Jeff,

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Jeff,

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While the terms total harmonic distortion or just harmonic distortion pop up pretty regularly. I seldom hear intermodulation distortion discussed or tested with audio or HF amplifiers.? It too is an interesting area to test. I was reading articles about IM distortion a few years ago and ran across this youtube demonstration of IM distortion. While shown with a huge amount of distortion added to the sound, it really drives home what IM is and how it affects a signal passing through a circuit with distortions or imbalances. Seeing it on a spectrum analyzer or scope screen does not provide the same impact.

Speaking of speakers, I looked into why Bose speakers were so popular over the years.? They are nothing great when it comes to music reproduction. So why have they always sold well? Turns out the appeal is that many people have an expectation of what the music should sound like, which generally has a bit more base and treble than normal and Bose speakers color the sound in these areas, I think by design.? So when most people hear music through them it sounds like they expect it or want it to sound.?

All this audio stuff is subjective and that is why most people don't get the search for music reproduction perfection. Perfectly reproduced sound may not be that appealing.

And, as many have pointed out, humans may be able to tell if a note is off my a hertz (some of us singers and musicians can often tell with a little more precision), but most cannot or don't notice a small amount of distortion. So how low of a distortion is practical in the design of an amplifier?? If an engineer needs to amplify a signal, usually an instrumentation amplifier is used, not a stereo amp so ultimate perfection does not have to be a goal.

The thing about power cords has always just been marketed to the non-technical, and I cannot blame some manufacturers/dealers. It is extra profit in a tight marketplace and some will fall for the pitch.? Same with speaker cables. It is not that hard to demonstrate the physics and electrical characteristics of speaker cables, but in the end 99.9% of people in blind tests cannot tell the difference between cables. It is mostly a problem with the speakers attached, hiding any benefit that might be there. This have been demonstrated since the 70s, but the debate just won't stop.

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On Wed, Nov 23, 2022 at 03:58 PM, Jeff Green wrote:

A friend showed me a crazy ad for adapters to convert the wires from the speaker out to a NEMA 5-15P and adapters to convert NEMA 5-15R at the other, the idea being you’d use a heavy duty extension cord.

I have visions of some guy connecting his power amp or speakers the AC mains...with interesting consequences.

When I was in my early teens, so nearly 55 years ago, some friends had a band and used those for the PA system speakers, with precisely the consequences you envision.? I? was there when it happened.? It was loud.? The magic smoke came out of the speakers.

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Although a bit OT there is a history? to Harmonic Distortion and Inter Modulation Distortion? measurements. The major need for distortion measurements was in sound reproduction, the transducers were often the weak links. HD was easy, a low distortion source and a very sharp notch filter was simple to implement. The sine signal? was filtered out completely leaving the distortion and noise which was then expressed as a ratio to the un-notched signal.

When audio waves were recorded on disc or on film ( from the start of the talkies) there was a lot of wow and flutter which frequency and phase modulated the sine wave carrier so it was impossible to notch out all of the tone energy now spread each side of the carrier.

So the SMPTE came up with intermodulation testing, a high frequency carrier was added to a low frequency ( 50 or 60 Hz) signal and sent through the recording system. The LF signal was removed by high-pass filtering and the high frequency tone was then demodulated as an amplitude modulated signal, low pass filtered to eliminate the carrier and then displayed as IMD.

There is a subtle difference between the tests, HD depends on notch depth, ideally at least 20dB below the lowest HD to be indicated so even with 0.1% distortion the notch should be at least 80dB down, this is quite deep! Automatic balance bridges were produced to avoid manual twiddling.? The HD measurement is a "Whole Wave" one, the distortion waveform gives some data on where the distortion is happening in the time domain.

IMD measurements normally use a large LF tone and around a quarter amplitude HF signal. Essentially the LF signal sweeps the HF carrier through the transfer characteristic of the system, local changes in slope modulate the carrier amplitude so again the recovered IMD can be related to the transfer curve.

