Occupy Waikīkī: pushing the borders of land, sea and storytelling in Kristiana Kahakauwila's This is Paradise (2013) Occupy Waikīkī: This is paradise (2013) di Kristiana Kahakauwila, oltre i confini della terra, del mare e del racconto Sylvie Largeaud-Ortega 1 First of all, I'd like to thank Kristiana Kahakauwila, the author of This is Paradise 1 , for her generous time reading this essay and sharing her thoughts on it. It wouldn't be what it is without our conversations (referred to as [START_REF] Kahakauwila | [END_REF], which I'm immensely grateful for. This is Paradise is the story of three groups of Oceanian women who, in rotating series, narrate their occupations in Waikīkī 2 over a 24-hour period. There's a group of local surfers in their 20s, a group of Hawaiian career women in their 30s, and a group of married and mother-of-a-family Micronesian hotel housekeepers in their early-50s. Through their eleven short sequential narratives, in turns, each group incidentally reports occasional encounters with a young American female tourist. Her name is Susan and she keeps saying to all around her, «This is paradise». She is ultimately found dead on the beach, murdered by a foreigner. The picture of a hula dancer stands on This is Paradise's cover. In the short story, prints of hula girls keep popping out, on T-shirts and restrooms walls. These «graphematic» (Spivak 2010: 22) icons, like Susan's leitmotiv and the title of the short story, reverberate and repeat hegemonic colonial discourse on Oceania. Since early Polynesian encounters, the West has constructed stereotypical narratives on Oceania revolving around the hula girl. Indeed, Teresia Teaiwa protests that Oceanian diversity has been «sacrificed at the feet of the 'hula dancer'» (Teaiwa 1999: 252).

2

I suggest reading Kahakauwila's narrative as an ecofeminist deconstruction of the hegemonic colonial discourse that says that Oceania "is paradise" and that constructs the hula girl 3 as an object for male consumption. While, in colonial discourse, predominantly white Western male narrators dot their stories with the character of a thinly-sketched sexualised hula dancer (Largeaud-Ortega 2018: 135), here, Oceanian female narrators dot their own stories with thinly-sketched sexualised Susan. As far as her narrative status is concerned, Susan seems to be the counterpart of the hula girl: this time, the girl is white mainland American, a visitor in Oceania, and the narrators are groups of autochthonous women.

Through references to the works of historians, anthropologists, critics in post-and decolonial studies and environmental humanities 4 , and with special references to Oceanian studies of autochthonous claims to sovereignty [START_REF] Grandinetti | Urban aloha 'aina: Kaka'ako and a decolonized right to the city[END_REF]Kajihra 2008;Teaiwa 2000;Trask 1999), I look at Susan as "the land that divides", and at the female narrators and author, as Oceanian agents attempting to decolonise land, sea, and story-telling. I claim that, in this counterhegemonic Oceanian identitarian narrative, Kahakauwila and her female characters all "Occupy Waikīkī" 5 each in their own ways, as colonials, as resistants, or as hybrid cultural agents.

Susan as the land that divides

Susan as colonialism

In Hawaiian colonial history, the land is what divides. The very concept of 'land' is divisive: to Hawaiians, land is «a living 'aina (literally 'that which feeds')» whereas to the Euro-Americans, it is «flat and lifeless real estate» (Kajihira 2008: 176;Kame'eleihiwa 1992: 25). The latter concept has been dominant in Hawai'i since, against Native Hawaiian wishes, Americans overthrew the Hawaiian monarchy (1893), annexed the islands (1898) and obtained their "territorial incorporation as a state of the United States" (1959). Hawaiian homeland has been unilaterally redefined, and Native Hawaiians, displaced and dispossessed of their own country. Many have been actively fighting for their rights to sovereignty, self-determination and self-governance (Trask 1993: 16-8;Walker 2008;[START_REF] Kame | Native Land, Foreign Desires: Pehea Lā E Pono Ai? How Shall We Live in Harmony?[END_REF].

Highly Americanised Waikīkī, on the island of O'ahu, is an epitome of the land that divides, since «access to beaches near hotels is strictly regulated or denied to the local public» and the tourist industry is the major cause of «land dispossession, and the highest cost of living in the United States» (Trask 1999: 143-144). This dividing process has sometimes been reciprocated by Hawaiian communities, as in their declaration of a «ban on all resorts» (Hawai'i Ecumenical Coalition on Tourism 1989;Trask 1999: 245-250). In Kahakauwila's short story, Susan is repeatedly referred to as "mainland" or "continental American" and I suggest that she embodies a colonialist -the land that divides. Indeed, she keeps to Americanised Waikīkī only. What's more, she holds on to her preconceived representations of the place as paradisiacal: «it's like Hawaiians are all pissed off. They live in paradise. What is there to be so mad about?» (Kahakauwila 2013: 23. Further references to this text list page numbers only). Susan therefore denies Waikīkī any situational context of history: she ignores «the real» (Barthes 1970: 239), alienates Hawaiians and sets them apart. This process is seen at work when she scathingly spurns the group of surfer girls' advice against Bryan (the man who's flirting with her and will eventually murder her):

Occupy Waikīkī: pushing the borders of land, sea and story-telling in Kristia... Archivio antropologico mediterraneo, Anno XXV, n. 24 (2) | 2022 "You girls really don't want visitors to have a good time, do you?" Susan shrugs. "Whateves." With a tight smile, she snaps her purse shut and brushes past Lani. The bathroom doors swings in Susan's wake, and we are left staring at the empty space. (28) By applying her own standards and definition to place and people, she metaphorically claims Waikīkī as her own (nomen est omen), she participates in its colonisation. Furthermore, by promoting the myth that Hawaiians are "happy Natives", she «disparage[s] Native resistance» to colonialism (Trask 1999: 42). She Occupies Waikīkī in the colonial sense.

Susan as 'militourism'

Susan also embodies 'militourism' (Teaiwa 2000(Teaiwa , 1999;;Gonzalez 2013) -an escalation on the concept of the land that divides. Militourism, as the word indicates, is the conflation of militarisation and tourism 6 , and Susan in her bikini embodies this conflation. All three groups of narrators repeatedly pinpoint her «white bikini with red polka dots» (9, and variants 12, 17, 20). In July 1946, the United States dropped a fifteen-megaton hydrogen bomb over the Bikini Atoll [START_REF] Maurer | Special Forum Introduction to Transnational Nuclear Imperialisms[END_REF]DeLoughrey 2010: 106). At the very same time, public attention in the Western world was drawn to the launching of a sensationally skimpy swimsuit called 'bikini'. Susan's bikini-clad female body therefore appears as the «effective tool for hiding colonial violence» (Walker 2008, 109) which «substitutes and domesticates the unrepresentable chaos of nuclear war» (Teaiwa 2000: 92). Militourism can also be observed at Susan's Waikīkī hotel, in the way management deals with the group of proletarian immigrant Micronesian female labourers. Tourist and military management work hand in hand, through treaties between the U.S. and the Federated States of Micronesia [START_REF] Kahakauwila | [END_REF]) which «allow citizens of Micronesia to live and legally work in the U.S. without a visa» as «compensation for the loss of life, health, land, and resources» on the atolls. In return, «the U.S. has sole access and military and veto power over these islands» (US Department of the Interior 1985). The crowning touch of militourism is that the American-style hotel management now require Micronesian workers to «report suspicious activity […] to fight terrorism» (13). Hotel management overexploits and segregates these workers. They toil through the day, starting at six in the morning. Their only authorised access to the hotel is through a basement back door on a sidewalk spotted with «the faint red splatter of a spilled shave ice» ( 14) -an uncanny reminder of Susan's red-polka-dot bikini.

