Geirr Tveitt's tonality theory (1937)

Geirr Tveitt's tonality theory (1937)

John Bjarne Grover

Geirr Tveitt (1908-81) from western Norway studied piano and composition in Leipzig, Paris and Vienna and had some career on the european continent. Here is a sample of his work - 'Welcome with honour' from the suite '100 folk tunes from Hardanger'. His 1939 book 'Tonalitätstheorie des parallelen Leittonsystems' seems (as far as I can determine) to tell that there are four basic scales going in parallel - principly like going from C to C on only white keys on the temperate piano (his own example has two sharps), from D to D, from E to E and from F to F - but he uses many examples from the work of Eivind Groven and I dont know how temperately-minded his discussion is. The four scales create an advanced tonality (quite different from the major-minor of recent centuries) which he explores and proves the systematic reality of in his book.

If the theory is something worth, and to me it looks serious and creative and I would guess it is a doctorate level work, it was anyhow not accepted for the doctorate in Norway (as his widow wrote in a 1987 letter to me - they could not find opponents, as seems to have been the story - they found one in Sweden but not enough for a doctorate) - and they put fire to his home and life work instead. (What caused the fire I dont know but one has the impression that it was arson that consumed most of his work). His book is listed for some libraries in the World Catalogue but it seems that it is not found in any norwegian library.

Could be the plan is or was to abuse this work of his on basis of the formula 'Geirr Tveitt' = 'Hughes/Kennedy Ted'. The fire was in 1970. Gro Harlem Brundtland entered the norwegian political scene when she became minister of environment in I think 1974 or thereabout - later hailed as 'the first female prime minister'.

A chapter in his book is 'Das Wesen der parallelen Leittonauflösung' - if this is read by faulty administative logic it could look like water pipes in the clay ('Ton') walls of the adobe house in Szolnok - according to official registers built in 1970. Things like that? Were the fire in the house of Tveitt an 'intelligence project'? The opposite of water pipes in adobe 'Ton' - for 'parallelen Leittonauflösung'? But that could tell of a damp and lockedup mood of thinking which secret intelligences could be forced to live in when they are not allowed to bring the knowledge to the fresh air.

If there are claims around that my own doctorate dissertation 'A waist of time' is about 'parallel processing', that is not right (except in the sense that studies in the interface to the collective consciousness necessarily are) - but there could perhaps be certain hints to the title of Tveitt's book therein? See discussion of this below. My doctorate was rejected in the summer when Gro Harlem Brundtland became chief of WHO, which is the reason why I make the observation on the fire in Tveitt's home in 1970. (There could have been a 'fire' in my 'home' body in 1959 - related at least to the name of 'Ted' Kennedy?)

It seems to be the sport to insinuate that Tveitt was 'nazi' before the war - he probably was not but of course he could have been to a concert with german music - and is it therefore that they do not want his book in norwegian libraries? Likewise there seems to be ideas around associating his theory with ideas of old norse roots in music - but that is not his thesis. His wife wrote that she - a decade after the doctorate had been rejected in probably 1937 - asked him if he wanted the book republished, to which he answered that some things may have been too 'youthful' and would need to be rewritten and he did not want to spend time on that - she herself in 1987 believed it was the old norse taste of the names of the four scales that was the problem. She included these comments from international musicologists which seem to have understood his work in more positive terms than the norwegians had.

I add the story from Fredrikstad - the famous 'raskolnikovian' axe murder in Valkyriengata/Knipleveien on christmas eve 1969 - two people were murdered with axe in the house next to Erik Ryr (later a fellow student at the high school I attended) - cp. the socalled RIR scale of Tveitt. The story attracted much attention and a man called 'Liland' served a lifetime in prison - he claimed to be innocent. One gets the idea that the bloodshed should represent the 'rejected doctorate'.

The 'Ton-ali-tät' of Tveitt's thesis can be seen to be encoded in the fire in his house as the third Kennedy brother ('Ted'), the 'tät' or 'tete' of the raskolnikovian story as the first Kennedy (John F.) and the 'ali' the second (Robert). This 1-2-3 from 3-2-1 could make for me as the 'Theorie' (cp. also the 3-2-1 attempt on the pope in 1981). 'Tonalitätstheorie' backwards = 'erotic tät in landnåm' = 'hymen'.

