Take a stand against EU bullies and our government cheerleaders – Lynn Boylan MEP

Sinn Féin MEP Lynn Boylan has taken a swipe at the EU and the Irish government’s ongoing reactions to the crisis in Greece.

Speaking in Dublin prior to Saturday’s protest in support of Greece, the Dublin MEP said:

“Every mainstream economist and even the IMF has quite clearly stated that Greek debt is unsustainable. And yet we have Enda Kenny, Joan Burton et al rigidly following the pro-austerity line pushed by their European masters in Brussels.

“While our government is clearly locked in that familiar position of kowtowing to Brussels, it is clear to those outside the bubble of establishment politics in Ireland that the bitterness Europe’s elite have towards Syriza stems from the Greek government being a dissenting voice to the EU’s failed austerity agenda while standing up for its people.

“Never has that fact been more clearly demonstrated than in the recent comments made by the President of the European Parliament Martin Schulz who said that negotiations with Greece should continue but only with an appointed technocratic government should the Greek people vote Yes in Sunday’s referendum.

“This is an example of the President of the European Parliament interfering in the internal politics of a member state. Europe’s dislike of Tsipras and Syriza has no boundaries.

“I am asking the Irish people to demonstrate support for the Greek people tomorrow. Please join us at 12 noon at the Central Bank and let Kenny & Co know that the Irish people will not stand idly by and watch Europe’s puppeteers quietly pull the strings of a political coup in a fellow member state.”

Source: Sinn Féin Newsroom

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Irish government must accept that Greek debt is unsustainable – Matt Carthy MEP

Sinn Féin MEP for the Midlands North West and member of the European Economic and Monetary Affairs Committee, Matt Carthy has today stated that the Irish Government should support calls for debt relief for Greece.  He said that almost every independent economist in the world has acknowledged the need for such relief and even the International Monetary Fund has acknowledged that Greek Debt is unsustainable.

Carthy said:

“The Irish government has invested more effort in blocking the Greek people from securing a debt deal that they did in fighting for one for Ireland.

“Refusing to consider any form of debt relief and steadfastly insisting on the imposition of even more Austerity on the Greek people has exacerbated the economic turmoil that has captured Greece.  The simple fact of the matter is that Greece requires debt relief and an end to Austerity if it is to have any hope of recovering from the current financial crisis.

“Even the IMF has recognised this fact, describing Greece’s debt level as “unsustainable” and calling for a significant grace period on debt repayments in order to allow the Greek economy to recover as well as large scale debt relief.  It is madness that the Irish government is not supporting this position.

“Of course, the irony is that any such deal for Greece would likely lead to an improved negotiating position for Ireland.  In the past when Greece has received improved terms Ireland has benefited and indeed Fine Gael and Labour sought to claim credit.  Unfortunately the Irish government position has been to act as cheerleader for the German government in the hope that a failure by the Syriza government to get a sustainable deal can in turn be used as a political stick to hit Sinn Féin with in Ireland.

“This has been about the politics of punishment – the Irish and EU leaders are making the Greek people suffer because they had the audacity to elect a government that sought an alternative to a crippling austerity agenda.  They are now turning the screws – refusing to even negotiate the latest proposal by the Greek government.  Ahead of Sunday’s referendum in Greece they have yet to state whether they will accept the outcome, whatever it is, in contrast to the Greek government who have bound themselves to the democratic will of their people.

“The Irish Government is on the wrong side of history and I am urging them to stand in solidarity with Greece and support their calls for debt write down as the only real solution to this crisis.”

Source: Sinn Féin Newsroom

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Sinn Féin to show solidarity with people of Greece in Athens

Sinn Féin MEP Martina Anderson will travel to Athens tomorrow to stand in solidarity with the Greek people in their battle against austerity.

Ms Anderson said;

“As a proud Irish republican and dedicated internationalist, I will be in Athens on Sunday with my party colleague Pearse Doherty to stand in solidarity with the people of Greece.

“The Greek people have an opportunity to send a clear message to the right wing elites of Europe that austerity is wrong and will not be tolerated.

“This referendum is democracy in action and stands in contrast to the anti-democratic actions of the ECB, IMF, and the European Commission in attempting to force further austerity on Greece.

“I wish the Greek people well in the referendum and encourage them to stand firm in the face of the relentless austerity regime imposed on them.

“Sinn Féin will continue to stand shoulder to shoulder with Syriza and the people of Greece in opposing austerity.”

Source: Sinn Féin Newsroom

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AP Shames Merkel on Greece; LaRouche Urges Story Be Spread

EIR Founding Editor Lyndon LaRouche, whose July 1 statement, “The Trans-Atlantic Financial System Is Bankrupt, Not Greece,” has circulated and been echoed widely from www.LaRouchePAC.com, today urged the widest circulation of an Associate Press article which recommends an emergency debt conference for Greece.

The article’s headline is “Germany resists debt relief for Greece, but benefited from such a plan after WWII,” referring to the 1953 London Debt Conference which arranged the writeoff of half of all German debt going back to the post-World War I period, and helped unleash the “German Economic Miracle” of the 1950s through 1970s.

Among others locations, the AP report appeared at USNews on July 2, just as the IMF reluctantly made public its [leaked] staff report which acknowledged that at least 50-60 billion euros of Greece’s unpayable debt has to be relieved. That would be only 20% of Greece’s current debt, but Germany received relief from nearly half of its debt in 1953, when Greece was one of its creditors.

The key section of the AP article reads:

“The 1953 agreement, in which Greece and about 20 other countries effectively wrote off a large chunk of Germany’s loans and restructured the rest, is a landmark case that shows how effective debt relief can be. It helped spark what became known as the German economic miracle….”So it’s perhaps ironic that Germany is now among the countries resisting Greece’s requests to have part of its debts written off.

“Greek Finance Minister Yanis Varoufakis claims debt relief is the key issue that held up a deal with creditors last week and says he’d rather cut off his arm than sign a deal that does not tackle the country’s borrowings.

“In a closely-watched report on Thursday, the International Monetary Fund backed the call to make Greece’s debt manageable.”

LaRouche was to discuss the situation of the euro system’s breakdown crisis with hundreds of activists around the United States Thursday night. He repeatedly emphasizes that the trans-Atlantic financial system cannot avoid collapse without imposing a “global Glass-Steagall” reorganization on the Wall Street and London-centered megabanks, and writing off their worthless debt “assets.” The bailouts of Greece were swindles which bailed out only these banks, he showed in analysis in late February, and the so-called “Greek debt” both unpayable and illegitimate.

Almost uniquely, LaRouche sees how this collapse leads to London using its puppet Barack Obama to provoke war with Russia and China. His conclusion to that February statement on the “Greek debt” swindle is worth quoting:

“Looting does not constitute legitimate debt. The debt is illegal, it is unpayable, and it is the fruit of a London-led criminal enterprise that must be shut down altogether, if the world is to survive the coming months without an eruption of general war in the center of Europe. This [issue] has to be put loud and clear on every doorstep in the United States. If you want to avoid World War III, that’s what you’ll do.”
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LaRouche: Regime-Change Assault on Greece Will Backfire; It’s the Trans-Atlantic System that is Set To Explode


The Troika and allied European heads of state have all fallen in line behind a suicidal scheme to use the upcoming Sunday referendum in Greece to overthrow the Tsipras government. This is the significance of the across-the-board refusal to take up the Greek government’s letter to the Troika on Tuesday night, proposing a major debt write-down, and modified economic reforms, based on the weekend proposal by the European Union. Schaeuble, Merkel, Renzi, and Hollande all rejected the Greek proposal out of hand, and following a conference call among EMU finance ministers, it was formally announced that there would be no discussions with Greece prior to the Sunday referendum.  The financial media, led by the Financial Times, put out a string of fraudulent stories, all aimed against Greek Prime Minister Tsipras, including wild claims that Greek voters were turning against the government.  The kind of regime change that was most recently employed in Ukraine, featuring military-style black propaganda, is now being unleashed inside the EU against Greece.

Lyndon LaRouche commented on Wednesday that this swindle is going to backfire against the relevant parties leading this attack on Greece.

“The relevant parties are setting themselves up…The euro was a swindle from the very beginning with the Maastricht Treaty.  It was a scheme by Mitterrand, Thatcher, and George H.W. Bush that was doomed from the outset, but was aimed against Germany, and against any prospect of a German-Russian economic partnership in the immediate post-Cold War period.”

LaRouche reiterated that the entire Greek so-called Troika debt is fraudulent.  Greece was raped and is now being pressured to pay off the rapists.  This cannot be tolerated, LaRouche declared.