10 Hawai'i is a major U.S. strategic place, as exemplified by Pearl Harbor. It has been until recently a key nuclear and missile testing ground. «The military is the second largest 'industry' behind tourism» and on O'ahu, the military controls about a quarter of the island [START_REF] Kajihira | The Militarizing of Hawai'i. Occupation, accommodation and resistance[END_REF]: 175, Trask 1999: 17). This much is implied by a narrative sequence on a dental convention being held in Waikīkī. What I argue, however, is that Susan's death epitomises the impasse where Western hegemony leads. Her death evidences that predominantly-American constructs -the «supposedly isolated» isles and islanders «safe» for bombing (DeLoughrey 2010: 106; Robie 1999: 143), the sexualised hula dancer and mainland female tourist -are murdered through the U.S.'s own doings. It foregrounds that American instrumentalisation and (self-reflexive) colonial gaze are fatally (self-)destructive. I therefore propose to see the groups of women's narratives on Susan and Bryan's relationship as an ecofeminist Oceanian response to Western hegemonic discourse. At the end of the tale, Bryan is eventually trapped in O'ahu: «On an island like ours, a man doesn't run. Can't run» (42). He is trapped by the island, the very supposedly female body the U.S. claims to possess and overpower. I will venture to say that he is also trapped by the Hawaiian goddess Pele who famously catches her runaway lovers within her destructive lava flows (Beckwith 1970: 190) -here, even after the lava has turned into stone. Bryan may be seen as a Western male «kapu 7 breaker» (Kahakauwila 2021). The latter, meanwhile, earns punishment from the Hawaiian female deity, who compellingly asserts her autochthonous/land power.

Female Oceanians reclaim land and sea

All three groups of Oceanian female characters -to varying degrees, and in each in their own fields -strive to reclaim the borders of land and sea. I suggest that, together, they Occupy Waikīkī, this time in the sense of protest. These groups are like metaphoric troops. Together they cover the whole range of land, beach and sea. Their strategic relation to space manifests their resistance to American hegemony. It also determines their ability to speak for Oceania: their runs of narrative may sound like patrol rounds.

The career women

The group of «career women» (42) left Hawai'i for college on continental U.S. -except one, Paula Gilbert, who will be discussed further down. Back in Waikīkī, they're now part of the Hawaiian white collar rising class supposed to bridge the worlds of Indigenous and continental people. They belong to urbanised Americanised Waikīkī. They are always indoors, in cars, bars, lobbies or offices. Whenever they come across still-alive Susan, they feel for her -they would like to advise her against shopping in her bikini, or against going out with a stranger at night, unescorted -but their compartmentalised urban lifestyle prevents them from connecting with her. The sea metaphors they use also reflect an urban perspective: the convention center is «a squared fishbowl» (15), and when they are caught in heavy traffic, their «heels and briefcases» "slide" in cars that «lurch to a stop» ( 14), an urban mimicry of sea surfing. At home, they sleep «beneath hand-stitched Hawaiian quilts» ( 16), symbols of an Oceanian appropriation of American missionary handicraft -yet now expensive "markers of success", in turn appropriated by the urban American tourist industry [START_REF] Kahakauwila | [END_REF]).

On the one hand, from a Spivakian perspective, they may be seen as the "Native Informant", «an instrument of colonial authority who speaks for the 'native' in service of efficient governing» (Birla 2010: 88). For instance, Laura, the group's architect, submits a project for an environmental-friendly resort. They celebrate her professional achievement but worry that this project of yet another tourist development «will push housing prices further upward, making it harder still for our people to remain on their land» (33). In that respect, they may be said to belong to the capitalist «middle class displacing the poor… pushing Indigenous geographies to the past or periphery, thereby precluding possibilities for a decolonial urban future» (Grandinetti 2017: 242-3).

On the other hand, these women may be seen as the 'Native Resistant'. Indeed, they do belong to native Hawai'i, and their active presence on Americanised Waikīkī and the strong bonds they maintain with their island are a political strategy.

It doesn't hurt that we're from here. We are considered by our peers to be local women who've done well, left but come back, dedicated their education and mainland skill to put this island right. We speak at civic club gatherings and native rights events. We are becoming the pillars of the island community. ( 16)

Laura's LEED-certified project will mitigate environmental damage to the island. These women's professional skills allow them to infiltrate the American system and fight it with its own weapons. But not only that. Through their highly committed choice to come back to Hawai'i, they also prove they have female mana or pono 8 leadership: the ability to speak for the people and the land on field (Trask 1999: 95). And when they select a «Modern. Moneyed. Mainland» (30) Waikīkī hotel bar for their social gatherings, they Occupy colonised land. They remind readers that city land was originally Indigenous, and can be claimed by Indigenous peoples as rightfully as rural spaces «with natural and cultural 'integrity'» (Grandinetti 2017: 228;Goeman 2009: 170). They stand for the women at the forefront of the Hawaiian sovereignty movement (Trask 1999: 191).

Occupy Waikīkī: pushing the borders of land, sea and story-telling in Kristia... Archivio antropologico mediterraneo, Anno XXV, n. 24 (2) | 2022

As they themselves acknowledge, the price they pay for this commitment is high: they are single and childless. They often struggle with belonging to both Americanised land, and Oceanian sea in the sense of Hau'ofa's We are the Ocean (2008). At night, each in their own homes, they have a collective dream:

we dream of the rolling ocean […] of waves, of room, […] and the space of the sea. We dream we are falling deep into the ocean.

[…] We need air, and none exists beneath the weight of all this water. We hear a woman screaming for help, and we're not sure if the voice is ours or someone else's. ( 36)

In their collective unconscious, these women are like Susan: they fear drowning. They may indeed fear being sucked into the vortex of neoliberal capitalism of Waikīkī -a vortex to which they participate. On the day after, when they learn about the murder, they sympathize with Susan. They identify with her as female victims of mainland U.S. male hegemony. Their last, inconclusive words may reflect their difficulty of existing on both «land for revenue and land for resurgence» (Grandinetti 2017: 241).

The housekeeping labourers

The group of «women of housekeeping» (11) are immigrant labour from Micronesia working in Waikīkī. Low-paid jobs are their only employment opportunity in Hawai'i, and that allows them to send remittances back to devastated home. Globalising capitalism strictly delineates their social space. They are unauthorised in most places in Waikīkī, cut off from other people by the international division of labour. It is only logical that Kahakauwila also «occluded» (Spivak 2010: 28) them from the runs of narratives about Waikīkī at night. At night, these women are in their humble homes a long bus-ride away. They are the victims of «the intersectionality of [the] classed and raced violence that has shaped urban Honolulu», of the «urban displacement» which has been heading for «indigenous erasure» (Grandinetti 2017: 234, 236).

Management orders them to «always start with 'Aloha'» (13) when answering the phone. This exercise in «subaltern ventriloquism» (Spivak 2010: 27) chimes in with what Trask calls «the prostitution of our culture by tourism» (Trask 1999: 143-4). Indeed, on the streets at night, prostitutes are likewise heard «whispering 'Aloha' in lilting voices» (34). The housekeepers are otherwise harshly and literally silenced by management. As unorganised urban proletariat, they try to transgress capitalist division through very small tactical moves: tucking tips into their shoes, passing leftovers on to night security. In their very limited ways, the subaltern staff join forces to outsmart their employers. Also, in an astute «strategy of mimicry» (Bhabha 2010: 122), they set down their own dividing criteria: they rank tourists according to their production of waste depending on nationalities/ ethnicities. This can't occult the fact that these women remain figures of the oppressed Global South.