I cannot assess the soundness or originality of Tveitt's theory but reproduce some (somewhat arbitrarily chosen) pages from his book in order to present a glimpse of the ideas - enough pages to make his work intelligible. The derivation of 'Familiarpolarität' reproduced briefly from p.109-115 continues with heavy formulaic stuff untill p.122 and much of the book is of this kind. The section 'FUM-Leiter mit SUM-tonalem Einschlag' p.198-204 I have reproduced in its totality - it includes some examples from his own ballet 'Baldurs draumar' ('Baldur's dreams').

I could not find the book in library online form anywhere.

Tveitt Front page
Tveitt Introductory page - the reason for the four scale names rir, fum, sum, tyr
Tveitt Page 20 - Tonalitätsbegriff des parallelen Leittonsystems
Tveitt Page 21
Tveitt Page 22
Tveitt Page 23
Tveitt Page 24
Tveitt Page 25 - Das Wesen der parallelen Leittonauflösung
Tveitt Page 26
Tveitt Page 27
Tveitt Page 28 - Funktionsterminologie
Tveitt Page 29
Tveitt Page 30
Tveitt Page 31
Tveitt Page 32
Tveitt Page 109 - Polarität - Familiarpolarität
Tveitt Page 110
Tveitt Page 111
Tveitt Page 112
Tveitt Page 113
Tveitt Page 114
Tveitt Page 115
Tveitt Page 198 - FUM-Leiter mit SUM-tonalem Einschlag
Tveitt Page 199
Tveitt Page 200
Tveitt Page 201
Tveitt Page 202
Tveitt Page 203
Tveitt Page 204

As to the idea of 'parallelism' in my doctoral dissertation 'A waist of time':

Tveitt's 1937 dissertation was about 'parallel' systems - and there seems to be the idea around that my own dissertation 'A waist of time' from 1997 should be about 'parallel processing'. That is not right. From the introduction to book 3 (out of 5) in my own doctoral dissertation I here quote from my discussion of the theme how to explain the strange similarity of the sculpture exhibition BRUDD (composed of 40 works made by former students of the sculpture class at the academy of arts in Bergen) with the fourth Duino elegy of Rilke - here a quote from vol.3 p.340-341:

"The conclusion I reach is that the correlations between the exhibition and the elegy must stem from some shared processing in the social space - in what I call the collective consciousness with a collective narrative. More specifically, I take it that the elegy has come to serve as the collective narrative for the project of the exhibition, and that this must be traced to the function of this elegy of representing an arbitrary sentential level sign referring to distributed objects in the social space rather than to some syntactically conjoined heap of referents and the words referring to them becoming meaningful through the syntactic composition of these parts in individual cognition. It is this new enlarged arbitrary sign (on the sentence level, when the sentence is of any finite length) which the book really is about.

Since the correlations are explained in terms of this arbitrary sentential sign, I should give the rationale for postulating such a level of signification in more detail. The concept of a distributed and parallel processing in the social space is essential for understanding this arbitrariness. Consider the following case: Two computational processes are running on two different computers (interconnected via a net or not), and both of them require participation from the user to carry out the computations. The users are prompted at intervals for a decision, and the choice which the users make is part of the computation. Given that humans have access to a collective consciousness, and that this is or may be consulted in situations of choice, we will find that these two parallel computations are consulting the collective consciousness when the users are prompted for input by choice. The basis for assuming such a computational device as the collective consciousness is discussed in the chapter which contains my lecture in the theory of science, and in the continuation in the chapter afterwards. Assume that the response which the user gives to the computation is dependent on the state of the collective consciousness, such that the total social state will influence the decision which the individual is making - this is a trivial implication from the assumption of such a collective consciousness, and that the total state will also depend on the individual choices. The parallel distributed processes which are running on these two computers can now be listed in temporal order for their inputs: We can decide, through the network connection or the recorded time for the input, which input is first and which is second of two temporally contiguous inputs to the two computers. We can also decide on the order of the internal computations in the two computers. The parallel distributed processes are therefore temporally enumerable. But we cannot decide on the temporal order of the individual choices which have been made while consulting the collective consciousness. Assuming that each such choice is dependent on the state of the collective consciousness, and that the state in this collective consciousness changes by each individual choice, it follows that the parallel distributed computation must depend on the order of the choices made by the two individuals. We can, though, not enumerate these choices, since we have no way of deciding when the choice was made and time it against the other choice. This is why the processes are not enumerable. The processing in the collective consciousness is, therefore, in the transfinite domain.

