Effect of temperature on tuning

[ttonon]

RAC, you're right, there is confusion. I myself made the mistake of thinking that Steve's tuner was a dedicated instrument and not a software concoction in an iPad. My apologies there.

On the other hand, Alex does say, "Oscillators are affected slightly by temperature changes though. Very accurate laboratory frequency references place the oscillator inside a thermostatically controlled oven." Thus, he was definitely talking about hardware, which justifies my comments.

Then again, you say, "From my understanding, everything realized in software - no matter what algrithm they implement - must use the underlying hardware for reference." This also justifies my comments.

So it seems there's confusion among all of us. I agree with your suggestion to have people conduct experiments and hopefully they will be done with enough rigor and explanation. 

Best regards,
Tom

[Richard Mellish]

This discussion is getting a little heated, but let's look at some numbers.

 

ttonon quotes Peterson strobe tuners as being accurate to within 0.1 cent. By my calculation that is about 58 ppm. The equivalent error in a clock or watch would be about 5 seconds per day. Those figures would be impractical to achieve with an R-C oscillator, but are reasonable with a crystal oscillator even without needing to put the crystal in an oven. A concertina reed can change its pitch considerably more than that with change of bellows pressure, never mind what happens with change of temperature.

 

BTW (thread drift alert) I would normally understand the word "strobe" to refer to a light that flashes at a controllable rate for viewing a rotating or vibrating object, so I am intrigued as to why Peterson chose it for their tuners.

 

 

 

[RAc]

13 minutes ago, Richard Mellish said:

This discussion is getting a little heated,...

 

 

Not at all, at least not on my side...

 

30 minutes ago, ttonon said:

On the other hand, Alex does say, "Oscillators are affected slightly by temperature changes though. Very accurate laboratory frequency references place the oscillator inside a thermostatically controlled oven." Thus, he was definitely talking about hardware, which justifies my comments.

Then again, you say, "From my understanding, everything realized in software - no matter what algrithm they implement - must use the underlying hardware for reference." This also justifies my comments.
 

Yes, we are almost in sync now, I may just have not made myself clear enough in this point - apologies, I hope the following paraphrase leaves no more room for confusion - what I meant to express is this:

 

No algorithm realized in software that relies on hardware input can be more accurate than what the hardware it runs on can provide. Thus, IF there is inaccuracy is a hardware time base, software can not compensate for it unless it has access to a different, more accurate secondary time base.

 

I hope we can put this debate to rest now. Overall, I believe we have had a technically rather fruit- and insightful debate and are now in basic agreement after communication errors on several sides have been ironed out.

Edited January 7 by RAc

[ttonon]

Richard, how did you determine that 0.1 cent is about 58 ppm? With the musical convention, an octave is broken into 12 tones, with each tone broken into 100 cents. There are thus 100 cents between each semitone. The question is, what are we measuring? Isn't it ultimately frequency?

Thus, by its definition, one cent is 1/100 of the frequency interval between semitones and 0.1 cent is 1/1000 of the interval, or one part in a thousand. You can go to online calculators if you want to very that. Such a result applies along the whole range of musical pitch.

The reason Peterson uses the strobe method is because it's so simple and foolproof, as long as you have a good frequency reference. The idea of strobe measurement goes back a hundred years, and for the Peterson instruments, an oscillator is used to accurately set the rotation speed of a wheel with markings. The signal from the musical instrument is used to strobe a light onto the rotating wheel. This will make the correct markings on the wheel appear stationary, and the circumferential distance from the zero along with the known speed of rotation tells you the frequency of the input signal. 
 

Here's from the manual of a Peterson 450 strobe tuner, which I have:

- - -
ACCURACY
The exceptional  accuracy of  the PETERSON STROBE TUNER, MODEL 450 is due to the fact that all of the pitches are controlled by a single oscillator circuit of unusual design (patented) using components of the highest stability.  The pitch is not affected by changes in power line voltage and the temperament is derived from precision counting circuits that are not subject to drift or variation. 

Recalibration should not be attempted in the field if an accurate standard is not available.  Tuning forks can vary greatly depending on quality, temperature and humidity.  Do not rely on these except for relative measurements.
- - -
From the manual of the iStroboSoft:
- - -
Calibrating iStroboSoft™
iStroboSoft will measure and display to within 0.1 cent accuracy throughout its full range. However, there may be instances when measurements do not match when compared to an external tuner. In such a case, the external tuner may be
inaccurate, or iStroboSoft may be subject to biasing introduced by an inaccurate
reference clock in its host device.