Instead of bringing down the Tsipras government, these actions are more likely to trigger the collapse of the entire trans-Atlantic financial system, including the entire Wall Street bubble, now officially assessed at $26.5 trillion in bailout obligations alone.

The only real solution is for there to be an immediate international conference, modeled on the 1953 London Debt Conference, to wipe out the fraudulent Greek debt and all of the gambling debt built up in the London/Wall Street system.  In the United States, this means the immediate reinstatement of Glass- Steagall, just as it was originally enacted in June 1933.  The Glass-Steagall model must be immediately adopted in Europe and globally.

The biggest danger, LaRouche warned, is that the London/Wall Street forces, led by the British Monarchy, will react to the backfire of the Greek showdown by going for war—against Russia and perhaps against China.  The elements of just such a war provocation are all in place, with the NATO deployments right up against the Russian borders in the Baltic and Balkan regions. Russia’s official representative to NATO, Alexander Grushko, delivered a pointed warning in a teleconference with journalists in Brussels on Wednesday, in which he declared that NATO had launched a containment campaign against Russia, prior to the launching of the US-NATO regime change operation in Ukraine.  He cited plans to establish NATO forward command posts in the three Baltic states, Romania, Bulgaria, and Poland, and warned that if NATO goes ahead with missile defense deployments following a P5+1 deal with Iran, it will be further evidence of the targeting of Russia.

The reality is that the entire trans-Atlantic system may not survive the week, as the result of the insane and desperate actions launched against Greece, and the imminent backfire.


Tsipras: Referendum Not about if Greece Stays or Leaves Euro

After a day of unbelievable psychological warfare and threats, Greek Prime Minister Alexis Tsipras made another public television address to the nation urging a “No” vote in the Sunday, July 5th referendum. He denounced the British Empire-run campaign of lies and blackmail.

Regarding the government’s decision to close the banks, he blamed “extreme circles” who “blackmail ordinary citizens” by refusing to extend liquidity to the Greek banks, reported Athens-Macedonia News Agency. He said:

“I have full knowledge of your difficulties, and I pledge personally to do everything I can to make them temporary…. The sirens of disaster are blackmailing you and asking you to say ‘Yes’ to everything…I never expected a democratic Europe not to give space and time [to hold the referendum]. It is a disgrace that we have these scenes of shame, because they closed the banks precisely because we wanted to give the people the vote.”

He called for Greeks to vote “No,” as representing the people’s clear choice of how they want to live on the day after, and for return to values in Europe, as well as strong pressure for a sustainable and fairer agreement. He said the referendum on July 5 does not constitute a coup, but that it’s the “appointed governments” who led to such an event. “I call on you to say no to memorandum formulas that are destroying Europe,” he said, adding that a “no” vote was an obligation to history. He also promised that wages, pensions, and the savings of those that had elected not to transfer their money abroad will not be lost.

Meanwhile, Productive Reconstruction, Environment and Energy Minister Panagiotis Lafazanis told Russia 24 TV network that Greece has a backup plan if the EU cuts off funding.  Lafazanis said: “The situation is very difficult but we shouldn’t allow [creditors] the opportunity to exploit us…The lack of funding from the European Union is not the end of the world. There are other sources of funding.”

Lafazanis said that Greece is not collapsing because banks have been closed. He said:

“Yes, banks are closed, but you can see that in Athens and other cities life goes on as usual…Yes, we shut down banks, but not on a whim. In the last few years, Europe has been using the wrong policy toward Greece. Now they don’t want to continue the Emergency Liquidity Assistance. We were forced to defend our people, people who have savings in the banks, so that our country can progress in the future…”the blackmailing techniques the European institutions are using have a specific purpose. They want our government to take measures that will bring us to our knees….

The banks may be closed, but we don’t have fuel or food shortages.”

Lafazanis said it was too early to reveal the details of Athens’ Plan B, because the government is still holding out the option of coming to an agreement with its European “partners.”

Predator ‘Institutions’ Knew Their Offer to Greece Was Made To Fail

The German newspaper Suddeutsche Zeitung obtained documents leaked by Bundestag deputies, which were an analysis by the IMF of the European creditors’ “last offer” to Greece on June 26. Intended to explain the offer to legislators who could have to vote on it, the analysis actually showed that the “really very generous” [per Angela Merkel] ultimatum plan, could never have gotten Greece below a debt/GDP ratio of 125%, with continuously deepening austerity sapping its economy and people. The analysis was published in full in the London Guardian July 1.

