Python/Musical intervals (numpy matplotlib)
< Python
This code creates three graphs of musical intervals that deviate from just intonation by a user-selected frequency. The graphs exhibit something analogous to an acoustical beat, except that these beats involve only phase shifts because each wave is a pure sinusoidal. To ensure that all three timescales are identical, it is important that the first graph plotted have the lowest beat frequency (here it is the perfect fifth.)
The code requires numpy and matplotlib. The modules scipy and sound file are called, but may be removed since they are not used in this version of the code. A sample output is shown below:
Plots
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Code
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importnumpyasnp#------------------------numerical operations on large arraysimportmatplotlib.pyplotasplt#-----------creates and displays plotsimportscipy,sys,os,time,math#----------scipy not used herefromscipyimportsignal#------------------signal not used hereimportsoundfileassf#--------------------soundfile not used herestart_time=time.time()#-------------------lets me see run time for code#FORMATTING CONSTANTS ----------------------these determine plot's appearancefigHigh,figWide=3,50#-----------------------figure Height and WidthAmp=1;samplerate=44100#--------------------standard CD sampling (not used)dt=1/samplerate#----------------------------dt to samplerate conversionslw=1#-------------------------------------slw signal's line widthbarx=1#------------------------------------barx quasi-period marker widthbarb=1.4#-----------------------------------barb beat marker widthfs=10#--------------------------------------fontsize, txp (latter not used?)show_images=False#--------------------------show_images: option to show imagesgraph_dots=False#---------------------------graph_dots plots dots (not lines)beat_dots=False#----------------------------beat_dots marks beats with dotsblu,pur="#0072B2","#CC79A7"#----------------colorblind friendly colorsver,sky,yel,bgr="#D55E00","#56b4e9","#F0E442","#009E73"MAR=2#--------------------------------------MAR-normalized margin#ESSENTIAL CONSTANTS------------------------these determine what gets plottedf_00=100#-----------------------------------Longest quasiperiodtmar=MAR/f_00#------------------------------margin at start and stopDf_q=.5#------------------------------------Df_p change p-tone pitchDf_p=0#-------------------------------------THIS SHOULD ALWAYS EQUAL ZEROBTS=1#--------------------------------------BTS=beats_to_showforcountinrange(3):#---------------------counts the three intervals plotted ifcount==0:#-------------------------- 3/2 fifthinterval="fifth 3-2"#--------------- p, q, f_0 definedp,q,f_0=3,2,f_00#-------- 1/f_0 = quasiperiodq_0=qifcount==1:#------------------------------ 7/5 tritoneinterval="tritone 7-5"p,q=7,5f_0=f_00*q_0/qifcount==2:#------------------------------ 8/5 minor sixthinterval="min_6th 8-5"p,q=8,5f_0=f_00*q_0/qprint("count =%i: %s"%(count,interval))T_0=1/f_0#---------------------------------- T_0 quasiperiod f_p=p*f_0#--------------------------------- Defines p-wave pitchf_q=q*f_0f_b=abs(p*Df_q-q*Df_p)#----------------- f_b=2*beat freqT_b=1/f_b#---------------------------------- Defines beat period#Next, I verify that the first graph requires the longest time periodifcount==0:T_M=T_b#----------------------- Check for margin errorifT_b>T_M:sys.exit("Margin error: i=%i"%i)#-cents=abs(1200*(np.log2(1+Df_p/f_p)-np.log2(1+Df_q/f_q)))#------ deviation from just (cents)tmax=BTS*T_b+2*tmar#------------------------ tmax=time plottedtwopi=2*np.pi# (twopi=2*pi)----------------- define twopi=2*piom_p,om_q=(f_p+Df_p)*twopi,(f_q+Df_q)*twopi#-define omega_p omega_q datapoints=int(round(tmax/dt))#------------- datapointsprint("%i datapoints"%(datapoints))#-------- not standard for CD playerst=np.linspace(-tmar,#------------------------create numpy array for timeBTS*T_b+tmar,#-----------------Define timespan with marginsnum=datapoints)yp=Amp*np.cos(om_p*(t))#------------------ yp (numpy array)yq=Amp*np.cos(om_q*(t))#------------------- y = yp + yqy=yp+yq#------------------------------------ (all are numpy arrays)plt.figure(figsize=(figWide,figHigh))#------ plt=variable name of ploti=0# --------------------------------------- initialize beat line locationwhilei*T_0<tmax:#------------------------ Plot quasiperiod markersplt.axvline(x=1/f_0+i/f_0,color=pur,linewidth=barx)i+=1ifgraph_dots:#------------------------------ Plot signal (dots or line)plt.scatter(t,y,s=dotsize,color="k")#--- I used dots to verify lineselse:plt.plot(t,y,color='k',linewidth=slw)#--Lines easier to seeplt.xlim(-tmar,BTS*T_M+tmar)#----------------Sets limits on axis plt.axhline(y=0,color='k',linewidth=slw/4)# Plot axis (y=0)a0=Amp#------------------------------------- Plot y_p and y_q signalsa1=Amp;offset=a0+2*a1#-------------------- Offset signals downwardarr=np.empty(datapoints);arr.fill(offset)#-- Numpy array speeds things upplt.plot(t,a1*yp-arr,color=ver,linewidth=slw)#Plot p-waveplt.plot(t,a1*yq-arr,color=bgr,linewidth=slw)#Plot q-wavei=0#----------------------------------------- Plot beats T_b=1/f_bwhilei*T_b<tmax:# Plots vertical markers for the beatsplt.axvline(x=i*T_b,color=sky,linewidth=barb)i+=1i=0#----------------------------------------- Label quasiperiods T_0whilei*T_0<tmax:s=int(i)#---------------------------------- s=string representing iplt.annotate(s,xy=(i/f_0,2.25*Amp),#------ Places s on t axis at i*T_0 xycoords='data',fontsize=fs,horizontalalignment='center',color=blu,verticalalignment='bottom')i+=1titlestring="%s%5.1f to %5.1f"%(interval,f_p+Df_p,f_q)titlestring+=" (%5.2f cents off)"%(cents)#-------Title for graphpath2image=titlestring+".svg"#-------------------Names svg filepath2image=os.path.join("images",path2image)#---Location for imageplt.xlabel(titlestring,fontsize=fs,loc="left")#---TITLEplt.savefig(path2image,dpi=1600,bbox_inches="tight")ifshow_images:plt.show()#----------------------Show imageprint("T_b=%f for %s"%(T_b,interval))print("---------------- %s seconds"%(time.time()-start_time))soundfile and playsound (pip installed packages)
[edit | edit source]I discoverd that soundfile cannot create large OGG files, probably due their compression. So instead I made WAV files. And I installed playsound so I could hear the interval each time I ran the code. The latest version of the code currently resides at:
