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Thread: Baroque "chord progressions"

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    Senior Member mikeh375's Avatar
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    Quote Originally Posted by millionrainbows View Post
    Use your logic, please.

    The concept of "chord function" cannot exist without knowing the root of a chord as related to a key or tonic note.
    Bach was not interesting in identifying by analysis or in his figured-bass notation any chords except by the voicings above a bass note, and this does not identify roots of chords.

    So he had to be doing it by ear. That's what I've been saying all along. That's not a form of "harmonic thinking" that is touted in the counterpoint textbooks. That's "using your ear" (both of them). That's "harmonic hearing."

    In this way, Bach MUST have been hearing root relations to a key note, in order to hear any sort of "function" which he might have heard. It's inescapable.

    This means my harmonic model (and all those charts I posted) are correct, because it is based on the perception of intervals, and not on codified theory.

    No one else has offered any explanation except ME.


    The ideas you express seem too black and white imv MR and miss the intimate relationship between counterpoint and harmony.
    Does this shed any light?.....

    oldroyd.tiff.pdf
    Last edited by mikeh375; May-16-2020 at 11:00.
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    Quote Originally Posted by Woodduck View Post
    Sorry, but that reads like a medieval text on alchemy. Are you saying that the perception of degrees of dissonance between the notes of a scale and a tonic note is a sufficient guide to the procedures of common practice harmony and "explains" how Bach knew how to write a cadence with a Neopolitan sixth in it?
    No one else has "explained" how Bach used harmonic function. You haven't. All you can do is invalidate other ideas. Why don't you do some work on this? You can't just narcissistically expect everyone to agree with your self-serving "rationality."

    There may be some stylistic non-essential procedures like "a cadence with a Neopolitan sixth" which were followed, but, yes, I'm saying that the more basic perception of degrees of dissonance between the notes of a scale and a tonic note is done by ear, and the consonance/dissonance corresponds.

    Here it is again.

    What is the most closely-related chord to I? V, and so on. The correspondences follow with each chord function:

    So a C major scale's horizontal functions correspond to these harmonic relations; and one can observe how these functions were derived:

    I — 1:1
    ii — 8:9
    iii — 4:5
    IV — 3:4
    V — 2:3
    vi — 3:5
    vii — 8:15

    Their importance in establishing the tonality is ranked by the order of consonance to dissonance, with smaller-number ratios being more consonant.

    I — 1:1
    V — 2:3
    IV — 3:4
    vi — 3:5
    iii — 4:5
    ii — 8:9
    vii — 8:15


    Using this model, a "function" hierarchy can be applied to any scale, after the degrees of dissonance are ranked.

    Furthermore, I'm asserting that "chord function" is not exclusive to CP harmony, but is an innate feature of any scale which can be used in a tonality.
    Last edited by millionrainbows; May-16-2020 at 12:55.

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    15/8 has higher complexity than 9/5, if you after consonant seventh degree. (And we get mixolydian mode, plus 9/5 is is close to seventh harmonic).And your given scale has wolf intervals, so some normal chords are ugly and modulate enharmonically, if you attempt typical progressions.
    IF you actually read some of the functional harmony theorists, you will understand why major and minor are the structurally important ones, but it's not because of highest degree of consonance for sure...

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    Quote Originally Posted by BabyGiraffe View Post
    15/8 has higher complexity than 9/5, if you after consonant seventh degree. (And we get mixolydian mode, plus 9/5 is is close to seventh harmonic).And your given scale has wolf intervals, so some normal chords are ugly and modulate enharmonically, if you attempt typical progressions.
    IF you actually read some of the functional harmony theorists, you will understand why major and minor are the structurally important ones, but it's not because of highest degree of consonance for sure...
    That's weird...I thought that you, of all people, would believe in the primacy of the ear. I'm disappointed in you, Baby.

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    Quote Originally Posted by millionrainbows View Post
    That's weird...I thought that you, of all people, would believe in the primacy of the ear. I'm disappointed in you, Baby.
    Check this graph.

    het01_16.gif

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    Quote Originally Posted by BabyGiraffe View Post
    Check this graph.

    het01_16.gif
    The octave is still king, and look how close 3/2 and 4/3 are, the "triumvirate" of Western tonality.

    This also corresponds to how closely related an interval (or root) is to "1" or tonic, as "functions."
    Last edited by millionrainbows; May-16-2020 at 16:14.

