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Playing 440 Hz, what are the approximate harmonics for a trumpet? For a flute? This to help students understand the differences when those instruments play the same note.

I've been to many website, including University of New South Wales. I would like spectrum in percentages. For example: --- Flute => 440 Hz - 100% | 880 Hz - 33% | 1320 Hz - 8% | 1760 Hz - 13% | 2200 Hz - 12% | 2640 Hz - 2% | 080 Hz - 12% --- Trumpet => 440 Hz - 100% | 880 Hz - 100% | 1320 Hz - 53% | 1760 Hz - 75% | 2200 Hz - 85% | 2640 Hz - 40% | 3080 Hz - 32% --- Same harmonics - different harmonic amplitudes.

I prefer percentages. Many students have no idea what dB means. Percentages they do understand.

I posted this question a few days ago.  I'm curious if no one has pursued this type of 
question.  Trumpets, etc. have been around for decades.
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  • You'll find plenty of waveform pictures of the sustain portion of trumpet and flute notes. Flute tends more to a sine wave, with predominately even-order harmonics. Trumpet is a rather more complex sound with more odd-order harmonics. But you might be surprised at how SIMILAR the sustained part of the two instruments sound, not how DIFFERENT. A lot of the characteristic of an instrument is in the initial attack. This displays as a very complex - even chaotic - waveform, difficult to analyse. I'm afraid your 'measure the harmonics of the sustain portion' approach may not be terribly useful. – Laurence Payne Nov 9 '20 at 23:50
  • (continued) This fact was exploited by the 'hybrid synthesis' generation of keyboards, notably the Roland D50 and the Yamaha SY range. Computer memory for samples was still limited and expensive, so they sampled the attack, synthesised the sustain and release. It was remarkably successful! This approach continues in the much-respected Kurzweil keyboards that manage to produce remarkably realistic instrumental sounds from remarkably low amounts of sample memory. – Laurence Payne Nov 9 '20 at 23:50
  • @LaurencePayne you may be thinking of clarinet, which (thanks to the cylindrical bore and half-open characteristic) has only odd harmonics. But that doesn't really apply to flute, which though also cylindrical is sufficiently open on both ends to support both even and odd harmonics – like trumpet, but with much lower amplitude. I don't think there's any instrument that has predominantly even harmonics, at least there's no simple physics reason why this would happen. – leftaroundabout Nov 10 '20 at 0:11
  • What kind of students? High school? University? What prevents them from understanding dB? What class? Physics? Music? Would they understand difference between power and amplitude percentages? What exactly are you trying to teach or demonstrate? – user1079505 Nov 10 '20 at 5:35
  • A quick Google search for "flute vs. trumpet spectrum" not only returned thousands of academic articles about this very topic, but also this: physics.stackexchange.com/questions/15385/… – Duston Nov 10 '20 at 14:20
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You can find detailed acoustic information on both trumpet and flute (and many others) on the Music Acoustics website for the University of New South Wales. Here are the pages for

In particular, the trumpet spectra

trumpet spectra

and the flute spectra

flute spectra

Similar information is available in The Physics of Music and Musical Instruments, by David Lapp, Chapter 3, "Modes, Overtones, and Harmonics" (pp. 27-39). (This site appears to be directly related to the UNSW site above insofar as it links to it directly for "further information".)

Again the trumpet spectrum

The first graph is a histogram of the power spectrum for that musical instrument. The first bar on the left is the power of the fundamental frequency, followed by the overtones. Be careful when comparing the relative strength of the overtones to the fundamental and to each other. The scale of the vertical axis is logarithmic. The top of the graph represents 100% of the acoustic power of the instrument and the bottom of the graph represents 80 dB lower than full power (†10-8 less power). The second graph is a superposition of the fundamental wave together with all the overtone waves. Three cycles are shown in each case.

trumpet spectrum

The corresponding flute graphs are not provided, but there are similar graphs for a variety of other instruments.

I did not find graphs corresponding to the two instruments at 440Hz

You may also find another post from SE Music Practice and Theory helpful.

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  • I don't see how this answers the question. Thanks! – Clyde Jan 10 at 14:03

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