From b9e1181a0fb5d8ece4d3c55a25798ed3445e1bec Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Lo=C3=AFc=20Gu=C3=A9gan?= Date: Mon, 28 Oct 2024 15:49:13 +0100 Subject: [PATCH] Minor changes --- source/music/code/pythagoricienne.R | 17 + source/music/figures/harmoniques.svg | 489 +++++++++++++++++++++++++++ source/music/figures/quinte_loup.jpg | Bin 0 -> 35716 bytes source/music/gammes.rst | 10 + source/music/harmoniques.rst | 88 ++++- 5 files changed, 601 insertions(+), 3 deletions(-) create mode 100755 source/music/code/pythagoricienne.R create mode 100644 source/music/figures/harmoniques.svg create mode 100644 source/music/figures/quinte_loup.jpg diff --git a/source/music/code/pythagoricienne.R b/source/music/code/pythagoricienne.R new file mode 100755 index 0000000..6e33967 --- /dev/null +++ b/source/music/code/pythagoricienne.R @@ -0,0 +1,17 @@ +#!/usr/bin/Rscript + +do=261.63 # do frequency convention +N=13 # Number de nouvelle notes +quintes=rep(do,N) # Les nouvelles quintes + +## Calcule l'ensemble des quintes de la gamme +facteurs=(3/2)^(0:(N-1)) # Facteurs relatif au do 261.63 +## On divise par 2 jusqu'à retombé dans notre octave +toOctave=function(x){ + if(x<(2*do+10)) # +10 car la dernière quinte n'est pas parfait et dépasse 2*261.63 + x + else + toOctave(x/2) +} +notes=sort(sapply(quintes*facteurs,FUN=toOctave)) # Generation des notes de la gamme + diff --git a/source/music/figures/harmoniques.svg b/source/music/figures/harmoniques.svg new file mode 100644 index 0000000..75ec212 --- /dev/null +++ b/source/music/figures/harmoniques.svg @@ -0,0 +1,489 @@ + + + + + + image/svg+xml + + + + + + + + + + + + + + + + + + + + + +1/2 + + + +1/3 + + + +2/3 + + + +1/4 + + + +3/4 + + + +1/5 + + + +2/5 + + + +3/5 + + + +4/5 + + + +1/6 + + + +5/6 + + + +1/7 + + + +2/7 + + + +3/7 + + + +4/7 + + + +5/7 + + + +6/7 + + + +1/2 + + + +1/3 + + + +2/3 + + + +1/4 + + + +3/4 + + + +1/5 + + + +2/5 + + + +3/5 + + + +4/5 + + + +1/6 + + + +5/6 + + + +1/7 + + + +2/7 + + + +3/7 + + + 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zw3DKMMyb4P%Ex@WG_5wY165Jd!2k6-$0rPYT4PYcwh1R1WTyVKnEmSa2n|IDj)lke zTc>gk@ra4e?UT-6V>>L__$W5X8Y?IU;P%`jxwo_QpYIu}bnkG+@6_`nU{CBVq$-uF zXoPrUszhPc!6Z+PxtMhLLobsYZ>BBqz*RH;qFYN8XOrlKF-gRLU@fs7nkBgzv+Ud| zUcD`Jf{OZ%KE%@#MpXdN9L}aT>?&e+#;GkDxt(vy*m~9;lz)am!6h&XFJ^N#Gq^`M zO_DTZxYfpir}c6WcdU|`O@jWv0RI30{{Y9m14ktibPr~~!B9v^D+(P5{xc#&Fk3~W zNl;Fd*kNg+icwILH5Hp+|M*&JD#wHdbGq3S?ol^MB z3dc5}1QTOs>MhU-wv;pgo05`_163&Uk=`__ + +Gamme Pythagoricienne +====================== + +En musique, un intervalle est la rapport de deux fréquences. +Un octave corresponds à deux fois la fréquence initiale :math:`f_{octave}=2f_0`. +Il s'agit d'un intervalle important car il sonne extrêmement juste lorsque l'on joue :math:`f_0` et :math:`f_{octave}` simulatanement. + +On note également que le passage à l'octave :math:`f_{octave_i}=2^i*f_0` est une opération qui ne change pas la note de départ! +Ainsi, diviser/multiplier une fréquence par 2, une ou plusieurs fois, laisse la note inchangée. +Un concept très important sur lequelle repose la gamme Pythagoricienne. + +En multipliant par 3 une fréquence :math:`f_0`, on obtient une note +qui correspond quasiment à la quinte de celle-ci. Pourquoi? Car si on +ramène cette quinte sur l'octave the :math:`f_0` (en divisant par 2), +on obtient une fréquence qui correspond quasiment la quinte de cette +octave. Pour rappel, diviser par deux ne change pas la note! + +En répétant ce principe, Pythagore ajoute 12 nouvelle notes l'octave. +En partant d'une fréquence :math:`f_0`, il créer une quinte :math:`f_a=3f_0`. Puis il prends à nouveau la quinte de :math:`f_b=3f_a`. +On oubli pas de divisé chacunes de ce nouvelles fréquences par 2 jusqu'a retomber dans l'octave de :math:`f_0`. +C'est à dire une fréquence :math:`f` tel que :math:`f_0`__, `ScienceÉtonnante `__ + +Gamme Tempéré +============== -game pythagoritienne -game tempéré