Of course, the creditors’ loyal staffs tried to blame their analysis of the plan’s guaranteed failure, on the Syriza government in Greece. “It is clear that the policy slippages and uncertainties of the last months have made the achievement of the 2012 targets [for debt/GDP ratios—ed.] impossible under any scenario,” they recited dutifully.

But even making the most optimistic, discredited, actually absurd assumptions about the deeper tax, wage, and pension austerity leading to rapid growth in the rest of this decade, the plan would not “work.” “Under all the scenarios looked at by the Troika,” wrote the Guardian, which all assume a third bailout program, Greece has no chance of meeting the target of reducing its debt” which was set in 2012. Its “unsustainable” level of debt would continue at least until 2030.

The reason this failure was planned — and why the IMF et al. thought the Bundestag would vote for it nonetheless — was in order to allow Greece no debt write-down. As the Guardian notes in its lead, “The documents … support Greece’s argument that it needs substantial debt relief for a lasting economic recovery.” Anything, including asking European parliaments to vote for a debt-payment plan self-described as unworkable, was preferable, for the Troika, to allowing Greece the kind of debt write-down given to Germany in 1953.

What was the really very generous plan? Greece was to achieve a primary budget surplus of 1% of GDP this year, rapidly rising to 3.5% of GDP (7 billion euros) by 2018; it was to raise VAT taxes by 2 billion euros immediately; cut annual pension payments by 2 billion euros immediately and cap them permanently; rescind the temporary increase in minimum wages; sell off state-owned islands, ports, etc. to raise 15 billion euros by 2016; etc.

Greek Prime Minister Tsipras effectively threw the vote on this made-to-fail plan from the Bundestag to the Greek population by referendum.

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Fireside Chat with Lyndon LaRouche, July 2, 2015

Join us this Thursday at 9PM Eastern for our Fireside Chat series featuring a live Q&A session with Lyndon LaRouche!

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Unheard Melodies: Harmonic Dissymmetry and Musical Inversion

by Megan BeetsMusic is not sound. Though it appears to us dressed in the attire of audible tones, music as such is not a consequence of those tones.1 In fact, many a tone has been sounded under the banner of “music” or “art” which in fact has nothing to do with it! Music which is rightly called such, as in the Classical tradition of Bach through Brahms, has characteristics drawn not from sound, but from the creative function belonging to the human mind, and stands above any particular sense domain.

While music per se is not dictated by the laws of sound, the lawfulness of Classical musical composition does have a relationship, as does a substance to its shadow, to the shape and ordered structure of the medium of musical composition, the interconnected system of major and minor keys. The discovery and development of the structure of the musical language2 has always originated from the insight of composers and performers into the creative mind of man. This insight drove breakthroughs in the use of the musical language, rather than any derivation from the “mathematics” of combining notes and intervals. The notes on the page, and the sounds that they correspond to, are merely stand-ins which demand the presence of a living idea on the stage of the imagination.

Here we will explore, in an introductory way, the relationship between the structure of the musical system and the soundless realm of ideas underlying it.

Harmonic Structure

The structure of the harmonic system, the medium of music, is inherently a paradoxical one. Though the system of major and minor keys is physically (and not arbitrarily) derived by lawful methods of construction,3 within it are discrepancies in tuning and ambiguities about exact note values which cannot be resolved except from the higher domain of musical composition and performance—the soundless domain of the creative action of the mind, rather than in anything derivable from sound and harmonics.4 The fact that there are hundreds of “answers” to the tempering problem5 is an indication of this.

Here we will focus on one of the ironical features of the musical system, its inherent dissymmetry,6 and related to that, the principle of inversion, to see how a physical system such as musical harmonics looks to a higher, noetic cause for its meaning; a cause to which it makes itself susceptible as a medium of expression.

In order for the dissymmetry of the musical system to become apparent, first look at its symmetry. Take, for starters, the harmonic (or consonant) intervals which come from the division of the string.

Here are the divisions of the string, by whole number fractions up to ½ (or the octave) which produce notes consonant with the sound of the whole string. These are tones of the major and minor musical scales.

