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Plus this idea that sometimes accidentals are just for colouration and should be ignored is unsettling: what tells us we should ignore mm. 12 and 14 in our essential analysis, but include mm. 6 and 10 with their F#'s as being important to that G major cadence story?
Not sure I am understanding why we want to look at various sections as being in a different key. A teacher I had once liked to do this and I always glanced over at him with a blank stare (he was blind so didn't notice my lack of enthusiasm.)
Clearly, we are not in a different key as the key signature has not changed. Is this just so the RN progression structure will make more sense to us structurally?
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M12 has the notes C# E G Bb, if we stack in 3rds. So if you want to think of this as C#dim7, I understand. But it will be written as Gdim7 because the bass note is G
This is exactly where my thinking was Gary, when we started on the Moonlight thread. Although I am more keen now on following a more universal and broadly accepted naming convention. At any rate, I am keen to see what other responses/perspectives (perhaps already posted and I have not come to yet) there may be to this.
Greener, the key can be indicated either by key signature or by accidentals. The first thing to learn is how to identify key from key signature. A new thing to learn is how to identify changes of key when accidentals are introduced (and the change of key is often confirmed by the chord progression). To make it a bit more complicated (of course) the introduction of accidentals does not always mean a change of key.
Can you see how the introduction of F# and the chord progression in mm.5-11 suggest that we are temporarily in the key of G?
I hesitate saying this because my foundations are bring rocked on this thread. I am sure Richard or Gary will be kind enough to correct me if I am being misleading.
Gary, thank you for writing out the more detailed information and ways of thinking about dim7. I am happy to report that, thanks to things you've said in the past about rootless (and extended) V chords, I had already found the root idea of A D G C for mm.12-15, so it is good to see that confirmed by you. (Wait, now I'm not sure I have the accidentals right here. I'll have to review this, and compare to what you said. Maybe I got it wrong after all.) (ETA: I did have the letters right. I got confused because I was remembering the C# minor from the Moonlight Sonata and forgot that we're now in C major in the Prelude.) So it is fun to see it happening in a piece. I have to think about the rest of what you said. I am trying to practice what you said about dim7 because I can see that it will make me more flexible and more aurally attuned in what I can understand, as well as practicing standard notation for communication purposes. My own private notation for m.12 includes ideas from your way of using roman numerals with conventions from the land of secondary dominants and figured bass: VIIdim7/IIm (43).
Gary, I really appreciate you explaining all these things. I have some questions but I need to organize my thinking a bit more before asking them.
The moment we hit our dim7 chord in M12, we sense that it is going somewhere. If we decide to label it as C#dim7/G, we have actually done something very functional. C#dim7 with this EXACT spelling is, as you know, vii°7 in the key of D major or D minor.
Do you follow so far? My apologies to everyone else. This SHOULD be its own thread.
No apology required. This is exactly what I need to understand better. I will need to come back to it, however for it to sink in. Glad I know where to find it.
Do you follow so far? My apologies to everyone else. This SHOULD be its own thread.
Excellent post, Gary, but this thread isn't currently being used by composers/arrangers doing analysis on the music and for whom the analysis is the thing.
This thread was developed as an offshoot to the Moonlight analysis thread that was showing holes in the understanding of the musical language and lack of knowledge in the notation systems. Its purpose is to elicit posts exactly like the one you've just given us. Kudos! _____________________________
The link from keystring to the Bach-Gounod Ave Maria works if you edit out the duplicate http bit at the start. _____________________________
Let me summarise where we are as I see it.
We looked at the first four bars where we saw a ii-V7-I cadence to establish the tonic key. We saw three things that help a V7-I to bring closure, the leading note effect (7-8) as it rises to tonic, the resolution inwards of the tritone (augmented fourth between 3 and 7 of V7 chord) and the descent in the bass by a fifth to tonic.
We then discussed scales, particularly the minor variant, which is best thought of as a major scale with b3. We may also get b7 as well and other times a further b6 and it's variable within a piece.
