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Your favorite modulation tricks and tips?

Emanuel Fróes said:
For Riemann the subdominant is the SUB-dominant: the dominant from below, from the inverted series... The inverted series is deducted from the inversion of the tonic triad. But why does he go here?
Click to expand...
I think he goes there because it makes a lot of sense on a certain level.

We usually consider the tonic as the first node in some kind of linear representation of functions. It is certainly the mainstream view in many countries and it is very convenient. It can be easily represented in a straight line, analogous to a scale. Something like this illustration (just a random image from Google) - a linear model I to VII:

1683473722035.png

But the other way of describing the same thing is by putting the tonic in the center and the mediants, subdominant and dominant as radiating outwards (or up and down) from the center:

1683467677875.png

This latter modeled is Riemann-derived and used (and enriched extensively) by the Russians, from what I understand. You can conceptualize this model as a kind of oscillation between S and D, crossing the T, with clearly defined and measurable tension qualities, and that eventually settles on the tonic. It can be compared to the oscillation of a string or a metronome. More recently, it's been described as something not unlike Fibonacci spirals to show how it can incorporate microtonality, temperaments and other types of sectioning and division.

In my opinion, this German-Russian model (in contrast to the familiar linear model) is far more visual, deep and elegant. It better explains the leading tones, chromatic alterations, the very concept of cadence and all of its types, plus chord substitutions. The Russians used it to explain the merger of the major and minor modes into a single mode, a far more elegant concept than "chord borrowing" the linear model uses even today.

"Negative harmony" is a very unfortunate and misleading term, but it's central idea - the mirror inversion up or down, is very reasonable. If you build a C major chord and then repeat the same exact intervals in the opposite direction from the tonic, you will indeed get an F minor chord. All of the major chords will become minor chords, the diminished chords will remain diminished. All authentic tensions will become plagal. All this is part of "negative harmony" but is more simply and elegantly explained by the Russians in the model shown above, and used by composers since well before 1895.

What Levy introduces that's totally new is the idea of an axis - a theoretical tone that's equal distance between the tonic and the dominant. This specific tone (and not the tonic any longer) is the point from which the inversions are created up or down, retaining all of the principles shown above. The entire subdominant group becomes displaced, so to speak. And:
- we get a whole new group of (mirrored) chord substitutions, while all of the leading tones and tensions of the given key are preserved
- the dissonances from layering of these polar chords are very striking (Bartok concerto for orchestra is a great example)
- we can reharmonize existing material differently and we can also deliberately modulate between the two groups in the same period or sentence and get even more color

I'm not a big fan of negative harmony but I do think it's an interesting inversion technique for enriching harmonic color and specifically progressions and chord layering. It sounds a little jazzy, often unusual and sometimes fresh. That's all it is, imho.
 
youngpokie said:
I think he goes there because it makes a lot of sense on a certain level.

We usually consider the tonic as the first node in some kind of linear representation of functions. It is certainly the mainstream view in many countries and it is very convenient. It can be easily represented in a straight line, analogous to a scale. Something like this illustration (just a random image from Google) - a linear model I to VII:

1683473722035.png

But the other way of describing the same thing is by putting the tonic in the center and the mediants, subdominant and dominant as radiating outwards (or up and down) from the center:

1683467677875.png

This latter modeled is Riemann-derived and used (and enriched extensively) by the Russians, from what I understand. You can conceptualize this model as a kind of oscillation between S and D, crossing the T, with clearly defined and measurable tension qualities, and that eventually settles on the tonic. It can be compared to the oscillation of a string or a metronome. More recently, it's been described as something not unlike Fibonacci spirals to show how it can incorporate microtonality, temperaments and other types of sectioning and division.

In my opinion, this German-Russian model (in contrast to the familiar linear model) is far more visual, deep and elegant. It better explains the leading tones, chromatic alterations, the very concept of cadence and all of its types, plus chord substitutions. The Russians used it to explain the merger of the major and minor modes into a single mode, a far more elegant concept than "chord borrowing" the linear model uses even today.

