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RE: Next Piece
What is the attraction of Burgmueller for analysis?
I had the impression that this was just "finger exercises",
not serious music, although I'm sure it illustrates many technical points.

I do think one of the problems of "analysis" of beginner music
is that the music has often been so modified in timing or harmony or voicing
to make it "easy to play" that some really interesting musical aspects
of the original composition have been lost or obscured.

I'd like to see a mix of popular and classical selections.
For classical, I'm fond of The Anna Magdalena Notebook,
but I think it might be more useful to cover a variety of composers and periods.
I have a book called Great Piano Music Vol 1 by Ada Richter (Theo. Presser, 1981)
with a variety of graded 1-2 page "easy" solos from 20 different composers from Bach to Bartok.

In the popular vein, I'd like to see some analysis of jazz.
(My teacher has been pushing me into it!)
I understand it uses different scales and more complex harmonies
(a lot of 7 9 11 and 13 chords)
but on the other hand is the basis for contemporary pop/rock and gospel/praise music.
But maybe that's a subject worthy of it's own "analysis" forum!

tinman1943, that was me who mentioned #Idim. I also mentioned vii°. But I didn't call it just vii°, I called it vii°/ii. The "/ii" is an important part of that chord name. These two names -- #Idim7 and vii°/ii -- are coming from two different systems of naming chords.

#Idim means it's the diminished triad built on the sharped tonic of the key: that is, C#dim. This comes from a system that always relates the roman numeral for the chord to the notes of the major scale for the piece. This is the system I will use on this thread.

vii°/ii comes from a different system which I will not normally use on this thread. The notations means: first look at the number after the slash, ii. That means find the minor key built on the second degree (that is, note) of the piece's scale. The piece is in C major, the second degree is D, and in particular the triad built on D out of notes in C major is D minor: DFA. So D minor is our temporary key for the purposes of interpreting this chord symbol. Next look at the number before the slash, vii°. That means consider the (temporary) key of D minor and find the diminished triad built on the raised seventh note of the D minor scale (or the seventh note of the harmonic D minor scale). This is C#dim.

So exactly the same chord is meant by both symbols, #Idim and vii°/ii.

Just to make things more complex, the slash notation with Roman numerals on both sides of the slash that I described in this post is different from the slash notation that we will normally use on this thread, e.g. C/G to mean a C chord with G as the lowest note.

You're right that a plain vii° in C major would have meant Bdim.

(I started this a while ago, so now it's cross-posted. I like keystring's reply to tinman above, because it talks about musically the progression of chords and how they're leading one to the next. My post here is a purely technical post focused on the mechanics of naming chords.)

tinman1943, good suggestions about pieces. Burgmüller's studies include some good pieces such as Ballade and Arabesque. It depends on your musical tastes as to whether you find most of the other studies interesing or not. I'm quite fond of orderly and straightforward music, so I like the studies, but I know I have some odd tastes.

Anyway, the reason for proposing to tackle Burgmüller before the Anna Magdalena Bach Notebook was that I think that the harmony is easier to analyze in Burgmüller than in AMBN. Also I think that for people who may be coming out of mostly chord playing, Burgmüller's style is easier than the counterpoint of the AMBN.

I think there's value in looking at simpler pieces to get the basics of analysis out of the way before tackling pieces that are more complex, in particular that are more complex in being able to identify the harmonies.

That said, I'm not attached to any exact piece. If pieces from your Great Piano Music Vol I are available on imslp, we can work on them too.

I know almost nothing about jazz, but maybe there are others on the thread who know more and could guide us in jazz analysis. Do you have any pieces in mind?

I do have a piece I want to do next, which is America (a.k.a. God Save The Queen for our Commonwealth pianists). The reason is to give us some more practice in identifying a wider variety of chords, and to continue looking at chord progressions.

And one more post: tinman1943, is this the book you have?

Indeed, why even be attached to the notion of doing complete pieces one at a time? To cover topics and make points, why not present them using little snippet examples, perhaps just a bar or two -- like the example from "White Christmas" above.

The problem with isolating fragments is that this thread becomes more like a course of instruction that could skip real world features and they can get swept under the carpet.

By looking at complete pieces every event comes under scrutiny and the learning is more homogenous with no stone unturned.

We move from learning the theory as an interesting by-product that aids understanding into learning theory, with a real world example or two, but scant idea of its effect within the larger context of a piece and thus devoid of interest, meaning or purpose.

Here we are looking at all the theory necessary to understand a particular piece and learning it by understanding its function rather than learning a dull checklist of how it can be used. The learning is motivated by the desire to understand a piece of music and its effects.

A course of instruction might look at a particular type of cadence and show its basic function. Then you come across real world examples that aren't so basic and you feel betrayed.

Here we look at all the cadences in a piece and build a catalogue of functions from real examples. No cadences get overlooked. The knowledge is empirical and more complete but also with doorways to other avenues, not a closed book.