Now that we can easily do spectral curves using accurate ADC's and FFT's it is easy to plot the harmonic structure of the distortion products. By using very narrow bandwidths and averaging it is possible to reach much lower levels than earlier methods which had much broader measurement bandwidths.

There was a unique early method that could be used with inverting amplifiers, the amplifier output was nulled against a sample of the input signal by very careful attenuation and phase adjustments leaving the distortion residuals. This had the advantage of being relatively frequency insensitive and very simple.

As for the audibility of distortion, I would never underestimate the superpowers of some to hear the inaudible. There are people who claim they can hear the difference between very good operational amplifiers yet it is very probable that they could not detect 1% second harmonics nor could they tell the difference between sine and square short tonebursts.

Regards, Alan G8LCO

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Hello Jeff,

Though J S Bach set up the equally-tempered scale in about 1720, he did not establish the basic pitch of instruments. The beauty of the equally-tempered scale is that when a piece of music required several keys, the musicians did not need separate instruments or to retune for each key change. However, when bands of musicians or orchestras travelled to other auditoria, in their own countries or overseas, if they were accompanying a local impresario, such as a pianist or organist, the whole orchestra would need to retune to the local pitch. In the 18^th and 19^th centuries, ‘Standard pitch’ varied between 420 and 450 Hz.?

For some brass instruments tuned to the higher pitch, there just wasn’t enough tubing to reach the lower, local ‘standard pitch’. Take for instance a trumpet designed for A = 450 Hz; its total length from mouthpiece to the end of the bell would be about 50” (1.28 m). To retune to A =420 Hz, the tuning slide would need to be extended about 1.8” (nearly 45 mm). Not all instrument makers allowed for this much retuning. There were worse problems for some stringed instruments whose strings and tuning pegs had been designed for the local standard pitch range. Establishing an international standard pitch made music production, international travel of musicians, and musical instrument manufacture much easier. Nonetheless, there are still groups of string players who will only play instruments designed for the original ‘classical pitch’ of A = 422 Hz.?

On my piano, the upper 60 notes (soprano and tenor) have three strings each , the next lower 20 (alto) have two strings each and the 8 lowest (bass) notes are produced by just one string per note. The pitch of each string is determined by its length, its mass per unit length and the string’s tension – remember the f = √(k/m) formula? When pianos were first produced they had just one string per note. So, the piano’s harp was very long to accommodate the bass notes, perhaps 8 to 10’. To reduce the size of the harp, in the late 19^th century, piano manufacturers wound copper around the steel inner string to increase the mass per unit length of the bass notes and some of the tenor notes. Such over-winding increased the vibrating area of the string thus lowering the impedance mis-match between the surrounding air, the sound board and the human ear. As a first approximation, when the hammer velocity is kept constant, the loudness of a piano note is determined by its vibrating area. So, the over-wound lower notes started to sound much louder. To get a more balanced loudness throughout the piano’s range, piano manufacturers added more strings per note in the upper ranges. This increases the amount of air vibrated. One manufacturer, Bosendorfer, employs four strings per note in the upper register.?

Fender, with its Rhodes piano, used a normal grand piano action with the hammers striking one steel tuning fork per note. Adjacent to the free end of each tuning fork there was a pickup coil whose electrical signal was fed to a preamplifier with suitable electronic filtering to ensure even loudness throughout the piano’s range. (I’ve used the past tense because I dealt with Fender Rhodes pianos over 50 years ago – Fender may have changed the design since.)?

The usual way string players achieve harmonics is by lightly touching the string, not pressing the string hard down on the finger board (violin family) or fret board (guitar). If you play a fretless acoustic guitar, you can achieve any pitch you want, including the disharmonious ones.?

Cheers, Brian, VK2GCE

Brian Clarke

BE, MBA, PhD, CPEng,?APEC Engineer, IntPE(Aus),?FIEAust?

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Jeff

1KHz = 2^3 x 5^3 Hz and

440Hz = 2^3 x 5 x 11 Hz

so the difference is? 5^2 and 11.

This gives rise to x11 then 1/25 to produce 440Hz. That is all you need.

