Harmonietöne

Siehe auch Schwebungen

Prof. Dr. Dörte Haftendorn, Mai 06, https://mathe.web.leuphana.de      Juni 2013

Die Posaunentöne

Clear[B1,B,f,b,d1,f1,as1,b1];fpos=58.3;

B1p= Play[Sin[2 π fpos*1*t],{t,0,3}];
            Bp= Play[Sin[2 π fpos*2*t],{t,0,3}];
            fp= Play[Sin[2 π fpos*3*t],{t,0,3}];
            bp= Play[Sin[2 π fpos*4*t],{t,0,3}];
          d1p= Play[Sin[2 π fpos*5*t],{t,0,3}];
          f1p= Play[Sin[2 π fpos*6*t],{t,0,3}];
      as1p= Play[Sin[2 π fpos*7*t],{t,0,3}];
  b1p= Play[Sin[2 π fpos*8*t],{t,0,3}];

Manipulate[
 Play[Sin[2 π fpos*n*t],{t,0,3}]
,{{n,4},1,12,1}]

Show[B1p,Bp,fp,bp,d1p,f1p,as1p,b1p]

das war:   B1,B,f,b  ,d1,f1,as1,b1

Jagdsignal

Show[f1p,d1p,f1p,bp,d1p,fp,fp,bp]

Tonleiter ab C

Tondefinitonen

Clear[CC,DD,B,f,b,d1,f1,as1,b1,d,f,a];

fgr=132

132

CC[td_]:=Play[Sin[2 π*fgr*1t],{t,0,td}, DisplayFunction->Identity];
c[td_]:=Play[Sin[2 π*fgr*2t],{t,0,td},
DisplayFunction->Identity];
g[td_]:=Play[Sin[2 π*fgr*3t],{t,0,td},DisplayFunction->Identity];
c1[td_]:=Play[Sin[2 π*fgr*4t],{t,0,td},DisplayFunction->Identity];
e1[td_]:=Play[Sin[2 π*fgr*5t],{t,0,td},
DisplayFunction->Identity];
g1[td_]:=Play[Sin[2 π*fgr*6t],{t,0,td},DisplayFunction->Identity];
x1[td_]:=Play[Sin[2 π*fgr*7t],{t,0,td},
DisplayFunction->Identity];
c2[td_]:=Play[Sin[2 π*fgr*8t],{t,0,td},DisplayFunction->Identity];
d2[td_]:=Play[Sin[2 π*fgr*9t],{t,0,td},DisplayFunction->Identity];
g2[td_]:=Play[Sin[2 π*fgr*12t],{t,0,td},DisplayFunction->Identity];
h2[td_]:=Play[Sin[2 π*fgr*15t],{t,0,td},DisplayFunction->Identity];
c3[td_]:=Play[Sin[2 π*fgr*16t],{t,0,td},DisplayFunction->Identity];

h1[td_]:=Play[Sin[2 π*fgr*15/2t],{t,0,td},DisplayFunction->Identity];
h[td_]:=Play[Sin[2 π*fgr*15/(2^2)t],{t,0,td},DisplayFunction->Identity];
H[td_]:=Play[Sin[2 π*fgr*15/(2^3)t],{t,0,td},DisplayFunction->Identity];
H1[td_]:=Play[Sin[2 π*fgr*(15/16)t],{t,0,td},DisplayFunction->Identity];
A[td_]:=Play[Sin[2 π*fgr*(5/3)t],{t,0,td},DisplayFunction->Identity];
a[td_]:=Play[Sin[2 π*fgr*(5/3)*2t],{t,0,td},DisplayFunction->Identity];
a1[td_]:=Play[Sin[2 π*fgr*(5/3)*(2^2)t],{t,0,td},DisplayFunction->Identity];
a2[td_]:=Play[Sin[2 π*fgr*(5/3)*(2^3)t],{t,0,td},DisplayFunction->Identity];
e[td_]:=Play[Sin[2 π*fgr*5/2t],{t,0,td},DisplayFunction->Identity];
e2[td_]:=Play[Sin[2 π*fgr*5*2t],{t,0,td},DisplayFunction->Identity];
x[td_]:=Play[Sin[2 π*fgr*7/2t],{t,0,td},DisplayFunction->Identity];
X[td_]:=Play[Sin[2 π*fgr*7/(2^2)t],{t,0,td},DisplayFunction->Identity];
x2[td_]:=Play[Sin[2 π*fgr*7*2t],{t,0,td},DisplayFunction->Identity];
d1[td_]:=Play[Sin[2 π*fgr*9/2t],{t,0,td},DisplayFunction->Identity];
d[td_]:=Play[Sin[2 π*fgr*9/(2^2)t],{t,0,td},
DisplayFunction->Identity];
DD[td_]:=Play[Sin[2 π*fgr*9/(2^3)t],{t,0,td},
DisplayFunction->Identity];
F[td_]:=Play[Sin[2 π*fgr*(4/3)t],{t,0,td},
DisplayFunction->Identity];
f[td_]:=Play[Sin[2 π*fgr*(4/3)t*2],{t,0,td},
DisplayFunction->Identity];
f1[td_]:=Play[Sin[2 π*fgr*(4/3)t*(2^2)],{t,0,td},
DisplayFunction->Identity];
f2[td_]:=Play[Sin[2 π*fgr*(4/3)t*(2^3)],{t,0,td},
DisplayFunction->Identity];

fgr=220;