This inaccurate reference clock inserts a 'bias' onto the audio signal during processing. This bias can be enough to sway an otherwise accurate measurement by as much as +/- 3 cents!

To allow these host devices to be used to accurately tune instruments, iStroboSoft has a calibration feature which will independently allow it to calibrate to an external audio source and measure the offset of the bias to ensure an optimal measurement. This calibration is remembered permanently until you remove it.
- - -
There are calibration notes for Steve and others who use this software.

- - -
RAc, why end the discussion when it continues to bring forth all kinds of insights? Thanks for clarifying your position and I take it to mean you have no objections to my technical comments and that they were justified.

Best regards,
Tom

[David Barnert]

2 hours ago, ttonon said:

Thus, by its definition, one cent is 1/100 of the frequency interval between semitones...

 

That’s a little misleading. A cent (like the octave and the semitone) is a unit of pitch, not frequency. The relationship between pitch and frequency is not linear, it’s algorithmic. Adding pitch multiplies frequency. Each octave doubles the frequency, each semitone multiplies it by approximately 1.06, each cent multiplies it by approximately 1.00058.

[Auldfellowmelad]

6 hours ago, ttonon said:

RAC, thanks for your impressions on my evaluation of Alex's suggestion, though your technical argument is not applicable to devices like Peterson strobe tuners.

 

I do agree that if Alex chooses so, he can be offended by my claim his suggestion could be a "little knowledge can be a bad thing." That would be his problem. But it seems you yourself chose to be offended. Am I right?

 

We all know of many such examples where people extrapolate true knowledge to erroneous belief, and I made that comment not just for Alex but to all of us who might benefit from the reminder. The web seems to invite such behavior from all of us.

 

And where are your relevant facts? You recite a convoluted story that doesn't explain all the key details necessary to make a scientific assessment of your conclusions, or part conclusions, or "sort of" conclusions, whatever conclusions. Then you extrapolate that into an argument why a Peterson strobe tuner could be inaccurate.

 

Here are the relevant facts: Electronic timing circuits are based on two technologies: RC circuits or crystals. (We also have atomic clocks, but we need not let that confuse us.) Resistors, capacitors, and crystals have strict specifications, according to the class they are assigned to, and that determines their cost. I repeat, do some homework, and find that both resistors and capacitors in IC circuits have temperature coefficients varying from zero to somewhat less than 100 ppm/C, over very wide temperature ranges, and crystal oscillators, depending on the crystal cut, vary from zero to up over 100 ppm/C. That's for the components themselves. Then add to it the facts that compensation circuits can eliminate any significant temperature effect and that typical room temperature variations are only a small fraction of the specification ranges, there's no reason whatsoever to blame the magnitude of the variations people see in tuning free reeds in their own homes. Unless of course they're using a faulty meter or some kind of homemade method to make the measurement.

 

I repeat, Peterson strobe tuners are accurate to within 0.1 cent, which is the smallest unit measured for musical pitch, and - no offense - I trust their engineers more than I trust you with your example. I've read that the top musical schools claim that most people can discern musical tones to within +/- 10 cents. I'd be surprised if people with perfect pitch could detect differences down to 0.1 cents. If I'm wrong, that would be a good example of a "little knowledge can be a bad thing." We do it all the time. 

 

I appreciate the comments you and Richard made regarding ways to test cell phone and computer circuits, and I have no idea how much software is integral to their mechanisms for measuring this. I encourage you to do such experiments. My comments here are restricted to devices with dedicated designs to measure musical pitch and sold with that in mind. Because of my arguments here, I think it not too likely that even cell phone or computer methods could result in the errors mentioned at the beginning of this thread, unless their designs are incompetent. But I could be wrong and would welcome correction.

 

A word on offense. If I told you, "You have a funny nose," and if you never thought about your nose in such a way, you'd either be curious or think I'm a nut. But if you had a history of people discussing your nose and you looking in the mirror with misgivings, you might choose to be offended by my statement.

 

So, if Alex isn't offended by my comment, he's thinking intelligently, understands why I said it, and takes no offense. If he chooses to be offended, he thinks I speak the truth.

 

Thanks for your good wishes,

Tom

 

I don't think there is any place on this website for this sort of pedantic annoying bad behaviour you are displaying ttonon. Stop it.