They don't have a career, but they have children. This is their force. It is in their relation to Susan as mother figures that, gradually, they break down land divisions.

When they first meet her they share a moment of laughter, which reminds them of their daughters. Laughter, in ancient Hawaiian Makahiki rituals 9 , was an experience of a «common humanity» which «destroy[ed] the taboos» (Valeri 1985: 218, 220) -and at this particular moment in contemporary Waikīkī, it does so, too. Also, this laughter allows the group of housekeeping women to hold on to their collective agency, at least for the day, and to make some transitory sense of Waikīkī: «We decide the American girl has brought us luck» (13, italics mine).

Family ties closely bind them to the ocean, their «home islands» (37), the «sea of islands» [START_REF] Hau | We are the Ocean: Selected Works[END_REF] which is constantly on their minds, and where they wish they could send their children back. They represent the ocean that unites. When the ocean washes Susan's corpse to their feet the next morning, they instantly translate their class status into 'motherhood' 10 : «We are here […]. All us mothers are here» (39). Without authorisation, they step out onto the material beach -reclaiming it as «public space that lies outside capitalism" [START_REF] Kahakauwila | [END_REF]. They become a stubbornly silent but physically powerful presence, «very still and very tall» (40). They stand in a protective circle around the corpse and, notwithstanding management and police injunctions, they will not move. They Occupy the beach, where they stamp their own standards: against capitalism, they demonstrate that human respect is not marketable. For a brief moment, they reaffirm Oceanian female agency on Waikīkī. Their strong collective mother figure transiently pushes land borders, and allows the ocean to unite female victims of both Global South and Global North together.

The surfers

The group of female surfers' zone is the ocean itself: ka po'ina nalu, the surf zone. The short story's opening lines present it as a hostile place: signposts read "CAUTION", "DANGEROUS UNDERTOW" (9). This expresses a typically mainland American perspective (Hau'ofa, 2008: 30-4). Antagonistically, the surfer girls declare: «We ignore it.

[…] We're not afraid of the beaches and breaks here in Waikīkī» (9).

Walker's 2008 article on the 1920s Waikīkī beachboys was at the forefront of Kahakauwila's mind when writing This is Paradise [START_REF] Kahakauwila | [END_REF], and indeed, the surfer girls are the beachboys' contemporary female variant. As in the early 20 th century, early-21 st -century ka po'ina nalu is a political place. Not only because surfing has been «an integral part of being Native Hawaiian» from time immemorial. But also because surf is «a pu'uhonua -a historic Hawaiian place of refuge from strict colonial laws», especially in ocean-based communities like Waikīkī (Walker 2008: 89-95). And from the very start, the surfer girls don't just Occupy the place: they rule it. 11

At sea, they decide who belongs or not. Clearly, Susan doesn't: «scared of da water. Haoles, yeah» (9). She is «label [ed] for what she i» (10) -a tourist -and they paddle out and leave her in the whitewash. In contrast, Mel Chun belongs: although she grew up in San Francisco, her keen practice of competitive Native Hawaiian canoeing has won her the status of «one of us locals» (21). Together they ride «on top of a social hierarchy on the ocean» (Walker 2008: 107). Keeping closely posted on weather reports, they can tell when «da swell» is going to be «mean» (34) and organize their lives correspondingly. In ka po'ina nalu they are free from «colonial encroachment» (Walker 2008: 89) and exercise full Hawaiian sovereignty. In symmetry to the career women on land, they stand at the forefront of the Hawaiian sovereignty movement on sea.

On land, at the Lava Lounge, they have to share their space with tourists, military, and college kids. But they are still the «local girls», the ones who know how to surf the place: when to «wait, bide [their] time», and when to «cruise» (19, 21). Their tactics rely on sea metaphors: Cora Jones calls her seduction dance «her come-and-get-it wave, but we think it makes her eye look like squid tentacles are growing from it» (22), and they

Occupy Waikīkī: pushing the borders of land, sea and story-telling in Kristia... Archivio antropologico mediterraneo, Anno XXV, n. 24 (2) | 2022 laugh at the tourists who copulate on the beach at night as openly as «mating monk seals» (35). They govern their powerfully sexualised bodies and defy tourist expectations of sexual conquest, in resistance to the Western construct of the hula girl. They thereby «subvert colonial categories -which insist on Native passivity and compliance -and assert anticolonial identities» (Walker 2008: 107). On land also, they decide who belongs or not. They dub a humble young haole 12 guitarist «one kanaka» ( 27) for his Native Hawaiian slack playing skills and honouring of his kūpuna 13 . But as soon as they spot Bryan as potentially dangerous, they deploy their troops to drive him away from Mel, and to warn Susan against him. They're also keenly aware of land issues: «Our families are barely affording a life here, the land is being eaten away by developers, the old sugar companies control water rights» ( 23). They stake a claim «to both urban space and Indigenous sovereignty… at the intersection between the concept of the 'right to the city' and the value of aloha 'aina» (Grandinetti 2017: 243). So they Occupy the Lava Lounge. And sometimes suffer setbacks, as with Susan.

Upon Susan's death, they decide to elaborate on a hotel-sponsored remembrance ceremony organised on Waikīkī beach. They reproduce the housekeepers' protective female family circle, this time at sea, sitting on their boards in a tight circle as her "sistas". They «pule» (45), they pray, then toss flowers into the centre of the circle. These flowers, «invariably associated with deity» in ancient Hawaiian times (Beckwith 1970: 93), might be an offering to Kanaloa, god of the sea, or to Kane, «the leading god among the great gods», and to the sea, the «tapu water of Kane» (wai tapu a Kane) 14 (Beckwith 1970: 43, 61). The white petals reflected in the sunset seem to replace Susan's red polka dot bikini. It looks as if their soothing light had replaced Bikini's blinding atomic light, installing sacred peace and natural harmony over the sea. The surfer girls' genuine, holistic aloha culture represents the ocean that unites.

Back on land, however, they have to tread on left-overs from the hotel-sponsored remembrance ceremony, «a confused jumble» of flowers «wilting» in the heat (46). These are the closing words of the short story.

To none of these groups is the political struggle to reclaim the borders of land and sea an easy one. And the fight isn't over.

Pushing the borders of storytelling

We, the women of Oceania

Probably the short story's most salient feature is the extensive use of "We". Not only do the three groups of Oceanian female characters-narrators speak collectively, always: they also think collectively, they even dream collectively! This is one step further than Sia Figiel's narrator's arresting statement: «'I' doesn't exist […]. 'I' is 'we'… always» (Figiel 1996: 137). This outstanding narrative strategy clearly highlights the women's sense of collective identity, or their Oceanian-ness -in sharp contrast with individual character Susan. Although collective, their identity is diverse: «even among locals and Natives, not everyone sees the islands the same», says Kahakauwila (McMahon 2013).

The three "we"s therefore weave multi-perspective narrative threads. The cyclical structure of their narrative runs may evoke the Oceanian collective weaving of a multiple-strand shroud around Susan, and around the people and land destroyed by Western militourism. It might also evoke the wave cycles of the ocean, their possibly restorative power.

Their collective identity is also eminently female, which enunciates the prominent role of women in Oceanian political activism. In the Hawaiian sovereignty movement, «both cultural and political restoration projects» were «more often headed by women than by men» (Walker 2008: 106;Trask 1999). Correspondingly, these female groups are highly protective. Their quality of caring, however doesn't subscribe to Western gendered essentialism, since the Hawaiian male characters -Paula's husband, the local boys at the Lava Lounge -are protective, too. Caring comes out, instead, as Oceanian expertise: «that's a job at which we are experts» (39). It perpetuates ancestral Oceanian caring for the land and the sea, Mālama 'Aina 15 in Hawaiian, as opposed to Globalising capitalist eagerness to «take-make-dispose» (Elisha 2020).