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    errr...where's the music? Where's Papa gone?
    Last edited by mikeh375; May-16-2020 at 20:57.
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  11. #233
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    Quote Originally Posted by millionrainbows View Post

    Furthermore, I'm asserting that "chord function" is not exclusive to CP harmony, but is an innate feature of any scale which can be used in a tonality.
    "Chord function … is an innate feature of any scale which can be used in tonality?" This is meaningless. Chord function is not a feature of scales. The statement makes no sense whatever. Try again.

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    Senior Member Woodduck's Avatar
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    Quote Originally Posted by millionrainbows View Post
    No one else has "explained" how Bach used harmonic function. You haven't. All you can do is invalidate other ideas. Why don't you do some work on this? You can't just narcissistically expect everyone to agree with your self-serving "rationality."
    Jiminy Crickets! Narcissistically? Back to labeling and name-calling (and now I have confirmation that your use of that term yesterday was aimed at me, even though you denied it). Ho hum...

    You're projecting mightily. I don't expect everyone to agree with anything, but apparently you do expect that, else you wouldn't repeat yourself over and over in exactly the same words, hoping that everyone who might consider questioning you will either adopt them as a mantra, be stuck with an earworm, or just give up from brain fatigue.

    Sorry, bubba, but what I'm really tryin' ta do is figger out what in the Sam Hill you're talkin' 'bout with this here "composition by ear" thang.

    There may be some stylistic non-essential procedures like "a cadence with a Neopolitan sixth" which were followed, but, yes, I'm saying that the more basic perception of degrees of dissonance between the notes of a scale and a tonic note is done by ear, and the consonance/dissonance corresponds.
    If that's all I thought you were saying, I'd have no argument with you (up until "and the consonance/dissonance corresponds"- but hang on...) OF COURSE we can perceive - "by ear" - different degrees of consonance and dissonance among the intervals between a tonic note and the other notes of a scale (though I dare say that most people wouldn't know whether, e.g., a major third or a major sixth is more dissonant). But you appear to be saying much more than that. You appear to be saying that this basic fact of perception "EXPLAINS HOW" Bach - and presumably other people writing harmonic progressions - have arrived at the tonal system we call "common practice" and are able to know, while composing, what chord should follow what. If this is the claim you're making, it's an extraordinaryone, and it strikes me as insufficiently reasoned, as welol as reductive in the extreme. It certainly cries out for concrete demonstration. "The consonance/dissonance corresponds" doesn't explain anything, even if there is actually a meaningful correspondence between something and something else.

    Here is what you've said in this thread:

    "Harmonic thinking did not exist in Bach's time, so no one has explained exactly how he thought about harmonic root movement or harmonic 'progressions.'"

    "It has already been acknowledged that Bach was 'thinking harmonically' without the benefit of a codified system of harmony, chord function, or root movement. There is only one possible conclusion: Bach was doing it by 'ear,' on the basis of what he was hearing harmonically. Bach's 'function' was derived by listening."

    "Bach was determining 'function' by ear."

    "Bach was doing it by ear. his linear rules were there, but any harmonic factors not covered by these rules were arrived at by listening."

    "What is called 'harmonic thinking' is just 'using your ear' to hear the 'harmonic truth.'
    It has less to do with harmonic rules or regulations. It is derived from the act of hearing, not rules."

    "'Harmonic thinking' is possible without any rules; it operates more on the level of the ear, as a directly perceived 'logic' of the senses."

    "'Harmonic truths' such as 'function' of roots and chords exists without any codification or established practices. It is a universal truth, one of the underlying principles of music."

    "'Harmonic hearing' is the underlying basis of all 'systems,' nomenclatures, and 'practices' or rules."

    "Tonal music is harmonic; music is vertical. It is based on vertical, harmonic factors which are instantaneous, based on hearing degrees of consonance/dissonance to a key or tonic note."

    "Melodies in counterpoint have a harmonic basis; they suggest triads, and can outline triads. Bach's unaccompanied violin sonatas show that he was thinking harmonically. But no one has offered an explanation of how this is possible, except me. It is done by ear, using intervals and their degrees of dissonance to a key note, and their other suggestions of triads. The intervals have a dissonant/consonant quality determined by their ratio, all in relation to a 'keynote' or unity of 1; our ears/brain experience this as an instantaneous visceral sensation. The intervals have a scale degree and place in relation to '1' or the Tonic, and triads can be constructed on these steps/notes. The chords thus constructed can then be given a 'function' which is modeled after this harmonic relation to the keynote. Function is dependent on forward progression in time, and context, and both rely on memory.

