Re: 9:04 - I can’t say someone has specifically written this, but in my experience, based on the harmony books I’ve read (harmony geek here) - and within the context of the harmonic series, having just the roots and fifths of the chord above the third makes the ratios of tones a much cleaner ratio. Having the third emphasised in a higher octave would make the simple octave ratio (1:2) of the two thirds the apparent auditory denominator of the harmony (ie making the ear bias towards some root position E sonority). C and G are not heard in the E harmonic series until like the 4th - maybe 5th - octave module of the overtones. Therefore, it makes this kind of voicing sounds ‘muddy’ due to our ear trying to perceive it as a harmonic relationship with respect to E. Transposing overtones heard a lot higher in the overtone series down a few octaves, forcing them closer to the fundamental, is a recipe for dissonance and more ‘vulgar’ ratios (ie big numbers - to put it imprecisely). This is what the ear’s bias is doing in that situation. If the C and G’s are stated with more emphasis (ie doubled), it makes the simple ratio of the fifth (2:3) in the C overtone series more prominent. Therefore, the ears interpret the sound as a redacted C overtone series (ie C major) where the fundamental tones before the 5th overtone (E) are missing, but the prominence of the higher C’s and G’s alludes to the ghost of a C overtone series as the harmonic context. I don’t want to suggest that there is a god-given truth about consonance. It’s all relative to compositional context. But if you play a passage with ‘6’ chords (first inversions) with doubled bass notes, and then again but now without (just roots and fifths above), I’d be interested to see anyone’s response. Undoubled first inversion bass note chords offer a delicate consonance that is completely overshadowed when the bass is doubled. It’s the sonic difference between aesthetic anime crying vs Kim Kardashian ugly crying (RUclips it) 🤣
@@bobfrog4836 I'd tend to agree, but (just for the sake of friendly conservation) I'm not of the general persuasion that mathematics can quantify harmonic consonance, as a conscious experience. Perhaps one day we will have a dynamic mathematical answer for every universal instance of conscious experience. But my fear is that saying that consonance and dissonance are mathematically true, will lead people to think within a framework of GCSE equations. I find the most common (western) language used to describe and denote music utterly arbitrary, colloquial, and in no where near refined enough to use as a means of integrating it with a pure mathematical model. It's not that the symbols we use aren't logical or mathematical in their essence, it's that the entire structure of our music as we perceive it (and as a consequence, turn into symbols and write on paper), is completely imaginary. Its all made up. It isn't'real'. So in short, I am open to the possibility that harmonic consonance could be explained with alarming accuracy through the correct mathematical structure, but I think that structure will have to integrate the conscious experience in some way, if it's to be accurate. Interestingly, experiencing the world being exposed to global cinema for the last few generations, it'd be canny to ponder over whether the sounds, harmonies, and rhythms we choose for certain emotional triggers in film are somehow experientially 'true' by means of mathematical simplicity, or if is it more like a feedback loop of relativity, where the human condition evolves to respond with the ideas it exposes to itself over time. If that were to be the case, consonance as a true fact is impossible. The math behind music would have to become quantum and chaotic if it wanted to make anymore headway with scientific explanation. Anyway sorry I got carried away again lol. In short (again), I'm inclined to agree, but don't tell anyone else that, cos they'll just get it wrong and turn it into a religion 🤣 Soz for getting too involved, just vibing. Peace ✌🏽
I've started and given up figured bass multiple times in the past. Going through the cycle of fifths sounds like it would really hammer it in. I did not know they used to practise this way. Your videos are very informative!
Great video! Easy to understand, thank you! :) I'm learning to compose and want more of a practice based guide to learning harmony at the keyboard so this video came at the right time
First inversion chords DEFINITELY sound better if you don't double the third. Probably because of how the perfect intervals in the top three voices really ring. It also makes the chord identity much more clear; doubling the third when it's already in the bass just brings it too much into the foreground. The empty fifth in the top voices makes it sound more balanced.