The short story gives these Oceanian women a voice -and, in literary terms, a supreme voice, to boot: the narrators'. Management forbids the housekeepers to speak -but they do speak directly to the readers. Susan silences the surfer girls -but with their assertive voices opening and closing the short story, they strike readers as the ones in charge. As to the career women, not only do they speak for their community, they also have Paula Gilbert. She is different because she chose not to study abroad and she doesn't have a white-collar job. Yet, as police officer, she is a figure of authority in Waikīkī: she stands as a Native female bulwark against destructive U.S. white male forces. Like the housekeepers, she is also a mother, bearing their second child to her Hawaiian husband. And like the surfer girls, she knows ka po'ina nalu: on the beach, they watch the waves together «with the same longing» (41).

Paula's voice binds the three groups of women together. She unites forces with the housekeepers, the surfers and the other career women, to identify Bryan: they / their voices / their bodies / their islands lay the female foundations to overpower the foreign male murderer. Under her clear-sighted and articulate leadership, the three groups of women make some headway towards Native sovereignty. In that respect, they may illustrate international / global resistance to militarism and capitalism that keeps erupting throughout the world -as in Hawai'i, the Philippines and Guam / Guåhan, to demand the closing and cleaning-up of US military bases. This resistance «proclaims a radical new vision for the world where genuine security is based on human needs, human dignity, cultural integrity, environmental preservation, and global solidarity» (Kajihira 2008: 189).

A hybrid tale

Kahakauwila is «a hapa 16 writer of Kanaka Maoli 17 (Native Hawaiian), Norwegian and German descent» [START_REF] Kahakauwila | [END_REF]. She went to mainland college, is now an academic at the University of Hawai'i Mānoa, and a mother and a surfer. Her storytelling is hybrid, like the Waikīkī beach which she «redefine[s] and reconstitute[s]» (Walker 2008: 91). To do so, she draws from both her "literary lineage" and her "Oceanian lineage" [START_REF] Kahakauwila | [END_REF]).

In This is Paradise, some lines -«Do we already know she is marked, special in some way?» (10) -seem to show that, like Aristotelian heroes, Susan has a tragic flaw. Other questions like «Haven't we hurled ourselves past this moment?» (19), «How did we drink so much? How did we laugh so hard?» (29) signal that some superior power is toying with the characters -is it the three Greek Fates, determining the three choruses' destinies? One of the surfers, Cora, the "group's academic" «majoring in theatre at the University of Hawai'i» (24), reads Bryan's tattoos (a smiling and a tearful mask) according to Greek drama. Her approach is overruled by the other surfer girls as inadequate: they see prison marks instead. Yet Cora's reading is proven equally adequate, by the plot itself. Like Bar Ambrosia in the Waikīkī hotel where the career women enjoy their night drinks, Kahakauwila seems to feed her readers the eponymous food of Greek and Roman gods. In our conversations, the author has kindly confirmed that she sees her groups of Oceanian female narrators as "a Greek chorus" commenting on the dramatic action. She also conceives of the tight unity of place, time and action, as Aristotelian [START_REF] Kahakauwila | [END_REF].

But the author also agrees that the short story's oral quality also stands in the line of Oceanian oratory and oral transmissions of (hi)story [START_REF] Kahakauwila | [END_REF]. I suggest that her masterfully orchestrated Oceanian polyphony delivers a modern mo'olelo, a multiple-meaning word which defines as "story, history, legend, chronicle, myth", etc. [START_REF] Kahakauwila | To Weave with Water», Presentation of Kauhakauwila's work in progress[END_REF]. In Hawaiian mo'olelo, «there are many examples of women as empowered agents» (Walker 2008: 109). This mo'olelo might be a profane contemporary Pele "legend", a genre where women play a leading role , standing «between the semihistorical figures of more or less authentic history and […] fictitious heroes, product of the free play of the imagination» (Beckwith 1970: 404).

Not only is Kahakauwila's story-telling multivocal, it is also multilingual. Each group of narrators has their own languages, and code-switch according to who is listening. Languages span from the career women's very posh «Thank goodness» (30) to the surfer girls' Pidgin -addressed to Paula, or spoken amongst the younger generationand vernacular Hawaiian, spoken only in ka po'ina nalu. I will therefore say that Kahakauwila's short story Occupies the contemporary Oceanian literary scene by appropriating division factors and subsuming them in cultural hybridity.

A founding tale

The short story's treatment of time is intriguing also because it narrates events that took place in the past and are reported in hindsight, but it narrates them… in the present tense, always. This seems to thrust readers somewhere outside diachronic time -time, that is, as conventionally represented in dominant historiography. But time is different in Oceania: «all time is now time», «centered in the being» and «the centered being in this now time simply reaches out in any direction towards outer circles, these outer circles being named 'past' and 'future' only for our convenience» (Grace 1986: 39).

In This is Paradise, the merging of past and present delivers «present history» (Kahakauwila 2016), a process of "re-membering" that links Hawaiians' past to their present (Walker 2008: 92).

The Hawaiian stands firmly in the present, with his back to the future, and his eyes fixed upon the past, seeking historical answers for present-day dilemmas. Such an orientation is to the Hawaiian an eminently practical one, for the future is always unknown whereas the past is rich in glory and knowledge (Kame'eleihiwa 1992: 22-3).

The narrative may be said to approach the quality of a "myth" -another meaning of mo'olelo -in the sense of a founding tale. In Oceanian epistemology, a myth is a «narrative of constant actuality» (Segal 2004: 179). It performs a fundamental social 7. Kapu (the Hawaiian variation of tapu) is a pan-Polynesian word originally meaning 'forbidden' to commoners because 'sacred'. Since contact with the West, it has been integrated the English language as 'taboo'.

8.

Mana is sacred spiritual energy of power and strength. Pono stands for righteousness and balance with all things in life.

9.

The Makahiki rituals celebrated the ancient Hawaiian New Year. They were days for resting and feasting. Today, the Aloha Festivals reactivate the Makahiki tradition.

10. The word 'proletariat' comes from the Latin proles meaning 'offspring, progeny'. Historically, it identifies producing offspring as one of the proletariat's major strengths.

11. They rule it, not as owners, but as guardians and caretakers.

12. Haole means 'foreigner'. In modern usage it has come to mean 'a white person'.

13. Kūpuna means 'ancestors', or here, 'forefathers'.

14. The particle a instead of o denotes direct handiwork rather than possession (Beckwith 1970: 61).

15. Mālama 'Āina means «serving and caring for the Land» and the adjoining Sea (Kajihira 2008: 176).

16.

Hapa is Polynesian transliteration of the English word 'half'. It refers to Polynesian islanders of mixed ethnic ancestry.

17. Kānaka Maoli translates as 'Polynesian people'.

ABSTRACTS

This essay explores Kahakauwila's short story This is Paradise from the angle of post-and decolonial studies and environmental humanities, and presents it as an ecofeminist and counterhegemonic Oceanian identitarian narrative. With special references to autochthonous antinuclear protests and claims to sovereignty (Trask, Teaiwa, Walker), it argues that female author and characters all Occupy Waikīkī, as colonials, as resistants, or as hybrid cultural agents.