We also lately covered modes, their construction and a bit of their history. Of the old Greek modes if the third note is minor it's a minor mode (Aeolian, Dorian, Phrygian, Locrian) and if the third is major, it's a major mode(Ionian, Lydian, Mixolydian) just like our diatonic scales. _____________________________
To find the end of the second section we looked for another V-I or ii-V-I cadence and found one at measure 7. But it wasn't really there. Well, the cadence was but the effect wasn't. So we learned that a sequence can override the effect of a cadence especially if, as here, the descending fifth isn't in the bass. (Either a descending fifth from dominant to tonic or a rising fourth from dominant to tonic octave.)
Note the stopping, resolving, relaxing, homely effect of arrival at tonic.
And we learned that to find a cadence we must use our ears. And listen predominantly to the bass. In bar 5 Bach introduced a descending sequence (a simple mathematical pattern) which our ears pick up as a descent to the dominant G. He adds a nice twist at the end (and just in time, I feel) to bring in the rising fourth.
In bar 12 he began a slower descent, via a slower moving pattern, to the tonic C in b. 19. This pattern needed a quick side step (to avoid F#, which would have obscured the target C) and deftly skirted the problem.
He has toyed with tension and release as the music comes at us in waves.
We have learnt the power of the sequence. The descent 3-2-1, the stronger 5-4-3-2-1 and the leading-note effect 7-8 are driving forces in music.
Note the moving, driving, tension-building, exciting effect of the anticipation of arriving at tonic.
And how the leading note wants to resolve to tonic and how the dominant chord/note dominates the key. ______________________________
In the ensuing discussions we have looked closely at the diminished seventh chord. It can resolve using the leading note effect to any of four points, it can resolve either of its two tritones inwards to a major third or its two outer notes inwards to a fifth, either major or minor. It is useful in cadences but also allows modulation within a passage. It's a tricky little blighter but so very, very useful!
Despite the many possible names, including enharmonics and double flats, there are only really three of 'em. Each one is formed from a stack of minor thirds repeating at the octave.
The way I remember and/or recognise them is thus: one has ONE black key, Ab, the middle of the group of three on the keyboard, and the other two use TWO black keys; one uses the first of the group of three (F#) and pairs it with Eb. The other uses the last (Bb) and pairs it with C#.
You are of course welcome to learn the first one as either Ab dim7, Bbb dim 7, B dim7, D dim 7, Ebb dim7, F dim7, E# dim 7 or G# dim7 and the others accordingly.
We have learned that the naming convention using the lowest note is the way forward. _____________________________
We looked at notation and note the convention of referring to notes within a scale or chord using Arabic numerals 1, 2, 3, etc. and for referring to chords using Roman numerals, I, IV, V etc. Some use mixed case (upper for major, lower for minor) some use upper and append an 'm' for minor. Some note inversions using figured base, V/3. I use letters b and c for first and second inversions etc. but am trying here to avoid using any inversion notation in RN's. I don't see their purpose.
Roman numerals are great for discussing the functionality of short passages but, for me, lose their worth beyond the length of a section because keys change and it's not always immediately clear what key the RN's refer to.
Once you know what key you're in and the chords associated with it you know the effect each chord has with the others in the specific case. ______________________________
I'm not trying to write a book, though sometimes I feel like it. I have more to say but am going to leave it for a little while.
We can progress from measure 20 or discuss further what's happened so far or any of the topics that cropped up on the way.
I think I can handle all three so it's up to you. If you're progressing on, remember to ignore the chords for this first run through the next section. Do it at the piano.
Greener, thank you for the Swingle Singers link. OMG, they do the Fugue too. I didn't particularly like the Prelude, actually, (too staccato, and I couldn't figure out what the high voice was doing -- probably if I could understand the role of the high voice and the comment it's making on the Prelude, I would like it better), but I LOVED the Fugue. Hearing the Fugue sung in actual different people's voices for the different voices of the Fugue helped me to start to hear those voice lines better. Fun fun fun.