    "This harmonic model is where all 'linear function' originates."


    I'm not about to analyze these statements one at a time, but I have to say that the general point they seem to be making would have much more credibility if they were accompanied by some explanation of HOW the imputed magical transformation of perception into music happens: how hearing different degrees of dissonance between scale notes and the tonic explains a composer's choice of harmonic progressions. Some musical examples might be useful in supporting your theory, but you don't even provide those.

    As I look over the history of music, I see a great variety of harmonic practice. Tonality is a near-universal characteristic of music, but harmony in Western music is said to date back to about 900 A.D., and a lot changed over the succeeding millennium. Across time and cultures the human ear has presumably been quite capable of perceiving degrees of relative dissonance in various intervals, yet the treatment of harmony has been immensely varied. We observe certain common features in disparate cultures and styles, such as a preference for the fifth scale degree, an easily audible overtone of the tonic, which eventually became our dominant. But our tonal hierarchy and conventions of harmonic progression underwent a long development. Why so long? What was "the ear" doing over all that time? What were composers' ears telling them to do? What was Machaut's ear telling him in this:

    https://www.youtube.com/watch?v=cu7-RV7XB9k

    In what way was Dufay's ear telling him what to write in this?

    https://www.youtube.com/watch?v=6mcxEtyEUw4

    How about Ockeghem's ear:

    https://www.youtube.com/watch?v=Ospfv3AP1_c

    Or Purcell's:

    https://www.youtube.com/watch?v=4AD96qnao5U

    Or Gesualdo's:

    https://www.youtube.com/watch?v=6dVPu71D8VI


    I presume these composers could hear degrees of dissonance as well as Bach could, but they certainly had different intuitions about proper "function" in deciding what harmonies sounded right at any given moment. The ear was busy for hundreds of years before modern harmonic theory was formulated. What exactly was it telling the musical minds attached to it? How does the perception of degrees of dissonance, which should not change over time if the human ear doesn't, result in different modes or tonal systems? And how does it guide specific procedures? How does it guide the use of chromaticism? How does it account for the aptness of an authentic cadence, or a plagal one, or a deceptive one? Music is built on the increase and decrease of tensions, and degrees of dissonance are basic in harmonic music's accomplishment of that, but beyond a crude level - say, tonic to dominant increasing tension, the reverse decreasing it - how much can relative dissonance tell composers how to structure their music? Assuming it can tell them anything at all, doesn't it seem to have told them very different things? How, for a more far-flung example, does the following music reflect the scale's hierarchy of consonance and dissonance?

    https://www.youtube.com/watch?v=4E0w1J6xe1k

    It probably isn't necessary to go outside the common practice tradition to make my point, which is that harmonic progression is so variable, and governed by so many factors, that there is no reason to suppose that composers arrive at a specific harmonic system, a codified or codifiable way of using harmony, solely or mainly by observing or sensing the acoustical properties of sound. And to go even farther (if that's what you're doing) and imagine that any composer is guided by that factor in the moment of composition to shape his work in any particular way is just inconceivable to me.

    You've claimed a local patent on being able to "EXPLAIN HOW" Bach, under the influence of some subliminal perception of relative dissonance between the tonic and the roots of other chords, could think in terms of a harmonic idiom without referring to a codified classification of chords. Well, I'm not looking to infringe that patent, since I don't see that you've explained any such thing. In fact I don't even see that an explanation of that kind is necessary. If Bach had lived in the time of Binchois, he would have written modal polyphony with Landini cadences, and if he had lived in the time of Schoenberg, God only knows what sort of harmony he would have written. Bach learned to think harmonically the same way everybody else does: by hearing, performing, reading and writing music in the harmonic idiom of his own day, not by listening to spirit voices from the Celestial Academy of Acoustical Science.
    Last edited by Woodduck; May-17-2020 at 01:01.

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    Quote Originally Posted by EdwardBast View Post
    "Chord function … is an innate feature of any scale which can be used in tonality?" This is meaningless. Chord function is not a feature of scales. The statement makes no sense whatever. Try again.
    It makes sense to me & my ear(s). You've never thought about it, apparently. If you can hear scale steps in relation to a tonic, you're hearing "function." All the classification in the world won't change that basic fact of perception. You're not an "ear guy," are you? Didn't think so.
    Last edited by millionrainbows; May-17-2020 at 02:54.