Each harmonic division, shown here as whole number ratios of the whole string, does not merely correspond to a number or a geometric division; it is, more importantly, a unique, physically-derived point of singularity and resonance within the whole of the vibrating string.7 Therefore, the notes of the musical scale are not arbitrary, but are a manifestation of an ordered resonance and structure within the physical world.

Now, having seen the set of harmonic divisions of the octave (those notes which form a harmonic interval with the whole string), take a look at how these divisions relate to one another: examine the intervals between them.8

The proportions between the harmonic divisions indicate the intervals between the harmonic intervals.

While in their construction, the harmonic divisions are derived one by one,9 you can see that taken together as a set they create a symmetrical division of the whole space of the octave (half the string), with the first and last intervals being identical, the second and second to last, etc.10

However, this sequence of intervals is not complete. When the harmonic divisions (containing both the major and minor 3rds and 6ths) are separated into the major scale and the minor scale, and the (dissonant) notes of the 2nd and 7th are added to complete the scales, the perfect symmetry is lost, and a simple dissymmetry emerges.11

Here are the harmonic divisions, plus the (dissonant) divisions of the 2nd and 7th, separated into the major and minor scales The corresponding musical notes are indicated below.

These two dissymmetrical scales are the most basic structure of the harmonic system of the octave, which the more complex, interconnected system of 24 major and minor keys is built upon. However, even these are merely shadows of something which can not be explained by the system’s structure. To get an insight into the “why”—why the musical system is constructed in this dissymmetrical way, and not otherwise—we must go to the substance, that which is prior, of which the sounds are a mere shadow: the living domain of music.

Musical Inversion

Let’s now put the system of harmonics, which we’ve so far considered only as a non-living system, into motion.

In a good musical performance (of a great—or at least adequate—composition) the notes are not chosen beforehand—a fact which will probably surprise most readers, considering that the score of a musical piece by Bach or Beethoven, for example, was written down centuries before. The music must come and the notes must be sounded anew, as if an improvisation, within the unfolding creative process of the performer. The notes, therefore, clothe and make perceptible something antecedent, which can only be found “between” the audible tones, so to speak: ironies which provoke the mind of performer and listener alike to an insight into the actual, unspoken and unutterable meaning of the piece. These types of unuttered thoughts, expressed outwardly and veiled in language, are what the poet Percy Bysshe Shelley referred to as “the interpretation of a diviner nature through our own.”

One of the ironies which appears often in Classical musical composition, not as a formal device, but rather a natural consequence of such artistic efforts, is the action of inversion. In music, as in poetry and other meaningful modes of communication, a statement and its inversion are not equivalent. This non-equivalence is built into the potential of the musical system itself, and more importantly allows the composer to create an experience for the listener which is neither the musical “statement” itself, nor its inversion, but something in between: the unhearable simultaneity of the two.

To begin, examine inversion first as it is built into the structure of the harmonic system.

Take the dissymmetry which appears when we invert the major scale. Below is the major scale, with the intervals between each note indicated by a W, whole step, or H, half step.

The intervals of the ascending major scale are: W W H W W W H. What happens if we take the same intervals, in the same order, beginning from the same note (in this case, C), but invert the direction to create a descending scale?

Inverting the major scale thus, we get the notes of a minor scale, built on the the fourth note of the original key (in this case F). The minor and major are not actually separate, but are inversions of one another. This is seen (among countless other places) in Bach’s Musical Offering.12

In this example, A is the puzzle posed by Bach, and B is its solution. In the puzzle, Bach indicates for two voices to play the lower line, entering in canon (one coming in later than the other, at the segno). However, he writes two clefs, one upside down and displaced.

The puzzle is solved as shown in B, with the second voice reading the music upside down, and so the descending C minor scale of the first voice is transformed an ascending G major scale in the second. (This is the same relationship between major and minor keys as the example above, where the C major scale inverted to F minor. The note F is the 4th above C, just as C is the 4th above G.) Set in canon, it is as if one voice is having a discussion with its reflection. The voice and the reflection play back and forth contrapuntally (i.e. in their rhythmic and melodic interactions) as two characters engaged in conversation, and come together harmonically in a beautiful duet, with something said by the two that couldn’t have been said by either individually. Bach’s joining of the major and minor together, in harmony and by inversion, shows in practice that they are not actually separate modes.

