Haha - that is exactly what I came down here to say! But despite there not being a single G to be seen in the whole bar, I think what he is trying to suggest is that, used in this context, it so strongly plays with the ambiguity of a C7 sound that the inclusion of a G is implied. But it's still an Italian 6th! :)
such a tricky was to achieve distant modulation. I love it. I have got to try this in my composing. Thanks for the quick explanation and the beautiful Beethoven example.
It's likely closer to the composers thinking to look at it in according to thoroughbass in the following way. Bar 21 is a 5 3 on C. Bar 22 the C becomes the 6 of E minor and takes a #6 3. Bar 23 B is the 5 of E minor and takes 5 3 but pendulums on a 6 4 suspension for a while. Only at bar 31 the scale changes to E major but thinking of dominant harmony until it resolves on bar 32. So all in all it's a relatively close modulation from C to E minor then at bar 31 modulates again to E major.
but the modulation doesnt happen until 32, right? i mean the scale implies it being a secondary dominant, then its reduced to the triad, in 32 its E major
What a great question! The modulation does happen at 23, but you're right that it is not confirmed until 32 when the tonic in E major arrives. The ten measures in between are functioning as what some would call "Standing on the Dominant" or others would call "Dominant Lock." In this case, it's the dominant of the new key that is used to transition into the second theme and new key area.
So are we are talking about two possible spellings of one note since in 12 equal intonation there is no audible difference between Bb and A#? Now in the various intonations used in Beethoven's day these notes may have been tuned differently, especially if they were played on keyboards in meantone (some with double black keys), or by a choir or by bowed strings. Today the two enharmonic notes are not supposed to be different so we are talking about the ghost of what was once available rather than an actual effect that is available today, we are really talking about something that was once physical which has been extracted from the music as though it were still there when it is not. An A# would have once been intoned flatter and a Bb would have been intoned sharper thus the German 6th chord would probably sound more "relaxed" than the dominant 7th chord, today they sound identical.
Bill, thanks for this! Beethoven's keyboard would have been equal-tempered, as equal temperament had been around for since the late Baroque. And this piece was written for piano, not a choir or instrumental ensemble that (I agree) would have (and still would, for that matter) treated the notes A-sharp and B-flat differently. So yes, B-flat and A-sharp do (and did) sound the same, but in the above example, the same sounding harmony is treated differently. We are set up for the expectation of the A-sharp (heard as B-flat by the listener who can't see the score and assumes the harmony is V7 of IV) to fall to A-natural. The interval of a minor 7th (between the bass and the 7th of the V7) has a strong tendency to resolve to a 3rd (the 7th falls by step and the bass skips up a 4th). In this case, Beethoven both spells and resolves the interval as an augmented 6th, and the tendency of an augmented 6th is to resolve out to an octave. The resulting harmonic motion allows for the modulation to E major. So in the end, it is one sounding interval (a minor 7th or an augmented 6th) that has the possibility to resolve in 2 different ways.
There is actually a great deal of evidence that although equal temperament was in existence it was not the norm, including extensive classic descriptions of the differences in the moods of various key signatures, since in mean tone each key signature has a unique tuning, there are many more than this one link regarding classic tuning schemes. www.kylegann.com/histune.html
That's an Italian Augmented 6th (C-E-A#). The German Augmented 6th contains the 5th (C-E-G-A#).
Haha - that is exactly what I came down here to say!
But despite there not being a single G to be seen in the whole bar, I think what he is trying to suggest is that, used in this context, it so strongly plays with the ambiguity of a C7 sound that the inclusion of a G is implied.
But it's still an Italian 6th! :)
such a tricky was to achieve distant modulation. I love it. I have got to try this in my composing. Thanks for the quick explanation and the beautiful Beethoven example.
It's likely closer to the composers thinking to look at it in according to thoroughbass in the following way.
Bar 21 is a 5 3 on C. Bar 22 the C becomes the 6 of E minor and takes a #6 3. Bar 23 B is the 5 of E minor and takes 5 3 but pendulums on a 6 4 suspension for a while. Only at bar 31 the scale changes to E major but thinking of dominant harmony until it resolves on bar 32. So all in all it's a relatively close modulation from C to E minor then at bar 31 modulates again to E major.
6:01 Jazz kids: Dm - Dm, E7/D - Am/C - Am/C - C7 - B7, Em/B
IMHO:
E Major Ger+6 : { 6b, 1, 3b, 4# }
It should be C E G A#
but the modulation doesnt happen until 32, right? i mean the scale implies it being a secondary dominant, then its reduced to the triad, in 32 its E major
What a great question! The modulation does happen at 23, but you're right that it is not confirmed until 32 when the tonic in E major arrives. The ten measures in between are functioning as what some would call "Standing on the Dominant" or others would call "Dominant Lock." In this case, it's the dominant of the new key that is used to transition into the second theme and new key area.
So are we are talking about two possible spellings of one note since in 12 equal intonation there is no audible difference between Bb and A#? Now in the various intonations used in Beethoven's day these notes may have been tuned differently, especially if they were played on keyboards in meantone (some with double black keys), or by a choir or by bowed strings. Today the two enharmonic notes are not supposed to be different so we are talking about the ghost of what was once available rather than an actual effect that is available today, we are really talking about something that was once physical which has been extracted from the music as though it were still there when it is not. An A# would have once been intoned flatter and a Bb would have been intoned sharper thus the German 6th chord would probably sound more "relaxed" than the dominant 7th chord, today they sound identical.
Bill, thanks for this!
Beethoven's keyboard would have been equal-tempered, as equal temperament had been around for since the late Baroque. And this piece was written for piano, not a choir or instrumental ensemble that (I agree) would have (and still would, for that matter) treated the notes A-sharp and B-flat differently. So yes, B-flat and A-sharp do (and did) sound the same, but in the above example, the same sounding harmony is treated differently. We are set up for the expectation of the A-sharp (heard as B-flat by the listener who can't see the score and assumes the harmony is V7 of IV) to fall to A-natural. The interval of a minor 7th (between the bass and the 7th of the V7) has a strong tendency to resolve to a 3rd (the 7th falls by step and the bass skips up a 4th). In this case, Beethoven both spells and resolves the interval as an augmented 6th, and the tendency of an augmented 6th is to resolve out to an octave. The resulting harmonic motion allows for the modulation to E major.
So in the end, it is one sounding interval (a minor 7th or an augmented 6th) that has the possibility to resolve in 2 different ways.
There is actually a great deal of evidence that although equal temperament was in existence it was not the norm, including extensive classic descriptions of the differences in the moods of various key signatures, since in mean tone each key signature has a unique tuning, there are many more than this one link regarding classic tuning schemes.
www.kylegann.com/histune.html
like tritone substitution?
Same notes, but the difference between an augmented 6th chord and a tritone substitution is what it resolves to.