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    Another gargantuan invalidation-fest from you-know-who! Wow! Where do I begin? I'm gonna have to break this one down into manageable chunks, otherwise I'll choke.

    Quote Originally Posted by Woodduck View Post
    Jiminy Crickets! Narcissistically? Back to labeling and name-calling (and now I have confirmation that your use of that term yesterday was aimed at me, even though you denied it). Ho hum...
    After observing your behavior on the "Religious Music Without Lyrics" thread, why do you even bother with "victim statements" like this?

    You're projecting mightily. I don't expect everyone to agree with anything, but apparently you do expect that, else you wouldn't repeat yourself over and over in exactly the same words, hoping that everyone who might consider questioning you will either adopt them as a mantra, be stuck with an earworm, or just give up from brain fatigue.
    No, it's just that I really feel you are unaware of the import of my ideas, and are hostile to me as a person, so it's a no-win situation. I just put my ideas out there, you can take 'em or leave 'em. It's not going to ruin my supper.
    Sorry, bubba, but what I'm really tryin' ta do is figger out what in the Sam Hill you're talkin' 'bout with this here "composition by ear" thang.
    Maybe it's my motivation that eludes you, but it's really very simple, all in the charts I posted. All you have to be able to do is hear scale steps in relation to a tonic, and you're hearing "function" in its basic, pre-theory form. All the CP classification in the world won't change that basic fact of perception. You play piano, don't you? I assumed you were an "ear guy," but apparently your "edjumacation" is getting in your way.

    If that's all I thought you were saying, I'd have no argument with you (up until "and the consonance/dissonance corresponds"- but hang on...) OF COURSE we can perceive - "by ear" - different degrees of consonance and dissonance among the intervals between a tonic note and the other notes of a scale (though I dare say that most people wouldn't know whether, e.g., a major third or a major sixth is more dissonant). But you appear to be saying much more than that. You appear to be saying that this basic fact of perception "EXPLAINS HOW" Bach - and presumably other people writing harmonic progressions - have arrived at the tonal system we call "common practice" and are able to know, while composing, what chord should follow what. If this is the claim you're making, it's an extraordinaryone, and it strikes me as insufficiently reasoned, as well as reductive in the extreme. It certainly cries out for concrete demonstration. "The consonance/dissonance corresponds" doesn't explain anything, even if there is actually a meaningful correspondence between something and something else.
    Well, I'm not a historian, but I think this is the way all good musicians hear things. Whether or not it adheres to later codified practices is of no concern to me. Since there is no written record by Bach on theory, then at least I offer an explanation which is innate and universal. If you think it sucks, so be it, it won't bother me in the least.
    Last edited by millionrainbows; May-17-2020 at 02:23.

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    Quote Originally Posted by Woodduck View Post

    Here is what you've said in this thread:

    "Harmonic thinking did not exist in Bach's time, so no one has explained exactly how he thought about harmonic root movement or harmonic 'progressions.'"

    "It has already been acknowledged that Bach was 'thinking harmonically' without the benefit of a codified system of harmony, chord function, or root movement. There is only one possible conclusion: Bach was doing it by 'ear,' on the basis of what he was hearing harmonically. Bach's 'function' was derived by listening."

    "Bach was determining 'function' by ear."

    "Bach was doing it by ear. his linear rules were there, but any harmonic factors not covered by these rules were arrived at by listening."

    "What is called 'harmonic thinking' is just 'using your ear' to hear the 'harmonic truth.'
    It has less to do with harmonic rules or regulations. It is derived from the act of hearing, not rules."

    "'Harmonic thinking' is possible without any rules; it operates more on the level of the ear, as a directly perceived 'logic' of the senses."

    "'Harmonic truths' such as 'function' of roots and chords exists without any codification or established practices. It is a universal truth, one of the underlying principles of music."

    "'Harmonic hearing' is the underlying basis of all 'systems,' nomenclatures, and 'practices' or rules."

    "Tonal music is harmonic; music is vertical. It is based on vertical, harmonic factors which are instantaneous, based on hearing degrees of consonance/dissonance to a key or tonic note."

