Objective measurements of tone?

[sgf]

When someone describes a tone, they say words like "bright", "muted", "full". I don't always know what that person means, or if we are even using the same terms for the same effects. So I did some recordings on different tubas and I felt this was a good place to share results and see if anyone has any interesting insights.

I had a few hypothesis going into this:

1. The larger (Bb / C) tubas would have more noise at higher pitches - Conclusion: False
2. The smaller instruments would have a more pure tone at higher pitches, but there would be visible distortion at lower pitches - Conclusion: False
3. The open-bugle notes would show some sort of better quality than notes with valves - Conclusion: False
4. The fundamental (2nd partial) would show some sort of better quality than higher partials - Conclusion: False

I recorded/compared four tubas:

1. Melton Mienl Weston 2250 (F)
2. Besson Soverign (Eb)
3. Melton 30 (C)
4. Besson Soverign (Bb)

Instead of a musical microphone, I used a spectral microphone which has been calibrated to have uniform frequency response from 20Hz to 15KHz.

Here's a fourier analysis of the F tuba playing its fundamental (F2):

Screenshot_20240106_152007.png

The first thing I liked was that the partials/harmonics are clearly visible. I added a few note names at the top. In the first octave, you only get the root note. But in the next octave, you get the fifth added. In the third octave, you get the major third and dominant seventh creating a reasonable chord! After that, the we start getting to the -80dB range, so it's pretty quiet. I was really surprised to see how loud those partials were. Volume here is in dB, so a 3dB drop on this plot represents the volume being half as soft. I repeated this with a few other instruments, and they all exhibit this in some form or another.

Here are the four tubas playing a Bb in the middle of the bass clef:

Screenshot_20240106_145529.png

If I compare these instruments, there are a few things that stand out. The main one is that you can actually see each tuba's quality. The best sounding tuba here was the C tuba. Here we can see that the space between partials is very low. This means there is very little noise between each partial. It also has the quietest 2nd partial (the others are much louder). The Bb and Eb really start to show a lot of noise from the 3000-5000 Hz range, and these were definitely the worst sounding tubas of the set.

I did a few other recordings and here were some of my takeaways:

I tried to play a pedal F (F1) with the F tuba, open-bugle and then with all five valves pressed and slides pulled. With the pedal, F1 was actually one of the quietest notes played. F2, C3, F3 ... were all louder than it, up until around C5. When comparing the two plots, the C4-F4 partials were quieter when played open-bugle, while they were about the same volume as the F2-A3 peaks when played with valves pressed.

In a lot of the notes, the Eb tuba had louder harmonics. I interpreted this as sounding "brighter". It also had more noise between each harmonic and a lot of noise above 1000 Hz which I interpreted as a "windy" sound.

I didn't see any tubas looking better than the others when playing in a certain range, or playing their fundamental. That surprised me. It seems that the tuba's quality dominates the differences. There were lots of cases where high notes looked just as good on the F as on the C and cases where low notes looked just as good on the F as on the Bb. I was expecting Eb would be a note that would shine for the Eb tuba (open) and compromise the C tuba (2+3).

I tried Bb3 on a few other instruments. Trumpet surprised me in that it was louder in its partials from Bb4 to Bb6 were all louder than Bb3. That goes well with the "louder harmonics=bright" theory.

Screenshot_20240106_151820.png

Curious if anyone else thinks this is interesting.

[circusboy]

I think it's interesting, though I can't say that I understand it terribly well. I'd be curious to see a similar test with, say, the BBb tubas from four different manufacturers.

[daktx2]

Love seeing these kinds of measurement, and I'd love to see a survey of a bunch of those compiled as some actual quantitative analysis on a DMA/PHD in music.

A couple of specific spectrograph comparisons that would be cool to see are:

1) an okay amateur and a real pro, playing the same notes at about the same volume on the same tuba. We all know it's not all about the equipment, and seeing that difference measured objectively would be informative!

2) a new and an old Miraphone 186 C tuba, and/or a new and old B and S Symphonie / PT8 F tuba. There have been rivers of ink spilled about the qualities of the old, sheet metal hand hammered versions of these tubas, and how their construction makes them play differently from the new ones. I'd love to see what the measurable differences there are, and I wonder if it's related to the ratio of high frequency junk noise to higher frequency harmonics.

[tylerferris1213]

A number of years ago someone did something very similar to this where they compared a Miraphone 186 to a York Master to try to quantify the difference between "German" and "American" sound. The researcher did find differences between them. I believe the York's American sound came from a much stronger overtone series and a comparatively weak fundamental, with the 186 being vice-versa.

I think it would be enlightening to gather a bunch of tubas from the same manufacturer that are all in the same key, but different sizes. I'm sure I'm not alone in my curiosity of why a BAT sounds so dang good lol. Something like comparing a Miraphone 184, 185, 186, and 188 for example.

On the point of open bugle vs valved notes being empirically the same, can we finally do away with the practice of pulling slides instead of using alternate fingerings!? lol. I'm tired of people telling me they "pull for purity of tone."

[daktx2]

It was Rick Denney who did the 186 vs York Master comparison, interesting stuff!

https://www.rickdenney.com/the_tuba_sound.htm

[sgf]

That 186 vs York looks interesting. I kept the whole spectrum in my plots, but Denney reduces that down to comparing the maximum of each overtone. I particularly like the last plot where he plots the relative differences. We see the York is stronger in the 2nd overtone, but weaker in the 4th and 5th.

[peterbas]

When someone describes a tone, they say words like "bright", "muted", "full". I don't always know what that person means, or if we are even using the same terms for the same effects. So I did some recordings on different tubas and I felt this was a good place to share results and see if anyone has any interesting insights.

I had a few hypothesis going into this:

1. The larger (Bb / C) tubas would have more noise at higher pitches - Conclusion: False
2. The smaller instruments would have a more pure tone at higher pitches, but there would be visible distortion at lower pitches - Conclusion: False
3. The open-bugle notes would show some sort of better quality than notes with valves - Conclusion: False
4. The fundamental (2nd partial) would show some sort of better quality than higher partials - Conclusion: False

I recorded/compared four tubas:

1. Melton Mienl Weston 2250 (F)
2. Besson Soverign (Eb)
3. Melton 30 (C)
4. Besson Soverign (Bb)

Not much objective going around. You decide that the Melton 30 is the best sounding based on what?
What is a pure tone? How do you define distortion on a complex wave like produced on an instrument?
There is research on what words used to describe sound quality that can be used meaning the same for most people but they are few.
A 3 dB drop isn't half the volume for our ears, it is more the limit of hearing a change in volume. -10 dB in sound level is sounding half as loud for our ears.

Science is hard!