 

With regards to the accuracy of free reeds, here is a quote from one of the greats of the original concertina manufacturing industry (who will remain un-named and is no longer with us) when he was questioned about the accuracy of tuning: He reminded the asker that the Concertina is not an electronic organ – and that the asker should “stop listening to the hi-fi and get on with playing some music. The instrument was designed in 1827 so any improvements we can make should be considered as a bonus”!

 

Basically what he was saying was "yes the pitch will fluctuate a bit depending on humidity or temperature but not by an amount that really matters, or can do anything about so just get on with it". We should all remember that. 

 

 

Edited January 7 by Auldfellowmelad

[Richard Mellish]

3 hours ago, ttonon said:

Thus, by its definition, one cent is 1/100 of the frequency interval between semitones and 0.1 cent is 1/1000 of the interval, or one part in a thousand. You can go to online calculators if you want to very that. Such a result applies along the whole range of musical pitch.

Thank you for explaining that the Peterson devices do actually use a strobe light. That isn't the most obvious way of measuring frequency but fair enough if they choose to do it that way.

 

I didn't use an online calculator. I used a spreadsheet.

1 semitone = 2^(1/12).

1 cent = 1 semitone ^(1/100).

0.1 cent = 1 cent ^(1/10).

That differs from unity by about 58 ppm.

[ttonon]

On 1/7/2024 at 3:35 PM, David Barnert said:

 

That’s a little misleading. A cent (like the octave and the semitone) is a unit of pitch, not frequency. The relationship between pitch and frequency is not linear, it’s algorithmic. Adding pitch multiplies frequency. Each octave doubles the frequency, each semitone multiplies it by approximately 1.06, each cent multiplies it by approximately 1.00058.

Dave, thanks for the comment and opportunity to clear up this issue. It can be confusing.

The pitch of a musical tone is the frequency we perceive. Although it doesn't make sense to say so, it may be instructive to view frequency as what a tuning instrument "perceives." It works by physical principles. Our brains work by who knows what?

Perception belongs to humans and frequency belongs to an objective nature, if we can call it that. Musical tones from real instruments contain multiple frequencies, called overtones, or partials, often with whole number ratios to a fundamental and in which case they are called harmonics. This is physics, Mother Nature.

When we hear a musical tone, we perceive the fundamental frequency of the (mathematical) Fourier Series that represents the actual tone and call it the musical pitch. This is mathematics, and miraculously, it's also nature, as our brain/ear system perceives. There usually isn't any difference in the pitch we perceive and this mathematical fundamental. But if the tone is so heavily laden by upper partials, we progressively fail to detect the correct fundamental, to the point that we wouldn't call it a musical tone. We'd then call it noise.

Thus the relationship between pitch and frequency is quite exact, but maybe not perfect. Your mention of the term "logarithmic" indicates you are confusing volume with loudness. Loudness, a perceived quantity, has a logarithmic dependence on volume, which is the physical measure of acoustic power per unit surface area. Loudness belongs to humans and volume belongs to nature.

"Adding pitch multiplies frequency." I understand what you mean, but it's not an edifying description. Yes, each semitone is the 12th root of 2 multiplied by the preceding note. [Each upper half tone = (Start.Freq)*(2^1/12)]. That means when you multiply the root frequency in succession 12 times, you must arrive at twice the original value; i.e., (Orig.Freq)*[2^(1/12)]^12 = (Orig.Freq)*2.

The cents definition is similar, and with the same geometric definition. Thus when you multiply the root by 2^(1/1200) you get one cent more frequency and for the entire octave, (Orig.Freq)*[2^(1/1200)]^1200, you again get (Orig.Freq)*2. This arises from the definitions of an octave (factor of 2), the division of the octave into 12 tones, and the definion of a cent being 1/100 of the tone interval. You might notice that your multiplication facto 1.059 = 2^1/12.

I believe you call this logarithmic because the geometric operation means you add exponents and closed form solutions to cents calculations require logarithms.

Edited January 9 by ttonon

[David Barnert]

1 hour ago, ttonon said:

Your mention of the term "logarithmic" indicates you are confusing volume with loudness.

 

Not at all. Volume and loudness were furthest from my thoughts. I was talking (as I thought I made clear) about pitch and frequency. Each interval in pitch (additive) is associated with a multiplicative change in frequency. Therefore pitch varies with the logarithm of frequency.