The beach becomes a place of Native political, environmental and cultural resistance, where American colonialism, 'militourism' and Globalising capitalism are being challenged. It defends the oppressed female figures from both global South and global North, metaphorically counters colonialism and restores their historical and spiritual polysemy to land, beach and ocean in Waikīkī.

In questo saggio, attraverso le prospettive teoriche postcoloniali e decoloniali, le proteste antinucleari e le rivendicazioni indigene per la sovranità di diverse realtà dell'Oceania, analizzo i modi in cui il racconto di Kristiana Kahakauwila, This is Paradise, decostruisce il discorso egemonico sulle Hawaii come paradiso. Tale vibrante opera polifonica e identitaria di gruppi di narratrici oceaniane, è impegnata a trasformare la spiaggia più famosa delle isole hawaiane in uno spazio di resistenza culturale e politica che ha generato vari movimenti sociali, raggruppati nell'espressione "Occupy Waikīkī". Attraverso la denuncia ecofemminista del colonialismo americano, del 'militourism', del capitalismo globale e dell'oppressione delle donne sia del Nord che del Sud del mondo, il testo di Kahakauwila restituisce alla terra, alla spiaggia e al mare di Waikīkī la loro polisemia storica e spirituale.

Occupy Waikīkī: pushing the borders of land, sea and story-telling in Kristia... Archivio antropologico mediterraneo, Anno XXV, n. 24 (2) | 2022

Occupy

  Waikīkī: pushing the borders of land, sea and story-telling in Kristia... Archivio antropologico mediterraneo, Anno XXV, n. 24 (2) | 2022

Occupy

  Waikīkī: pushing the borders of land, sea and story-telling in Kristia... Archivio antropologico mediterraneo, Anno XXV, n. 24 (2) | 2022

  Occupy Waikīkī: pushing the borders of land, sea and story-telling in Kristia...

Archivio antropologico mediterraneo, Anno XXV, n. 24 (2) | 2022

  Occupy Waikīkī: pushing the borders of land, sea and story-telling in Kristia...

Archivio antropologico mediterraneo, Anno XXV, n. 24 (2) | 2022

  Occupy Waikīkī: pushing the borders of land, sea and story-telling in Kristia... cultural function, that of explaining the world, defining each person's place within that world(Wood 2007: 119). It is «repeatable, since it serves as a model, and also a justification, for all human acts»(Eliade 1957: 22). This short story may be seen as a profane variant of a founding tale, as it narrates and explains features of Waikīkī / Hawai'i / Oceania in their 21 st century context.42 The plot hinges around the Banyan Hotel, i.e. a metaphorical tree, or kumu. The first banyan tree was introduced in Hawai'i in 1873 by American missionaries, to commemorate their arrival on the archipelago. The banyan species is remarkable for its expanding aerial roots which «embrace and ultimately envelop the host tree […] forming a compound trunk»(Perez 2021: 39-40). It has indeed expanded into Hawaiian landscape, and history (and Waikīkī boasts a magnificent banyan tree outside its oldest hotel). But kumu also, and more prevailingly, means 'teacher', or 'source'. In that respect, kumu is knowledge sourcing from the base, from the land, from the islands' original foundations. With the Banyan Hotel as its «textual tree trunk»(Perez 2021: 57), This is Paradise explores the epistemic sources of Waikīkī, both Western and Oceanian.Conclusion 43In protest against mainland Americans occupying the land, Kahakauwila's groups of Oceanian women Occupy Waikīkī, which becomes a place of Native political and cultural resistance. They denounce American colonialism and militourism, and Globalising capitalism. They defend the oppressed female figures from both Global South and Global North, they metaphorically reinstate a Hawaiian goddess's autochthonous supremacy. Through their powerful narrative voices, This is Paradise weaves together land and sea, annexation and resistance, the material and the spiritual, the literary and the oral, the present and the past, and by doing so, it masterfully and militantly accounts for aspects of Hawai'i's present situation. It restores their historical and spiritual polysemy to land, beach and ocean in Waikīkī. A counterhegemonic source of knowledge, this ecofeminist tale deconstructs the colonial statement, This is Paradise. It allows readers to explore, instead, multiple facets of Oceanian identities, under the guidance of a leading contemporary Hawaiian female author who stakes a claim on the cultural and political field and powerfully declares: "This is Waikīkī".Occupy Waikīkī: pushing the borders of land, sea and story-telling in Kristia...

	BIBLIOGRAPHY
	Bhabha H., 2010 [1994] The Location of Culture, Routledge, New York.
	Barthes R., 1970 [1957] Mythologies, Point Seuil, Paris.

Archivio antropologico mediterraneo, Anno XXV, n. 24 (2) | 2022 and Beckwith M., 1970 Hawaiian Mythology, University of Hawai'i Press, Honolulu. Beckwith M. 1972 [1951] (transl. and ed.) The Kumulipo, a Hawaiian Creation Chant, University of Hawai'i Press, Honolulu. Archivio antropologico mediterraneo, Anno XXV, n. 24 (2) | 2022

Teaiwa T., 1999 «Reading Paul Gauguin's Noa Noa with Epeli Hau'ofa's Kisses in the Netherends: Militourism, Feminism, and the 'Polynesian' Body», in V. Hereniko, R. Wilson (eds.), Inside Out; Literature, Cultural Politics, and Identity in the New Pacific, Rowman & Littlefield, Lanham: 249-263. Teaiwa T., 2000 «Bikinis and other S/pacific N/oceans», in Hanlon D. and White G. (eds.), Voyaging through the Contemporary Pacific, Rowan and Littlefield, Lanham, MSD: 91-112. Thompson D., 2013«Occupy movement in Hawai'i», in Honolulu Magazine, April 8 www.honolulumagazine.com/field-notes-occupy-movement-in-hawaii-2, accessed 11/21/2022. Trask H.-K., 1999[1993] NOTES 1. This is Paradise is the title of Kristiana Kahakauwila's collection of short stories. This essay only examines the volume's first, eponymous short story, This is Paradise. I have chosen to parse Kahakauwila's work because so far, it has not been subject to any extensive scholarly examination, and it is important that this new voice in Oceanian literature should start gaining the international academic recognition it deserves. The reason why I focus on the eponymous short story only is, as I'll try to demonstrate, that this specific narrative resonates, with particular accuracy, with the rationale of this Archivio Antropologico Mediterraneo special issue -"The sea unites what the land divides".

2.

Waikīkī was the first capital of the Kingdom of Hawai'i from 1795 to 1796, on the south shore of the island of Oʻahu. It is now a neighborhood of Honolulu, capital and largest city of the US state of Hawai'i. Waikīkī is most famous for its seafront filled with high-rises and resort hotels, and its surf with long rolling breaks ideal for long boarding.

Popularized images of the female hula dancer -as a gentle, scantily-clad and alluring

Polynesian woman who gives a welcoming smile as she shimmies her hips -have deviated far from their origins and perpetuated stereotypes of the sexualized Polynesian woman.

4.

Given the current colonial situation of Hawai'i, this essay refers to postcolonial studies as a means of engaging with decolonisation.

5.

