what is an a7

[Chris Fitzgerald]

I don't know that you understand what I am saying. I would agree that the tendency is more for the 7th to resolve downward, but, and you can play this on a piano/bass/guitar if you like, if the 7th moves upward to the 5th of the tonic does it still resolve? I would argue that it does. The leading tone on the other hand can't go anywhere else and still resolve the dominant.

No, in the case cited above it does not resolve, or resolves deceptively.

So what I am saying is that what the 7th of the chord does is irrelevant in term of directing resolution back to the tonal centre. Even if I am in the minority I would like to see a stronger empirical argument against what I am saying than what everyone else thinks is right, if possible.

Even if the "everyone else" in the above statement includes the greatest tonal composers the human race has ever known, and whose broad shoulders we all stand on, harmonically speaking? The "empirical argument" can be found in the music of Bach, Haydn, Mozart, Beethoven, Brahms, Schubert, Mendelssohn, etc. Their 7ths resolved down. Look at the music, and if you'd like to pursue this point, please cite examples where their 7ths resolved up to the 5th. This simple empirical fact tells me that what the 7th does is far from irrelevant. If it were irrelevant, the greatest composers in the history of western music would not have treated them as consistently as they did. The music bears this out. You are free to argue that their opinion isn't worth any more than yours on the subject, but I'm also free to point out that when trying to determine the answers to questions such as this, it is wise to consider your sources.

 

[mutedeity]

No, in the case cited above it does not resolve, or resolves deceptively.



Even if the "everyone else" in the above statement includes the greatest tonal composers the human race has ever known, and whose broad shoulders we all stand on, harmonically speaking? The "empirical argument" can be found in the music of Bach, Haydn, Mozart, Beethoven, Brahms, Schubert, Mendelssohn, etc. Their 7ths resolved down. Look at the music, and if you'd like to pursue this point, please cite examples where their 7ths resolved up to the 5th. This simple empirical fact tells me that what the 7th does is far from irrelevant. If it were irrelevant, the greatest composers in the history of western music would not have treated them as consistently as they did. The music bears this out. You are free to argue that their opinion isn't worth any more than yours on the subject, but I'm also free to point out that when trying to determine the answers to questions such as this, it is wise to consider your sources.

Well that is your opinion and you are entitled to it. Mozart would have probably felt violently ill when confronted with the ideas behind George Russell's Lydian Dominant theory, so I will take the opinion of the romantic and classical period composers under advisement.

I did give you an example, and you refute it by claiming that it resolves deceptively. So how is it that you seemingly think that dominants only resolve to the second inversion of the tonic?

I mean all things being equal you don't even need the 3rd or 5th of the tonic chord to resolve a dominant. the one thing you do need to do is resolve to the tonic or at least imply the tonic in the resolution.

 

[Chris Fitzgerald]

Well that is your opinion and you are entitled to it. Mozart would have probably felt violently ill when confronted with the ideas behind George Russell's Lydian Dominant theory, so I will take the opinion of the romantic and classical period composers under advisement.

Mozart would have had zero trouble with George Russell's concepts. How many George Russell albums do you own? How many times have you heard George Russell compositions performed live?

I did give you an example, and you refute it by claiming that it resolves deceptively. So how is it that you seemingly think that dominants only resolve to the second inversion of the tonic?

Please point out where I have ever said or even implied that dominants resolve only to the second inversion of the tonic. I'm asking you to go look at actual tendencies of the seventh in hundreds of years of music history, and your counterargument is to maintain that I "seemingly think" something that I never said.

I mean all things being equal you don't even need the 3rd or 5th of the tonic chord to resolve a dominant. the one thing you do need to do is resolve to the tonic or at least imply the tonic in the resolution.

One of the most common resolutions in tonal music is sometimes referred to as the "frustrated leading tone" cadence. When V7 and I are both in root position (an extremely common occurrance), it is common for the voice leading to go as follows:

F -->E
D -->C
B -->G
G -->C

The B and D of the V chord in this instance are a third apart, and the D resolves down to the C, taking over the aural resolution of the leading tone and allowing the B to move down to the 5th. This is certainly more common in tonal harmony than the 7th resolving up to the 5th.

 

[mutedeity]

Mozart would have had zero trouble with George Russell's concepts. How many George Russell albums do you own? How many times have you heard George Russell compositions performed live?

