Blowing, twanging, strumming, plucking and thumping musical instruments all create magic. In this article I take a cursory look at some of the acoustic properties behind this
Did you ever have a book called "The Physics of Musical Sounds"? My dad gave me a copy in the 70s which I have mislaid. Went into all this stuff. Very good
Thanks for the post, love it. Readers may realize that the bugle, as a single-length tube, also exhibits this harmonic series. The perfomer increases air speed and lip vibrations to excite the higher modes (partials).
After many years of trumpet playing, it dawned on me that the trumpet is comprised of seven differently-lengthed bugles. There are 7 fundamemtals in play. The design is clever as only 3 incremental lengths of tubing, judiciously chosen, are needed. The 3 pistons provide 7 combinations of those 3 incremental tubes, ranging from all engaged (lowest fundamental) to none engaged (highest fundamental).
The use of just 3 tubes does introduce tradeoffs in terms of the resulting pitches at higher partials. Hence professional trumpets allow for the movement of two of the three tubes so the performer can fine-adjust to pitch of the partial (of the selected fundamental) being played.
“Alternate fingerings” are alternate selections that can be chosen by the performer that might be closer to the frequency of the intended note. Different trumpet designs and pitches may yield better or worse results with specific alfernate fingerings.
The primary tube also has a tuning slide that is only used to tune up, generally using the highest fundamental. It is a fine adjustment applied at once for all seven fundamentals.
A Bb trumpet’s highest fundamental will sound a Bb on the piano (written as “C” on Bb trumpet sheet music). An Eb trumpet’s highest fundamental will sound Eb on the piano (also written “C” on Eb trumpet sheet music and “F” on Bb trumpet sheet music).
Haydn and Hummel concertos were written for Eb trumpet. However the ‘natural’ trumpet they were faniliar with uses different means than modern trumpet (just described) for generating the desired fundamentals.
Trumpet vs cornet? Cylindrical vs conical tubing, from the mouthpiece receiver to the tuning slide. It is then cylindrical through the piston section. Upon exiting the pistons the tube can then begin its slow flare out to the bell.
Unlike atrings, there are no fixed endpoints. The fundamental’s “effective” length is measued from a few inches past the bell. I’m told it may begin within the performer’s oral cavity.
The “bore” of a trumpet reflects the choice of diameter of tubing at the pistons (ML = Medium Large is common, L reguires more blowing capability on the part of the performer, and smaller bores require less air but can feel stuffy to someone better matched to larger bores).
What a splendid and informative comment - love it! Yep, tubes do the same thing (essentially). As it so happens I learned trumpet at school but got seduced by the guitar.
Wailing violin string indeed! lol. String players use the sympathetic vibrations of the fundamentals and the harmonic series(consciously or unconsiously) to improve the sound. So we are naturally tending to use the harmonic series, which is not the same as equal temperament. Indeed, when a violin (and presumably the other bowed instruments) is played well, and in tune, using the resonances, the instrument actually improves over time. I don't know the physical reason for this. Also, will you be looking at the Pythagorean comma? it makes tuning the instrument in 5ths very interesting.
LOL - I was being very cheeky when I wrote that! Improvement over time will come about through ageing of the wood. Those breathtaking examples that now command millions were made from trees growing during the little ice age - growth rings are so tightly packed it's tricky to count but this structural density is the basis for that amazing tone. I haven't got plans to take the physics of music further than part 2 of this series because I've got a tremendous amount of material to cover as it is.
The comma comes about because a circle of fifths takes 12 steps in 12-tone western music, each step multiplying the frequency by 1.5 (3/2), which yields an overall factor of 129.75 (1.5^12). Whereas only 7 octaves match this same range, each step multiplying the frequency by 2.0, which yields an overall factor of 128.00 (2^7); this small difference being the comma, with a ratio 129.75/120.00 = 1.01364. To get round this physical discrepancy we have to stretch the tuning one way or other.
The root of the problem essentially lies with 1/3 being an infinite fraction of 0.3333333333...; that is to say man cannot reach the perfection of God, and this reminds me of that famous gap between the fingers on the Sistine Chapel ceiling. That gap is like the comma!
An instrument actually improves over a short period of time if played really well and in tune. It can also quite quickly get very unhappy and unco-operative if played badly. So in some way the vibrations are affecting the whole structure. I like the Sistine Chapel simile :)
Did you ever have a book called "The Physics of Musical Sounds"? My dad gave me a copy in the 70s which I have mislaid. Went into all this stuff. Very good
Sounds like something I need to put on my treats list!