    "Melodies in counterpoint have a harmonic basis; they suggest triads, and can outline triads. Bach's unaccompanied violin sonatas show that he was thinking harmonically. But no one has offered an explanation of how this is possible, except me. It is done by ear, using intervals and their degrees of dissonance to a key note, and their other suggestions of triads. The intervals have a dissonant/consonant quality determined by their ratio, all in relation to a 'keynote' or unity of 1; our ears/brain experience this as an instantaneous visceral sensation. The intervals have a scale degree and place in relation to '1' or the Tonic, and triads can be constructed on these steps/notes. The chords thus constructed can then be given a 'function' which is modeled after this harmonic relation to the keynote. Function is dependent on forward progression in time, and context, and both rely on memory.

    "This harmonic model is where all 'linear function' originates."


    I'm not about to analyze these statements one at a time, but I have to say that the general point they seem to be making would have much more credibility if they were accompanied by some explanation of HOW the imputed magical transformation of perception into music happens: how hearing different degrees of dissonance between scale notes and the tonic explains a composer's choice of harmonic progressions. Some musical examples might be useful in supporting your theory, but you don't even provide those.
    It seems simple to me. If a composer wants to move away from the tonic and create a chord progression, he does it on the basis of how closely-related the roots are to the tonic, and creates the progressions. This can be done with any scale, based on the degrees of relation (those ratios in the chart, and the rankings):

    Their importance in establishing the tonality is ranked by the order of consonance to dissonance, with smaller-number ratios being more consonant.

    I — 1:1
    V — 2:3
    IV — 3:4
    vi — 3:5
    iii — 4:5
    ii — 8:9
    vii — 8:15

    As I look over the history of music, I see a great variety of harmonic practice. Tonality is a near-universal characteristic of music, but harmony in Western music is said to date back to about 900 A.D., and a lot changed over the succeeding millennium. Across time and cultures the human ear has presumably been quite capable of perceiving degrees of relative dissonance in various intervals, yet the treatment of harmony has been immensely varied. We observe certain common features in disparate cultures and styles, such as a preference for the fifth scale degree, an easily audible overtone of the tonic, which eventually became our dominant. But our tonal hierarchy and conventions of harmonic progression underwent a long development. Why so long? What was "the ear" doing over all that time? What were composers' ears telling them to do?
    Thanks for the examples anyway.

    I presume these composers could hear degrees of dissonance as well as Bach could, but they certainly had different intuitions about proper "function" in deciding what harmonies sounded right at any given moment. The ear was busy for hundreds of years before modern harmonic theory was formulated. What exactly was it telling the musical minds attached to it? How does the perception of degrees of dissonance, which should not change over time if the human ear doesn't, result in different modes or tonal systems? And how does it guide specific procedures? How does it guide the use of chromaticism? How does it account for the aptness of an authentic cadence, or a plagal one, or a deceptive one?
    I guess you could say that this is up to the individual's own taste and knowledge of styles and what went before. I don't deny this legacy, I'm simply getting down to the root of it, pardon the pun.

    Music is built on the increase and decrease of tensions, and degrees of dissonance are basic in harmonic music's accomplishment of that, but beyond a crude level - say, tonic to dominant increasing tension, the reverse decreasing it - how much can relative dissonance tell composers how to structure their music? Assuming it can tell them anything at all, doesn't it seem to have told them very different things?
    Thanks for the example anyway.

    It probably isn't necessary to go outside the common practice tradition to make my point, which is that harmonic progression is so variable, and governed by so many factors, that there is no reason to suppose that composers arrive at a specific harmonic system, a codified or codifiable way of using harmony, solely or mainly by observing or sensing the acoustical properties of sound. And to go even farther (if that's what you're doing) and imagine that any composer is guided by that factor in the moment of composition to shape his work in any particular way is just inconceivable to me.
    Well, this sort of deep logic is also the subject of Arnold Schoenberg's textbook "Structural Functions of Harmony."

    You've claimed a local patent on being able to "EXPLAIN HOW" Bach, under the influence of some subliminal perception of relative dissonance between the tonic and the roots of other chords, could think in terms of a harmonic idiom without referring to a codified classification of chords.
    That's an exaggeration, but I am the only one who has offered any concrete explanation. You're probably a close second. I would be wrong to say Bach wasn't influenced by the practices of his day (even though he rejected Rameau's ideas), but I've never said that.

    Besides, my explanation gives the benefit to Bach "using his ears" rather than him simply "parroting" the procedures of the day.