I agree. As a keyboard player, something about a D-flat major sixth chord with F in the left hand and A-flat - D-flat - A-flat in the right hand just feels dynamically balanced and satisfying. I think there are vertical reasons for preferring this kind of doubling, as you put very well, as well as horizontal reasons. Doubling the chordal third seems to narrow the options for what kind of chord can follow (frustrated leading tones, etc.).
I only started playing the piano after 65 years of age and joking all my life that I was born with two left ears. You sir have guaranteed that I will not be influenced to join a gang now.
@@JacobGran Hello Mr. Gran. I would kindly like to ask regarding the second (A minor) Bach exercise (min 8:05). There are 2 consecutive parallel Octaves between the A - Bb - G positions (all in third position). I can assume that the first Parallel octave is there to avoid a dissonant (Augmented 2nd) in the melody (???). but wouldn’t it be possible to avoid the second Parallel octave if we treat the G with a fifth position chord, then the A with a third position, and ending the exercise with the D in an Octave position? I will appreciate if you could explain the choice of voicings in this case. Thank you.
Ofer Wetzler Yes, Bach is avoiding the augmented second that would result with the more “normal” contrary motion hand positions (third position over A, octave over Bb, third over G). I would say that the easiest solution (and the one Bach likely had in mind) would be to double the chordal third in that Bb chord (D-F-D in the right hand). Deceptive resolutions of applied dominants often require special hand positions like this. I would have mentioned this in the video but it didn’t occur to me, so thank you for the perceptive question.
As I keep practicing, I noticed the patterns that patterns of the hand when moving a second up, a second down, a third up, etc, either going from a 5-3 chord to a 6-3 chord, or going from a 5-3 chord to another 5-3 chord, starging from an 8th, 5th or 3rd position. It is not very hard to memorize those changes, and it seems possible to have fluency in the exercises you gave us this way. But it is an absolutely mechanical way of doing it. Is it ok to practice like that?
Yes, I think what you are calling "mechanical" is actually what I was referring to as physical muscle memory. The less mental energy spent finding the voices of the next chord, the better.
I worked out the CPE Bach exercises, and the only way that I can see to harmonise the Bb in the second one while avoiding parallel octaves and fifths entering and exiting, especially as he specifies three chords in row (including a pair moving by step!) as third position chords, is with a right-hand fingering that you don't mention, i.e. 3-5-3 = D-F-D here. This seems reasonable, because in classical harmony when V-VI is an interrupted cadence, one usually doubles the third. Is there a less ungainly solution, or is that it? Thanks.
Yes, I agree that is the solution. Those hand positions are sort of like the default assumption and they usually work, but I should have been more explicit in stating that you can't get by only using those few hand positions.
I'm going through all of your videos to find all sheet music sources. I'm having trouble with a few. I'd also mention that I'm doing this to add excerises in a text book I'm writing. May I use your videos as a source?
In the Am Exercised from "The true art of playing keyboard instruments" There are two chords in third position in a row. Isn't that parallel 5ths / 8th? ... I don't understand.
Yes! For the B-flat chord on the last beat of the first full measure, you will need to use a less typical hand position to avoid parallels. You could either double the third of the chord (D F D in the right hand) or drop into a three voice texture (just F and D). Normally, when the bass moves by step between root position triads, we would want our right hand chord to move in contrary motion to the bass line, but, when the keyboardist is asked to realize a "deceptive cadence" in a minor key like we have here, moving to an octave position B-flat chord would create a leap of an augmented second in the top voice. "Frustrating" the leading tone would otherwise be fine in an inner voice in a major key (where there is no augmented second to worry about), but here it would be way too prominent, so Bach recommends simply changing the hand position to meet the demands of the voice leading.
