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Thanks, JimF. It's been a pleasure but it's not all been me.





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Thanks so much, Richard for putting up with me throughout with your tremendous patience and expert coaching.

I am relatively new to PW and this is the first exercise I have participated in. I'm looking forward to more now.

I will be back on this thread tomorrow and likely for some time to come as there are a lot of notes that I still need to digest.

Special acknowledgement and thanks to PS88 as well. It is always productive to see things from varying perspectives and this insight was sometimes just what was needed to flip the switch, for me.

Also, to everyone else who participated in this thread, especially Carol and Jim, it was fun working with you on this.

I understand there is another analysis coming soon. The composition is unfamiliar to me (Bach.) However, I will be interested to participate and may actually give a go at learning something from wrote.

Thanks so much again, everyone and good night.

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I'm back from my choir concert.  Standing ovation, and nobody fainted.  Very satisfying.

Measures 63 and 65 look to me like the same G#7b9 that we saw before: G# B# D# F# A.  Wouldn't G#9 require A#?

Circle of fifths in measures 55-58:
55. C#; F#.
56. B7 (1st inv); B7 (1st inv), E
57. Amaj7 (1st inv), D#; G#7 (1st inv), C#m
58. F#m6; ...

Notice each root is a fifth below the previous root (by note names, not necessarily by exact pitch on the keyboard).  We get a long string, starting from C# and progressing through every note of the C# minor scale, accelerating to one chord per half beat part way through.  Then it hurtles straight past C# and continues to F#.  By alternating seventh chords in first inversion with triads in root position, Beethoven gets a nice bass line in mm. 56-58: up a half step, down a minor third, up a half step, down a minor third, etc.

Strictly speaking it's not a pure circle of fifths because Beethoven stays diatonic in C# minor (notice he gets both B natural and B# within the minor tonality), so there is a hitch from A down to D#, which is a diminished fifth instead of a perfect fifth.  Every diatonic circle of fifths progression has a tritone hitch like this.

I think that's gorgeous.  Shorter common progressions, like vi-ii-V-I or ii-V-I or V7-I are shorter fragments of this full circle of fifths progression.


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I want to follow up on something that I said way back in my post about exercises to get familiar with dim7 chords, and then follow up on what keystring said about alternate spellings and they're not always stacked minor thirds.

Originally Posted by PianoStudent88
Hint: if the root of your dim7 chord is a black note, call it by its sharp name, not its flat name. For example, A#dim7, not Bbdim7. There's a reason for this which I'll explain in a later post.

The dim7 chord appears diatonically (that is, using the notes of a standard scale) only as the dim7 chord built on the raised leading tone in the harmonic minor scale.  So for example, in C# harmonic minor the raised leading tone is B#, and B#dim7 is B# D# F# A, and those four notes all appear in C# harmonic minor.

Now, considered as sound only, or physical keys on the keyboard, B#dim7 is part of a family of four dim7 chords which all use the exact same physical keys: B#dim7, D#dim7, F#dim7, Adim7.  Oh yes, and B#dim7 could be enharmonically named Cdim7 as well.  Notice that all of those five dim7 chords have different spellings if you're using picky precise spellings.  I want to stay in the world of picky precise spellings for now.

In the world of picky precise spellings, let's reverse the process.  Instead of starting with a minor scale and finding its leading tone and dim7 chord, let's start with the dim7 chord.  Let's say, F#dim7.  What minor scale does this go with?  F# is the leading tone, so the tonic is one half step higher (and the next letter name).  In this case, G.  Let's check it out.  The picky spelling for F#dim7 is F# A C Eb, and sure enough those four notes appear in G harmonic minor.

That's why I said for dim7 chords rooted on black keys to use their sharp names.  For example, F#dim7.  If you use the flat name for the root such as Gbdim7, then you're considering Gb as the leading tone of a harmonic minor scale whose tonic is... oh dear, the note a half-step up from Gb looks like G, but we have to use the next letter after Gb so the tonic has to be a type of A.  Abb to the rescue (if rescue it can be called).  That's right, Gbdim7 naturally occurs in the key of Abb harmonic minor.  OK, I'm crazy and I'm intrigued by how we might find ourselves in Abb minor, but it's hardly an everyday occurrence.

