{"id":1017,"date":"2019-11-29T11:52:49","date_gmt":"2019-11-29T10:52:49","guid":{"rendered":"https:\/\/blogs.futura-sciences.com\/lehning\/?p=1017"},"modified":"2019-11-29T11:53:21","modified_gmt":"2019-11-29T10:53:21","slug":"le-code-des-luthiers-et-la-loi-de-benford","status":"publish","type":"post","link":"https:\/\/blogs.futura-sciences.com\/lehning\/2019\/11\/29\/le-code-des-luthiers-et-la-loi-de-benford\/","title":{"rendered":"Le code des luthiers et la loi de Benford"},"content":{"rendered":"

Les registres d’un grand luthier parisien du XIX\u00b0 si\u00e8cle, Gand & Bernardel, se trouvant de nos jours au mus\u00e9e de la musique, montrent d’\u00e9tonnantes parties chiffr\u00e9es.<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

La ligne de registre ci-dessus concerne la vente d’un violon au prix de 8000 F. Dans la premi\u00e8re partie figure le prix de 10000 F, sans doute le prix demand\u00e9 par le luthier avant n\u00e9gociation. Entre parenth\u00e8ses apr\u00e8s ce prix figure quatre lettres : (exzx) puis ensuite ohxz. Le nombre de lettres incite \u00e0 penser que l’un des deux repr\u00e9sente le prix d’achat du luthier et l’autre le prix de r\u00e9serve en dessous duquel il ne faut pas descendre. Ces indications ont alors un r\u00f4le \u00e9vident : permettre la n\u00e9gociation du prix sans erreur de la prt du vendeur et sans donner le prix de r\u00e9serve \u00e0 l’acheteur. Il est alors logique de penser que le prix de r\u00e9serve est entre parenth\u00e8ses et que l’autre est le prix d’achat.<\/p>\n

La loi de Benford<\/h2>\n

Le mus\u00e9e de la musique a demand\u00e9 l’aide d’un cryptologue, en la personne de Pierrick Gaudry, pour casser le code utilis\u00e9. Pour ce faire, il a examin\u00e9 les lettres se trouvant en t\u00eate des codes en pensant que, comme toutes donn\u00e9es comptables, elle suivait la loi de Benford . Cette loi donne les fr\u00e9quences d’apparition des chiffres en t\u00eate d’un nombre :<\/p>\n\n\n\n\n
Chiffre<\/td>\n1<\/td>\n2<\/td>\n3<\/td>\n4<\/td>\n5<\/td>\n6<\/td>\n7<\/td>\n8<\/td>\n9<\/td>\n<\/tr>\n
Fr\u00e9quence en %<\/td>\n30<\/td>\n18<\/td>\n12<\/td>\n10<\/td>\n8<\/td>\n7<\/td>\n6<\/td>\n5<\/td>\n4<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

(voir une discussion de cette loi dans Toutes les math\u00e9matiques du monde<\/em>, page386)<\/p>\n

En utilisant les fr\u00e9quences d’apparition des lettres dans les codes, on trouve que h repr\u00e9sente 1 et a repr\u00e9sente 2. Des t\u00e2tonnements\u00a0 donnent le reste et la clef est lumineuse pour un marchand de violons puisqu’il s’agit du mot harmonieux :<\/p>\n\n\n\n\n
h<\/td>\na<\/td>\nr<\/td>\nm<\/td>\no<\/td>\nn<\/td>\ni<\/td>\ne<\/td>\nu<\/td>\nx<\/td>\n<\/tr>\n
1<\/td>\n2<\/td>\n3<\/td>\n4<\/td>\n5<\/td>\n6<\/td>\n7<\/td>\n8<\/td>\n9<\/td>\n0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

 <\/p>\n

Dans les diff\u00e9rents registres, on trouve \u00e9galement le code z. Des additions montrent qu’il vaut 0, comme x. Le fait de coder 0 de deux fa\u00e7ons diff\u00e9rentes s’expliquent car le 0 se trouve souvent dans les prix.<\/p>\n

