Six musical tones

«Ut queant laxis
resonare fibris,
mira gestorum
famuli tuorum,
solve polluti
labii reatum,
Sancte Iohannes.»

[«Para que lassas
ressoem as fibras,
mira os gestos aos
fâmulos teus,
solve a poluição dos
lábios reactivos,
São João.»]

[So that loosened
resound the fibers,
look at the gestures of
your famuli,
solve the pollution of
reactive lips,
Saint John.

– Paulus Diaconus (720-799), “Hymnus in Ioannem“, written in Sapphic stanzas.

The first syllable of each hemistich (half line of verse) from Ut queant laxis were used by Guido of Arezzo, in the eleventh century, to name the successive six musical tones. The “si” was added much later, in the 18th century.

The hymn was usually sung on June 24, the Feast of the Nativity of John the Baptist, and was divided into three parts, with:
– “Ut queant laxis” sung at Vespers (18h-21h),
– “Antra deserti teneris sub annis” sung at Matins (0h-3h),
– “O nimis felix, meritique celsi” sung at Lauds (3h-6h).

Guido of Arezzo also used a mnemonic system to teach musical reading, where note names corresponded to parts of the human hand:



The AntiOedipus and An Ndembu Doctor in Practice


«In primitive families, the father, mother, and sister always also function as something other than father, mother, and sister; families are coextensive with the social field. (8)

Deleuze and Guattari present Victor Turner’s case of a shamanistic cure in “An Ndembu Doctor in Practice” (Turner 1964) as an example of a primitive cure that, unlike psychoanalysis, works through a wide range of social investments rather than remaining fixated on a personal story about familial positioning. (9)

When Kamahasanyi, a resident of a small village of the Ndembu tribe in northern Rhodesia studied by Turner in the 1950s, became ill (rapid palpitations of the heart, severe pains in the back, limbs, and chest, and fatigue after short spells of work [Turner 1964, 255]), Ihembi, a “ritual specialist” was called in to rid Kamahasanyi of the ancestral “shades” that his illness indicated were afflicting him. Turner emphasizes Ihembi’s skill in studying the various networks of relationships affecting Kamahasanyi, diagnosing “the incidence and pattern of tensions” (Turner 242) in those relations, and reducing them by presiding over collective rituals in which a general atmosphere maximizing sympathy for the patient is generated through drumming, singing, prayers, and the airing of grievances (259). Some of the tensions in the various networks of relations arose, according to Turner’s description of Ihembi’s diagnosis, from colonial relations between whites and blacks (the chieftainship that entitled the village to certain resources from the British had been abolished, creating various resentments due to resulting shifts in power), power struggles between two branches of the lineage of chieftainship (affected by the colonial situation), relations among the villagers that threatened to divide the village, and Kamahasanyi’s life’s history (which included shirking duties toward his matrilineal kin [Turner 1964, 253]). As Turner explains,

the Ndembu “doctor” sees his task less as curing an individual patient than as remedying the ills of a corporate group. . . . The patient will not get better until all the tensions and aggressions in the group’s interrelations have been brought to light and exposed to ritual treatment. . . . The doctor’s task is to tap the various streams of affect associated with these conflicts and with the social and interpersonal disputes in which they are manifested—and to channel them in a socially positive direction. (262)

Deleuze and Guattari point out that Ihembi’s analysis is never oedipal, but rather directly plugs into social organization and disorganization. Through the intense affect created in hours of drumming, the patient’s rhythmic shuddering as the afflicting shades are exorcised, rituals various participants are asked to perform, and induced confessions testifying to hidden resentments, social synergy is revitalized. Ihembi creates “a veritable group analysis centering on the sick individual” that discovers

the preconscious investments of a social field by interests, but — more profoundly — its unconscious investments by desire, such as they pass by way of the sick person’s marriages, his position in the village, and all the positions of a chief lived in intensity within the group. (AO 168)

It is never a question for Ihembi of determining Kamahasanyi’s desires and position in an oedipal triangle considered independently of his position in multiple social networks, but rather of directly accessing those social networks through rituals that tap into various flows of the social field in order to address blockages and thus allow the various members of those networks to successfully perform their allotted social roles. (10)

Deleuze and Guattari add that the Ndembu analysis only becomes oedipal “under the effect of colonization”: “The colonizer says: your father is your father and nothing else, or your maternal grandfather—don’t mistake them for chiefs . . . your family is your family and nothing else” (AO 168–69).