Was it this book?
https://amzn.eu/d/0p0vwR2
Nope - I think this was it - https://www.ebay.co.uk/itm/364762713267
They were closing down the technical library at his place of work and were going to bin everything.
Btw my comp sub to almanac has expired
Sorted!
Cheers… and passion too by the looks… had to do a 7day trial to get back I . Managing this looks like hard work
Sorted. Yep, there's a fair bit of peddling behind the scenes!
Thanks for the post, love it. Readers may realize that the bugle, as a single-length tube, also exhibits this harmonic series. The perfomer increases air speed and lip vibrations to excite the higher modes (partials).
After many years of trumpet playing, it dawned on me that the trumpet is comprised of seven differently-lengthed bugles. There are 7 fundamemtals in play. The design is clever as only 3 incremental lengths of tubing, judiciously chosen, are needed. The 3 pistons provide 7 combinations of those 3 incremental tubes, ranging from all engaged (lowest fundamental) to none engaged (highest fundamental).
The use of just 3 tubes does introduce tradeoffs in terms of the resulting pitches at higher partials. Hence professional trumpets allow for the movement of two of the three tubes so the performer can fine-adjust to pitch of the partial (of the selected fundamental) being played.
“Alternate fingerings” are alternate selections that can be chosen by the performer that might be closer to the frequency of the intended note. Different trumpet designs and pitches may yield better or worse results with specific alfernate fingerings.
The primary tube also has a tuning slide that is only used to tune up, generally using the highest fundamental. It is a fine adjustment applied at once for all seven fundamentals.
A Bb trumpet’s highest fundamental will sound a Bb on the piano (written as “C” on Bb trumpet sheet music). An Eb trumpet’s highest fundamental will sound Eb on the piano (also written “C” on Eb trumpet sheet music and “F” on Bb trumpet sheet music).
Haydn and Hummel concertos were written for Eb trumpet. However the ‘natural’ trumpet they were faniliar with uses different means than modern trumpet (just described) for generating the desired fundamentals.
Trumpet vs cornet? Cylindrical vs conical tubing, from the mouthpiece receiver to the tuning slide. It is then cylindrical through the piston section. Upon exiting the pistons the tube can then begin its slow flare out to the bell.
Unlike atrings, there are no fixed endpoints. The fundamental’s “effective” length is measued from a few inches past the bell. I’m told it may begin within the performer’s oral cavity.
The “bore” of a trumpet reflects the choice of diameter of tubing at the pistons (ML = Medium Large is common, L reguires more blowing capability on the part of the performer, and smaller bores require less air but can feel stuffy to someone better matched to larger bores).
What a splendid and informative comment - love it! Yep, tubes do the same thing (essentially). As it so happens I learned trumpet at school but got seduced by the guitar.
We had guitar class at school but my hands were mittens. More suited to trumpet, my passion. Cheers.
A friend passed this, which you may enjoy, to me overnight. https://x.com/interesting_aIl/status/1798698654271766647
Oh, that is sensational!
Wailing violin string indeed! lol. String players use the sympathetic vibrations of the fundamentals and the harmonic series(consciously or unconsiously) to improve the sound. So we are naturally tending to use the harmonic series, which is not the same as equal temperament. Indeed, when a violin (and presumably the other bowed instruments) is played well, and in tune, using the resonances, the instrument actually improves over time. I don't know the physical reason for this. Also, will you be looking at the Pythagorean comma? it makes tuning the instrument in 5ths very interesting.
LOL - I was being very cheeky when I wrote that! Improvement over time will come about through ageing of the wood. Those breathtaking examples that now command millions were made from trees growing during the little ice age - growth rings are so tightly packed it's tricky to count but this structural density is the basis for that amazing tone. I haven't got plans to take the physics of music further than part 2 of this series because I've got a tremendous amount of material to cover as it is.
The comma comes about because a circle of fifths takes 12 steps in 12-tone western music, each step multiplying the frequency by 1.5 (3/2), which yields an overall factor of 129.75 (1.5^12). Whereas only 7 octaves match this same range, each step multiplying the frequency by 2.0, which yields an overall factor of 128.00 (2^7); this small difference being the comma, with a ratio 129.75/120.00 = 1.01364. To get round this physical discrepancy we have to stretch the tuning one way or other.
The root of the problem essentially lies with 1/3 being an infinite fraction of 0.3333333333...; that is to say man cannot reach the perfection of God, and this reminds me of that famous gap between the fingers on the Sistine Chapel ceiling. That gap is like the comma!
An instrument actually improves over a short period of time if played really well and in tune. It can also quite quickly get very unhappy and unco-operative if played badly. So in some way the vibrations are affecting the whole structure. I like the Sistine Chapel simile :)