On this general idea: When I began harmony theory the traditional way, each book that I got had something missing. All of them restricted themselves to common patterns while real music is not that narrow. Even for the "traditional in Bach's time", when they finally showed Bach, they warned us not to break the rules that Bach broke! One of the books has a tiny note for teachers saying that it is all simplified, and if they want to expand with their students, please go ahead.

Meanwhile, what we did was exercises. You learned about primary (I, IV, V) and secondary (ii,iii, vi, viio) chords, and how each was used, and then you wrote exercises. You never actually saw this applied in music. Well, then I found a book that did try to do what JohnSprung suggested - use small excerpts. Now this was still from the point of view of the theory being taught, rather than figuring things out from a piece. So this book taught the same chord-thing as Sarnecki, but it added pieces. For every item of theory, there were around 40 (!) excerpts from music. If it taught about I64 V7 I (which they name V64 V7 I) then you found it in those 40 pieces and saw how it was applied. If the tritone that you find in any V7 (BF) moves to a give place in a V7 I progression, then you drew arrows in these excerpts, to catch the movement.

There was a huge weakness! They had to search far and wide, and the excerpts were out of context. As a student I wasn't familiar with the pieces, but my teacher spotted it. He would say that excerpt X was near the end of some section in that movement, where there was a modulation and other things going on, and musically the example was wrong. If a student were learning to hear and understand music, this killed that kind of hearing and understanding. It was great for passing tests (my opinion) but not for being a musician.

Therefore I do tend to endorse the wholeness idea. There are weaknesses in doing theory in this form, and some real study of each item should probably be done as well.

Wow! I never thought of it that way. So if you create a sequence of Dom7 around the circle of fifths, then the 3-7 (alternately inverted) of those chords forms a chromatic sequence of aug4/dim5/tritones! So is that why the circle of fifths (or a dim progression) "works"?

Example: bold are the Dom7 roots; cols 2 and 4 are the dim5, "=" means natural
E= G# B= D=
__ G= A= C# E= G=
D= F# A= C=
__ F= G= B= D= F=
C= E= G= Bb
__ Eb F= A= C= Eb
Bb D= F= Ab
etc.

Good explanation.
I don't recall ever seeing the roman/roman notation before;
I had it confused with the "normal" one.

But it relates to an interesting point: why does the 'leading tone" lead?

I'm thinking that trying to do analysis in terms of chord name of whatever system just leads to a lot of seemingly arbitrary rules.

But doing the analysis in terms of actual intervals (concurrent and sequential)
expressed as "just" frequency ratios (such as 2:3 for a "fifth") might lead to an actual understanding of why the music works.

In the end, we'll have the same rules, but we might have a better understanding of why they are the rules.

Next Piece?


That's it: Great Piano Music, ed. Ada Richter
JCF Bach: Country Dance
JS Bach: Minuet
Bartok: Copy Cat; Indian Dance
Beethoven: Rondo a Capriccio
Diabelli, Moderato
Gretchaninoff, Sailing
Gurlitt: Landler; Micchievous Child
Haydn: Minuet
Krieger: Bourree
Loeschhorn: Song without words
Mozart: aria; Minuet in F major
Mueller: Andantino
Neefe: Canzonet
Notebook for Anna Magdalena Bach: Chorale 8
Ornstein: Listen to the Drums
Rameau: Menuet
Schumann: Canzonetta
Schytte: Cantibile; Polka
Wanhal: Theme from a Sonatina

Integer frequency ratios are a natural consequence of the physics of vibrating strings, air columns, metal bars on a glockenspiel, etc. The physics and math may make an interesting appendix to the book for those who can follow that stuff. But it doesn't do much to illuminate why we like ii - V - I chords in that order.

At this point, I'll refrain from a very long tangent on overtones, equal and other temperaments, the circle of fifths, and all that.... (Except maybe to remark that only the first two overtones really matter, 2:1 for the octave, and 3:1 which is an octave and a fifth. Going up and down octaves and fifths you can put the whole circle together from that.)

No, you can't - and it's not my style to refrain from long tangents...

Using the 3:2 ratio on A = 110Hz you get to A = 14272.1 hz approx.
(E=165, B=247.5, F# = 371.25 etc.)

Going up the octaves you get (via 220, 440, 880, 1760, 3520, 7040) to 14080 - not 14272.1

That's why we had to develop mean, well, and equal temperaments. Most pianos are now tuned to a stretched equal temperament to compensate for the way our ears work but that's a subject for another time.

The octave was divided into twelve equal tones with each frequency being a multiple of the twelfth root of 2 (1.059463)

We lost the pure fifths, though they are very close (off by 0.11%) and we created a very dissonant interval at the seventh (off by almost 3%, nearly 30 time worse).

Because it's so dissonant! It wants to resolve to consonance. The nearest point of resolution is the semitone above.