Due to what Gary has said about dim7 chords, I will stop pestering you about "can you find a chord name that matches Bach's spelling". Instead I will pester you about "now that you've found a low-note-based chord name for the dim7 chord, notice that the notation Bach uses suggests a certain emphasis coming next, out of all the possible ways this chord might move. Our ears may not be able to predict where it is going, which is part of the fun, but Bach chooses his accidentals for a particular reason here." Aren't you glad I'm going to change ?
There's a dim7 chord coming up which I haven't yet been able to fit into my usual way of thinking about dim7 chords and their spelling. I'll look forward to asking about it when we get there.
Not sure I am understanding why we want to look at various sections as being in a different key.
Ah, Jeff, the key question!
It was when we developed equal temperament and our modern scales that we were able to change key within a piece. Up until this time music was confined to short pieces but changing key allowed the composer to write longer pieces of music without the listener losing interest. Compare the length of the movements in a Bach suite to those in a sonata by Mozart and then again to Beethoven's Hammerklavier.
Compare the lengths of Bach's Orchestral Suites and Brandenbergs to Mozart's Symphonies and Concertos and those of Beethoven.
Having a key gives music a tone centre or tonality. This is why we call it tonal music (from very roughtly 1590 to the atonality of Berg and Schoenberg).
Very, very very brief description of what's happening here: we develop the ability to change key and move away from the key centre to another one; baroque moves step by step (or accidental by acidental), Beethoven moves up to three accidentals at a time, Wagner and Liszt are falling over themselves trying to add more sharps and flats at every bar while Debussy is developing a whole tone scale. Finally Schoenberg introduces the 12 tone system where every note is visited once before any note is repeated thereby removing all traces of tonal centre.
Think of it like C7 in the key of E major. Yes, we could write it C(#6), bectause it’s going to be written C E G A# (German 6th), but C7 is all that is necessary for any musician who knows that in the key of E, C7 moving to B/E demands an A# for spelling reasons.
So letters imply both no knowledge (very practical for people who just want to push the right keys) but also a HUGE amount of knowledge (allowing people who have really deep knowledge of theory to intuitively know how to spell the chords that are notated based on sound only).
I think this has been my problem. I know the basic kinds of things: VIIdim7 implies the minor key a half-step up, V7 implies the major triad a fifth down; and slightly more advanced things: German 6th implies a resolution outwards. Now I have to learn these all over with more flexibility about spelling. For example: dim7 can imply any of four minor keys a half-step up from any of the four notes, and if I have Gdim7 (say) I have to first think of what those 3 other notes are besides G, and I don't have instant recall of them, nor do I see them instantly as a pattern on the keyboard (more things to learn). Plus it can resolve all those other ways that Richard mentioned. Dominant 7 can resolve out instead of in, and not be part of the key a fifth lower at all.
So now I have a lot of exercises to do, at the piano, looking at and feeling the physical keys and listening to the results and moving notes up and down by half-steps and whole steps, and then incorporating that into a vastly larger vocabulary of chords and what they can imply about what might come next. (I can do most of these exercises on paper as well, but I think it's probably important to listen to them. I don't have confidence that I'll hear/feel any sense of inevitability about any of the moves, but I'm thinking that it can only help to get the sounds in my ears at least once, and also to see the progressions as physical moves on the keyboard as well as paper juggling of letters.)
The question I was going to ask you was about which places a dim7 chord can typically move next, but I see that Richard has listed a lot of possibilities. So I'll just ask if you have anything you'd say in addition to what Richard said, and/or if you'd say it a different way:
Originally Posted by zrtf90
In the ensuing discussions we have looked closely at the diminished seventh chord. It can resolve using the leading note effect to any of four points, it can resolve either of its two tritones inwards to a major third or its two outer notes inwards to a fifth, either major or minor. It is useful in cadences but also allows modulation within a passage.