Ainsi, dans le cas de la ligne de registre cit\u00e9e plus haut, ohxz signifie 5100 F, ce qui correspond bien \u00e0 un prix d’achat vraisemblable puisque le prix de vente final a \u00e9t\u00e9 de 8000 F. Le prix de r\u00e9serve exzx \u00e9tait de 8000 F aussi ce qui prouve que l’acheteur a bien n\u00e9goci\u00e9.<\/p>\n

 <\/p>\n

 <\/p>\n

<\/h2>\n

<\/h2>\n

 <\/p>\n","protected":false},"excerpt":{"rendered":"

Les registres d’un grand luthier parisien du XIX\u00b0 si\u00e8cle, Gand & Bernardel, se trouvant de nos jours au mus\u00e9e de la musique, montrent d’\u00e9tonnantes parties chiffr\u00e9es. La ligne de registre ci-dessus concerne la vente d’un violon au prix de 8000 F. Dans la premi\u00e8re partie figure le prix de 10000 F, sans doute le prix … Continuer la lecture de Le code des luthiers et la loi de Benford<\/span> →<\/span><\/a><\/p>\n","protected":false},"author":12,"featured_media":1019,"comment_status":"open","ping_status":"open","sticky":true,"template":"","format":"standard","meta":{"footnotes":"","_links_to":"","_links_to_target":""},"categories":[5,9,63,29],"tags":[387,59,386,384,388,385],"class_list":["post-1017","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-arts","category-cryptologie","category-histoire","category-maths-2","tag-code-secret","tag-cryptologie","tag-luthier","tag-musique","tag-negociation","tag-violon"],"yoast_head":"\nLe code des luthiers et la loi de Benford, par Herv\u00e9 Lehning<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/blogs.futura-sciences.com\/lehning\/2019\/11\/29\/le-code-des-luthiers-et-la-loi-de-benford\/\" \/>\n<meta property=\"og:locale\" content=\"fr_FR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Le code des luthiers et la loi de Benford, par Herv\u00e9 Lehning\" \/>\n<meta property=\"og:description\" content=\"Les registres d’un grand luthier parisien du XIX\u00b0 si\u00e8cle, Gand & Bernardel, se trouvant de nos jours au mus\u00e9e de la musique, montrent d’\u00e9tonnantes parties chiffr\u00e9es. La ligne de registre ci-dessus concerne la vente d’un violon au prix de 8000 F. Dans la premi\u00e8re partie figure le prix de 10000 F, sans doute le prix … Continuer la lecture de Le code des luthiers et la loi de Benford →\" \/>\n<meta property=\"og:url\" content=\"https:\/\/blogs.futura-sciences.com\/lehning\/2019\/11\/29\/le-code-des-luthiers-et-la-loi-de-benford\/\" \/>\n<meta property=\"og:site_name\" content=\"MATH'MONDE, le blog d'Herv\u00e9 LEHNING, agr\u00e9g\u00e9 de math\u00e9matiques\" \/>\n<meta property=\"article:published_time\" content=\"2019-11-29T10:52:49+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2019-11-29T10:53:21+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2019\/11\/violin.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"570\" \/>\n\t<meta property=\"og:image:height\" content=\"380\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u00c9crit par\" \/>\n\t<meta name=\"twitter:data1\" content=\"\" \/>\n\t<meta name=\"twitter:label2\" content=\"Dur\u00e9e de lecture estim\u00e9e\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/blogs.futura-sciences.com\/lehning\/2019\/11\/29\/le-code-des-luthiers-et-la-loi-de-benford\/\",\"url\":\"https:\/\/blogs.futura-sciences.com\/lehning\/2019\/11\/29\/le-code-des-luthiers-et-la-loi-de-benford\/\",\"name\":\"Le code des luthiers et la loi de Benford, par Herv\u00e9 