{"id":194,"date":"2020-05-06T13:25:21","date_gmt":"2020-05-06T11:25:21","guid":{"rendered":"http:\/\/www.jacques-rougemont.ch\/?p=194"},"modified":"2020-05-06T20:33:37","modified_gmt":"2020-05-06T18:33:37","slug":"les-intervalles-diatoniques-et-les-autres","status":"publish","type":"post","link":"http:\/\/www.jacques-rougemont.ch\/?p=194","title":{"rendered":"Les intervalles diatoniques (et les autres..)"},"content":{"rendered":"\n

L’harmonie est fond\u00e9e sur un certain nombre d’intervalles bien d\u00e9finis<\/a> mais ne correspondant qu’approximativement \u00e0 des multiples de demi-tons. La Table 1 ci-dessous r\u00e9sume les intervalles essentiels (qui forment les gammes majeures et mineures): chaque intervalle est d\u00e9fini par un rapport rationnel (colonne Rapport<\/strong>) entre la fr\u00e9quence la plus aigu\u00eb et la plus grave. Ce rapport peut \u00eatre approxim\u00e9 par un nombre entier de demi-tons (colonne Chromatisme<\/strong>). La diff\u00e9rence (4e colonne) entre la d\u00e9finition exacte (rationnelle) et l’approximation chromatique<\/a> est: $r-2^{n\/12}$ o\u00f9 $n$ est le nombre de demi-tons et $r$ le rapport exact. On exprime souvent cette diff\u00e9rence sur une \u00e9chelle logarithmique de 100 cents par demi-ton (derni\u00e8re colonne: $\\delta c=100\\cdot(12\\cdot\\log_2(r)-n)$).<\/p>\n\n\n\n

Intervalle<\/th>Rapport<\/th>Chromatisme<\/th>Diff\u00e9rence<\/th>Cents<\/th><\/tr><\/thead>
Seconde min.<\/td>16\/15<\/td>1<\/td>0.007204<\/td> 11.731290<\/td><\/tr>
Seconde maj.<\/td>9\/8<\/td>2<\/td>0.002538<\/td>3.910002<\/td><\/tr>
Tierce min.<\/td>6\/5<\/td>3<\/td>0.010793<\/td>15.641287<\/td><\/tr>
Tierce maj.<\/td>5\/4<\/td>4<\/td>-0.009921<\/td>-13.686286<\/td><\/tr>
Quarte j.<\/td>4\/3<\/td>5<\/td>-0.001507<\/td>-1.955001<\/td><\/tr>
Quarte augm.<\/td>7\/5<\/td>6<\/td>-0.014213<\/td>-17.487810<\/td><\/tr>
Quinte j.<\/td>3\/2<\/td>7<\/td>0.001693<\/td>1.955001<\/td><\/tr>
Sixte min.<\/td>8\/5<\/td>8<\/td>0.012599<\/td>13.686286<\/td><\/tr>
Sixte maj.<\/td>5\/3<\/td>9<\/td>-0.015126<\/td>-15.641287<\/td><\/tr>
(Septi\u00e8me min. basse)<\/td>7\/4<\/td>10<\/td>-0.031797<\/td>-31.174090<\/td><\/tr>
Septi\u00e8me min.<\/td>9\/5<\/td>10<\/td>0.018203<\/td>17.596288<\/td><\/tr>
(Septi\u00e8me min. temp.)<\/td>16\/9<\/td>10<\/td>-0.004020<\/td>$-3.910002<\/td><\/tr>
Septi\u00e8me maj.<\/td>15\/8<\/td>11<\/td>-0.012749<\/td>-11.731285<\/td><\/tr>
Octave<\/td>2<\/td>12<\/td>0<\/td>0<\/td><\/tr><\/tbody><\/table>
Table 1: D\u00e9finition des intervalles purs<\/figcaption><\/figure>\n\n\n\n

Pour illustration, si l’on fixe le la<\/strong> \u00e0 440 [Hz], alors les fr\u00e9quences des notes autour de ce la<\/strong> sont indiqu\u00e9es dans la Table 2, accord\u00e9es selon le rapport exact de l’intervalle correspondant (colonne Naturel<\/strong>) o\u00f9 selon l’\u00e9chelle des demi-tons (colonne Temp\u00e9r\u00e9<\/strong>).<\/p>\n\n\n\n

\n\n\n\n
Note<\/th>Naturel<\/th>Temp\u00e9r\u00e9<\/th><\/tr>\n<\/thead>\n
do<\/td>264<\/td>261.626<\/td><\/tr>\n
r\u00e9<\/td>297<\/td>293.665<\/td><\/tr>\n
mi\u266d<\/td>316.8<\/td>311.127<\/td><\/tr>\n
mi\u266e<\/td>330<\/td>329.628<\/td><\/tr>\n
fa<\/td>352<\/td>349.228<\/td><\/tr>\n
sol<\/td>396<\/td>391.995<\/td><\/tr>\n
la\u266d<\/td>422.4<\/td>415.305<\/td><\/tr>\n
la\u266e<\/td>440<\/td>440<\/td><\/tr>\n
si\u266d<\/td>475.2<\/td>466.164<\/td><\/tr>\n
si\u266e<\/td>495<\/td>493.883<\/td><\/tr>\n
do<\/td>528<\/td>523.251<\/td><\/tr>\n<\/tbody>\n<\/table>
Table 2: Fr\u00e9quences des notes accord\u00e9es sur un la<\/b> \u00e0 440 [Hz]<\/figcaption><\/figure>\n","protected":false},"excerpt":{"rendered":"

L’harmonie est fond\u00e9e sur un certain nombre d’intervalles bien d\u00e9finis mais ne correspondant qu’approximativement \u00e0 des multiples de demi-tons. La Table 1 ci-dessous r\u00e9sume les intervalles essentiels (qui forment les gammes majeures et mineures): chaque intervalle est d\u00e9fini par un rapport rationnel (colonne Rapport) entre la fr\u00e9quence la plus aigu\u00eb et la plus grave. Ce […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[18,16],"tags":[],"_links":{"self":[{"href":"http:\/\/www.jacques-rougemont.ch\/index.php?rest_route=\/wp\/v2\/posts\/194"}],"collection":[{"href":"http:\/\/www.jacques-rougemont.ch\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.jacques-rougemont.ch\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.jacques-rougemont.ch\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.jacques-rougemont.ch\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=194"}],"version-history":[{"count":16,"href":"http:\/\/www.jacques-rougemont.ch\/index.php?rest_route=\/wp\/v2\/posts\/194\/revisions"}],"predecessor-version":[{"id":405,"href":"http:\/\/www.jacques-rougemont.ch\/index.php?rest_route=\/wp\/v2\/posts\/194\/revisions\/405"}],"wp:attachment":[{"href":"http:\/\/www.jacques-rougemont.ch\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=194"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.jacques-rougemont.ch\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=194"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.jacques-rougemont.ch\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=194"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}