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SYOS

Shouldn't harmonics be exactly in tune?

Colin the Bear

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12,648
We all go through the tuner stage. Tuners aren't in tune. Octave divided into 12. Not on my saxophone.

I use harmonics to tune the saxophone.

Having said that a tuner is handy to tune a banjo or any stringed instrument with a moveable bridge.
 

randulo

Playing alto 2.25 years
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I misread the graphic you posted and thought it was the app I mentioned in the other thread. Yes, Audacity is a workhorse, one of the best free, multi-platform apps ever.
 

jbtsax

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In "Fundamentals of Musical Acoustics" Arthur Benade writes to "avoid confusion" the term "harmonics" should be used only for frequencies that are an exact whole number multiple of the frequency of the fundamental. Those "overtones" that are not exact he calls "partials".

So using Bende's terminology the answer to the question posed in the title of this thread is YES. :)
 

Hipparion

Member
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242
Shouldn't it also depend on the definition of "in tune" too? (As others underlined before)
In "Fundamentals of Musical Acoustics" Arthur Benade writes to "avoid confusion" the term "harmonics" should be used only for frequencies that are an exact whole number multiple of the frequency of the fundamental. Those "overtones" that are not exact he calls "partials".

So using Bende's terminology the answer to the question posed in the title of this thread is YES. :)
 

randulo

Playing alto 2.25 years
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I'd take it one step further. By the laws of physics, they are in tune. Our concept of tempering the scale is not. However none of it matters, what you want is to sound good.
 

jbtsax

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Shouldn't it also depend on the definition of "in tune" too? (As others underlined before)
I see your point. In terms of "pure tuning" when harmonics are whole number multiples of the frequency of the fundamental: The 2nd harmonic is a perfect octave, the 3rd harmonic is a perfect fifth above that, the 4th harmonic is a perfect fourth above that, and the 5th harmonic is a major third above that. From there on I think it gets a bit "dicey".
 

Dibbs

Member
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659
Here we go again.

Harmonics has two meanings.

1. The harmonic component frequencies of a sound.
2. Notes produced by a string or air column vibrating in a higher mode.

The former are perfectly in tune in the sense that they are integer multiples of the fundamental. The latter typically aren't.

Also, just to make it more confusing, the (meaning 1) harmonics of a (meaning 2) harmonic are perfectly in tune.
 

Pete Effamy

Senior Member
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2,027
Here we go again.

Harmonics has two meanings.

1. The harmonic component frequencies of a sound.
2. Notes produced by a string or air column vibrating in a higher mode.

The former are perfectly in tune in the sense that they are integer multiples of the fundamental. The latter typically aren't.

Also, just to make it more confusing, the (meaning 1) harmonics of a (meaning 2) harmonic are perfectly in tune.
Then why do upper fingerings differ from the fundamentals? Is it merely that the pipe has been cut into with the tone holes?
 

Dibbs

Member
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659
Yes, and a few other things as explained here.

Taken from here: How harmonic are harmonics?

"
Real pipes
have inharmonic resonances because of their finite diameter: the end effects are frequency dependent. The pipes of musical instruments are complicated by departures from cylindrical or conical shape (valves and tone holes). Some of these complications are there to improve the harmonicity, but the results are rarely perfect. For any one note, however, the lip or the reed performs the same (strongly non-linear) role as the bow: the lip or reed undergoes periodic vibration and so produces a harmonic spectrum. Again, the operating mode of a brass or woodwind instrument playing a steady* note is a compromise among the tunings of all of the (slightly inharmonic) pipe resonances (mode locking again.)
"
 

Admitone

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139
the lip or reed undergoes periodic vibration and so produces a harmonic spectrum.
No doubt the reed starts things off and vibrates at a fundamental frequency, but is it the reed itself that produces the rest of the harmonics, or is it the sax?

