequence, and that sequence has a note or note(s) that are non-diatonic to the key of the overall song.

I assume this means there has been a modulation of some kind. I am learning (through another thread I posted on r/piano) that you need to use your ears to determine what the key of the part of the song you are in is, and then you can more accurately use that context to determine the chord progressions.

Take for instance, this song:

https://www.youtube.com/watch?v=4liWweR89uo

In another thread, it was pointed out to me that the first four measures sound like they are in the key of F major, and also that all the tones are diatonic to F major, so its likely that part began in F major. Hence, we would interpret the progression as being in the key of F and name the chords accordingly. Separately, someone argued it is in the key of C major.

I, on the other hand, erroneously assumed that because the overall piece is in G major, and the notes in the first four measures are diatonic to G minor, then its not a shock that the song begins in the parallel minor.

Of course, my analysis omits what I actually hear to determine the key, which I know is far more important then just figuring it out on paper/logic like I did.

But what am I supposed to be hearing to determine the key? I totally understand that a key is the center, and its what a sequence resolves to. If we look at measures 5 and 6, I can definitively say that those are in the key of G major even just using my ears, as both measures so strongly resolve at G, and well, the piece is in G major (correct me if I'm wrong though).

But what about the first measure am I supposed to "hear" that tips me off to it being in Fmajor?

Audio: https://youtu.be/jaf-kmdIHns

I'm transcribing this piece. Growing up I always heard the intro and main melody in 3/4 (~96 bpm), because many of the melody notes and harp chords land cleanly on beat 3, but as the piece goes on, it feels more and more like it should actually be in 6/8 (~64 bpm), with a fair amount of hemiola, culminating at 1:52 where it's pretty unambiguous compound meter.

To me the bodhran part seems more stilted in 6/8, with most first beats split into two, right until a later section makes the exact same rhythm feel better in 6/8 (to me).

So I turn to you: Do you feel the piece entirely in 6/8, or does it switch from 3/4 to 6/8 part of the way through? Entirely in 3/4 (nah)?