So my greatest hits of George Russell box edition set would validate him as a theorist?

Please point out where I have ever said or even implied that dominants resolve only to the second inversion of the tonic. I'm asking you to go look at actual tendencies of the seventh in hundreds of years of music history, and your counterargument is to maintain that I "seemingly think" something that I never said.

Sorry, I was just making that assumption on the fact that you said that resolving the 7th upwards (and therefore playing an inversion of the tonic chord other than the 2nd inversion) would be unresolved.

One of the most common resolutions in tonal music is sometimes referred to as the "frustrated leading tone" cadence. When V7 and I are both in root position (an extremely common occurrance), it is common for the voice leading to go as follows:

F -->E
D -->C
B -->G
G -->C

The B and D of the V chord in this instance are a third apart, and the D resolves down to the C, taking over the aural resolution of the leading tone and allowing the B to move down to the 5th. This is certainly more common in tonal harmony than the 7th resolving up to the 5th.

I think, once again, we are arguing about what is common over what is functional. Tell me am I right or wrong that the function of the dominant is to resolve to the tonic? Am I right or wrong to say that it is the leading tone that directs the movement of the chord back to the tonic? That the leading tone doesn't tend to resolve to the tonic it must move to the tonic to resolve? The 7th of the dominant tends to move to the third but whether it is major or minor doesn't matter as long as it is in the relative key?

 

[onlyclave]

One of the most common resolutions in tonal music is sometimes referred to as the "frustrated leading tone" cadence. When V7 and I are both in root position (an extremely common occurrance), it is common for the voice leading to go as follows:

F -->E
D -->C
B -->G
G -->C

The B and D of the V chord in this instance are a third apart, and the D resolves down to the C, taking over the aural resolution of the leading tone and allowing the B to move down to the 5th. This is certainly more common in tonal harmony than the 7th resolving up to the 5th.

I think what usually happens when writing out SATB harmonies and observing strict 4-part rules is in the tonic your triple the root note and omit the 5th. It prevents parallel 5th/octave motion.

 

[Chris Fitzgerald]

So my greatest hits of George Russell box edition set would validate him as a theorist?

By about the same token that your certainty of Mozart's stomach ache would place Russell on the the same plane in terms of historical importance.

Sorry, I was just making that assumption on the fact that you said that resolving the 7th upwards (and therefore playing an inversion of the tonic chord other than the 2nd inversion) would be unresolved.

Well, that was quite an assumption. The direction of the 7th resolution has absolutely nothing to do with the inversion of the chord it resolves to.

I think, once again, we are arguing about what is common over what is functional. Tell me am I right or wrong that the function of the dominant is to resolve to the tonic? Am I right or wrong to say that it is the leading tone that directs the movement of the chord back to the tonic? That the leading tone doesn't tend to resolve to the tonic it must move to the tonic to resolve? The 7th of the dominant tends to move to the third but whether it is major or minor doesn't matter as long as it is in the relative key?

I never argued any of this, which can be found in the first few chapters of any tonal harmony text. My point is that music theory is the study and analysis of music that has already happened, and that most of our current theory books show us what is functional by showing what was common practice when the particular concept in question was becoming codified.

During the time that "resolving" dominant seventh chords (as opposed to non functional/non-resolving dominants, as in Debussy and Ravel. etc.) became established as an important part of the musical language, the simple fact is that composers went to great pains to ensure that they resolved down. This was my point, and I only brought it up because you claimed on several occasions that the resolution of the seventh is irrelevant. Several hundred years of the musical output of the world's greatest composers would seem to disagree with this, and at this point many decades of tonal harmony books writing about these composers specifically instruct us that, for hundreds of years, 7ths have resolved downward. If you want to hold up George Russell to validate something you said in a thread where the OP wanted to know what an A7 chord is, that's your right, but claiming that 7ths resolve up or that the direction of the 7th resolution is irrelevant is not in any way helping the OP, IMO.

 

[Chris Fitzgerald]

I think what usually happens when writing out SATB harmonies and observing strict 4-part rules is in the tonic your triple the root note and omit the 5th. It prevents parallel 5th/octave motion.

The resolution you describe is also common. However, in the example I posted, the bass voice would have been a 10th below the tenor and would have resolved upward to avoid the parallels.