Lehning\",\"isPartOf\":{\"@id\":\"https:\/\/blogs.futura-sciences.com\/lehning\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\/\/blogs.futura-sciences.com\/lehning\/2019\/11\/29\/le-code-des-luthiers-et-la-loi-de-benford\/#primaryimage\"},\"image\":{\"@id\":\"https:\/\/blogs.futura-sciences.com\/lehning\/2019\/11\/29\/le-code-des-luthiers-et-la-loi-de-benford\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2019\/11\/violin.jpg\",\"datePublished\":\"2019-11-29T10:52:49+00:00\",\"dateModified\":\"2019-11-29T10:53:21+00:00\",\"author\":{\"@id\":\"\"},\"breadcrumb\":{\"@id\":\"https:\/\/blogs.futura-sciences.com\/lehning\/2019\/11\/29\/le-code-des-luthiers-et-la-loi-de-benford\/#breadcrumb\"},\"inLanguage\":\"fr-FR\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/blogs.futura-sciences.com\/lehning\/2019\/11\/29\/le-code-des-luthiers-et-la-loi-de-benford\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"fr-FR\",\"@id\":\"https:\/\/blogs.futura-sciences.com\/lehning\/2019\/11\/29\/le-code-des-luthiers-et-la-loi-de-benford\/#primaryimage\",\"url\":\"https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2019\/11\/violin.jpg\",\"contentUrl\":\"https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2019\/11\/violin.jpg\",\"width\":570,\"height\":380},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/blogs.futura-sciences.com\/lehning\/2019\/11\/29\/le-code-des-luthiers-et-la-loi-de-benford\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Accueil\",\"item\":\"https:\/\/blogs.futura-sciences.com\/lehning\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Le code des luthiers et la loi de Benford\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/blogs.futura-sciences.com\/lehning\/#website\",\"url\":\"https:\/\/blogs.futura-sciences.com\/lehning\/\",\"name\":\"MATH'MONDE, le blog d'Herv\u00e9 LEHNING, agr\u00e9g\u00e9 de math\u00e9matiques\",\"description\":\"Comment comprendre le monde moderne sans culture math\u00e9matique ? Acc\u00e9der \u00e0 celle-ci n\u2019exige cependant pas d\u2019apprendre \u00e0 r\u00e9soudre la moindre \u00e9quation.\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/blogs.futura-sciences.com\/lehning\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"fr-FR\"},{\"@type\":\"Person\",\"@id\":\"\",\"url\":\"https:\/\/blogs.futura-sciences.com\/lehning\/author\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Le code des luthiers et la loi de Benford, par Herv\u00e9 Lehning","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/blogs.futura-sciences.com\/lehning\/2019\/11\/29\/le-code-des-luthiers-et-la-loi-de-benford\/","og_locale":"fr_FR","og_type":"article","og_title":"Le code des luthiers et la loi de Benford, par Herv\u00e9 Lehning","og_description":"Les registres d’un grand luthier parisien du XIX\u00b0 si\u00e8cle, Gand & Bernardel, se trouvant de nos jours au mus\u00e9e de la musique, montrent d’\u00e9tonnantes parties chiffr\u00e9es. La ligne de registre ci-dessus concerne la vente d’un violon au prix de 8000 F. Dans la premi\u00e8re partie figure le prix de 10000 F, sans doute le prix … Continuer la lecture de Le code des luthiers et la loi de Benford →","og_url":"https:\/\/blogs.futura-sciences.com\/lehning\/2019\/11\/29\/le-code-des-luthiers-et-la-loi-de-benford\/","og_site_name":"MATH'MONDE, le blog d'Herv\u00e9 LEHNING, agr\u00e9g\u00e9 de math\u00e9matiques","article_published_time":"2019-11-29T10:52:49+00:00","article_modified_time":"2019-11-29T10:53:21+00:00","og_image":[{"width":570,"height":380,"url":"https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2019\/11\/violin.jpg","type":"image\/jpeg"}],"twitter_card":"summary_large_image","twitter_misc":{"\u00c9crit par":"","Dur\u00e9e de lecture estim\u00e9e":"2 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/blogs.futura-sciences.com\/lehning\/2019\/11\/29\/le-code-des-luthiers-et-la-loi-de-benford\/","url":"https:\/\/blogs.futura-sciences.com\/lehning\/2019\/11\/29\/le-code-des-luthiers-et-la-loi-de-benford\/","name":"Le