In coining this expression, I'm nodding both to 'Occupy Wall Street', and to the Hawaiian '(de)Occupy' movement, originally called 'Occupy Honolulu' -the «(de) was added in solidarity


Paul Goutmann

Alain Bonardi
email: alain.bonardi@univ-paris8.fr

Alain Bonardi Approaching

Paul Goutmann Artec

Approaching Spatial Audio Processing by Means of Decorrelation and Ring Modulation in Ambisonics

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

The spatial dimension of sound is essential in the field of contemporary music creation, especially in electroacoustic and electronic music. Today, concert halls and studios are equipped with multipoint diffusion systems. Since the 1990s, software implementing sound spatialization models have been created and shared by the community of compositors, computer music designers and audio engineers [START_REF] Garcia | Interactivecompositional Authoring of Sound Spatialization[END_REF]. The development of these technologies feeds new paradigms of representation and ways to think about space in music [START_REF] Fober | Les nouveaux espaces de la notation musicale[END_REF]. Most of the spatialization techniques are based on point sources in close relationship with spatial hearing models [START_REF] Blaeurt | Spatial Hearing: The Psychophysics of Human Sound Localization[END_REF] [4] [START_REF] Colafrancesco | Spatialisation de sources auditives étendues : applications musicales avec la bibliothèque HOA[END_REF]. Accessible musical operations for creators are the placement of sources, designing movements and room acoustic simulation. However, other approaches of interaction with spatial attributes of sound exist [6] [7] [START_REF] Bonardi | Composer l'espace sonore[END_REF]. The project HOALibrary contributed to those approaches in synergy with many years of research and creation about the spatiality of sound at CICM. The Cen-tre d'Informatique et de Création Musicale created by Horacio Vaggione in 1992 accommodates researches which have interactions 1 between creation, technologies and computer sciences especially spatialization since the beginning of the 2000s [START_REF] Sedes | Espaces sonores actes de recherche[END_REF]. Developed by J. Colafrancesco, P. Guillot and E. Paris between 2012 and 2015 in the context of the Labex Arts H2H projects, HOALibrary is a library of spatial audio processing tools in ambisonics [START_REF] Sèdes | The HOA library, review and prospects[END_REF]. One of the particularities of this library for Max and Pd is the insertion of signal processes (well known in electroacoustic and mixed music) such as granulation, ring modulation or decorrelation into the ambisonic model. Unfortunately the Pd version is obsolete since 2019. In order to formalize twenty years of work on mixed music and to address the obsolescence of HOALibrary, Bonardi began to transcribe treatments of the object hoa.process∼ in Faust (as well as ambisonic basics and multichannel processes) grouped in the library abc.lib [START_REF] Bonardi | La librairie abclib : un ensemble de codes Faust rassemblant 20 ans de recherche, enseignement et création en musique mixte[END_REF] 2 . In this context, we began new developments and fine-tuning around the decorrelation and the ring modulator in ambisonics lean on a research-creation practice 3 . The musical interest of those two treatments is in part linked to the fact that they allow complex sensitive results through the manipulation of just one parameter, the factor. The decorrelation produces progressively diffuse sound fields from one mono source (Sound 6.1) and the ring modulation creates the sensation of complex movement from one mono source (Sound 6.2). We refer to sound examples all along the article which are indexed in the appendix (6) and available on the platform HAL of the Centre pour la Communication Scientifique of the CNRS. 1 The interactions take place in research projects where the activity of creation permits to test in sensitive and qualitative ways the results of audio digital processes. https://cicm.mshparisnord.fr Accessed on: April 6, 2022 2 The library is currently compiled for Max and Pd and available here with the Faust code: https://github.com/alainbonardi/ abclib Accessed on: April 6, 2022 3 A state of the art of 'research-creation' or 'artistic research' is beyond the scope of this paper. 'Research-creation' refers to a large set of practices and methods. For this paper, its doing research in interaction with creation in an academic context. Both part emerges from and merges with the other. Composing is here a manner to handle tools (theoretical and technological) and to produce knowledge in music, musicology and computer music sciences. Composing as a research activity is at the core of CICM and ArTeC. We explain in fact the methodology in section 3.

INTERACTING WITH SPATIALITY

In the practices of electroacoustic, mixed and electronic music, the work on the spatial dimension of sound cannot be reduced to spatialization [START_REF] Stroppa | Accorder musicalement un espace réel et un espace inventé[END_REF] [13] [START_REF] Vaggione | L'espace composable. Sur quelques catégories opératoires dans la musique électroacoustique[END_REF] [15]4 . Designing treatments as a way to design instruments is at the core of musical practices in digital environments. The HOALibrary project approached space in terms of spatial process of sound. The library has been conceived to give access to musicians to the operations in the framework of the HOA (High Order Ambisonic) model. In this section we will first present the way to create treatments in HOALibrary and their transcriptions in the Faust language. Then we will present the design of macro parameters as controllers for digital processes. Finally, we will go further and expose how the design of functions is an important step to give access to operations.

Spatial Processing

The B-Format proposed by M.Gerzon and HOA proposed by J.Daniel are techniques to record, synthesize, process and reproduce acoustic fields. These techniques are based on three steps: encoding, optimisation and decoding. The encoding principle is based on the description of the spherical functions (in 3D) or circular functions (in 2D) corresponding to the acoustic field at one point of space using an ensemble of reference functions. These reference functions are called 'harmonics', their number depends on the encoding order. The more harmonics are used, the more precise the encoding will be. In a 2D encoding there are 2(N +1) harmonics and in 3D encoding there are (N +1) 2 harmonics. They are organized in order m (line) and degree l (row) as -l ≤ m ≤ +l and can be represented as in the Figure 1. The decoding stage consists of calculating the projection of the spherical function on the loudspeaker setup. In other words, calculating the gain sent to each speaker depending of a diffusion system which needs to include more speakers (set on a circle or a dome) than the number of harmonics. Processes in HOALibrary consist of applying digital audio treatment to each harmonic. Inspired by the object poly∼, the objects hoa.2d.process∼ or hoa.3d.process∼ -takes as first argument the order of encoding -instances a patch of treatment for each harmonic [START_REF] Bonardi | Concevoir des traitements ambisoniques en 2D et en 3D : l'exemple de Pianotronics 2[END_REF]. For example, the object hoa.2d.process∼ in the Figure 2, instances the patch hoa.fx.decorrelation∼ (as in Figure 3 for Y 0 ) fifteen times corresponding to the numbers of harmonics in HOA 2D 7 th order. The process parameters are generally proportional to an harmonic coefficient which depend on the order, the degree and the number of harmonics. Since 2020 patches instantiated by the hoa.process∼ are grouped in abc.lib in Faust. This functional language for signal processing gives the opportunity to clear operations especially with the primitive function 'par' which creates indexed operations in parallel. Multiple windows encapsulated in Max or Pd correspond to a few lines in Faust that can be edited using an embedded compiler.

The Factor

Designing treatments is a way to build a part of our 'composable space'. This notion originally developped by Horacio Vaggione is the environment allowing composers to generate and control sound morphologies. Composable spaces are multidimensional and are themselves morphologies that can be designed [START_REF] Vaggione | L'espace composable. Sur quelques catégories opératoires dans la musique électroacoustique[END_REF]. The composable space offers controllers to operate on and compose sound. In HOALibrary and abc.lib, the controllers which are designed for decorrelation and ring modulation are accessible parameters, and notably the 'factor'. The 'factor' parameter is a meta-parameter which controls the depth of the treatment. The idea of Guillot and Paris was to begin to process higher harmonics for low values of the 'factor' up to the harmonic 0 for the maximum of the 'factor'. When these treatments are applied after a mono source encoding, the result can be described by a transition from point source to a diffuse sound field with a color chart behind these two states for the decorrelation [START_REF] Goutmann | Traitement spatial du son par décorrélation des signaux en ambisonie d'ordre élevé[END_REF] and a transition from point static situations to larger source and complex movements for the ring modulation.