I assume it is the reed, but although at a much reduced level, sax harmonics extend past 15,000 Hz. That seems a bit much for a piece of cane:

G4.png


And then there's a sax in a tube:
 

aldevis

Surrealist Contributor.
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No doubt the reed starts things off and vibrates at a fundamental frequency, but is it the reed itself that produces the rest of the harmonics, or is it the sax?
It is the air column contained in the sax
I guess the reed produces a lot of them, but it's the air column that defines which ones are stronger.
 

aldevis

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Also "harmonics" are an abstraction, used to describe the actual soundwave
With a sinusoid there would be no harmonics, but soundwaves have funny shapes
 

Dibbs

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659
It's the combination of reed and air column cooperating to form what Woolf calls an operating mode and Benade calls a regime of oscillation.

A reed itself has resonances way up into the ultrasonic region so it's not problem for it get to 15KHz.
 

BigMartin

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No doubt the reed starts things off and vibrates at a fundamental frequency, but is it the reed itself that produces the rest of the harmonics, or is it the sax?
I think at least some of it is driven by turbulence within the mouthpiece. Hence the influence of mouthpiece design on tone.
 

Admitone

Member
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139
it's the air column that defines which ones are stronger.
I agree. the column resists frequencies which do not correspond to its wavelength.
With a sinusoid there would be no harmonics
A sine wave (Continuous Wave) radio transmitter produces multiple harmonics which must be suppressed or the operator could be arrested.
It's the combination of reed and air column cooperating to form what Woolf calls an operating mode and Benade calls a regime of oscillation.
No doubt, the air column strongly influences, along with the player, the reed's vibration. But does the complex resulting sound precisely mirror the reed's vibration, or does the air column provide some harmonics of it's own?
 

Admitone

Member
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139
I think at least some of it is driven by turbulence within the mouthpiece.
This and another thread here has changed my view of how sound is produced with a sax.

It now seems to me that it's all about the vibration of the reed. Everything else, mouthpiece, sax, fingering, embouchure, throat, etc., acts together to control the reed's complex (fundamental plus harmonics) vibration.

Tomorrow, I may well have a different theory.
 

jbtsax

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My current understanding is that on a reed instrument the "natural resonant frequency" of the length of the tube being used "couples" with the reed to vibrate at that frequency. The soundwave produced in the column of air inside a conical instrument vibrates at the fundamental frequency with twice the wavelength of the length of the tube since a "complete" wave travels down and back. In a conical reed instrument the vibrating air column also vibrates at frequencies that are "in the area of" whole number multiples of the fundamental. The closer the harmonics are to whole number multiples determine the "harmonicity" with which the instrument plays.

In a cylindrical reed instrument closed on one end the air column vibrates at the fundamental frequency with a wavelength three times the length of the tube since it makes three "trips". The vibrating air column also vibrates "in the area of" odd number multiples of the fundamental. [even number multiples also exist but they are very weak compared to the odd number multiples].
 

Admitone

Member
Messages
139
My current understanding is that on a reed instrument the "natural resonant frequency" of the length of the tube being used "couples" with the reed to vibrate at that frequency. The soundwave produced in the column of air inside a conical instrument vibrates at the fundamental frequency with twice the wavelength of the length of the tube since a "complete" wave travels down and back. In a conical reed instrument the vibrating air column also vibrates at frequencies that are "in the area of" whole number multiples of the fundamental. The closer the harmonics are to whole number multiples determine the "harmonicity" with which the instrument plays.

In a cylindrical reed instrument closed on one end the air column vibrates at the fundamental frequency with a wavelength three times the length of the tube since it makes three "trips". The vibrating air column also vibrates "in the area of" odd number multiples of the fundamental. [even number multiples also exist but they are very weak compared to the odd number multiples].
But does the sound from a sax contain any frequencies not initially generated by the reed?
 

Dibbs

Member
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659
Four times not three for cylindrical reed instruments. The length is a quarter of the wavelength.

A high pressure pulse starting at the "closed" end is "reflected" at the open end but as a low pressure pulse. 180 degrees out of phase. This low pressure pulse is reflected with no phase change at the closed end. When that pulse hits the open end it is reflected again 180 degrees a high pressure pulse again. The reflection of this pulse with no phase shift at the closed end starts the cycle over again.
 
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