This is why a parallel distributed processing in the social space may essentially transcend the computational power of a Turing machine. In comparison, a parallel distributed processing in a closed system, imitating a neural network, has the same computational capacity as a Turing machine. This is because it does not consult the collective consciousness".

These ideas of 'computation' were mainly presented for giving rationale to my concept of a 'Cantor machine' - they had otherwise a rather marginal role in the dissertation. It seems that the committee (Jens Erland Braarvig, Jens Erik Fenstad, Anders Holmberg) evaluating my dissertation had read this and had opinions on it, perhaps due to their own competence in the field - their 'raskolnikovian' rejection of my 5-volume work starts as follows (translated by me - here from my 1998 book 'The doctorate' with the papers from the rejections):

"Let us with the author take as a point of departure the case where two computational processes are running in parallel on two machines, which well may be interconnected. In what the author calls a closed system - and for him a neural network is a typical example of this - such computations have the same capacity as computations on a Turing machine. But suppose that each of these processes requires interaction from a user in the form that these users, from time to time in the course of the computation, actively must perform some action (e.g., answer a question, choose between various alternatives, etc.) as a part of the computational processing. We can then have a process which transgresses the limitation inherent in absolute Turing-computability.

This is standard theory, and there is much literature on socalled relative Turing-computability. The special suggestion which the author makes is to consider a computation relative to what he calls "the collective consciousness"; see e.g. the description on pages 7 and 8 in Vol.III. The concept of a collective consciousness, as "a level of shared knowledge which individuals communicate with and may consult when they are making choices (Vol.III, page 4)", is of course not an unknown concept, neither in anthropological analyses of the concept of culture, nor - to take an example from philosophy - K.Popper's concept of World 3. But here the concept is given a particular shape. We must distinguish between the author's vision and motivating description of the collective consciousness and his technical construction of the collective consciousness as a definition of the Cantor machine.

Motivating for the author is the collective consciousness, or at least parts of the collective consciousness, as a common 'platonic region', which individuals can communicate with "even if they are in considerable geographical distance from the source of this revelation (Vol.III, page 34)". This motivation stands centrally in the author's interpretation of Kuhn's dissertation [should be 'article'? - JG] "Energy conservation as an example of simultaneous discovery" and in his discussion of the non-evclidean geometry. But one thing is motivation and interpretation, another thing is the author's attempts at definition and technical construction as a basis for a precise theory. Grøver himself emphasizes strongly that formalization is possible and that there exists a "computational device", which he calls a Cantor machine.

In the author's attempts at formalization, Cantor's diagonal argument stands centrally. He connects this with Tarski's analysis of the concept of truth in formalized languages (- see also a commentary in 4.2.2 to the author's assertion on the relationship between Tarski and Gödel). Tarski was led to a hierarchy of languages, where a language on level n+1 expands the language on level n by giving a formalized definition of truth to this level n language. The author then wants to identify what he calls the diagonal language to such a Tarski hierarchy, as a version of "the collective consciousness" for use in a Cantor machine processing; see in particular the pages 52-53 in Vol.III. The assertion that "the achievement of Cantor was, as I see it, that he proved the existence of the collective consciousness, and showed that it could be formally described (Vol.III, page 9)" seems right away entirely unfounded. But one understands the author's intentions when one sees the "collective consciousness" tentatively constructed as a diagonal language.

But even if one understands the author's intentions, the analysis and constructive description are all too imprecise to meet scientific critic".

This 'Cantor machine' in my reasoning is a 'diagonal' in the trivial non-formal down-to-earth sense that the two users A and B of two computers connected in an electronic network can have all interaction with the machine level wellordered - but not their choices and interaction with the collective consciousness - that is why this 'butterfly' of A and B relative to the collective consciousness makes for a 'diagonal language' - but that is intuitive and non-formal in my dissertation - which does not make it 'imprecise'. Of course it could be made quasi formal if the dissertation were in logic or mathematics - but that is not what my dissertation is about. To reject it as 'too imprecise to meet scientific critic' could have been an argument if this were a thesis in the theory of logic but not in my study. (And neither do Tarski or Gödel make for anything important in my work - at best a page or two among the 600). It rather looks as if the committee had 'understood something' when reading the passages I quoted above - and therefore have rejected the dissertation.