Good question. A couple do occur in the Handel and Tchaikovsky bass lines at the end, but in 6/3 position (built on ^2 in the bass). I suppose the avoidance of 5/3 position leading tone chords is done in order to prevent forming a diminished fifth above the bass, as in strict counterpoint. These examples happen to remain strict, although in thoroughbass generally we are thinking in terms of free composition, so in other exercises you may well see a 5/3 position leading tone chord.
@@JacobGran Oh ok that makes sense... The diminished triad does sound better in 1st inversion to my ears but when I studied harmony, my teacher was a jazz guitarist so I always learned 7th dimished chords on the guitar because they are very common shapes on the guitar.... however, when I switched to piano and now learning from your videos I definitely can hear the difference and mcuh prefer the sound of the 1st inversion dim chord.. on piano at least :)
How do we name the 63 chord shapes? For example, if the 6th of the 63 chord is in the soprano do we say the 63 chord is in octave position since the 6th is the chordal root?
That’s a great question. I don’t think there is a commonly accepted norm. My best guess would be to be as specific as possible (“chordal third” vs “third position”) to differentiate between figured bass intervals and chord members.
Good question. No, all of the textbooks recommend avoiding the parallel fifths that could occur in parallel 6/3 chords by either 1) dropping into a three-voice texture and using parallel fourths (or doubling a voice at the unison, which amounts to the same thing) or 2) alternating very awkward hand positions to avoid the fifths. When you see a stretch of parallel sixths, you should just think, "that means parallel fourths."
Re: 9:04 - I can’t say someone has specifically written this, but in my experience, based on the harmony books I’ve read (harmony geek here) - and within the context of the harmonic series, having just the roots and fifths of the chord above the third makes the ratios of tones a much cleaner ratio.
Having the third emphasised in a higher octave would make the simple octave ratio (1:2) of the two thirds the apparent auditory denominator of the harmony (ie making the ear bias towards some root position E sonority). C and G are not heard in the E harmonic series until like the 4th - maybe 5th - octave module of the overtones. Therefore, it makes this kind of voicing sounds ‘muddy’ due to our ear trying to perceive it as a harmonic relationship with respect to E. Transposing overtones heard a lot higher in the overtone series down a few octaves, forcing them closer to the fundamental, is a recipe for dissonance and more ‘vulgar’ ratios (ie big numbers - to put it imprecisely). This is what the ear’s bias is doing in that situation.
If the C and G’s are stated with more emphasis (ie doubled), it makes the simple ratio of the fifth (2:3) in the C overtone series more prominent. Therefore, the ears interpret the sound as a redacted C overtone series (ie C major) where the fundamental tones before the 5th overtone (E) are missing, but the prominence of the higher C’s and G’s alludes to the ghost of a C overtone series as the harmonic context.
I don’t want to suggest that there is a god-given truth about consonance. It’s all relative to compositional context. But if you play a passage with ‘6’ chords (first inversions) with doubled bass notes, and then again but now without (just roots and fifths above), I’d be interested to see anyone’s response.
Undoubled first inversion bass note chords offer a delicate consonance that is completely overshadowed when the bass is doubled. It’s the sonic difference between aesthetic anime crying vs Kim Kardashian ugly crying (RUclips it) 🤣
Thank you; that’s the best explanation that I’ve heard for this preference that doesn’t simply appeal to authority.
I would think that the harmonic series (ie. physics) would be as close to a god-given truth about consonance one can get. LOL.
@@bobfrog4836 I'd tend to agree, but (just for the sake of friendly conservation) I'm not of the general persuasion that mathematics can quantify harmonic consonance, as a conscious experience. Perhaps one day we will have a dynamic mathematical answer for every universal instance of conscious experience. But my fear is that saying that consonance and dissonance are mathematically true, will lead people to think within a framework of GCSE equations. I find the most common (western) language used to describe and denote music utterly arbitrary, colloquial, and in no where near refined enough to use as a means of integrating it with a pure mathematical model. It's not that the symbols we use aren't logical or mathematical in their essence, it's that the entire structure of our music as we perceive it (and as a consequence, turn into symbols and write on paper), is completely imaginary. Its all made up. It isn't'real'. So in short, I am open to the possibility that harmonic consonance could be explained with alarming accuracy through the correct mathematical structure, but I think that structure will have to integrate the conscious experience in some way, if it's to be accurate.