The takeaway here is really this, though: if a composer is using picky precise spellings, and you find a dim7 chord, it makes sense to start looking for evidence of the related minor key.  Check it out in the Moonlight Sonata: B#dim7 followed by C#m, E#dim7 followed by F#m, etc.


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I was going to say something about the alternate appearances and resolutions of dim7 chords, but I need to clarify my own thinking on this first.


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Off topic - PianoStudent88, congratulations on tonight's concert. Standing ovation - wow!

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Originally Posted by PianoStudent88
I want to follow up on something that I said way back in my post about exercises to get familiar with dim7 chords, and then follow up on what keystring said about alternate spellings and they're not always stacked minor thirds.

I’d like to make a few points, and this will be disorganized. I apologize in advance, but you can take any point and enlarge upon it. My points are not meant to build. I’m not teaching here. I’m just throwing out odd facts, tricks, shortcuts. I’m not correcting, criticizing, playing the master. If anything, I want to show just how difficult this whole subject is, for students to learn, and for teachers to explain.

1) For reasons that are very obvious, people who play solely by ear do all the things we make a big deal about, notationally, with NO notation. So obviously notation is not necessary for all people. But for many it is a way in. For some it is the only way in. Most of my students need a lot of help with notation to get to the essence.
2) Of all the foundation chords in music, I believe the dim chord is the most tricky. First, it is present in both a three note and a four note form – a diminished triad (if it is spelled that way) and a fully diminished chord.
3) The assumption is that 3 notes is the triad, but there are a ton of situations in which only three notes are not spelled in thirds, and that already causes a headache: C Eb F#, which I simply call a Cdim chord, does not stack. In order to stack it, you have to add a missing note: C Eb F# **A**, then restack the chord as F# A C Eb.
4) Even in the case of a diminished triad, spelled in thirds – such as C Eb Gb – a huge amount of time we will see this as something like Eb C Gb, spread WAY out, and to make the third-stacking the Most Important Thing we would have to call it Cdim/Eb. Is anyone else getting a headache yet? Some may see why it is always easiest for me to view a three note dim chord as incomplete. Mentally I tend to complete it either as a fully diminished chord or as a dominant seven chord; B D F, moving to C E sounds like a rootless V7 I in the key of C major, to me.
5) If the concept of diminished is viewed as a set of pitches first, with no defined spelling, then we have a very different thing. And make no mistake about it. A fully diminished chord will have at least one note doubled most of the time, outside of SATB writing, and that results in this kind of thing: B D F *Ab B*
6) It is the 5TH note, the OCTAVE, that shows the bump in the system. There will ALWAYS be an augmented 2nd. Above it is *Ab B*.
7) The only way to construct a fully diminished chord that does not have an augmented 2nd, or an octave extension of that interval, is to limit your chord to four and ONLY four notes. This is the default in theory books explaining it. It is rather rare in music.
8) The best way to find that “root” of a chord, if you need one, is to always scan for the aug 2nd. The top note of that will be your answer.
Examples: C *Eb F#* A--> F# is the root, thus F#dim7. *Gb A* C Eb--> A is the root, thus Adim7.
9) You can make up the most ridiculous chords you wish, but they will always have min 3rds and one aug2. The aug2 gives you the root? No aug 2? Then you know you have only four notes, they are stacked, and the bottom note is the root (C Eb Gb Bbb)
10) You can theoretically construct dim7 chords by starting with the 7th note of the harmonic minor scale and stacking 3rds, and that does show the relationship to the key: B D F Ab, coming from C harmonic minor is an example, and it does want to go to Cm, though it can also go to C major, the chord.
11) For me it is more logical to think this way: I want to go to C or Cm, the chords, but also possible as a final chord. How can I backtrack?
B to C
D and F converge on Eb or E
Ab to G
thus B D F Ab to C Eb G. The spelling of the dim7 chord is dictated by the next chord, what key area it is in.
That same idea can be used for inversions: F Ab B D to Eb G C. Here the aug 2nd in the dim7 chord, Eb B, gives the root (B).
12) An easier way for me to get TO a chord FROM a dim7 chord is to consider the my destination chord, consider the key that this chord would fit in, then build a dim7 chord on the leading tone. For example, if the chord I am move TO is B or Bm, I simply consider the leading tone in the keys the belong to, A#, use that as he dim7 root and stack it: A# C# E G, min 3rds, and I have the right chord and the right spelling. What about C# E G A#--->B D F# B? I’m going to call that C#dim7 to Bm, but I will automatically know how to spell it because A# remains the leading tone, and THAT determines the notation.