Wasn't there enough empty 'jargon' in my work to make it look sufficiently 'impressive'?

The committe's argument is no reason to reject it as a dissertation about 'parallel processing' - it was not a study in logic or mathematics - but I had used the concept of 'Cantor machine' (not old norse!) and explained why.

It seems that Tveitt could have got his dissertation rejected because the four scales he propose needed names and he chose names borrowed from old norse 'Håvamål' - and therefore he was rejected as quasi 'nazi'? Likewise, I needed a name for the level of reasoning I propose in the collective consciousness and called it a 'Cantor machine' - and was it therefore it was rejected - because of lack of precision and formalisms in the logic?

What are the real sources of old norse mythology? It is not a parallelism made around the time of Henry VIII's BREXIT from the catholic church? If old norse is a 'joke' only, made for 'political' reasons, it is high time that the intrigue be brought to daylight.

Stories like these doctorate rejections could contribute to the construction of a very unhealthy paradigm of 'numinous' political 'beasts' in the mythological consciousness of the people - haunting them (from way down into viking mythology) with quasi authorities that could deprive people of their elan vital, a spirituality a la the respiration of the corona virus pandemic that make people lose their life. (That was, by the way, when I got my pension - after 'Leif' had died).

The sad story could be that the committee had 'seen something' when they read my simple account of why I called it a 'Cantor machine' and they felt haunted by this 'beast' arising there from the darkness of old norse unknowingness and claimed that it is a very common and wellknown beast which must be rejected right away before it comes to be something. Could be the dangerous beast later could be tamed and brought up by somebody else, could be the logic. Then it is high time with some self-understanding first.

Nelly Sachs could have waited for me on my way to school in Volda at the stairs to the shop of 'Jarle'. That is no reason to reject my work by the strategic arguments of 'jåle' = 'affectedly picky' - or even PTRSIM PIKy in the perspectives of british fear of ridicule on background of theories that the pope was 'affected' by things but 'picky' in his mediator role? I notice that my high school biology teacher Lauvstad had a certain laughter that perhaps could be associated with 'yar le'. Could be that is why I have fancied that Sachs stayed overnight at Lauvstad.

One sometimes gets this feeling that the better a work is, the more prone it is to be rejected: It could be just this 'fear of something from the dark mythos world'. It could be just this policy which now can have become so far developed in the administration of arts and sciences that 'politics' can drive people across the border of life due to their religious creed by even only minor infections.

It is this political attitude that is a 'dark medieval beast' - not the scientific treatise or work of art that leads to enlightenment and enhanced understanding. If the committee rejected my dissertation because they got the sudden feeling of 'something arising there in the deep darkness of unknowing', then it is the committee that should have been rejected, not the doctorate work.

This could have been Tveitt's fate as well. It is all too tragic that the many hundred works of his went lost in the fire - as if the society feared that enlightenment of some sort could hide therein.

I hope this is not the fate they have planned for my work as well. Norway may have a problem of that kind. Is it the antisemitic 1814 constitution that was constructed from fear of ridicule by Henry's BREXIT? 'Klipr-a connection'? But then it is not right to put fire to Tveitt's work only because they were too impressed by the advanced level in his study of tonality in the doctoral dissertation.

It is too primitive to reject an enlightening study only for leading the wild beasts into the circus ring ('manesje') by some other lion tamer (domesticator) from the arts or research council than the original author: That corresponds to the solution of scare by mythos gods + 'homo' = engineered copy of somebody - a combination which could deprive people of their breath (including their laugh?).

If this structure (from this file) is the background of the norwegian constitutional problems, is there something similar in Austria? Could be the Burgenland border power phenomenon is the comparable phenomenon. I may have solved this in this study. 'Dirty Beast' could be the power that Hitler exported to UK/US via this triadic structure.

If 'Jekyll/Hyde' resembles 'James/Bond', that is not me - even if the Bond character could be seen to have been modelled on my name 'Bjarne John'.