 

If we arbitrarily assign a reference note to have pitch (P) = 0 and frequency (F) = f and count by half steps,  when P=12 (an octave) F=2f. When P=24 (two octaves) F=4f etc.

 

So P = 12 x log(2) F

[ttonon]

5 hours ago, Richard Mellish said:

Thank you for explaining that the Peterson devices do actually use a strobe light. That isn't the most obvious way of measuring frequency but fair enough if they choose to do it that way.

 

I didn't use an online calculator. I used a spreadsheet.

1 semitone = 2^(1/12).

1 cent = 1 semitone ^(1/100).

0.1 cent = 1 cent ^(1/10).

That differs from unity by about 58 ppm.

Richard, I'm surprised that you haven't heard of the several applications of strobe lighting. There's a strobe instrument that can very accurately measure the speed of a rotating part. It's flawless and simple. You just change the frequency of the strobe until you see the part freeze in view. It can measure deviations from a mean, etc. Strobe techniques were used when they first figured out how different animals pace. You take a series of photographs of an animal walking or running in dim light, using a bright flash in a strobe. People were able to see very clearly the different kinds of gates horses and most other animals use. Until then, no human had a fast enough response to see the sequence of steps in a full gallop. People also learned much about how high speed projectiles penetrate targets. With the very high frequencies available, you can stop a bullet, then see it a mm later in its path and measure how fast debris is flying away.

I believe the man most associated with it was Harold Edgerton, in 1931. His bulb is a discharge bulb, mostly powered by a large bank of capacitors, with responses in nanoseconds. The flash speed is normally so short, you need an inductor to slow down the discharge of the capacitors to expose the film, or CCD. I know because although some else in my company brought the idea into the company, I built a strobe system to measure the power of solar cells. They can illuminate the entire area of the cells with one-sun intensity, over a period long enough to electronically scan the terminal voltage from negative to greater than open circuit voltage over varying load and get the power curve.

Edgerton was a good guy. I read he made all his patents free so that German and Japanese photo industries could rebuild themselves after WWII.

I see the calculation you made and thanks for the correction. I failed to raise the number 2 to the appropriate power. Silly me. These results hold throughout the musical range.  

Best regards,
Tom

[ttonon]

4 hours ago, David Barnert said:

 

Not at all. Volume and loudness were furthest from my thoughts. I was talking (as I thought I made clear) about pitch and frequency. Each interval in pitch (additive) is associated with a multiplicative change in frequency. Therefore pitch varies with the logarithm of frequency.

 

If we arbitrarily assign a reference note to have pitch (P) = 0 and frequency (F) = f and count by half steps,  when P=12 (an octave) F=2f. When P=24 (two octaves) F=4f etc.

 

So P = 12 x log(2) F

Dave, sorry but I don't understand your last equation. 

 

Question: If your concertina is tuned to A 440, that means that the octave A above it is 880. Correct? Are you saying that the second note is not twice the pitch of the first note?

[Richard Mellish]

7 hours ago, ttonon said:

Richard, I'm surprised that you haven't heard of the several applications of strobe lighting

Misunderstanding! I am perfectly familiar with that. As I said " I would normally understand the word "strobe" to refer to a light that flashes at a controllable rate for viewing a rotating or vibrating object".

 

What I had not encountered before was using a strobe light to measure the frequency of a musical note.

[ttonon]

2 hours ago, Richard Mellish said:

Misunderstanding! I am perfectly familiar with that. As I said " I would normally understand the word "strobe" to refer to a light that flashes at a controllable rate for viewing a rotating or vibrating object".

 

What I had not encountered before was using a strobe light to measure the frequency of a musical note.

Sorry. Forgive me for my unnecessary elaboration. But yes, Peterson was a clever dude and was able to exploit the idea in applications that never saw it before. I bought the 490 Tuner about 20 years ago and now it's worth twice the price. The rotation speed of the disc, which is set according to their stable oscillator, differs for different ranges of frequencies, as you might expect, with the higher frequencies requiring faster rotations.

 

The company then went a step further, with the iStroboSoft, used on ipads and computers, which doesn't have a mechanically rotating disc, but I believe LCD's are sequentially illuminated by updating the screen at the correct rate. It makes it look like there's something rotating, and the speed of that rotation is again set by the oscillator, with the strobe light determined by the musical instrument. At least that's how I think it works.  