Lower notes: Starts out with a drop from tonic C to a fifth lower: F. I guess this drop of a fifth, or move to the subdominant to use the big fancy words, is perhaps supposed to have a kind of comfortable feel to it. I don't know if I hear that, or if I just hear notes. Anyway, it's followed by a chromatic waffling around with F# and Ab, which turns out to be a way of leading to the dominant, G. (Again, I don't hear the G as any particularly important note except that it's nice and low and gets repeated over and over, but I don't hear it *functionally* as "oooh, wow, the fifth degree of the scale, how delicious and important and meaningful".) The G gets repeated a ton and then drops a fifth to low C (and I notice the nice lowness of the C, but I'm not sure I hear the drop of a fifth as implying any kind of finality, among other things because I can't hear what a tonic is, I just hear C as a note). And then the C continues to the end.
So mm.20-35 is pretty simple for the low bass line, and it basically goes: C G C. Very tonal and simple and I suppose it's supposed to sound nice and inevitable and like "wow, look how I'm confirming we're really in C and heading to the end" but I can't hear that part.
Upper notes of the bass line: Bach abandons the close intervals here, and the upper notes seem to move around with no clear logic that I can find yet. At the very end they end with C B C, and this is one of the very few things where I can hear the function: I can hear how that "do ti do" gives closure on C.
The notes that stand out to me the most in this section are the top notes of the arpeggios, and these move up and down gently in a pleasant way, although the overall feel of this passage is down. The other notes that stand out to me are the low bass notes G and C (except, reminder, I don't hear them as G and C, nor as "note, and note a fifth lower", I just hear them as "a low note" and "an even lower note"). This is the same as when I'm listening to choral music: I hear the soprano most, and can hear the bass if I pay attention, but usually find it hard to distinguish the alto and tenor lines (and this, even though I sing alto).
Incidentally, on that F# Ab G in mm.22-24, I looked at it on paper first and wondered what the accidentals were for. Then I came up with the idea that they're revolving around G, and maybe pointing the way towards G by not quite being at G, and by being chromatic hence out of key, so after we circle around G and then settle on diatonic G, that's a way of highlighting the arrival on G.
Then I listened to the piece, and played it and listened some more, and found myself able to hear that effect.
Just listening to the piece without priming myself by reference to, and thinking about, the notes on paper, I just heard notes followed by more notes. Maybe now that I have learned about this kind of pattern, and listened to it with understanding, I will be more ready to pick it up purely aurally the next time I hear something like it.
mm. 20-end. ...I don't know if I hear that ...Again, I don't hear the G as any particularly important note ...I'm not sure I hear the drop of a fifth ...I suppose it's supposed to sound nice ...but I can't hear that part. ...the upper notes seem to move around ...with no clear logic that I can find yet ...The notes that stand out to me...move up and down
So, found nothing then?
Originally Posted by PianoStudent88
The G gets repeated a ton...
My score has considerably less than hundred. Which edition are you using?
Originally Posted by PianoStudent88
I can hear how that "do ti do" gives closure on C.
In England we use 'doh'. What you write over there sounds like 'dooty-doo' to me and I can't help laughing!
I want to quickly extract and highlight a couple of things (for myself, pardon me please) so as to keep a closer eye on it and locate more readily ...
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Instead I will pester you about "now that you've found a low-note-based chord name for the dim7 chord, notice that the notation Bach uses suggests a certain emphasis coming next, out of all the possible ways this chord might move. Our ears may not be able to predict where it is going, which is part of the fun, but Bach chooses his accidentals for a particular reason here." Aren't you glad I'm going to change laugh ?
Yes, PS88 you are always a fun addition to the party.
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It's kind of important, really! smile
Yes, it sounds it. Yet one I was totally missing the boat on.
Those of us that aren't yet as accomplished in RN's and theory couldn't place the section end.
I don't understand this sentence (literally).
Those of us without practise in RN's couldn't SEE a V-I cadence on paper and also couldn't HEAR the section end (whether playing or listening) unless they isolated the bass. They couldn't locate it on the score OR at the piano.