I want to take this idea from 88:
Quote

That's right, Gbdim7 naturally occurs in the key of Abb harmonic minor. OK, I'm crazy and I'm intrigued by how we might find ourselves in Abb minor, but it's hardly an everyday occurrence.

Anything is possible, but Abb minor, of any kind, is weird enough so that we would be justified at cursing at any composer who chose something that insane. First, minor adds flats to a key signature. Then lowering any flat key adds 7 flats.

Consider that A minor, no sharps or flats, becomes 7 flats as Ab minor. Abb minor has 14. Abb Bbb Cbb Dbb Ebb Fbb Gbb. So if you wanted to construct a diminished chord using the harmonic minor scale method, start with Ab minor. The dim chord would be:

G Bb Db Fb, and that would be seen. It is used. But then you have to flat it for the chord beloning to Abb minor:

Gb Bbb Dbb Fbb

INSANE!!! But would Satie do something like that? <gulp> … maybe laugh

In general it is best to start FROM sane keys and construct dim7 chords moving backwards or you are going to get some pretty weird stuff. wink

Bottom line: THIS STUFF IS HARD!!!!!!!!!!!!!!!

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Originally Posted by zrtf90
This repeats the E minor question we had in measure 16. Both chord names are correct. I too am going with F# minor but I can't say that D major 7 is wrong.

Technically, every note in a chord can form the root of a chord and therefore be configured to be the chord name. Some of the names can thus be really awkward. The right one to choose is the one that makes most sense to you as a player looking to hit the right chord in a hurry, or as a performer looking for a better understanding of the harmonic progression or whatever suits your needs.

I try, when there's an option, to give most weight to the bass note and least weight to the melody.


I'm sorry to be so late in this whole discussion. I was so sick last week, I didn't even know it was going on.

In the measures you are talking about, two here, two earlier in the key of B, Beethoven is just doing a IV I combo. F#m to C#m. iv to i for people who use case, IVm to Im the way I use RNs.

The melody notes, in the recap D and B#, are non-harmonic, color tones that revolve around the 5th, C#. You could stack it as D F# D C#, Dmaj7, but that's just not what the composer is doing because he insistently pounds out the F#m chord in the LH.

It creates more tension than a turn (D C# B# C#) by jumping over the C# melodically, so in his time this was VERY dissonnant.

The idea is so basic, so simple, that it seems like everyone would have used it, but I think that is a huge part of genius. smile

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Originally Posted by zrtf90


Our chord then is a B#dim7 with a G# pedal or a G# 7b9.

This is for M32. Your chord is 100% correct, but I think there is a much easier way to get there.

I would label this section and the the four measures before it a development section, but a very free-form one. We are in the key of C# minor. What is the most common chord in any key? A V or V7. The only thing that makes this tricky is that everyone knows a G7, not so many people are equally familiar with G#7.

But it just takes a G7, G B D F, and sharps everything.

G# B# D# F#. If you know to look for those notes, you see them immediately. And it only takes one low bass note to make a chord what it is. So the only problem is in figuring out what the extra note is, the A.

But there is a trick to that too. Whenever you see a dominant 7 chord, all the notes, with an extra note that is 1/2 step higher than the root but one letter higher, you know you have a flat nine chord. And it is VERY common in minor keys, not too unusual in major keys.

To me this is an incredibly powerful and important chord, and you find it everywhere.

The other thing about it, which you pointed out, is that if you throw out the root, you have a fully diminished chord left. That's why B#dim7/G# is the same chord as G#7b9.