[David Barnert]

20 hours ago, David Barnert said:

So P = 12 x log(2) F

 

I was trying to express it without the subscript required to do it correctly, but I now realize it is possible to render subscripts in this medium. So this is what I meant:

 

P = 12 log₂ (F) or Pitch is twelve times the logarithm (base two) of the frequency.

 

16 hours ago, ttonon said:

Question: If your concertina is tuned to A 440, that means that the octave A above it is 880. Correct?

 

Correct.

 

16 hours ago, ttonon said:

Are you saying that the second note is not twice the pitch of the first note?

 

Exactly. It is 12 semitones higher. Additive, not multiplicative.

 

To get from one octave to the next you ADD 12 semitones to the PITCH or you MULTIPLY the FREQUENCY by 2. But you DO NOT multiply the pitch.

[ttonon]

48 minutes ago, David Barnert said:

 

17 hours ago, ttonon said:

Are you saying that the second note is not twice the pitch of the first note?

 

Exactly. It is 12 semitones higher. Additive, not multiplicative.

What note above middle "A" is twice the pitch of middle "A."

[David Barnert]

5 hours ago, ttonon said:

What note above middle "A" is twice the pitch of middle "A."

 

The phrase “twice the pitch” has no meaning. I’ll say it again: You can’t multiply pitches. It’s like trying to multiply colors or temperatures. [I’m trying very hard not to make a joke about your hearing loss, but as you see, I’m not being very successful 😉 ]

 

Here’s another way to look at it: On a piano, pitch varies linearly with distance from the left end of the keyboard. Every time we go an octave higher, we add a constant distance (number of inches) from the left end of the keyboard, so we’re adding a constant interval of pitch (in this case an octave). The only thing we’re doubling is the frequency.

[Little John]

On 1/7/2024 at 10:09 PM, ttonon said:

... overtones, or partials, most often an octave apart. And the ones an octave apart are called harmonics.

 

This is a curious assertion. In my experience "overtone", "partial" and "harmonic" are virtually interchangeable (with some slight differences in usage between the scientific and musical communities). I've never come across "harmonics" as being reserved for the overtones at octave intervals. Also they are not the most common. If F is the fundamental frequency of a note its harmonics are at 2F, 3F, 4F, 5F etc. The ones at octave intervals are 2F, 4F, 8F, 16F etc. So "most" harmonics/overtones/partials are not at octave intervals: 3F, 5F, 6F, 7F, 9F, 10F, 11F, 12F, 13F etc.

 

It is from these "non-octave" harmonics that we derive the intervals and notes of the natural scale we use: 3F gives us the fifth note, 5F gives us the (major) third note for example. [These are the pure, natural or Pythagorean intervals, which differ slightly from the intervals derived from adding 100, 200 etc. cents to the pitch, but that's a discussion for a different place!]

[David Barnert]

52 minutes ago, Little John said:

This is a curious assertion. In my experience "overtone", "partial" and "harmonic" are virtually interchangeable (with some slight differences in usage between the scientific and musical communities). I've never come across "harmonics" as being reserved for the overtones at octave intervals. Also they are not the most common. If F is the fundamental frequency of a note its harmonics are at 2F, 3F, 4F, 5F etc. The ones at octave intervals are 2F, 4F, 8F, 16F etc. So "most" harmonics/overtones/partials are not at octave intervals: 3F, 5F, 6F, 7F, 9F, 10F, 11F, 12F, 13F etc.

 

It is from these "non-octave" harmonics that we derive the intervals and notes of the natural scale we use: 3F gives us the fifth note, 5F gives us the (major) third note for example. [These are the pure, natural or Pythagorean intervals, which differ slightly from the intervals derived from adding 100, 200 etc. cents to the pitch, but that's a discussion for a different place!]

 

I agree with all of this except that the Pythagorean system doesn’t include the pure third at the 5th harmonic. Pythagorean thirds (3^4/2^6 = 81/64 = 1.265625) are much higher than pure thirds (5/4 = 1.25) or equal tempered thirds (approx. 1.26). They sound out-of-tune and thirds were considered dissonant back in the day. The ancient Mesopotamians knew Pythagorean tuning (although of course they didn’t call it that). Pure 3rds and the 5th harmonic is more of a 16th Century phenomenon.

 

https://en.wikipedia.org/wiki/Pythagorean_tuning