Interestingly, experiencing the world being exposed to global cinema for the last few generations, it'd be canny to ponder over whether the sounds, harmonies, and rhythms we choose for certain emotional triggers in film are somehow experientially 'true' by means of mathematical simplicity, or if is it more like a feedback loop of relativity, where the human condition evolves to respond with the ideas it exposes to itself over time. If that were to be the case, consonance as a true fact is impossible. The math behind music would have to become quantum and chaotic if it wanted to make anymore headway with scientific explanation.
Anyway sorry I got carried away again lol. In short (again), I'm inclined to agree, but don't tell anyone else that, cos they'll just get it wrong and turn it into a religion 🤣
Soz for getting too involved, just vibing. Peace ✌🏽
I've started and given up figured bass multiple times in the past.
Going through the cycle of fifths sounds like it would really hammer it in. I did not know they used to practise this way. Your videos are very informative!
Great video! Easy to understand, thank you! :) I'm learning to compose and want more of a practice based guide to learning harmony at the keyboard so this video came at the right time
Thank you! Glad you enjoyed it.
First inversion chords DEFINITELY sound better if you don't double the third. Probably because of how the perfect intervals in the top three voices really ring.
It also makes the chord identity much more clear; doubling the third when it's already in the bass just brings it too much into the foreground. The empty fifth in the top voices makes it sound more balanced.
I agree. As a keyboard player, something about a D-flat major sixth chord with F in the left hand and A-flat - D-flat - A-flat in the right hand just feels dynamically balanced and satisfying. I think there are vertical reasons for preferring this kind of doubling, as you put very well, as well as horizontal reasons. Doubling the chordal third seems to narrow the options for what kind of chord can follow (frustrated leading tones, etc.).
Very very very very good!
Thank you very much, Dr. Jacob Gran!
I only started playing the piano after 65 years of age and joking all my life that I was born with two left ears. You sir have guaranteed that I will not be influenced to join a gang now.
Thank you Doctor Gran
Thank you master
Thank you very much for this !!!
Amazing video and lesson. Thank you Mr. Gran!
You’re very welcome!
@@JacobGran
Hello Mr. Gran.
I would kindly like to ask regarding the second (A minor) Bach exercise (min 8:05).
There are 2 consecutive parallel Octaves between the A - Bb - G positions (all in third position).
I can assume that the first Parallel octave is there to avoid a dissonant (Augmented 2nd) in the melody (???).
but wouldn’t it be possible to avoid the second Parallel octave if we treat the G with a fifth position chord, then the A with a third position, and ending the exercise with the D in an Octave position?
I will appreciate if you could explain the choice of voicings in this case.
Thank you.
Ofer Wetzler Yes, Bach is avoiding the augmented second that would result with the more “normal” contrary motion hand positions (third position over A, octave over Bb, third over G). I would say that the easiest solution (and the one Bach likely had in mind) would be to double the chordal third in that Bb chord (D-F-D in the right hand). Deceptive resolutions of applied dominants often require special hand positions like this. I would have mentioned this in the video but it didn’t occur to me, so thank you for the perceptive question.
@@JacobGran Thank you very much for the reply.
It’s totally clear now…and the voicings sounding beautiful this way!
As I keep practicing, I noticed the patterns that patterns of the hand when moving a second up, a second down, a third up, etc, either going from a 5-3 chord to a 6-3 chord, or going from a 5-3 chord to another 5-3 chord, starging from an 8th, 5th or 3rd position. It is not very hard to memorize those changes, and it seems possible to have fluency in the exercises you gave us this way. But it is an absolutely mechanical way of doing it. Is it ok to practice like that?