 

[mutedeity]

During the time that "resolving" dominant seventh chords (as opposed to non functional/non-resolving dominants, as in Debussy and Ravel. etc.) became established as an important part of the musical language, the simple fact is that composers went to great pains to ensure that they resolved down. This was my point, and I only brought it up because you claimed on several occasions that the resolution of the seventh is irrelevant. Several hundred years of the musical output of the world's greatest composers would seem to disagree with this, and at this point many decades of tonal harmony books writing about these composers specifically instruct us that, for hundreds of years, 7ths have resolved downward. If you want to hold up George Russell to validate something you said in a thread where the OP wanted to know what an A7 chord is, that's your right, but claiming that 7ths resolve up or that the direction of the 7th resolution is irrelevant is not in any way helping the OP, IMO.

Actually, my reference to George Russell is not a validation of anything I am saying. It is more of a commentary that musical composition has continued and evolved since the period of who the world's greatest composers are in your opinion. It think it's important to note that it is your opinion that these classicists and romanticists are the world's greatest composers, since you seem to be using them to validate your point.

Now whether 7ths tend to resolve downward or not is absolutely irrelevant to the point I am making. The point I am making is that the movement of the 7th does not resolve the dominant. It is the movement of the leading tone that must move to the tonal centre for resolution to occur.

The reason I brought this up in the first place is because the diagrams supplied by Alvaro Martín Gómez A show the dominant moving to the second inversion of the tonic and he says, "The way to resolve it is raising the third by a semitone and lowering the seventh by the same amount if the dominant chord resolves to a major chord, or by a whole tone if it resolves to a minor chord".

In my opinion this is a very confusing way to explain what is happening and explains the "what" without explaining the "how"
What I would have said is that the tension is released because the leading tone directs the more dissonant chord back to the more consonant tonic chord. All this stuff about thirds resolving down because they tend to, so say the "greatest composers", but it might be major or it might be minor, really doesn't give a clear cut picture of the function of the dominant. You can say all of that stuff once the student knows what is going on.

 

[Chris Fitzgerald]

A It think it's important to note that it is your opinion that these classicists and romanticists are the world's greatest composers, since you seem to be using them to validate your point.

I'll live happily on that continent.

Now whether 7ths tend to resolve downward or not is absolutely irrelevant to the point I am making.

I strongly disagree, and so do most of the theory books I've ever read. I teach college level theory for a living, so I feel strongly about refuting what I believe to be misinformation when I find it. YMM, and obviously does, vary.

The point I am making is that the movement of the 7th does not resolve the dominant. It is the movement of the leading tone that must move to the tonal centre for resolution to occur.

The resolution of the seventh helps resolve the dominant. It's one piece of the tension puzzle involved in any dominant 7th chord.

The reason I brought this up in the first place is because the diagrams supplied by Alvaro Martín Gómez A show the dominant moving to the second inversion of the tonic and he says, "The way to resolve it is raising the third by a semitone and lowering the seventh by the same amount if the dominant chord resolves to a major chord, or by a whole tone if it resolves to a minor chord".

In my opinion this is a very confusing way to explain what is happening and explains the "what" without explaining the "how"
What I would have said is that the tension is released because the leading tone directs the more dissonant chord back to the more consonant tonic chord. All this stuff about thirds resolving down because they tend to, so say the "greatest composers", but it might be major or it might be minor, really doesn't give a clear cut picture of the function of the dominant. You can say all of that stuff once the student knows what is going on.

You are entitled to your opinion. IMO, saying that the direction that the 7th resolves is "irrelevant" is a blatant bit of misinformation which I hoped to counter with my posts. Obviously each reader will have to decide for themselves.

 

[HaVIC5]

The resolution of the seventh helps resolve the dominant. It's one piece of the tension puzzle involved in any dominant 7th chord.

It's not essential, however. If you consider the historical lineage of cadences in modal music in the Renaissance, it was the resolution of the leading tone to the tonic of the mode that made the cadence. Even if it was in a mode that didn't have a leading tone, like dorian or whathaveyou, the note was altered to fit the cadential melodic movement. Many theorists (especially jazz-minded ones) will have you believe that the resolution of a dominant comes from the resolution of the tritone - this was a harmonic device that was added to the theoretical canon much later. Dominant-tonic relationship originally stemmed from contrapuntal melodic tendencies, namely the resolution of the leading tone to the tonic. You can have dominant resolution without the seventh (just the triad, as it originally was), but not without the third.

