FFT What are the other frequencies when a single piano note is played

Question

I have recorded a piano note G#4/ Ab4 in wav file. I am using the scipy read to read this wav file and plot the FFT, i was expecting just the dominant frequency of 415Hz. The FFT is displaying this frequency but with that there are other frequencies closer to it, which i am not sure why they are seen. Please explain

Original Signal from wav file

FFT of the Original Signal

The peak Frequency is 415.2012138678529 and Amplitude at 2271 bit

But when i check the FFT frequency sequence, i also see these values which are closer to 415 Hz

Following is my code

import scipy.io.wavfile as wavfile
import scipy
import scipy.fftpack as fftpack
from matplotlib import pyplot as plt
import pandas as pd
import numpy as np
import csv

def plotGraph(figNum,x,y,xlabel,ylabel,graphlabel,color,isFFT):
    plt.figure(figNum)
    plt.xscale('log')
    plt.xlabel(xlabel)
    plt.ylabel(ylabel)
    if(isFFT=='true'):
        plt.stem(x, y, label=graphlabel,use_line_collection=True)
    else:
        plt.plot(x, y, color=color,linewidth=4.0,label=graphlabel)    
    plt.legend()

def exportToCSV(x,y,xlabel,ylabel,csvfilename):
    df = pd.DataFrame({xlabel : x, ylabel : y})
    df.to_csv(csvfilename, index=False)

def filtersignal(x,y,xlabel,ylabel,csvfilename):
    mask = y >0
    signal_with_mask = abs(y[mask])
    mean=np.mean(signal_with_mask,dtype=np.float64)
    standard_deviation=np.std(signal_with_mask,dtype=np.float64)
    third_standard_deviation=3*standard_deviation
    df = pd.DataFrame({xlabel : x[mask], ylabel : signal_with_mask - mean})   
    # print(third_standard_deviation,df[df[ylabel] > third_standard_deviation])
    signal_after_filter = df[df[ylabel] > third_standard_deviation]
    signal_after_filter.to_csv(csvfilename,header=None,index=False)

def setPlotParams():
    params = {'legend.fontsize': '20',
          'font.family': 'Times New Roman Bold',
          'font.size': '15',
          'axes.labelsize': 'x-large',
          'axes.labelweight': 'bold',
          'axes.titlesize':'x-large',
          'xtick.labelsize':'x-large',
          'ytick.labelsize':'x-large',
          'font.weight':'bold'}
    plt.rcParams.update(params)

  
def plotBarGraphFromCSV(figNum,csvfile1,csvfile2,xlabel,ylabel):
    Original_X = []
    Original_Y = []
    
    Reconstructed_X = []
    Reconstructed_Y = []
    
    with open(csvfile1,'r') as csvfile:
        plots = csv.reader(csvfile, delimiter=',')
        for row in plots:
            Original_X.append(float(row[0]))
            Original_Y.append(float(row[1]))
            
    with open(csvfile2,'r') as csvfile:
        plots = csv.reader(csvfile, delimiter=',')
        for row in plots:
            Reconstructed_X.append(float(row[0]))
            Reconstructed_Y.append(float(row[1]))
    
    plt.figure(figNum)
    lenx=len(Original_X)
    rlenx=len(Reconstructed_X)
    ind = np.arange(lenx) 
    indr = np.arange(rlenx)
    width = 0.35 
    plt.bar(ind, Original_Y, width, color='blue', label='Original Sample')
    plt.bar(indr + width, Reconstructed_Y, width,color='green',label='Reconstructed FFT Sample')
    plt.xlabel(xlabel)
    plt.ylabel(ylabel)
    plt.legend()
    plt.show()
    
# -----------------------Read the wav file to generate Time---------------
# wavFileName ="latest/PuriyaWOTanpura.wav"
wavFileName ="piano_Ab4.wav"
sample_rate, sample_data = wavfile.read(wavFileName)
print ("Sample Rate or Sampling Frequency is", sample_rate," Hz")
print(sample_data.dtype)
l_audio = len(sample_data.shape)

print ("Channels", l_audio,"Audio data shape",sample_data.shape,"l_audio",l_audio)
if l_audio == 2:
    sample_data = sample_data.sum(axis=1) / 2
N = sample_data.shape[0]
length = N / sample_rate
print ("Duration of audio wav file in secs", length,"Number of Samples chosen",sample_data.shape[0])
time =np.linspace(0, length, sample_data.shape[0])
sampling_interval=time[1]-time[0]
#---------------FFT of Original signal-----------------------
fft_amplitude=2.0*np.abs(fftpack.fft(sample_data)/len(time))
fft_freqs=fftpack.fftfreq(len(time),sampling_interval)
idx = np.argmax(np.abs(fft_amplitude))
freq = fft_freqs[idx]
freq_in_hertz = abs(freq * sample_rate)
print('Frequency ',freq,' Amplitude ',idx)
mask = fft_freqs > 0
#---------------Inverse FFT------------------------------------
inverse_fft_amplitude = scipy.ifft(fftpack.fft(sample_data))
#-----------------------Graph plotting----------------------------
setPlotParams()
plotGraph(1,time,sample_data,'Time [s]','Sample Data [bits]','Time vs Sample Data','red','false')
plotGraph(2,fft_freqs[mask],fft_amplitude[mask],'Frequency [Hz]','Sample Data [bits]','Frequency vs Sample Data','blue','true')
plotGraph(3,time,inverse_fft_amplitude,'Time [s]','Sample Data [bits]','Time vs Sample Data','green','false')
# -----------------------Exporting Results to CSV-----------------------------
exportToCSV(time,sample_data,'Time','Sample Data','OriginalData.csv')
exportToCSV(fft_freqs[mask],fft_amplitude[mask],'Frequency','Sample Data','FFTDataSet.csv')
exportToCSV(time,inverse_fft_amplitude,'Time','Sample Data','ReconstructedDataSet.csv')
# -----------------------Plot Original and Reconstructed Signal-------------
filtersignal(time,sample_data,'Time','Sample Data','OriginalDataWithMask.csv')
filtersignal(time,inverse_fft_amplitude,'Time','Sample Data','ReconstructedDataSetWithMask.csv')
plotBarGraphFromCSV(4,'OriginalDataWithMask.csv', 'ReconstructedDataSetWithMask.csv','Time [s]','Sample Data [bits]')