Accessing Controls in Faust

One of the advantages of the Faust language is the possibility to define a user interface which will be automatically rendered at compilation. Primitives like buttons, sliders, and number boxes are generated. These primitives are parameterized when they are declared: initial value, minimum, maximum, interval. For example in the function abc 2d f x decorrelation ui(n) presented in the Listing 1, the function fxDecorrelation is called with four parameters which are the variables 'delay', 'factor', 'fdbk' and 'functiontype'. Those variables take the value of the associated primitive 'hslider' (horizontal slider). If the function abc 2d f x decorrelation ui(n) is called in the 'process', at compilation the program will include a horizontal slider labeled 'delay', 'factor', 'fdbk' and 'functiontype' corresponding to the string. In abc.lib, graphic user interfaces are dissociated from audio process functions (the fxDecorrelation function in this example). Already at this step, the controllers are defined. For example the decorrelation is based on delay lines which can be feedback: should we leave the possibility to control the amount of feedback in the interval [0, 1] or [0, 1[? In the same way, if the interval for the factor is 0.1 or 0.001, the perceived result will not be the same. We will see in the next section that the controllers of the composable space are already designed in the function implementation.

DESIGNING DIGITAL OBJECTS

Interactions between composers, performers or computer music designers and sound qualities when computers are involved are multilayered. Building setups of hardware controllers, sensors or GUI is common in the computer music practice as well as the building of audio processors with such high level graphical environments as Pd, MaxMsp or Max4Live. Thinking about the interactions between all the layers of musical environments and the sonic user feedback is essential to understand the music made with these environments. The term 'digital object' used in the title encapsulates all these layers. In this section, we highlight a methodology of experimental practice to build treatments in a musical way. With the new developments and fine tuning on decorrelation and ring modulation we want to show the multi-scale aspect of designing digital objects that gather: implementation, design of the controllers, GUI and activation by the user. Our method is based on an iterative prototyping loop always linked to listening and composition: we develop audio processes with musical goals, tested them in the studio and used them in compositions. These studies tools are handled in works of Musicology Bachelor students (Paris 8 University) as well as in experienced composers' works. The results of the interactions between developments, the self used, feedback from students and from experienced composers are not quantitative but observed in a qualitative way 5 . All the tests were done in HOA 2D 3 th on 8 speaker (Genelec 8030A) portion of a 16 speaker dome in the studio of the CICM at the MSH PN and example are grouped in the appendix.

Decorrelation

The terms correlation and decorrelation refer to mathematics tools used in digital audio processing among other disciplines for musical purposes and for analyzing perception of space. We can think of correlation as similarity. For example, the cross-correlation function is a way to calculate the similarity between two signals. The decorrelation in digital audio applied to musical purpose consists in dephasing signals or applying all-pass filters. Extending 5 We saw that this tools affect the students' approach of composition. Moreover the decorrelation takes a large place in the Anne Sèdes works. She documented her approach of decorrelation in ambisonics in [START_REF] Sèdes | Approche musicale de la decorrelation microtemporelle dans la bibliothèque HOA[END_REF] and the last version of the ambisonics decorrelation was implemented and tested in her last work Écoute/Expension for the choreograph Kitsou Dubois. Plus, as a part of his PhD research, Goutmann is working on an electroacoustic piece which handle the decorrelation in ambisonic Compression/Dilatation in the examples is a binaural version of the first part of this piece originally for a 3D setup of speakers (Sound 6.6). The piece was performed at the Les visites insolites du CNRS (October 4 2021) and during an electroacoustic concert Séance d'écoute (March 4 2022) at the MSH PN Maison des Sciences de l'Homme Paris Nord the works of Kendall and Vaggione [START_REF] Kendall | The decorrelation of audio signals and its impact on spatial imagery[END_REF] [21], the decorrelation in HOALibrary (and then in abc.lib) is based on the dephasing of the harmonics after the encoding process with the insertion of delay lines. Inserting some delays between harmonics breaks the correlation of post-encoding signals and gives a rich perceptive result of a diffuse sound field. The decorrelation has initially two parameters: 'delay', 'factor'. We add two more: type of distribution of the delays ('functiontype') and feedback ('fdbk'). The factor determines how many harmonics will be delayed, the delay is the maximum delay time applied to the harmonics, the distribution of delay is the function used to spread the delays between the harmonics. The decorrelation is defined for each spatial component among:

P = 2.N + 1 in 2D, (N + 1) 2 in 3D ( 1
)
where P is the number of harmonics at the ambisonic order N , by the delay d i :

d i = 0 if f a < 1 -i+1 P , delay.f ( i+1 P ) else ( 2
)
where f (x) is the function of distribution called abc th in the library. The blockdiagram of the decorrelation in Figure 4 shows that we hear the signal delayed or not according to the factor and the index of the harmonic, thanks to the two envelopes env1 and env1c -when one is equal to zero the other is equal to one. In this situation, if the factor value is in the interval [0, 1 P ] the last harmonic is delayed with the maximum delay time and all the others won't be delayed. Therefore, as the factor increases, the second to last harmonic will be delayed starting from a factor equal to 2 P , the third to last will be delayed starting from 3 P , etc. The sensitive result isn't a progressive generation of a diffuse sound field but a progressive insertion of static delay lines (Sound 6.3). Figure 5 illustrates the coefficient of delay time applied to each harmonic when the factor increases in 2D 3 th order: when the factor increases we first hear the last harmonic delayed (Y -3,3 ), then second to the last (Y 3,3 ) and this until the first (Y 0 ). In consequence, we decided to introduce the factor in the delay equation of each harmonic. That leads to the reduction to the gap between the delays of harmonics already delayed and harmonics that begin to be delayed when the factor increases. Moreover, the delays progressively increase as the factor increases as illustrated in the Figure 6 and that amplifies the effect of progressive generation of diffuse sound field (Sound 6.4). We have chosen to duplicate each signal corresponding to the harmonics and add a gate as a binary wet/dry controlled by the factor. The delay time is equal to 0 when the factor is under a threshold and the feedback introduces coloration and saturation. So when the factor is under the threshold we hear the signal without delay line and when the factor is higher the threshold we hear the signal with a delay line. Figure 6. Plot of the delay coefficient per harmonic versus the factor when including the factor in the delay equation.

The distribution choice

The calculation of the delay time for each harmonic depends on the factor, the maximum delay time and the coefficient of the harmonic. The higher the order of the harmonic is, the deeper the treatment. But the delay time applied if the factor is higher than the threshold increases linearly from the first harmonic to the last. Based on experiments on graphic user interfaces to control the decorrelation [START_REF] Goutmann | Traitement spatial du son par décorrélation des signaux en ambisonie d'ordre élevé[END_REF], we proposed to control the type of distribution with 21 functions called abc th that are in the range [0, 1] when x ∈ [0, 1] (Sound 6.5).

Ring Modulation

Ring modulation consists in modulating a bipolar signal by another bipolar signal. In ambisonics, ring modulation consists in modulating each harmonic with a sinusoidal signal and has two parameters: the factor of modulation and the frequency of the carrier. If the factor is greater than the threshold:

(P -i -1) P ( 3
)
the i th ring modulator is active with a carrier c of:

c = f 0. (i + 1) P ( 4
)
where P is the number of harmonics. If the factor is under the threshold, the original signal is provided. Therefore, ring modulators are progressively revealed when the factor increases. For example, after an encoding at third order in 2D, there are seven harmonics. The harmonic 0 will have a modulation with a carrier of f0 7 and will be modulated between a factor of [ 6 7 , 1]. Continuing the example, if the frequency of modulation is 10Hz the frequency of modulation of each harmonic will take the value shown in the Table 1 The sensitive result of this process ranges from complex movements to timbre modification thanks to the behaviour of the ring modulation with a frequency modulation higher than 20 Hz.