 

[onlyclave]

I look at it like this:

Kodaly hand signals are for the most part useless to me however the signal for leading tone is your index finger pointing up and the signal for the subdominant tone is the thumbs down sign and these show where these notes resolve.

Therefore in a V7-I cadence, leading tone resolves up and the 7th resolves down.

 

[Chris Fitzgerald]

It's not essential, however. If you consider the historical lineage of cadences in modal music in the Renaissance, it was the resolution of the leading tone to the tonic of the mode that made the cadence. Even if it was in a mode that didn't have a leading tone, like dorian or whathaveyou, the note was altered to fit the cadential melodic movement. Many theorists (especially jazz-minded ones) will have you believe that the resolution of a dominant comes from the resolution of the tritone - this was a harmonic device that was added to the theoretical canon much later. Dominant-tonic relationship originally stemmed from contrapuntal melodic tendencies, namely the resolution of the leading tone to the tonic. You can have dominant resolution without the seventh (just the triad, as it originally was), but not without the third.

No one is arguing this. However, throughout the history of functional tonal harmony, *when the 7th of the V chord is present*, it resolves down, and strengthens the resolution. This thread isn't entitled, "What is an A Major chord?", but rather, "What is an A7?". Clearly, the direction of the 7th resolution is irrelevant when the 7th isn't present - it goes without saying.

 

[mutedeity]

I'll live happily on that continent.

You can live happily on that continent, but I do think it is important pedagogically to understand that opinions are not justifications without a cohesive empirical argument.

I strongly disagree, and so do most of the theory books I've ever read. I teach college level theory for a living, so I feel strongly about refuting what I believe to be misinformation when I find it. YMM, and obviously does, vary.



The resolution of the seventh helps resolve the dominant. It's one piece of the tension puzzle involved in any dominant 7th chord.



You are entitled to your opinion. IMO, saying that the direction that the 7th resolves is "irrelevant" is a blatant bit of misinformation which I hoped to counter with my posts. Obviously each reader will have to decide for themselves.

I think the difference here is that you are talking about what the tendency of the 7th is to do based on precedence over what I am saying must happen in order for resolution to occur. You yourself aren't saying that the seventh must move downwards for resolution to occur. I think it is beyond argument that for resolution to occur the leading tone, or third of the dominant must move upwards to the tonic on the other hand.

Also, you are taking what I said about irrelevance out of context. What I am saying is that the direction of the 7th is irrelevant in causing resolution, not that it is irrelevant in resolution. There is actually a difference. I am fully aware that the 7th is a primary factor in the tension/release mechanism and should be obviously so when I say things like, "the tension is released because the leading tone directs the more dissonant chord back to the more consonant tonic chord". Keeping in mind that I think I said previously that the dissonance is cause by the tritone.

What it all boils down to is that using the language "The way to resolve it is raising the third by a semitone and lowering the seventh by the same amount if the dominant chord resolves to a major chord, or by a whole tone if it resolves to a minor chord," in my mind leads the student to make an outcome based judgement before they really understand the mechanics of the function of the dominant.

I would be very surprised also, if there was never a case of a dominant resolving where the 7th moved upward. I'm not going to read through score after score to prove that point but I don't really think precedence proves or disproves something that is a matter of function over a matter of preference anyway.

 

[Chris Fitzgerald]

I would be very surprised also, if there was never a case of a dominant resolving where the 7th moved upward. I'm not going to read through score after score to prove that point

Interesting take for someone who continually calls for empirical evidence.

but I don't really think precedence proves or disproves something that is a matter of function over a matter of preference anyway.

On this we disagree.

 

[mutedeity]

Interesting take for someone who continually calls for empirical evidence.



On this we disagree.

Well once upon a time people used to walk on the earth and even sail in boats. They thought that if you went too far you would fall off the edge. Everyone agreed, it was a fact. Some people argued that it was round but no-one took them seriously because everyone else knew better. One day someone proved otherwise. The empirical evidence was that someone found that the earth was round by not falling off the edge.

Empirical evidence is not what everyone else thinks. Just because you hold up "the world's greatest composers" as validation for your argument in an arbitrary supposition about what a 7th of a dominant tends to do doesn't make it truth that 7ths must move downwards. Must they? I mean is it a matter of must or are you just arguing this point for the sake of not admitting that I have a valid point?