Added on 7 june 2020:

I have little knowledge of musicology but noticed the passage in Tveitt's book on page 114. It is the conclusion in the derivation which calls for attention, as far as my limited understanding can evaluate:

This looks like a major achievement indeed - but Tveitt only points to the fact and does not raise the war-cry. It may be like me pointing to the explanatory force in my blue book - but I take it that the facts say more than boasting can. It may be that Tveitt had reasons for beating his chest with a shout of being the world's best kingkong for the moment, and then perhaps the norwegians would have given him the doctorate with admiration glittering in their eyes. It may be that instead of this, since he did not raise the kingkong warcry, they rejected the attempt to make a doctorate and constructed instead out of it a 'Familiar-Polarität' in the sense of a division-making between the 'families' of the society and a polarising of the relation between them - that is, an ordinary class division jack. The jack construction seems to have been based on the book title of Tveitt and the principle of Polarität in the form of the way of thinking in the 'services' by 'isomorphies' and 'parallel constructions' and used this against 'Kennedy'-me ('ton-ali-tät-s-theorie') - and jacked up the split and distance between the two 'classes' by way of the little word 'des' (in the title) which even has come to invade postwar chinese language (the sign 'de' - from Manser 2004 - which looks like somebody helping themselves with something from a cupboard or chest of drawers - or rather Tveitt himself running into the flames for getting out of the burning house the material in that cupboard where he stored his manuscripts) like a class division spreading a la coronavirus all over the world - mine being burdened down by 16 stories (8 child abuses + the octogon) of 16 Familiar-Polarität type. Instead of harvesting recognition for his work (although the internationals seem to have understood it), it was 'Arnuldo' of the services who harvested the glittering admiration. That could in fact be the political history, ah ja.

It could also be the story of what Tveitt's wife (in her 1987 letter to me) could have meant with 'magistre' (such as the doctorate committee) of modern research administration - if you do not beat your kingkong chest after such an achievement, then we will have to help ouselves with a piece of cake, unthanks. It is kingkong who has the power, they say. Could be it is only the ageold lax morals that lead to class divisions. This again developed into the postwar Kennedy story - reaching its peak with Brundtland as chief of WHO while NATO bombed Kosovo and the 'bell-grade' (of the 'Potenz-formel'?).

In the worst case, the entire Kennedy story - with Vietnam war etc - could derive from this single point on page 114.

But maybe Tveitt's formula is not so much news - I cannot evaluate that. It looks like. (Does it even constitute a proof that his account of the four scales has high explanatory force?)

Were Tveitt such a talent already at age 18-20 (when he was admitted to the conservatory in Leipzig in 1928) that Noam Avram Chomsky was given this name to date the sad story of the 1970 burning family farmhouse in Nordheimsund ('Noe-rheim-sund-sky' - even the Kosovo bombing from the sky could have been for this single formula - and the chinese embassy for that little 'de')? That is probably not likely - that the fire was planned already in 1928 - it is rather that the name of Chomsky could have been used as a part of the background for putting fire to the house - lending reason to the idea that this had been planned down in the 1920's long before he wrote his book - in which case it could have served to hide away the role of the book in the postwar construction with the Kennedys.

In 1966 the Ferrari P.Ward chair of linguistics was established at MIT and Chomsky was appointed for it. 'Ferrari P.Ward' could perhaps mean 'Geirr Tveitt', in which case the fire in Nordheimsund could have been planned 4 years in advance - but that does not mean that it was planned in 1928.