Hi everyone. I haven't fallen off the face of the earth. Life has taken me away from my keyboard for a couple of days.
Wow!!! things have really progressed and I was able to follow along for a while. I am able to see the ii V I progressions and hearing the patterns and resolutions, but when we got to harmonizing, modes, alternate chord names for dim 7 chords, I became lost and a bit overwhelmed.
I'm still carefully reading through everything and I'm still here though.
Don't be overwhelmed. The stuff will still be here to read later. It's best to let it just filter in through your subconscious. Understanding doesn't come overnight. One day the penny drops and everything seems to fall into place.
We've covered several weeks worth of music theory in just a couple of days. There's a limit to how much you can absorb at once.
G bass repeated from m.24 for eight measures. A ton, colloquially speaking.
I'm not at a keyboard so I can't check this out, but I think the three note descending sequence C G C would sound complete to me played as just three notes. But when it's stretched out over 13 measures as in the Prelude, I don't hear it. I guess I could try repeating the initial C in my head, and then comparing it when the G arrives, and then adding the final C to the whole sequence once it shows up but that seems awfully artificial, plus if I were really just listening to a piece I wouldn't know in advance which notes I should be trying to remember and which ones I can let float away (like F# and Ab). And without looking at the score I also wouldn't know which notes I should choose to try to remember.
Maybe this idea of remembering notes is stupid but I don't know how people hear things over such long stretches. Like in a sonata, after all the modulations and the whole thing ends on the tonic: how does anyone know that it's ending in the same key it started in? Or even in this Prelude. I can tell on paper that it starts and ends in the same key, but I don't know how to hear that.
I can sometimes hear accidentals (or at least, what I think are accidentals, but who knows, they might just be an extended or diminished chord or something) but I don't know how to hear if the net effect of the accidentals is just local colour while staying in the same key, vs. modulating to a new key. I've been noticing on the radio that sometimes music changes and sounds higher, but I can't tell if that means it has modulated up (say, to the dominant), or if it's still in the same key, but just playing something higher.
I wish I felt more positive about the things I do hear, but thinking about music theory always leads me to feel so negative about the things I can't hear. But it's progress at least to identify that there are some patterns I do hear, like do ti do, do sol do, sol fa mi re do, and similar. I think this experience of working back and forth from paper to ear is good, because it might be able to teach me the meaning of what I hear. And it's not like I don't hear anything: I can hear when I play things wrong on the piano, even if I can't name why it's wrong, I can still hear that it's wrong.
Carol, AIUI our basic task right now is to be focusing on the bass notes. So harmonization, modes, and alternate chord names are all tangential to the current core mission.
Speaking of the current core mission, I may be all wrong about what I think mm.20-35 are about. If so, I'm completely stumped because I've listened to this and played the bass notes, and the pairs of notes, and except for the chromatic notes, the long stay on one note, and then the descent to a lower note, I just don't hear anything else. I especially don't hear anything going on (other than random motion) when I listen to both notes in the bass together, instead of just the lowest note alone.
You may not hear that a section ends in the dominant. You might not tell the dominant from any other modulation. But you know it's not the tonic. It just doesn't feel complete. You can't stop there and walk away.
Stop this video at 1:02 and see if you feel satisfied that it's complete after it's ii-V-I cadence. Don't listen FOR this. Just see if you feel musically satisfied. Later you'll get to recognise that feeling and want to know what's caused it.
When you get home try playing (back to BWV 846 now) from 20 - 30 using the LH only (á tempo) the second time change the 2nd bass note to the last note (the highest) of each half-bar but keep the same tempo (ta-da <pause>, ta-da <pause>).
From the dominant pedal onwards (bar 24) try the left hand alone again to the end. Use the first and last note of the full measure for 33-34 and hold them longer. Use the chord for 35.
If you don't recognise anything when you get to the end try playing bars 1-4 (bass note only) again and then repeat the exercise.
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