    Well, I'm not looking to infringe that patent, since I don't see that you've explained any such thing. In fact I don't even see that an explanation of that kind is necessary.
    Well, I do, especially when academicians pull things out of their hats like "chords were not used in the Baroque" and stuff like that.

    If Bach had lived in the time of Binchois, he would have written modal polyphony with Landini cadences, and if he had lived in the time of Schoenberg, God only knows what sort of harmony he would have written. Bach learned to think harmonically the same way everybody else does: by hearing, performing, reading and writing music in the harmonic idiom of his own day...
    I agree, I don't doubt that at all.

    ...not by listening to spirit voices from the Celestial Academy of Acoustical Science.
    Yes, and be careful when you go to sleep tonight! I've heard that these "spirit voices" enter into you through the ears!
    Last edited by millionrainbows; May-17-2020 at 02:52.

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    ^^^ You're evading the elephant in the room, which I tried to place front and center: the variety of tonal systems, with their diverse conventions, throughout a long history of which common practice occupies only a portion. Your dismissal of this with "thanks for the examples anyway" tells me you're not capable of dealing with the problem they raise for your theory.

    Your statement, "If a composer wants to move away from the tonic and create a chord progression, he does it on the basis of how closely-related the roots are to the tonic," is not true. Unless you have a special meaning in mind for the expression, "on the basis of," a composer does not have to concern himself with degrees of relationship to the tonic or be compelled by them in any way. There are certainly conventional relationships between chords, and it's true that the most commonly used chords and progressions use the chords closest to the tonic; the tonic-dominant relationship is basic to common practice, and the subdominant root is to the tonic root as the tonic root is to the dominant root. It isn't surprising that this "triumvirate" should have come to dominate common practice tonality (at least for a while), since the overtone of the fifth above the tonic is so audible and the harmony created between them so satisfying. But a composer who wants to move away from the tonic may do so in a number of directions - he can move to the supertonic or the mediant chord, for example - and he may proceed in any number of directions from there. Not even at a final cadence is there a necessity of sticking to the common V - I or IV - I formulas. In exactly what way do you feel composers are constrained by your hierarchy of dissonance?
    Last edited by Woodduck; May-17-2020 at 03:35.

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    Quote Originally Posted by Woodduck View Post
    the tonic-dominant relationship is basic to common practice, and the subdominant root is to the tonic root as the tonic root is to the dominant root.
    Overtone relationships are one, voice leading relationships - another topic, that's why subdominant relationship has more validity as natural move of chords, related to a key (but it's not major/minor "key"). The only legal moves that don't imply modulation and don't introduce enharmonics are these found in the C-Eb-E-F-G-Ab-A scale. There is no dominant chord there. This is the 5-limit hexagonal lattice. Many-many scales can be derived, if we use selection polygons that go around pitches that are close on this lattice.
    Here is the tempered version in 12 equal.

    https://en.wikipedia.org/wiki/Neo-Ri...an_Tonnetz.svg

    If you want dominant and typical classical music progression, you want hidden 80/81 (or inverse) and prooobably meantone temperament to get rid of them. If you want "romantic" chord progressions, you will deal with both 81/80 and 128/125 and their product - 648/625, so the whole basis of classical music is artificial construct.
    Last edited by BabyGiraffe; May-17-2020 at 05:12.

  19. #240
    Senior Member millionrainbows's Avatar
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    Quote Originally Posted by Woodduck View Post

    Your statement, "If a composer wants to move away from the tonic and create a chord progression, he does it on the basis of how closely-related the roots are to the tonic," is not true. Unless you have a special meaning in mind for the expression, "on the basis of," a composer does not have to concern himself with degrees of relationship to the tonic or be compelled by them in any way.
    I think that's incorrect. As Schoenberg demonstrates in his book, certain root movements are stronger than others ands do different things. I think this is what Bach was doing, in addition to obvious voice-leading.

    For instance, a root movement a fifth up (a fourth down), say, from C to G suggests a movement away from the tonic, because the ear hears fifths with "root on bottom."

    A root movement a fourth up (a fifth down), say, G to C suggests a movement to a tonic, because the ear tends to hear fourths as "root on top."

    But a composer who wants to move away from the tonic may do so in a number of directions - he can move to the supertonic or the mediant chord, for example - and he may proceed in any number of directions from there. Not even at a final cadence is there a necessity of sticking to the common V - I or IV - I formulas.
    True; that doesn't negate anything I've said.
    Last edited by millionrainbows; May-17-2020 at 16:01.

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