Take another, related example of inversion, which hints at the major/minor relationship—the division of the fifth. The interval of a fifth (the relationship between the whole string and ⅔ of it) can be divided harmonically13 in only one way: into the two thirds, major and minor. Said differently, a major third plus a minor third equals a fifth. Moving from one note via the major third, followed by the minor (to reach a fifth above) generates a major triad (the skeleton of a major scale),

and inverting that motion, starting from the fifth above and moving back down to the starting note, generates a minor triad.

Once again, the major and minor prove to be inversions of one another, and while the fifth remains the same, the inversion gives the two results very different meanings, musically (i.e. when you hear these two triads, they are quite distinct)! The same space (the fifth) has been traversed with the same intervals, but something completely different was said. The musical system is a space in which A+B ≠ B+A!

Now look at a more general example, where the same action taken in different directions generates something new.

In this example, C is the tonic (or basis) of the scale. Motion upwards in pitch by the interval of a fifth generates G, the fifth note of the C scale. The same action downwards generates a different note, F, which is not the fifth, but the fourth note of the C scale (as counted when moving upwards).

In order to invert the motion, but arrive at the same note of the scale (G) below the tonic, the interval of action must be truncated from a 5th to a 4th.

When we move up by the interval of a 4th, we arrive at F. When we move down by a 4th, we arrive at the G below, the 5th of the scale. Thus, the 4th and the 5th are inversions of one another.

Inherent to the musical system there are complementary pairs, like the 4th and 5th, which together add up to an octave, or said differently, are inversions of one another.

In practice, in the composing and experiencing of great music, these pairs are actually inseparable. One does not exist without, implicitly, its inversion. As we’ll see in a few examples below, composers from Bach through Brahms use the ambiguity of these pairs and their inversions to create a type of transformation and development which cannot be heard by the sensuous ears, but only by the “ears” of the mind.

Begin with Bach

Take the example below from Bach’s The Art of the Fugue.

Here are the first few measures of two fugues from Bach’s The Art of the Fugue, for comparison.

At the top is the opening of Contrapunctus I, with the four-measure opening theme (outlined in blue). The theme rises by a 5th from D to A, then descends, outlining a D-minor triad (D-F-A) and continues down by a half-step to the leading tone C#. It then rises back up to the minor 3rd (F) before finally returning to the tonic, just as the second voice enters. Look at a few things that Bach does to transform and develop that theme which play with the relationship of the 5th and 4th.

The Emerson String Quartet plays Contrapunctus I from Bach’s The Art of the Fugue.

First is the way that the second voice enters in measure 5 (outlined in red). This second voice echoes the opening theme, but rather than beginning on the same note as the first voice, D, it enters a 5th higher, on A. If the second voice rose by a 5th, in exact imitation of the first voice, it would land on the note E and would declare itself as being in a different key entirely (the key of A). Therefore, it rises just a 4th, reaching the D an octave above where the first voice started, and the space of the fugue is defined as the octave D-d, built on the D-minor arpeggio D-F-A-d, with the element of the C# leading tone below. Ironically, if this voice had risen a full 5th (as it does later in the fugue’s development, in measures 29-31), it would sound more distant from the original theme than does this slightly transformed version, because of the modulation in key.

The effect of the second voice rising a 4th rather than a 5th, due to the fact that two fifths cannot fit within the space of an octave, is that the space in which it unfolds the theme is compressed, and the theme is slightly changed by operating within a smaller space. The second interval becomes a 2nd from D to C♮, rather than a full 3rd, as in the first voice. The changed theme of the second voice introduces an element of sameness-and-difference right at the opening of the fugue.

Now look at what Bach does in Contrapunctus III, where his subject is an inversion of the theme. (See image above.)

The Emerson String Quartet plays Contrapunctus III from Bach’s The Art of the Fugue, where an inversion of the original theme becomes Bach’s subject matter.

As we saw with the simple inversion of the major scale, the musical system is naturally ordered and structured such that it is not possible to move in perfect inversion14 and stay in the same key. Here, as with the entrance of the second voice in Contrapunctus I, Bach chooses to keep the theme’s inversion in D-minor, and so the first interval is not the descending 5th, D to G, but is truncated to a descending 4th (making this more like an inversion of the second voice’s entrance in Contrapunctus I).