"Negative harmony" is a very unfortunate and misleading term, but it's central idea - the mirror inversion up or down, is very reasonable. If you build a C major chord and then repeat the same exact intervals in the opposite direction from the tonic, you will indeed get an F minor chord. All of the major chords will become minor chords, the diminished chords will remain diminished. All authentic tensions will become plagal. All this is part of "negative harmony" but is more simply and elegantly explained by the Russians in the model shown above, and used by composers since well before 1895.

What Levy introduces that's totally new is the idea of an axis - a theoretical tone that's equal distance between the tonic and the dominant. This specific tone (and not the tonic any longer) is the point from which the inversions are created up or down, retaining all of the principles shown above. The entire subdominant group becomes displaced, so to speak. And:
- we get a whole new group of (mirrored) chord substitutions, while all of the leading tones and tensions of the given key are preserved
- the dissonances from layering of these polar chords are very striking (Bartok concerto for orchestra is a great example)
- we can reharmonize existing material differently and we can also deliberately modulate between the two groups in the same period or sentence and get even more color

I'm not a big fan of negative harmony but I do think it's an interesting inversion technique for enriching harmonic color and specifically progressions and chord layering. It sounds a little jazzy, often unusual and sometimes fresh. That's all it is, imho.
Click to expand...
His own argument is based on other things, like natural scale and harmonic series. I ask how these concepts fundament his hypothesis of inversion of harmonic series. Your text is good as such, but I guess it goes out from the subject of the question.

You speak about F Minor chord, but , except the A minor, Riemann considers just major chords and main functions in the stage of fundamentation of his theory. II. There are only three kinds of tonal functions {significance within tfie key), namely, tonic, dominant, and subdominant. In the change of these functions lies the essence etc.. The F Minor comes later, meaning the minor variant of the subdominant after the (for me) doubtful basis of inverted sub-harmonic series is set on stone.

IN this sense, what you say looks to be the "neo" thing, but not his thing. In his world a minor dominant is questionable, and a F minor does not correspond to the generative idea of the SUBdominant: the chord built from the inverted interval structure starting from the fifth of the tonic triad.

Another thing: it looks that you confuse the theory of tonality with its techniques. Negative harmony means a technique at the end of your text, but when you started it meant a theory. Things like this create the confusion and the "glamour" of this magic word " negative harmony" i was talking about.

Same happens when people speak about polytonality, i guess they want the audience to believe they are talking about another planet with different laws... I find you reply very informative, but my question is really about the axiomatic behind the "birth" of thinking things dualistically and especially like this: inverting things downwards hypothetically.

Schenker did also a big IF , if i remember well. A common error in theories is to never confirm the hypothesis, or justify it by valid arguments ; people start talking about this hypothesis for years, developing it, and suddenly they think it is a real big deal.

In this sense, the theorist who are more driven by practical side, and focus on the "how to" do not fly so far away from actual music. But let´s see, personally i find the main insight and. concepts of Riemann useful in the modern reception (of Diether de la Motte and T. Kuhn precisely), and it helped me as composer and teacher ; just philosophically i put him on interrogations (yet). Regarding the axis theory of or any other theory after this, i prefer to stop here ; ) I brought H. Riemann as a good theorist of modulation and the tonal relationships as we hear in the music used to learn the basics of music.

*The thing about horizontal representation is very good and very important; the function theory is yes more "3d"
"Negative harmony" is a very unfortunate and misleading term, but it's central idea - the mirror inversion up or down, is very reasonable. If you build a C major chord and then repeat the same exact intervals in the opposite direction from the tonic, you will indeed get an F minor chord. All of the major chords will become minor chords, the diminished chords will remain diminished. All authentic tensions will become plagal. All this is part of "negative harmony" but is more simply and elegantly explained by the Russians in the model shown above, and used by composers since well before 1895.
Click to expand...
 
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Use the upward sequence to go out from tonic, and the downwards to confirm the tonic or to go to a the dominant pedal point of a minor key, like here .

The easiest is to frame any major chord as dominant or subdominant, and any minor as subdominant

Of course you can split this knowledge into 10902 youtube videos... "how to modulate from C to C#..." viva!


I never made thoughts about this . Since modulation means a cadence elsewhere or a transit into another region from tonic. I cared about finishing and opening sections of music better.


I find interesting how many people do not care much about mastering this before modulation, since most problems come in these moments...
 
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