If you watch a pair of flashing blue lights on an ambulance, for example, they go in and out of synch. You can see that one just needs to increase a little or decrease a little to get back in synch. The ear does this with sound waves.

Play a major scale and observe the tension that develops as it almost propels you to get to the tonic. It establishes the tonic centre. Try not singing the final note of Lili Marleen, a classic 7-8 resolution.

7-8 resolution: using the 7th note of the scale going to the 8th note of the scale. E.g. B to C in the key of C major, or F# to G in the key of G major, etc.

Hi Everyone, It's been a busy week wrt to other realms of life and so I'm only now getting to some of the latest in this thread.

Thanks keystring for the suggestion of going through the chords for major and minor on all the keys, and pianostudent88 for the notes about the perfect and diminished fifths. I went through and found the chords. One thing i'm wondering is how do you know when to describe the chord in terms of sharps or flats? I think this will become clearer once I learn to recognize all the key signatures.

i went through and tried to go from the diminished fifth to the tonic chords. so the diminished fifth is always part of a 7th chord...and the root of that chord is always the fifth note of the key that the tonic is in? i made sense of it at the piano, but now sitting away from the piano, i can't quite remember what i did. anyway while I was at the piano, i realized how they fit together. But again i wasn't sure how to name some of the chords I found because I wasn't sure whether to describe them in terms of flats or sharps.


and thanks johnsprung for explaining the 7ths in white christmas, that makes sense!!

I haven't quite understand the question about describing chords in terms of sharps or flats. When you are considering whether a cord is major or minor, you are simply going by the intervals. Example: in root position, a major chord has a major 3rd (4 semitones) from root to third, and a perfect 5th (7 semitones) from root to 5th. This is the same regardless of how a chord is notated.

Example (try on piano and observe your intervals):

CEG - count all your piano keys, both white and black
DF#A - as you scoot over 4 piano keys, you'll land on F#.
FAC
F# A# C# - three black keys, remembering that the # brings the notes to the right (F to F#, A to A#, C to C#).

Gb Bb Db - the same black keys, but this time you've moved from G to Gb to the left; from B to Bb, from D to Db, to find those three notes.
-------------------
Your major chord will always have the 3rd being 4 semitones over. So for example from C to E, you move from C to C#, C# to D, D to D#, D# to E - those are 4 piano keys.

How about finding some on your own, starting with piano keys.

Find these major chords on your own:

Example:
Ab C__ E___
If you go 4 piano keys from Ab what kind of a C do you land on? It should be C. If you go 7 piano keys from Ab what kind of E do you land on? You should land on the black key to the left of E, which makes it Eb.
So the answer is: Ab C Eb is the Ab major chord.

E G__ B___
A C__ E___
Db F__ A___

Can you get this one:
B D__ F__

I just invented this exercise following your question, so please let me know if it works or if it's confusing.

Velencia, you might be interested in a little chart Greener has put together. It's a ribbon of fifths, based upon an opened out circle of fifths.

Major chords are formed from the letter on the top row; the fifth is the box to its right and the third is the box below the fifth.

Minor chords are formed from the letter in the middle row; the fifth is again the box to its right but the third is the box above the tonic rather than below the dominant.

Major chords:
| 1 | 5 |
|---|---|
| - | 3 |

Minor chords:
| 3 |
|---|---|
| 1 | 5 |

The minor seventh (note) is two squares to the left. That makes a minor seventh chord with a letter from the middle row and a dominant seventh chord, or plain seventh, with a letter from the top row. The note for a major seventh is a knight's move away, down 2, left 1.

There are other uses for the grid. You might become familiar with the middle of it from usage but I still refer to the extremities while analysing pieces in remote keys.

That chart helps people find at a glance the functional chords in each key so that they can instantly get answers to analysis questions. They don't have to understand what a IV chord is, or how to find one. Valencia's question was on a very basic level, involving major chords and how they relate to accidentals and key signatures. I don't know if the exercise I suggested will work, but if it does I think it will give this understanding. Will using a chart give that understanding?

Actually, I studied that chart. Maybe it is handy for some people to quickly see what the Dominant (V) and Subdominant (IV) chord is by looking left and right, but is it meant to aid understanding of basic theory? Can you get the nature of a major chord, and why the A major chord has a sharped note in the middle, through this chart?

No, that's not why I posted it.

Having found the chord I thought the chart might help clarify whether the notes in it are sharps or flats.

It won't build understanding on its own but it might help by seeing the patterns and relationships that lead to it and that it leads to. When I first saw this chart, or a subset of it, it led to an 'aha' moment when so many things fell into place.

I was no longer searching in the dark for lots of little things not knowing where I was headed. Seeing this made everything finite and achievable. There are many paths to understanding. Few of us all tread the same one.

As I thought. That gives an idea of usage.

At this stage, charts or the circle of fifths serve as a summary or picture of things I've discovered in stages. It's like after a journey you look at a map and get the big picture. I see what you're saying.