This means that the Kennedys relative to me could have been constructed on basis of Wittgenstein's 'Wörterbuch' (1926) as well as Tveitt's "Tonalitätstheorie' (1937) - and that the fire in Tveitt's house 1970 could have been made in order to hide away this role of Tveitt for Kennedy - by way of the name of 'cognitive-revolution-leader' Noam Avram Chomsky - pretending that he was made for the name of 'Nordheimsund'-sky. This hideaway could even have been fuelled by the Kosovo bombs from the sky on background of Kofi Annan as chief of UN - if one takes it that the name of 'annan' imitates the sound of a small child driving or fantasizing a toy 'ferrari'. And then 'Antonio Guterres' could be a name inspiring the coronavirus to be an apparent reference of 'Mister Grover'. Annan was chief of the UN peacekeeping forces in 1994 when the Rwanda genocide broke out - and UN waited and let it pass, so to speak - which could mean just the name of 'Jens-Erik Fenstad': When I met the man-on-wagon in 2011 (having just completed my 'Caruso', the first part - or second part if vol.3 chapter 9 is included as part 1 - of the red-metre book 'My mention e Anna'), I stood on a sidewalk 'vranda' waiting to let him pass while he slammed into the curbstone and climbed up on it - and I believe that I do remember some poles (a meter high or so) in a series along that curbstone (as if they had been going through the holes along the edge or 'side' of the potato peel filter which is found in the kitchen sink drainhole where the 'lapis philosophorum' is found - the white stone which seems to have the man-on-wagon as a 'quasi-historic transform' on archetype level), and he manouvred himself up between two of these (when the series of poles already had become 'less important', so to speak, or had faded somewhat in the attention, so to speak), but when I went back to inspect the place on a later occasion they were gone - or had never been there on this level of existence. But was it not the other way round - that the poles were in the physics but not the metaphysics? Could be it was - in which case it would have been opposite directionality. (See also this file). Could be they exist on one mystic level of existence of the man-on-wagon but not on the other, and you won't see the fence again if you see it from the other side. '[G]jenser-ikke fens-ta[d]' = 'sees-not-again fence-take' could be a name meaning just this strange phenomenon on the curbstone = 'vranda [geno?]side'. Ah, such mysticism used for political intrigue is spiritualism gone astray.

The Rwanda genocide was in 1994 and I got the university stipend for writing the doctorate thesis in 1995.

'John Fitzgerald Kennedy' rewrites similarly to 'John Sweet-yer-old Kennedy' - like 'sweetheart/süszhártja' = 'HYMEN' if the heart is in the 'old'(?).

It seems that the Kennedy era now can come to an end - rather than being turned into a new powerful air-factor (a la the 'smiting' coronaviruses).

It could be a good thing to accept my dissertation 'A waist of time' for the doctorate degree (PhD).

I add that these observations on a potential quite massive importance of a single formula on p.114 in Tveitt's book are not based on a thorough study of the work - I just happened to notice this page and the political echos there could happen to be.

Added on 8 june 2020:

It is observed that the name of 'Geirr Tveitt' well can be the reason for the political strategy of 'homo marriage'. ('Gay' used to be a word meaning 'happy' - it is probably only in recent decades that it has got the taint of 'homo'). 'Justice for Geirr Tveitt!' could be a slogan of considerable public appeal - not the least in order to get the big construction down. It could be this which certain political interesters have turned into 'justice for homo marriage' = 'legalize homo marriage' (which for certain political interesters even could serve to mean the horrendous program of 'legalize engineered copies of people' - that is, agents who take people's place while the original and authentic person is murdered). More recently the same could perhaps apply to 'justice for George Floyd!' And thereby the public support for my case could be tacitly switched over onto a public support for Geirr Tveitt in the sense of 'homo marriage' - which then could rest upon the role of the fire in his house which could be related systematically to a 'fire' in my body in january 1959 - and the Kennedy power thereby. This is why the stories must be told - people get so nervous when the politicians do not tell the whole truth that they can barely breathe from time to time. John 'Sweetheart' Kennedy - with the heart in the behind? The underpants are perhaps the rescue in these corona times.

A pity indeed if people bite the hook which lets the US democrats harvest the public support to my work - could be even on basis of an old injection of horror chemicals in my young body.

I do not have the resources to squeeze the money out of ÖVP, Kennedy Democrats, England - and that could be the reason why this continues. But somebody else could run that case against them in some court on my behalf - somebody who has knowledge of what this really is.

ÖVP can then perhaps be sentenced to close. Could be US democrats as well? And the english government?

Sources

Braarvig, J.E., Fenstad, J.E. and Holmberg, A: The doctorate committee's evaluation of the dissertation - in Grover, J.: 'The doctorate', Bergen 1998.

Manser, M.H.: Concise english-chinese chinese-english dictionary. (Third edition). The Commercial Press / Oxford University Press 2004.

Tveit, Geirr: Tonalitätstheorie des parallelen Leittonsystems. Gyldendal Norsk Forlag, Oslo 1937.