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Sekunde & $3$, $4$, $5$ & $\frac{25}{24}$, $?$, $\frac{16}{15}$ \\ - große Sekunde & $8$, $9$ & $\frac{10}{9}$, $\frac{9}{8}$ \\ - kleine Terz & $13$, $14$ & $\frac{32}{17}$, $\frac{6}{5}$ \\ - große Terz & $17$, $18$ & $\frac{5}{4}$, $\frac{81}{64}$ \\ - Quarte & $22$ & $\frac{4}{3}$ \\ + große Sekunde & $8$, $9$ & $\frac{10}{9}$, $\frac{9}{8}$& $\checked (\frac{9}{8})$, $-4 ct$ \\ + kleine Terz & $13$, $14$ & $\frac{32}{17}$, $\frac{6}{5}$ & $(\checked) (\frac{32}{27})$, $+6ct.$\\ + große Terz & $17$, $18$ & $\frac{5}{4}$, $\frac{81}{64}$ & $(\checked) (\frac{81}{64})$, $-8ct.$ \\ + Quarte & $22$ & $\frac{4}{3}$ & $\checked$, $+2ct.$\\ Tritonus & $26$, $27$ & $\sqrt{2} \approx \frac{7}{5}, \frac{10}{7}, \frac{17}{2}$ \\ - Quinte & $31$ & $\frac{3}{2}$ \\ + Quinte & $31$ & $\frac{3}{2}$ & $\checked$, $-2ct.$\\ kl. Sexte & $35$, $36$ & $\frac{128}{81}, \frac{8}{5}$\\ - gr. Sexte & $39$, $40$ & $\frac{5}{3}, \frac{27}{16}$\\ - kl. Septime & $43$, $44$, $45$ & $\frac{7}{4}$, $\frac{16}{9}$, $\frac{9}{5}$\\ + gr. Sexte & $39$, $40$ & $\frac{5}{3}, \frac{27}{16}$ & $(\checked) (\frac{27}{16})$, $-6ct.$\\ + kl. Septime & $43$, $44$, $45$ & $\frac{7}{4}$, $\frac{16}{9}$, $\frac{9}{5}$ & $\checked (\frac{16}{9})+4ct.$\\ \end{tabular} \end{table} + + +\todo{Aufgabe 2, Stück in EDO53} + + \begin{definition} + \vocab{leittönig} $\coloneqq$ keine großen Halbtonschritte + + \end{definition} + + + Buchempfehlung: ``A Geometry of Music'' - Dmitri Tymoczko + + \begin{definition} + Wir definieren eine Metrik auf der Menge der Tonvorräte, wobei $\text{dist}(T, T')$ die minimale Anzahl an Halbtonschritten sei, die geändert werden müssen, um von $T$ zu $T'$ zu gelangen. + \end{definition} + + + \begin{definition} + Eine \vocab{Modulation} ist ein Wechsel c$\sharp$\footnote{Enhamonisch auch als $d\flat$ bekannt} Tonvorrates, der nicht auf komplett absurde Weise geschieht. (``lokal sinnvoll'') + \end{definition} + + Tonvorräte: + \begin{itemize} + \item $n=2$ : + \begin{itemize} + \item 6,6 (Halbtonschritte EDO12) + z.B. $C, F\sharp$ + \item $7,5$ + z.B. $C,G$ + \end{itemize} + \end{itemize} diff --git a/music_bg.pdf b/music_bg.pdf new file mode 100644 index 0000000000000000000000000000000000000000..428f53a689229a544274ad6d5e1fefaa771dfd25 GIT binary patch literal 47314 zcmaf(1yo$gwy=W-celpf-QC^YY24l2-3cDt-Gc>phv4o3f(4iSWai%c-#0Vsz0-?D z^{!J@TfV*PoLWt$C@N0JM9&IOw!1ey4-dn{0bm5!8(YEi@-oO;+5wH6EWLoH044@m z04oOz6DxxPfQgGi48X$1!OqAa|K6brU}fiG=3tNn=m0ob*a6IpoO=BH@IX7$-_rp8 zcEQ7VI04Q6Sc#bf9)|H>7ZW?+j~2l0-!dj&X~R~b7K^WXGi=Vbrex*TkOvzLX5 zh4HVturRT){dFu06Bi@bU)E(|VdeO{jN@Zoi3R zVrS4)2AZk3*aCh}#Gq_%?*d?YR~n$qAZ2G}4|t#FcT-e{my?N=g^Qh;jYUXUNK~9v zNLW-@gqc&6OPGsMn3Ib`grAp-Swx(Tk)4%;Lx@$Jm6eT)U7U%XgOyc;O;m)Pja8KY zH_%}`rFc(8w9W53t1Zi#ah*E(@umpN_`A~;VY>$+)# zA&QY9656Lpz|iMd#s+ix1q*KgB+ka|2Vs^Up*np-U+Zo;MN^FE1Oq@mn4F@%8}gp1 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