FX/SYN

There are two modes of applying in abc.lib: FX and SYN. FX mode applies the process to the harmonics postencoding. The idea is to be able to control the depth of the treatment on the sound field from a directional sound field to a diffuse sound field. The idea of the SYN mode is that it doesn't matter if the signal is not ambisonic encoded before applying the treatment because the process distorts the coherence of the intermediate representation of space. SYN mode is thought to synthesize directly a diffuse sound field from one mono source. But when the factor is equal to zero, the same signal is sent to all the decoder inputs as if a localized sound field was synthesized the source is localized in one direction6 : 45°. For example, in the first order case, if the same signal is sent to all the entries of a decoder it get close to an encoding of a source at 45°(when the source angle is 45°, the output of Y -1,1 and Y 1,1 are 0.707) and the intermediate representation of space (circular function) has shown in the Figure 7. Consequently, we decided to cut all harmonics except the first when the factor is equal to 0. The objective was to create a strong mono when the factor is equal to zero and to go progressively to a diffuse sound field. We apply gain compensation and progressively fade in the other harmonics when the factor increases between [0, 1 n ]. The Figure 8 shows the gain compensation of the Y 0 per ambisonic order (until 7) versus the factor.

CONCLUSION

In this article we highlighted the potential of 'treatment' oriented approach for spatial audio processing in HOALibrary and abc.lib. We presented the richness of a researchcreation methodology based on an iterative prototyping loop guided by listening with two examples: decorrelation and ring modulation in ambisonics. In the part 2 'Interacting with spatiality' we first provide a summary on ambisonics and the approach of space in HOALibrary. In the section 2.2, we presented a new paradigm to compose and Figure 8. gain compensation per ambisonic order versus the factor control spatial attributes of sound based on the design of macro-parameters. We then suggested that attention given to the access to the functions (the controllers) take a part in the design of that Vaggione calls our 'composable space'. Based on two examples, we explained our methodology in part 3 'Designing digital objects'. First, we presented in the section 3.1 the fine tunings on the delay time equation, then in the section 3.1.2 the different types of distributions between the delay lines that we use in the library. We presented in the section 3.2 the ring modulation and a way to distribute all the frequencies of modulation to the spatial harmonics. Finally, we presented two modes of treatment in HOALibrary and abc.lib: FX and SYN ; we explain our choice to use only the first spatial component when the factor is equal to zero for the SYN mode. In future work, we plan to investigate other treatments of the library7 using the same methodology, combining tests and musical experiments to improve and tune the parameters/metaparameters of the processes. Furthermore, we will investigate the particularity of the ambisonic situation in different multi-channel situations. If processes of abc.lib are applied to the signals associated with harmonics or other multichannel signals, it will be the same mechanism. Nevertheless, we could imagine processes working per order and per degree or other logics that we would need to design.

Figure 1 .

 1 Figure 1. Spherical harmonics indexed by the ACN (Ambisonic Channel Number) in [16] .

Figure 2 .

 2 Figure 2. Help patch of the hoa.fx.decorrelation∼ spatial process.

Figure 3 .

 3 Figure 3. hoa.fx.decorrelation∼ patch.

1 8 functiontypeListing 1 .

 81 abc_2d_fx_decorrelation_ui(n) = fxDecorrelation( n, delay, winfreq, factor, fdbk, functiontype) 2 with { 3 delay = hslider("v:synfxdecorrelation/delay [unit:samples]", 48000, 10, 262144, 1); 4 window = 10; //by default a window of 10 milliseconds for the interpolation of delays // 5 winfreq = 1000. / window;6factor = hslider("v:synfxdecorrelation/ factor", 0, 0, 1, 0.001); 7 fdbk = hslider("v:synfxdecorrelation/fdbk", 0, 0, 0.99, 0.001); example of GUI with Faust in the abc.lib

Figure 4 .

 4 Figure 4. Blockdiagram of the decorrelation in abc.lib

Figure 5 .

 5 Figure 5. Plot of the delay coefficient per harmonic versus the factor.

Figure 7 .

 7 Figure 7. Intermediate representation of space with Y 0 , Y -1,1 and Y 1,1 equal to one. In red the positive and in blue the negative part of the function.

Table 1 .

 1 (Sound 6.2). Modulation frequency per harmonic for 2D 3 th order

	Y ith	f req mod
	Y 0	1.42 Hz
	Y -1,1 2.85 Hz
	Y 1,1	4.28 Hz
	Y -2,2 5.71 Hz
	Y 2,2	7.14 Hz
	Y -3,3 8.57 Hz
	Y 3,3	10.0 Hz

These four papers are written by composers (except the last) which cover electroacoustic, mixed music, electronic music and musical installation. They are focused on their own approach to the spatial dimension of sound, and gives an idea of the range of approaches.

In Head-Related Coordinate System, and the angle is given in anticlockwise

like granulation, wider and rotation of the sound field.

Acknowledgments

This research has been supported by the EUR ArTeC financed by the French National Agency for Research ANR through the PIA ANR-17-EURE-0008. The author would like to thank Atau Tanaka for his advice and proof-reading. The author would like to thank also the Maison des Sciences de l'Homme Paris Nord for hosting this work and specially Anne Sèdes for her advice.

List of sound examples quoted in the paper with short descriptions and links to HAL repository. All audio examples are mono sound encoded and processed in 2D 3 th order, and decoded in binaural (48kHz, 24bits).

Sound 1

• source: loop of an audio excerpt (10sec.) from the composition Compression-Dilatation 6.6 • description: the sound is presented five times, first without decorrelation (10sec.), second with the factor increasing, third with the factor at 1, fourth with the factor decreasing in 10 seconds and finally the sound without decorrelation (10sec.) ;

• parameter: delay = 1000ms, functiontype = 0, factor goes from 0 to 1 in 10 seconds then return to 0 in 10 seconds ; • https://hal.archives-ouvertes.fr/ hal-03637787 6.2 Sound 2

• source: loop ofa clarinet playing A3 ordinario ;

• description: we hear the effect of the factor of ring modulation ; • parameter: f0 = 10, factor goes from 0 to 1 in 10 seconds and after 5 seconds returns to 0 in 10 seconds after 5 seconds ; • https://hal.archives-ouvertes.fr/ hal-03637789 6.3 Sound 3

• source: looped sample of a doublebass doing a Bartok pizzicato ; • description: we hear the insertion of static delay line when the factor increases. First one echo, then two,etc., until we heard seven distinct echos (each harmonic -at the third order in 2D) ; • parameter: delay = 1000ms, functiontype = 0, factor goes from 0 to 1 in 25 seconds ; • https://hal.archives-ouvertes.fr/ hal-03637800 6.4 Sound 4

• source: looped sample of a doublebass doing a Bartok pizzicato ; • description: we hear the delay time of each harmonic increasing progressively when the factor increases ; • parameter: delay = 1000ms, functiontype = 0, factor goes from 0 to 1 in 25 seconds ; • https://hal.archives-ouvertes.fr/ hal-03637802 6.5 Sound 5

• source: looped sample of a doublebass doing a Bartok pizzicato ; • description: we hear the effect of the different delay distribution between the ambisonics component ; • parameter : delay = 1000ms, factor = 1, fd = 0, functiontype goes from 0 to 22 ; • https://hal.archives-ouvertes.fr/ hal-03637803 6.6 Sound 6

• title: Compression -Dilatation ;

• description: this is a sketch of electroacoustic piece composed in the context of the Ph.D research of Goutmann ; • https://hal.archives-ouvertes.fr/ hal-03642163