Hereafter I report the experiment I performed, in non-scientific conditions, to have a better understanding of the overtone differences between instruments.
I used the instruments i own, while with different level of expertise, and played on them the same C4 or C5 ( concert pitch), recording and analyzing the results using the trial version of the "Overtone Analyzer", although the same could also be achieved using freeware such as "Audacity" and then applying spectral analysis. To generate a plain reference tune I used the app "Tunable".
Yamaha ( Tenor Saxophon, Soprano Saxophone, Clarinet, French Horn)
Mollenhauer ( Sopran Recorder , Alt Recorder )
Jupiter ( Flute )
Holton ( Trombone )
Roth & Junius (Piano)
The diagram confirms that the tune generated by the app indeed has very little overtones. Addditionally, it also shows that all sources generate the same overtones, however with different intensities, and therefore confirms the often mentioned teachings.
Unfortunately, I am not as versed in all those instruments to the same extent, and therefore I am pretty confident that experienced musicians will be able to produce much richer overtones than what I reported in this afternoon experiment at home. I hope that others will make use of this simple demonstration for performing their own experiments in classes and orchestra, and also in this way raise more awareness on the importance of overtones. Perhaps musicians could train themself also in increasing the intensity of the overtones through special techniques - alike overtone singers do. Composers and arrangeurs will also benefit from simple practical experiments such as the one here performed in order to better understand why and how a specific instrument or chord played by different instruments could influence the final music.