 

[HaVIC5]

Empirical evidence is not what everyone else thinks. Just because you hold up "the world's greatest composers" as validation for your argument in an arbitrary supposition about what a 7th of a dominant tends to do doesn't make it truth that 7ths must move downwards. Must they? I mean is it a matter of must or are you just arguing this point for the sake of not admitting that I have a valid point?

Rules exist for the purpose of recreating an aesthetic. If your goal is to create the aesthetic of common practice composers and learn what they had to say with the music that they wrote, you should follow a series of guidelines to help you. Of course in jazz or popular music the direction of the resolution of the 7th can be inconsequential, but that isn't what we're talking here - we're talking common practice period sensibilities and understanding of melodic and harmonic considerations, and that is how we create rules, following precedent. Even if you find evidence of a seventh whose resolution wasn't downward by one of the masters (good luck, I for one SERIOUSLY doubt you will), that doesn't change the fact that the entire strong tendency for 7ths to be resolved downward should be utterly ignored. It is an important factor in creating an aesthetic and order from which to create music. Its not an absolute when creating music in general, but remember, we're not, we're dealing with specific tendencies with a specific form of music. Music isn't without form, and we have to look to the music itself to see how its structured. And in this particular case, it's structured with 7ths resolving downwards.

 

[mutedeity]

Rules exist for the purpose of recreating an aesthetic. If your goal is to create the aesthetic of common practice composers and learn what they had to say with the music that they wrote, you should follow a series of guidelines to help you. Of course in jazz or popular music the direction of the resolution of the 7th can be inconsequential, but that isn't what we're talking here - we're talking common practice period sensibilities and understanding of melodic and harmonic considerations, and that is how we create rules, following precedent. Even if you find evidence of a seventh whose resolution wasn't downward by one of the masters (good luck, I for one SERIOUSLY doubt you will), that doesn't change the fact that the entire strong tendency for 7ths to be resolved downward should be utterly ignored. It is an important factor in creating an aesthetic and order from which to create music. Its not an absolute when creating music in general, but remember, we're not, we're dealing with specific tendencies with a specific form of music. Music isn't without form, and we have to look to the music itself to see how its structured. And in this particular case, it's structured with 7ths resolving downwards.

Actually we aren't talking about either. I am talking about why saying that to "resolve a dominant you move the 7th downwards" is not accurate. The tendency is nothing to do with causing resolution. I am talking about what must occur not about what tends to be the case. I am doing this because telling a beginner that the 7th moving downwards resolves the chord gives them a false understanding of the mechanics of the dominant function.

As far as rules go, I don't believe there are any general rules in music. There are only paradigms affected by precedence, conditioning and context. Rules are subject to conforming to a paradigm, which is clearly not what I am discussing. If I was I would have said "in classicism, baroque and romantic composition..." etc.

I am talking about the general function of a dominant and how I believe that what was posted about 7ths moving downwards is misleading. You have to ask yourself this, and apparently by your posts you understand this point, is it absolutely necessary to tell the student that 7ths tend to move downwards in order to resolve the tonic? Or, is that something they can learn about once they understand that the leading tone directs the dominant back to the tonal centre and thus causes the V to return to the I?

It is also a matter of the language too. We know that the leading tone must move upwards to the tonic for resolution to occur. The tendency of "great composers" doesn't create a "must" in regards to what the 7th does. On top of that as I said before I would be willing to bet that one of those great composers at some stage moved the 7th upwards.

 

[Chris Fitzgerald]

Actually we aren't talking about either. I am talking about why saying that to "resolve a dominant you move the 7th downwards" is not accurate. The tendency is nothing to do with causing resolution. I am talking about what must occur not about what tends to be the case. I am doing this because telling a beginner that the 7th moving downwards resolves the chord gives them a false understanding of the mechanics of the dominant function.

Show me a person in this thread who claimed what you claim they claimed - namely, that the dominant resolution is caused by the downward movement of the 7th alone. I don't remember anyone claiming that at all.

As far as rules go, I don't believe there are any general rules in music.

If there are no rules, then why argue so strongly about the best theoretical way to describe a dominant chord?

I am talking about the general function of a dominant and how I believe that what was posted about 7ths moving downwards is misleading. You have to ask yourself this, and apparently by your posts you understand this point, is it absolutely necessary to tell the student that 7ths tend to move downwards in order to resolve the tonic? Or, is that something they can learn about once they understand that the leading tone directs the dominant back to the tonal centre and thus causes the V to return to the I?