Yes, I think what you are calling "mechanical" is actually what I was referring to as physical muscle memory. The less mental energy spent finding the voices of the next chord, the better.
Great stuff.
I worked out the CPE Bach exercises, and the only way that I can see to harmonise the Bb in the second one while avoiding parallel octaves and fifths entering and exiting, especially as he specifies three chords in row (including a pair moving by step!) as third position chords, is with a right-hand fingering that you don't mention, i.e. 3-5-3 = D-F-D here. This seems reasonable, because in classical harmony when V-VI is an interrupted cadence, one usually doubles the third. Is there a less ungainly solution, or is that it? Thanks.
Yes, I agree that is the solution. Those hand positions are sort of like the default assumption and they usually work, but I should have been more explicit in stating that you can't get by only using those few hand positions.
@@JacobGran Thanks!
I'm going through all of your videos to find all sheet music sources. I'm having trouble with a few. I'd also mention that I'm doing this to add excerises in a text book I'm writing. May I use your videos as a source?
Trombone: it's not as bad as it sounds.
what is intro music from?
👍🙂
In the Am Exercised from "The true art of playing keyboard instruments" There are two chords in third position in a row. Isn't that parallel 5ths / 8th? ... I don't understand.
Yes! For the B-flat chord on the last beat of the first full measure, you will need to use a less typical hand position to avoid parallels. You could either double the third of the chord (D F D in the right hand) or drop into a three voice texture (just F and D). Normally, when the bass moves by step between root position triads, we would want our right hand chord to move in contrary motion to the bass line, but, when the keyboardist is asked to realize a "deceptive cadence" in a minor key like we have here, moving to an octave position B-flat chord would create a leap of an augmented second in the top voice. "Frustrating" the leading tone would otherwise be fine in an inner voice in a major key (where there is no augmented second to worry about), but here it would be way too prominent, so Bach recommends simply changing the hand position to meet the demands of the voice leading.
@@JacobGran Wow thanks for the explanation! I'm used to playing jazz / rock charts but avoiding parallel fifths / octaves is a really difficult art
Thank you very much. Why is the leading tone triad not used in these exercises? All the other scale degrees are provided but not the leading tone (B)
Good question. A couple do occur in the Handel and Tchaikovsky bass lines at the end, but in 6/3 position (built on ^2 in the bass). I suppose the avoidance of 5/3 position leading tone chords is done in order to prevent forming a diminished fifth above the bass, as in strict counterpoint. These examples happen to remain strict, although in thoroughbass generally we are thinking in terms of free composition, so in other exercises you may well see a 5/3 position leading tone chord.
@@JacobGran Oh ok that makes sense... The diminished triad does sound better in 1st inversion to my ears but when I studied harmony, my teacher was a jazz guitarist so I always learned 7th dimished chords on the guitar because they are very common shapes on the guitar.... however, when I switched to piano and now learning from your videos I definitely can hear the difference and mcuh prefer the sound of the 1st inversion dim chord.. on piano at least :)
How do we name the 63 chord shapes? For example, if the 6th of the 63 chord is in the soprano do we say the 63 chord is in octave position since the 6th is the chordal root?
That’s a great question. I don’t think there is a commonly accepted norm. My best guess would be to be as specific as possible (“chordal third” vs “third position”) to differentiate between figured bass intervals and chord members.
*Western Eurocentric Tonal Voice Leading Style
At 10:00, can I use the first two hand positions as fauxbordon, despite the parallel 5ths?
Good question. No, all of the textbooks recommend avoiding the parallel fifths that could occur in parallel 6/3 chords by either 1) dropping into a three-voice texture and using parallel fourths (or doubling a voice at the unison, which amounts to the same thing) or 2) alternating very awkward hand positions to avoid the fifths.
When you see a stretch of parallel sixths, you should just think, "that means parallel fourths."