code des luthiers et la loi de Benford, par Herv\u00e9 Lehning","isPartOf":{"@id":"https:\/\/blogs.futura-sciences.com\/lehning\/#website"},"primaryImageOfPage":{"@id":"https:\/\/blogs.futura-sciences.com\/lehning\/2019\/11\/29\/le-code-des-luthiers-et-la-loi-de-benford\/#primaryimage"},"image":{"@id":"https:\/\/blogs.futura-sciences.com\/lehning\/2019\/11\/29\/le-code-des-luthiers-et-la-loi-de-benford\/#primaryimage"},"thumbnailUrl":"https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2019\/11\/violin.jpg","datePublished":"2019-11-29T10:52:49+00:00","dateModified":"2019-11-29T10:53:21+00:00","author":{"@id":""},"breadcrumb":{"@id":"https:\/\/blogs.futura-sciences.com\/lehning\/2019\/11\/29\/le-code-des-luthiers-et-la-loi-de-benford\/#breadcrumb"},"inLanguage":"fr-FR","potentialAction":[{"@type":"ReadAction","target":["https:\/\/blogs.futura-sciences.com\/lehning\/2019\/11\/29\/le-code-des-luthiers-et-la-loi-de-benford\/"]}]},{"@type":"ImageObject","inLanguage":"fr-FR","@id":"https:\/\/blogs.futura-sciences.com\/lehning\/2019\/11\/29\/le-code-des-luthiers-et-la-loi-de-benford\/#primaryimage","url":"https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2019\/11\/violin.jpg","contentUrl":"https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2019\/11\/violin.jpg","width":570,"height":380},{"@type":"BreadcrumbList","@id":"https:\/\/blogs.futura-sciences.com\/lehning\/2019\/11\/29\/le-code-des-luthiers-et-la-loi-de-benford\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Accueil","item":"https:\/\/blogs.futura-sciences.com\/lehning\/"},{"@type":"ListItem","position":2,"name":"Le code des luthiers et la loi de Benford"}]},{"@type":"WebSite","@id":"https:\/\/blogs.futura-sciences.com\/lehning\/#website","url":"https:\/\/blogs.futura-sciences.com\/lehning\/","name":"MATH'MONDE, le blog d'Herv\u00e9 LEHNING, agr\u00e9g\u00e9 de math\u00e9matiques","description":"Comment comprendre le monde moderne sans culture math\u00e9matique ? Acc\u00e9der \u00e0 celle-ci n\u2019exige cependant pas d\u2019apprendre \u00e0 r\u00e9soudre la moindre \u00e9quation.","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/blogs.futura-sciences.com\/lehning\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"fr-FR"},{"@type":"Person","@id":"","url":"https:\/\/blogs.futura-sciences.com\/lehning\/author\/"}]}},"_links":{"self":[{"href":"https:\/\/blogs.futura-sciences.com\/lehning\/wp-json\/wp\/v2\/posts\/1017","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.futura-sciences.com\/lehning\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.futura-sciences.com\/lehning\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.futura-sciences.com\/lehning\/wp-json\/wp\/v2\/users\/12"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.futura-sciences.com\/lehning\/wp-json\/wp\/v2\/comments?post=1017"}],"version-history":[{"count":13,"href":"https:\/\/blogs.futura-sciences.com\/lehning\/wp-json\/wp\/v2\/posts\/1017\/revisions"}],"predecessor-version":[{"id":1036,"href":"https:\/\/blogs.futura-sciences.com\/lehning\/wp-json\/wp\/v2\/posts\/1017\/revisions\/1036"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/blogs.futura-sciences.com\/lehning\/wp-json\/wp\/v2\/media\/1019"}],"wp:attachment":[{"href":"https:\/\/blogs.futura-sciences.com\/lehning\/wp-json\/wp\/v2\/media?parent=1017"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.futura-sciences.com\/lehning\/wp-json\/wp\/v2\/categories?post=1017"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.futura-sciences.com\/lehning\/wp-json\/wp\/v2\/tags?post=1017"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}