Comparing this inverted theme to the second voice in Contrapunctus I, where that voice descends a 4th from D to A (measures 5-6), the inversion rises a full 5th, via the minor triad A-C-E. Bach then utilizes the rising half-step within the scale from E to F to mirror the descending D-C# half-step of the original theme. From F, it then descends down to C#, before resolving to D in the first beat of measure 5.

The second voice, entering in measure 5, descends a 5th, and outlines the D-minor triad D-F-A, followed by the half-step up to B♭, a near-exact inversion of the first voice in Contrapunctus I.

There are a few things which can be pointed out here about the ambiguities which Bach makes use of in the opening measures of the Contrapunctus III inversion. First is the already stated one, that upon inverting the theme, Bach alters the first interval from a 5th to a 4th, thus staying in the key of D-minor, rather than a perfect inversion which would change the key to G-major.

On the bottom is a “perfect inversion” of the original D minor theme. The intervals between the notes are identical, only inverted in direction, and so the D minor theme becomes a G major inversion.

However, already by measure 4, the minor has been inverted to the major, further erasing the distinction of major and minor.

Adding to this ambiguity, after introducing the inverted theme in Contrapunctus III, the first voice goes into a completely “keyless” chromatic passage, played against the second voice’s inverted theme.

Note that the use of inversion in Classical composition is not a formulaic thing! Bach does not simply invert what is already there; he is constantly transforming and developing the theme beyond what would be given by a simplistic or mechanical inversion. It is not the notes which dictate the music—first there must be creative insight into the implications of a musical idea, and the ironies to be unveiled, which demand the use of inversion as a driver of the musical development.

Beethoven and Brahms

Now look at how Beethoven and Brahms use these complementary pairs, in inversions, in a way which more dense than the previous example.

While there is only one type of 4th and one 5th within the scale (with little flexibility in tuning15), the 3rds and 6ths are less determined—they can be either major or minor, and have much more variability in tuning.
Here we’ll look at two related examples which are based on the complementary pairs of thirds and sixths, in which the interval and its inversion are not treated separately, but as one unfolding process of development, such that each heard interval implies the unheard presence of its partner.

In Beethoven’s Opus 106, Piano Sonata No. 29 (“Hammerklavier”), there’s a short but gripping passage in the “Adagio sostenuto” movement where Beethoven alternates falling 3rds with rising 6ths, each pair separated by the interval of a third. The surprisingly moving “theme” of the pairs is carried through a series of transformations, driving to a point of dissonance16 from which a new line of development emerges. As the passage unfolds, and the 3rds and 6ths evolve into one another, the inversions are no longer understood as separate entities, but a unified process of change.

The black circles above the notes indicate the intervals between the two notes of the pair. M3=major 3rd, m3=minor 3rd and M6=major 6th.
Daniel Barenboim plays the “Adagio sostenuto” movement of Beethoven’s Op. 106. The relevant passage begins at 24:35 and ends at 25:20.

Underneath the 3rds and 6ths is a sequence of sweeping arpeggiated sixteenth notes of the left hand which, while ordered, cannot be pinned to simple sequence of major or minor keys, further adding to the transcendental quality of this passage.

It is known that Brahms had access to some of Beethoven’s sketchbooks (or at least copies of them) through his friend and Beethoven scholar Gustav Nottebohm, and studied the sections from those sketchbooks where Beethoven worked out the passage of 3rd and 6ths for the “Hammerklavier”.

Brahms opens his 4th Symphony with this exact passage of alternating falling 3rds and rising 6ths, with two (minor) changes: 1) while Beethoven has falling minor 3rds (for the most part) and rising minor 6ths, Brahms uses the “exact” complementary pair of falling major 3rds and rising minor 6ths; 2) after the first two pairs, Brahms quickly transforms the theme into pairs of a descending octave, and a rising major 3rd.

The black circles indicate the intervals between the notes of each pair. M3=major 3rd, M6=major 6th, and 8va=octave.
Wilhelm Furtwängler conducts the Berlin Philharmonic Orchestra in this live 1949 recording of Brahms’ 4th Symphony.