In tonal theory III and IV (romantic through 20th century), we tell them that both are important since we're studying "common practice" western harmony. Again, no one is discounting the importance of the resolution of the 3rd. Rather, folks are just pointing out that the seventh also has a strong resolution tendency, as demonstrated by hundreds of years of tradition.

It is also a matter of the language too. We know that the leading tone must move upwards to the tonic for resolution to occur. The tendency of "great composers" doesn't create a "must" in regards to what the 7th does.

The fact is that music theory only exists because of music that has already been created; it is basically a language of labels designed to describe what has been done in the past so that it may be understood, analyzed, and imitated. When common practice theory books are written, the language they create and use, which you are also using yourself in this thread, becomes the language of music theory. What is being described and analyzed in these books is the music of many of the composers I mentioned earlier - Bach, Mozart, Beethoven, Brahms, etc. - and for this reason, they created the "rules" by the tendencies they displayed in their works. In effect, they "wrote the book" on theory. That's about as empirical as it gets right there.

On top of that as I said before I would be willing to bet that one of those great composers at some stage moved the 7th upwards.

Knock yourself out finding one. If they're as common as you think, it should be easy.

 

[mutedeity]

Show me a person in this thread who claimed what you claim they claimed - namely, that the dominant resolution is caused by the downward movement of the 7th alone. I don't remember anyone claiming that at all.

It's only the 4th time, I think, that I posted it but;

"The way to resolve it is raising the third by a semitone and lowering the seventh by the same amount if the dominant chord resolves to a major chord, or by a whole tone if it resolves to a minor chord:"

Case closed

If there are no rules, then why argue so strongly about the best theoretical way to describe a dominant chord?

Firstly, once again you have taken what I said out of context. Secondly where rules are involved the rule is not that the 7th MUST resolve downwards it is that it has a TENDENCY to do so. I think the difference there is kind of obvious. Rules or not, due to conditioning, we tend to hear tension and expect resolution, on a psychological level this is true of any of the arts and even of our day to day lives. That resolution is tonally caused by the upwards movement of the leading tone to the tonic.

In tonal theory III and IV (romantic through 20th century), we tell them that both are important since we're studying "common practice" western harmony. Again, no one is discounting the importance of the resolution of the 3rd. Rather, folks are just pointing out that the seventh also has a strong resolution tendency, as demonstrated by hundreds of years of tradition.



The fact is that music theory only exists because of music that has already been created; it is basically a language of labels designed to describe what has been done in the past so that it may be understood, analyzed, and imitated. When common practice theory books are written, the language they create and use, which you are also using yourself in this thread, becomes the language of music theory. What is being described and analyzed in these books is the music of many of the composers I mentioned earlier - Bach, Mozart, Beethoven, Brahms, etc. - and for this reason, they created the "rules" by the tendencies they displayed in their works. In effect, they "wrote the book" on theory. That's about as empirical as it gets right there.

You are talking about COMMON PRACTICE. I made this point about four times now as well, but common practice is not what I am talking about. I am talking about the general mechanics of resolution. Yes, yes, the "great composers" made rules etc. Parallel 5ths is bad voice leading too but show me a rock band that doesn't use parallel motion of 5ths and octaves. It's still music and it still functions. Does a dominant resolve without the 7th moving down? Yes, it does. Does it resolve without the leading tone resolving to the tonic or the tonic at least being implied in resolution? No, it does not.

As far as empricism goes, empirical evidence is when the aliens land and open their doors and walk out and there is no doubt that they exist. It is not consulting the opinion of the experts who believe aliens are out there based on their calculations for life existing elsewhere in the universe or on the mathematical rules they have set up as a means of endorsing such a possibility.

Common practice or belief does not provide empirical evidence.

Knock yourself out finding one. If they're as common as you think, it should be easy.

I never said it was common. If and when I do though, trust me, you will be the first to know.

 

[Chris Fitzgerald]

It's only the 4th time, I think, that I posted it but;

"The way to resolve it is raising the third by a semitone and lowering the seventh by the same amount if the dominant chord resolves to a major chord, or by a whole tone if it resolves to a minor chord:"

Show me a person in this thread who claimed what you claim they claimed - namely, that the dominant resolution is caused by the downward movement of the 7th alone. I don't remember anyone claiming that at all.

Case closed

Indeed.