But the really cool thing is that he uses this idea, then flips from one dim7 chord to another, so two measures later he goes to an Fx dim7 chord. And what is that? But all you do is add a D# to the chord and suddenly you have D#7b9, D# Fx A# C# E, and that explains the spelling. He then goes back to his G#7b9 chord he plays around with it for a long time until finishing with A to D# half-diminished/F# to G# to G#7.

The half-diminished chord can also be written as F#6, which would be my choice.

But look how easy it is in Cm:

G7b9, Cm, F#dim7 (rootless D7b9) back to G7b9, drag it out, Ab, Fm6, G, G7, Cm.

He really isn't doing anything complicated, or new. Any hack could use those chords. I always tell my students, "Take it apart, find out how little is there, think how easy it would be for anyone else to use those same chords, then try to figure out why it turns into genius in his hands. Because if anyone else tried it, it would be ordinary, cliche. That's the miracle. You'll never figure out where the magic is. It's just there... smile

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Gary, thanks for that excellent insight into what we're doing. (Glad to see you up and about, so to speak smile )

These diminished chords can be tricky but I think between yourself, keystring and PianoStudent88 we'll get these little suckers under our belts.

Originally Posted by Gary D.
The half-diminished chord can also be written as F#6, which would be my choice
Coming from such a source I look forward to quoting this at PianoStudent88 smile but I think she was coming around to this way of thinking anyway.



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Originally Posted by PianoStudent88
I'm back from my choir concert. Standing ovation, and nobody fainted. Very satisfying.

I didn't know you were GIVING the concert! Well done.

Originally Posted by PianoStudent88
Measures 63 and 65 look to me like the same G#7b9 that we saw before: G# B# D# F# A. Wouldn't G#9 require A#?

One of the reasons this thread has kept on track is because you've been there with me all the way and catching all my stumbles.

Most road accidents happen within a few miles of home. This is no exception. I saw that B# and thought major! What an ass!

Yes, it's our old friend the domninant minor ninth. I've edited the summary.
Another round of applause!

Originally Posted by PianoStudent88

Circle of fifths in measures 55-58:
...
Strictly speaking it's not a pure circle of fifths

And that's why I paid it little attention.

To me this is a melodic step pattern with off beat appoggiaturas. The changing harmony underneath is not exact enough to fit the pattern that you're trying to squeeze it into. If you can see it, then enjoy. I neither see it nor hear it.

The dominant ninth is indeed an important chord and it's a shame in a way that we haven't gone into detail about the dominant seventh first. I suspect in the not too distant future we'll be looking at them up to the dominant thirteenth in the big man's later works and the Romantics, of course.

I guess I'm thankful that we haven't had to deal with it here.



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Well, friends, we've torn this work into a number of pieces and worked out the chords, and many of them were tricky little blighters, but the next step - and we needn't take it just yet - should be to take all these, let me see, eight or nine little pieces and look at them more closely to see what's happening in each.

You know now that the first phrase closes into the relative major at bar 9, then into the dominant (of the relative major) at bar 15 and the second phrase closes into the dominant of that, the subdominant of the tonic key, in bar 23 and then moves into the dominant of the tonic key at bar 28.

Now try and hear those changes while you're playing through the piece (at the keyboard or following the score while listening).

We need to look at the relationship all these chord progressions have with each other by seeing how they fit to the key at the start of the phrase and again to the key at the end of the phrase and how they affect the mood of the piece.

Look at the first phrase, for example, bars 5-9. There's a simple i-V-i progression followed by a iv-III-bvii-III but if we look at the last four chords in relation to the target key of E, they become a ii-I-V-I (perfect cadence) in E.

We haven't gone too much into cadences yet but PianoStudent88 has brought up the ii-V-I perfect cadence. We don't have one here, we have a simple I-V-I but look how the melody notes F#, B, E form steps ii-V-I of a scale in E. Can you feel the closure that this brings to the phrase? Play the phrase a few times to feel the tension of the B# in the bass at bar 6 and the release in the bar 7 (it's not very pronounced because we're in a minor key but) see how different it is going in to bar 9.