Ihembi’s purpose, contrary to a psychoanalytic analysis, is to reveal the hidden tensions and unconscious investments of the social field as they converge on the specific location of the affected individual. It follows that the cure also must address the social field itself rather than the psychic structure of an individual subject considered in isolation from the assemblages of which that individual forms a part

– Lorraine, Tamsin E., “Deleuze and Guattari’s immanent ethics: theory, subjectivity, and duration“, 2011.


8. “[T]he individual in the family, however young, directly invests a social, historical, economic, and political field that is not reducible to any mental structure or affective constellation” (AO 166).
9. They call this cure an example of schizoanalysis—their preferred alternative to psychoanalysis (AO 167).
10. As Turner puts it, Ihembi’s “main endeavor was to see that individuals were capable of playing their social roles successfully in a traditional structure of social positions. Illness was for him a mark of undue deviation from the norm” (1964, 262).

Turner, Victor. 1964. An Ndembu Doctor in Practice. In Magic, Faith, and Healing, Ari Kiev, editor. New York: Macmillan.

Do up the third button of your expensive jacket

“The cook, the thief, his wife and her lover” (1989), Peter Greenaway.

«- It’s dark in the restaurant.
– Yes, Phillipe.
– Thanks to Mr. Spica’s generosity, it is dark everywhere. No power, no light. (…)

– If you spent as much money on the meal, Mr. Spica, as you waste on the decor, your taste in good food must surely improve. (…)

– Two vans full of good stuff, just right for your kitchen.
– I would not touch it.
– Why on earth not?
–  I insist on buying my own food, Mr. Spica. Then I can be sure of its quality.
– I represent quality round here, my name is known for it. I offer quality and protection.
– Protection against what, I wonder, Mr. Spica? And whom?
– Protection, Boarst, against the rash temper of my men. Against a sudden arrival of food poisoning. Against rats. Against the public health inspector. (…)

– Do up the third button of your expensive jacket, Mr. Spica. You’ll feel less empty inside, Mr. Spica. (…)»

We are ‘hopelessly poor’

Shakuntala Devi, interview. She says European and American are “hopelessly poor” in Mathematics (compared to Chinese and Indian people).


The Guinness Book of Records (1982) reports:

“Mrs. Shakuntala Devi of India demonstrated the multiplication of two 13-digit numbers of 7,686,369,774,870 × 2,465,099,745,779 picked at random by the Computer Department of Imperial College, London on 18 June 1980, in 28 s. Her correct answer was 18,947,668,177,995,426,462,773,730.”

An article in the New York Times (November 10, 1976, cited in Smith, 1983, p. 306) reported that Shakuntala Devi added the following four numbers and multiplied the result by 9,878 to get the (correct) answer 5,559,369,456,432:


She was reported to have done this calculation in “20 seconds or less.”

Her fame grew manifold when she beat one of the world’s fastest computers by 10 seconds, while multiplying two 13-digit numbers in 28 seconds.

Shakuntala Devi never attended school in her younger days, but her father noticed and nourished her abilities in Mathematics since the age of three. He taught her Arithmetics. Numbers were her favorite toys and she would play and calculate with them every day, encouraged by her father, who soon made her a part of his professional act as a stage magician, with Devi performing card tricks and calculations. She soon became the whole show and her father then simply acted as her manager.

The question everyone asks is: how does she do it?

Devi’s own answers to this question, given at different times:
– “an inbom gift”;
– “I think anyone could do it if they loved numbers the way I do”;
– “Perhaps anyone could do it if they had played with numbers for hours every day since early childhood”.
So, remember, a remarkable performer (or genius, if you prefer) usually combines these three things: natural ability, desire guidance and early practice.

Now, do you understand why our standard school education is “hopelessly poor” (not only in Mathematics)? It wastes natural abilities, despises individual desire and privileges too much theory over practice.