Nochmal die Naturtonreihe (nicht nötig)

fgr=440*(6/5)*(2^(-3))
%//N

Show[CC[3],c[3],g[3],c1[3],e1[3],g1[3],x1[3],c2[3]]

Tonleitern anhören

Play[c[2],d[2],e[2],f[2],g[2],a[2],h[2],c1[2]]

fgr:=110;
Show[c1[2],d1[2],e1[2],f1[2],g1[2],a1[2],h1[2],c2[2]]

Akkorde definieren und anhören

Quinte

fgr=440;
Play[{Sin[2 π*fgr*1*t]+Sin[2 π*fgr*3/2*t]},{t,0,3}]

akkord[fgr_,fak1_,fak2_, td_]:=Play[{Sin[2 π*fgr*fak1*t]+Sin[2 π*fgr*fak2*t]},{t,0,td}];
akkord[fgr_,fak1_,fak2_,fak3_, td_]:=Play[{Sin[2 π*fgr*fak1*t]+Sin[2 π*fgr*fak2*t]+Sin[2 π*fgr*fak3*t]},{t,0,td}];

Show [akkord[220,1,5/4,3/2,3]]

quinte[fgr_,td_]:=akkord[fgr,1,3/2,td];
quarte[fgr_,td_]:=akkord[fgr,1,4/3,td];
terzG[fgr_,td_]:=akkord[fgr,1,5/4,td];
terzK[fgr_,td_]:=akkord[fgr,1,6/5,td];
sekundeG[fgr_,td_]:=akkord[fgr,1,8/9,td];
sexte[fgr_,td_]:=akkord[fgr,1,5/3,td];

tonikaDur[fgr_,td_]:=akkord[fgr,1,(5/4),(3/2),td];
subdomDur[fgr_,td_]:=akkord[fgr,1/2,(4/3),(5/3),td];
dominanteDur[fgr_,td_]:=akkord[fgr,(3/2),(9/8),(15/16),td];
tonikaMoll[fgr_,td_]:=akkord[fgr,1,(6/5),(3/2),td];

fgr=440;

Kadenz

Show[tonikaDur[fgr,3],subdomDur[fgr,3],
dominanteDur[fgr,3],tonikaDur[fgr,3]]

Alle Vögel sind schon da

fgr=440

Show[tonikaDur[fgr,3],subdomDur[fgr,1.5],tonikaDur[fgr,1.5],dominanteDur[fgr,1.5],tonikaDur[fgr,1.5],
dominanteDur[fgr,1.5],tonikaDur[fgr,2]]

Ton mit Klangfarben

klang[fgr_,a1_,a2_,a3_,a4_,a5_,a6_]:=Play[a1 Sin[2 π*fgr*1t]+a2 Sin[2 π*fgr*2t]+a3 Sin[2 π*fgr*3t]+a4 Sin[2 π*fgr*4t]+a5 Sin[2 π*fgr*5t]+a6 Sin[2 π*fgr*6t],{t,0,5}];

klangp[fgr_,a1_,a2_,a3_,a4_,a5_,a6_]:=Plot[a1 Sin[2 π*fgr*1t]+a2 Sin[2 π*fgr*2t]+a3 Sin[2 π*fgr*3t]+a4 Sin[2 π*fgr*4t]+a5 Sin[2 π*fgr*5t]+a6 Sin[2 π*fgr*6t],{t,0,0.01}];

floe=440;
floeteEcht    =klang[floe,1000,100,100,100,10,1];  (* Dasselbe eintragen *)
floeteEchtp=klangp[floe,1000,100,100,100,10,1];

Show[floeteEcht]

Show[floeteEchtp]

Weitere

Show[floete3]

Show[floete0]

Show[floete1]

Show[floete2]

Show[floeteEcht,floete0,floete1,floete0,floete2]

Show[klang[300,200,0,50,0,10,1]]

Show[klang[300,200,0,0,0,0,0]]

floe=440;
floeteEcht=klang[floe,1000,700,400,70,10,1];
floete1=klang[floe,200,70,50,20,10,1];
floete2=klang[floe,400,0,50,0,10,1];
floete3=klang[floe,400,100,400,0,10,1];
floete0=klang[floe,200,0,0,0,0,0];

floe=440;
floeteEchtp=klangp[floe,1000,700,400,70,10,1];
floete1p=klangp[floe,200,70,50,20,10,1];
floete2p=klangp[floe,400,0,50,0,10,1];
floete3p=klangp[floe,400,100,400,0,10,1];
floete0p=klangp[floe,200,0,0,0,0,0];

Plot dazu

floe=440;
floeteEchtp=klangp[floe,1000,700,100,70,10,1];
floete1p=klangp[floe,200,70,50,20,10,1];
floete2p=klangp[floe,400,0,50,0,10,1];
floete3p=klangp[floe,400,100,400,0,10,1];
floete0p=klangp[floe,200,0,0,0,0,0];

Show[floeteEchtp]

Show[floete3p]