Feel the tension and release of the tonic-dominant-tonic harmony of the second theme in bars 15-19.

It would be good if we took interludes while analysing the next few pieces to build up our harmonic vocabulary looking at the scales and chord construction, chord progressions and modulation and how they change the tension and mood, cadences that form the punctuation of music, the dominant seventh (and the other sevenths) and the extended dominants (ninths, elevenths and thirteenths).



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Good Morning fellow Moonlighters,

(that is what I feel like now as hardly touched any paying work last week)

Quote
The final analysis!
60. C# minor
61. G# 7
62. C# minor
63. G# 7b9 (dominant minor ninth.)
64. C# minor
65. G# 7b9
66 - 69. C# minor


I see we have preference to the dominant minor ninth and corresponding notation of this chord vs the B#dim7. I will go back to this lesson.

Quote

Originally Posted By: zrtf90
This repeats the E minor question we had in measure 16. Both chord names are correct. I too am going with F# minor but I can't say that D major 7 is wrong.

Quote
Technically, every note in a chord can form the root of a chord and therefore be configured to be the chord name. Some of the names can thus be really awkward. The right one to choose is the one that makes most sense to you as a player looking to hit the right chord in a hurry, or as a performer looking for a better understanding of the harmonic progression or whatever suits your needs.

I try, when there's an option, to give most weight to the bass note and least weight to the melody.


I took this one to heart and started wandering off with +- 5's. However, it makes sense to me that a standard is determined for chord notation and have a possitively enlightened perspective to this now.

Quote
1) For reasons that are very obvious, people who play solely by ear do all the things we make a big deal about, notationally, with NO notation. So obviously notation is not necessary for all people. But for many it is a way in. For some it is the only way in. Most of my students need a lot of help with notation to get to the essence.


Yep, that was the team I was on ... smile ... but no more.

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And, following on from that, Jeff, at the end of the day, the composer is trying to make sounds. How we choose to name them is semantics.

When I play B D F (B diminished triad) on the piano, either I want it to change to a C major chord (second inversion, G C E) or IT wants to change (I'm not sure which) and when it changes to C major I feel relieved.

And then again, maybe 'it' wants 'me' to change to a C major chord? Philosophy, anyone?

When I add an Ab/G# at the bottom to form a diminished seventh it wants to change just a little bit more. If I add the note at the top it's no more insistent but IT prefers to close to a C major root position (C E G) rather than the inversion.

If instead of the Ab/G# I add a G to form a dominant seventh the change isn't as insistent but the resolution is more emphatic.

If I do what Beethoven did here and add a G below AND and Ab/G# on top (dominant minor ninth) it screams at me to change. It really doesn't care whether I change to a root position or an inversion. It just wants me to get to C major.

The upshot is that since I stopped doing this stuff at university, and without an academic objective I really don't care what you call the chord. I know what it does and how it affects the music. I suppose, ideally, that is where we all need to get to.

But communication, whether between musicians or between teachers and students, is easier if we use recognised and more uniform notation, spelling and nomenclature so we need to get there too.



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When I add an Ab/G# at the bottom to form a diminished seventh it wants to change just a little bit more. If I add the note at the top it's no more insistent but IT prefers to close to a C major root position (C E G) rather than the inversion.


I understand that this is how Beethoven's mother used to get him out of bed in the morning. She would hammer out a G#dim7 without resolving it.

Poor Beethoven laugh

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But communication, whether between musicians or between teachers and students, is easier if we use recognised and more uniform notation, spelling and nomenclature so we need to get there too.


I'm with you 100% on that.

Can we play something else soon?

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Thank you Gary for adding far more than I ever could about dim and dim7 chords! I said earlier that what I have learned about dim7 chords I learned from you, but it comes out coloured by my predilection for precise spelling, and I have not fully absorbed the lesson about sound and alternate spellings all being OK. And my predilection for interpreting dim7 as VIIdim7 comes purely from my basic music theory course covering only the conservative basics.

I want to pick up on the Cdim triad C Eb F#.