The multiplication by 11 from 1 KHz square wave to 11 KHz is very much better than trying to multiply 10Hz to 110Hz, an 11 KHz tuned circuit of good Q is much easier, cheaper and smaller than a 110 Hz tuned circuit. The division by 25 is very simple, either two locked multivibrators ( two double triodes or two blocking oscillator dividers and one double triode to do 1/5 and 1/5 to get down to 1/25 and 440 Hz.

You would loose your bet, two or three? double triodes would complete the job and should be quite stable. A very good crystal oscillator , oven and divider chain AND the 1K to 440Hz? synth would easily go into a single thin rack panel or a small box in the 1950's.

There is something much more interesting than 440Hz about musical notes. A good enough equal temperament scale can be produced by dividing a frequency around 2 MHz by integers to produce top notes then dividing by octaves. The sequence:-

239? 253? 268? 284* 301? 319? 338? 358? 379? 402? 426? 451 gives a workable set of approximations to the ratio of 1.059463094 between adjacent notes.?? 284 is for A,? the exact drive frequency is 1999.360 Hz for 440 Hz but 2 MHz is close enough.? 12 different dividers were contained in one I.C.? and replaced 11 L-C oscillators in electronic organs in the 1970's. The idea is earlier, Hammond organs used gears to multiply up and down from a synchronous motor driven by mains frequency. Gears are more versatile than dividers, machinists have used some clever gear combination for over 200 years to cut specific threads however the last Hammond did use top octave dividers instead of gears.

But distant Musical History now but very little to do with Test Equipment apart from the frequency synthesis aspect.

Regards, Alan G8LCO

On Wed, Nov 23, 2022 at 03:58 PM, Jeff Green wrote:

Another snake oil sale pitch is special purpose power cables. The AC mains passes through so many miles of transmission line, transformers, etc, that magical thinking a 6 foot special power cord will be of any help is silly.

Love it. I remember going into a consumer electronics store needing a power strip and sales person insisting some almost $100 dollar power strip was what I absolutely needed. Based on the amazing power cord technology.?

I bough an inexpensive power strip a while back with $50,000 damage insurance. For the insurance to be valid, you could not plug the equipment and power strip into a wall plug farther than 10 feet from the power panel. Could not have any other extension cords or power strips plugged into the same wall plug or the power strip. And on and on.

The truly sad thing is these marketing/"business" people that pull this magical thinking out of their behinds, also find their way into decision making positions in companies that produce things that really do need to conform to the laws of physics and nature.?

Sad when they are fleecing consumers but otherwise causing no harm. But, horrible when they find their way into fields such as medicine, aeronautics, and computer fields like artificial intelligence.?

Tom, wb6b

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On Sat, Nov 26, 2022 at 06:57 AM, Jeff Green wrote:

I have a 196Hz tuning fork, open “G”, that I used until my EE friend showed me a $25(US) Deltalabs CT-30 clamp on tuner.

I have a Pickboy tuner, manufactured by Seiko/Epson (I'm going from memory, I don't have the tuner handy) that I bought over 30 years ago.? At the time it was, as far as I know, the only electronic guitar tuner worth buying, at least of the "consumer" devices.? I had an A 440 fork, which I checked against an expensive and recently calibrated HP frequency counter.? My fork was dead on 440 Hz.? I? went to every music store in the greater Raleigh, NC area and checked every electronic tuner they had.? Any tuner that said my fork was off pitch was rejected, and if they had more than one tuner of the same model in stock, if any tuner of that model said my fork was off, that model was rejected.? I had gotten so sick of going to jam sessions and such where no two instruments were tuned to the same pitch, and so many of them weren't even in tune with themselves, that I decided I had to find something that actually worked.? And the arguments at jam sessions were ridiculous: "My instrument is right, because I am tuned to my electronic tuner."? Some tuners had a selector switch to select the note to be tuned, and they might be correct (or close to it) on one note, but not on others.? Some tuners varied unacceptably with ambient temperature, while others varied with battery voltage.? I have done a lot of electronic design, and many of the tuners I encountered over the years were so bad that if I were asked to design a tuner that worked so poorly, I'm not sure exactly how I would do it, and of course I would turn the assignment down.

