# What are the approximate harmonic amplitudes for a trumpet vs flute?

Playing 440 Hz, what are the approximate harmonic amplitudes for a trumpet? For a flute?
This is 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 the frequency 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'm curious if anyone has pursued this type of question.

berkeman
Mentor
Playing 440 Hz, what are the approximate harmonic amplitudes for a trumpet? For a flute?
This is 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 the frequency 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'm curious if anyone has pursued this type of question.
Welcome to PhysicsForums.

One way to figure this out would be to download a free audio spectrum analyzer to your smartphone, and play those tones either live or with a recording. Here is one such app that appeared first on my Google search list:

If you prefer the peaks in percentages, just use the dB readings and convert them. It's pretty easy math, and you could just put the formulas into an Excel spreadsheet to make it more convenient to do repetitively.

DennisN and BillTre
I am creating video clips for students.

Recordings can be misleading. Is it an analog recording or a digital recording of the instrument? A digital recording analyzed with a spectrum analyzer that uses FFT can also add additional unwanted harmonics.

I'm seeking accurate numbers (dB numbers would be fine too). Thanks!

hutchphd
Homework Helper
I am creating video clips for students.

Recordings can be misleading. Is it an analog recording or a digital recording of the instrument? A digital recording analyzed with a spectrum analyzer that uses FFT can also add additional unwanted harmonics.

I'm seeking accurate numbers (dB numbers would be fine too). Thanks!

berkeman
Mentor
A digital recording analyzed with a spectrum analyzer that uses FFT can also add additional unwanted harmonics.
Presumably the app would use an anti-alias pre-filter before performing the FT. You might even be able to set the Lowpass Filter cutoff frequency for the anti-alias filter manually, depending on the app.

https://en.wikipedia.org/wiki/Anti-aliasing_filter

Staff Emeritus
I prefer percentages. Many students have no idea what dB means. Percentages they do understand.
Well, those percentages don't sum to 100%, so I am not sure I understand them.

A clarinet has only odd harmonics (mostly), so that would be a good comparison with flute. Brass is quite complicated, especially with real instruments and not (e.g.) a section of PVC pipe and a funnel.

etotheipi
A trumpet playing 440 Hz sounds different than a flute playing 440 Hz. They sound different because they generate different harmonic amplitudes.

To analyze, I am using MuseScore to create the trumpet sound and the flute sound. Unfortunately, those instruments have vibrato which adds unwanted harmonics (I cannot find instruments that generate sound without harmonics).

I use Audacity to view the sound as a spectrum plot. I use Excel to analyze the end result and generate plots. I convert the dB into percentages - the max volume is 100%.

The attachment provides a summary. I'm seeking information about the procedure to obtain accurate numbers.

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An ideal situation would be to have a trumpet and a flute play 440 Hz => into a high quality microphone => connected to a spectrum analyzer.

=======
My initial perception was that an Swept Spectrum Analyzer would be more accurate than an FFT Spectrum Analyzer.

Then I discovered the KeySight U8903B Performance Audio Analyzer [originally Hewlett Packard] --- https://www.keysight.com/en/pcx-x205218/audio-analyzers?nid=-32511.0.00&cc=US&lc=eng.

This equipment has a 24-bit resolution and two million point FFT. FFT must be ok for this type of analysis.

Know anyone who has this equipment?

#### Attachments

• 196.7 KB Views: 44
berkeman
Mentor
Know anyone who has this equipment?
Nice instruments! Unfortunately, all my analyzers now are for RF. I used to have a swept audio frequency analyzer many years ago, but that is long gone. Plus, as you say, for this application an FT analyzer would work better.

Although, even with a swept analyzer, you can usually put it in "zero span" mode and watch a single frequency. You might try that to get a feel for the vibrato performance of those different instruments. It seems like the different volumes of the resonant chambers between a flute and horn, as well as the different material characteristics, would affect the resonant behavior and sounds.

Klystron
tech99
Gold Member
I don't think we can expect digital audio to provide a correct spectrum due to the use of vocoder compression technique.

tech99, what do you recommend? Thanks!

hutchphd
Homework Helper
I'm seeking accurate numbers (dB numbers would be fine too). Thanks!
Do these numbers need to be "real time" or ex poste facto?
What do you mean by "accurate"? Result will depend upon the individual player. I'm lost on the vibrato...isn't this also player specific.? I must be missing something here: this shouldn't be this hard....a 1 sec input digitized at 44kHz and FFT should do you 1Hz to 20 kHz .

tech99
Gold Member
I should have though that a simple spectrum analyser, such as a software version on a sound card or the i-Phone App mentioned previously, and listening to real instruments, would be satisfactory. I think a reflection free environment is necessary, measure close to the instrument in a "dead" room.

hutchphd
I understand. Yes, there will be different harmonics. However, what harmonics / amplitudes make a trumpet sound like a trumpet, and a flute sound like a flute?

hutchphd
Homework Helper
Do you not think the folks who make synthesizers know these answers? It is what they do.
You could also run this the other way and add in overtones (and maybe more nuances?) to create instrument simulacra. All this data certainly exists. Dr Robert Moog (Ithaca College) unfortunately died in 2005 but there is one place to start your research.

Tom.G
hutchphd
Staff Emeritus
However, what harmonics / amplitudes make a trumpet sound like a trumpet, and a flute sound like a flute?
This assumes facts not in evidence. Only part of what makes a trumpet sound like a trumpet is the steady-state harmonics. A good part of this is the evolution of the sound, particularly the attack. If you ignore this and just go with the harmonics, it won't sound like a trumpet. It will sound like an organ.

tech99, etotheipi, berkeman and 1 other person
atyy

Staff Emeritus