I'm still in the conservative world of picky spellings, so if I saw that I would tend to call it F#dim7, second inversion (with the third, A, left out). I would be guided to that name by the neigbouring letter names Eb F# which would guide me to pick F# as the root and make Eb the seventh. I would be expecting G minor (the key or the chord) to show up. The augmented second doesn't throw me because I simply use it as a clue to an inversion of a seventh chord.

This is convenient for me because VIIdim7 is a familiar chord name and it clues me into what key to expect to be in.

On the other hand, there are various advantages to calling this Cdim -- it may be faster to play Cdim than F#dim7/C, because it's an easier chord name to process; also Cdim makes it clear that the A is omitted while F#dim7/C does not. Also one might simply prefer naming dim chords by their lowest note as standard practice.

Also, and here is where I don't have experience yet, and what I think is the most important reason for me to learn to use alternate dim and dim7 chord names. B#dim7/Cdim7/D#dim7/Ebdim7/F#dim7/Gbdim7/Adim7 (to give the family of related names) doesn't have to go to G minor. Because it is a completely symmetrical chord, it can go to any one of a number of places. So a composer can use what I would call F#dim7/C (with A omitted), know that as far as sounds goes it's exactly the same as Cdim, or B#dim, and go to C# minor instead of G minor. Or any of several other places.

An exercise I need to do is work out all the places a dim or dim7 chord could go to fairly naturally, and (because I like RNs) match these up with keys and RN names. For example Cdim in the key of G minor is IVdim.

This leads to needing to revise my comment about dim7 chords only showing up diatonically as VIIdim7 of a minor key. This is true if you're using picky conservative spelling requiring stacked thirds, but if you go by sound, and allow looser spelling, which composers do, then for example Cdim (C Eb F#, IVdim) also uses notes diatonic to G harmonic minor.

The thing is, I think there's a balance.

If a composer is using precise spellings and using VIIdim7 chords in the basic way, I think it's really helpful to be able to pick up on that quickly. "F#dim7/C, expect G minor" bang, done. No fussing about with "Cdim, or maybe it's Ebdim, and that could be going to one of 8 different places, hmmmm, what could it be, oh look, here's G minor, is that one of the 8 different places Cdim can normally go?"

On the other hand, if a composer is working more freely, then it helps to be able to pick up on that quickly too. "C Eb F#, followed by C# minor, no problem, that's one of the 8 places I would expect that dim triad to possibly go" rather than getting flummoxed by "F#dim7/C, I expect G minor, how the heck did the composer get to C# minor instead?"

I need more experience with the looser way of working with dim and dim7 chords, to start to find principles for when to work in one world or the other. Or maybe I'll become skilled enough in the loose world that I won't need the strict world's language any more.

(I think I recall that a dim7 chord has 8 natural places it can go, but I may have misremembered.)


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In the beginning I didn't know if I could get through analyzing this piece. It seemed so far over my head. Because of the people involved with this thread I have learned so much. I still have a long way to go recognizing chords but, because of the knowledge and patience of everyone here, I'm much further along. This has been a lot of fun.

Thanks everyone. I'm looking forward to the next piece.


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I'm delighted, Carol, that you carried on and had fun on the way.

I don't know how we approach the next piece.

Are we going to continue in this thread so that we can find earlier references more easily or are we going to start another thread for every piece?

If we're staying here then here's the link for the score in IMSLP.

http://erato.uvt.nl/files/imglnks/u...ach_Praeludium_No_1_in_C-Mjaor__RSB_.pdf

The piece is Bach's Prelude No 1 in C from the Well Tempered Clavier, Book I.

Nearly everyone knows it and it's not a lifetime's work on the piano. I can sight read it! smile

I imagine if you already have a copy of the score there will be no discrepancies between versions that are going to stand out.

Don't spend time on bars you can't solve.

Save them up for the end and we'll fill them in later.



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Originally Posted by zrtf90
Are we going to continue in this thread so that we can find earlier references more easily or are we going to start another thread for every piece?

I just started a new thread before reading Richard's post. I thought it would help new people to realize we're starting a new piece.

If we decide to keep it all in one thread, can we start a new thread anyway with a generic title, so people will know we do different pieces, not just the one listed in the title?


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