Hello Jeff,?

In the pendulum frequency formula, the factor ‘k’ includes the force of gravity. For a stretched string, the ‘k factor becomes a function of the string tension. Of course, it’s not as simple as that because stringed instruments – harp, guitar, piano, violin – anchor the stretched string at both ends. At the fundamental frequency, the string is one half-wavelength long, with nodes at each end. Natural strings, those with uniform distribution of mass per unit length, will therefore only produce odd harmonics – 3^rd, 5^th, 7^th … Violinists can choose to emphasise or attenuate specific harmonics by choosing exactly where to bow or pluck. Hence, the ‘sweetness’ of the violin’s sound depends almost entirely on the violinist’s skill. You can do the same with your guitar.???

In order to suppress that most disharmonious 7^th harmonic on the piano, the hammer strikes at the node of the 7^th harmonic. Re-tuning a vintage piano, that is, one designed for A = 420 Hz, to bring it up to modern standard pitch of A = 440 Hz, the additional tension on the harp will shorten the harp and automatically shift the hammer strike point away from the node of the 7^th harmonic. The tension on the harp is measured in tonnes – several! The sound board to which the harp is attached may well crack under such insult. Good piano tuners often refuse to raise the pitch of older pianos.?

The formula for the fundamental frequency, f1, of a string anchored at both ends is:?

f1 = ? √(T / mL)

where:

T = string tension

m = string mass

L = string length?

Now you can see why I referred to the pendulum formula – I was using a mathematician’s shorthand.?

For over-wound strings, the mass per unit length is not uniform, and hence the harmonics are not exactly 3^rd, 5^th and so on. The amount and style of over-winding gives each piano manufacturer’s design its specific ‘voice’. Over time, the repeated striking of the over-wound strings results in relaxation of the over-winding pattern, and the note sounds increasingly dull. A cunning piano tuner will then release the tension on the dull string, rotate the string at the end furthest from the hammer, re-tension and re-tune to get some of the previous harmonic richness back; this method is cheaper than getting a new string wound.?

For string basses, some players like to use over-wound strings because of the smaller tension on the tuning peg. A further benefit is a ‘richer’ sound from such over-wound strings – the string excites more air. Purists will still prefer non-over-wound strings. You know that over-wound strings are available for tenor and bass guitars.?

More grist for your mental mill.?

Now that you know about the equally-tempered scale, you know that G should actually be 199.59977 Hz. So, if your tuning fork is exactly 196.0000 Hz, and if you could tune accurately to that tuning fork, fellow musicians whose instruments had been fine tuned to the equally-tempered scale would sound about 0.4 Hz flatter than you. This would be experienced as a beat approximately every 2.5 seconds. Unless you use an electronic device to stretch tone level over several seconds (eg, a sustain pedal), neither you nor your fellow musos would know. However, if you play a G a couple of octaves higher, the 0.982 Hz beat will be more noticeable over a shorter time period, ie, less than a second. Some string players attempt to get around this problem by rocking the ball of their finger over the string on the finger board, or fret board, to induce a frequency tremolo.?

When I tune my piano, I use an electronic tuning fork that I have compared, using my oscilloscope, with the tones from WWV. Even when I get within 1 cent, I still listen for beats for 13 seconds. I don’t look forward to tuning my piano because it takes me several hours. My piano invariably goes flat. I pull up the middle octave of 12 notes, the harp compresses, all the adjacent notes go flat. So, I then do the octaves above and below the middle octave, and then retune that middle octave. And so on, leap-frogging back and forth.?

Cheers, Brian.?

From: [email protected] [mailto:[email protected]] On Behalf Of Jeff Green
Sent: Sunday, 27 November 2022 1:57 AM
To: [email protected]
Subject: Re: [Test Equipment Design & Construction] Two interesting projects

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