Finally, take Brahms’s incredible “Vier Ernste Gesänge” (“Four Serious Songs”). Brahms composed this set of songs at the very end of his life, after his lifelong friend and dearest collaborator Clara Schumann suffered a stroke. She would die a few weeks after the composition’s completion, as would Brahms himself just a year later. The third song is set to the following text taken from Ecclesiastes (Sirach):

Ecclesiastes (Sirach), 41:1-2

O Tod, wie bitter bist du,
Wenn an dich gedenket ein Mensch,
Der gute Tage und genug hat
Und ohne Sorge lebet;
Und dem es wohl geht in allen Dingen
Und noch wohl essen mag!
O Tod, wie bitter bist du.

O Tod, wie wohl tust du
dem Dürftigen,
Der da schwach und alt ist,
Der in allen Sorgen steckt,
Und nichts Bessers zu hoffen, Noch zu erwarten hat!
O Tod, wie wohl tust du!

O, death, how bitter you are,
in the thoughts of a man
who has good days, enough
and a sorrow-free life
and who is fortunate in all things,
and still pleased to eat well!
O, death, how bitter you are.

O death, how well you serve
him who is in need
Who is feeble and old,
and is beset by all sorrows,
and has nothing better to hope for or to expect;
O death, how well you serve.

The great baritone Dietrich Fischer-Dieskau sings “O Tod” in a 1949 performance.

In the song, the singer directly address death, first in its effect on the man who “has good days…and a sorrow-free life,” and secondly, in the relief brought to one who is “beset by all sorrows.” Both sections begin with: “O Tod,…” (“O, death,…”). With the first, Brahms uses two descending 3rds as the piano moves from E-minor down to A-minor.

He reverses that motion with a rising minor 3rd on “wie bitter…”, as the vocal line shifts to the high register of the singer’s voice.

When the speaker (singer) shifts, to address the contrary quality of death, Brahms inverts the “O, Tod…” from a descending 3rd to its companion, a rising 6th, against the piano’s E major.

At the singer’s final line, Brahms again sets “O, Tod,” to a rising 6th, not once, but twice, moving in just a few moments from the very low register of the singer’s voice to the highest on the “wie” of “wie wohl.” He then reverses the motion with a beautiful falling sixth on “wie wohl…”, before finally coming to rest in E-Major.

Music, which deserves the name, is not composed note by note, each tone caused by the one which came before, or selected because of how it sounds when heard against its neighbors. The mind hears and creates both in and across space and time, with the entirety of the composition implied in the unfolding of every moment. The singer of Brahms’ “Vier Ernste Gesänge” hears in the mind, in the moment of silence before he or she begins, the simultaneity of both statements of “O Tod,” each full of the potential of the other. In this way, the intervals which appear to us as inversions of one another are unfolded as an interconnected manifestation of a single idea.

Pipe to the Spirit Ditties of No Tone


Hopefully these few offerings have given the reader a glimpse into the soundless domain of ideas which lies behind and beyond the audible tones of the music, per se. The use of inversion in Classical composition provides an example of that soundless domain, in which the mind can hear not only what is there, the interval or statement, but also what is not there, its inversion, as an integrated one—a one which the ears will never hear. As with the major and minor, the two, which seem separate from the standpoint of the notes, are resolved into a unity, subsumed by a single generating concept which only exists in the closing silence following the final, audible tone.

Any competent composition or performance of music must originate from its proper place: the soundless realm of the imagination, of which the ears receive but a passing shadow.

Afterword: The Lydian Interval

Everything that’s been discussed so far on inversion and the dissymmetry of the harmonic system is only part of the story. We have examined sets of intervals which are inversions of one another, and together add up to the octave—the 4th and 5th, 3rd and 6th (major and minor), and the second and seventh. All of these intervals create a dissymmetrical division of the octave. Said otherwise, there is no interval or note within the scale which cuts the octave perfectly in half!

However, such an interval does exist, though it makes a jarring dissonance with the tonic—the so-called Lydian interval. There are six possible Lydian pairs in the system of 24 major and minor keys, and each is its own inversion.

Here is one way of writing the six Lydians pairs.

In Part II, we’ll explore the transcendental characteristics of the Lydian interval, both in the construction of the harmonic system, and more importantly in its use in musical composition. Bach’s revolutionary use of the Lydian set loose an incredible wealth of potential for precise poetic expression within the musical language which was carried forward by composers such as Mozart, Beethoven, and Brahms.


1. For more on tempering, see: http://science.larouchepac.com/kepler/harmony/book3/11

2. For a demonstration of the physical points of resonance of a vibrating string, see: http://science.larouchepac.com/kepler/harmony/book3/3

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