Et tu Brute?

This post might seem like a "poor me" or parts of it even like boasting. Think that if you want, but I am trying to make a point.

If you know me or you've followed my blog you'll know that I excelled in my school A-levels. My parents told me to do my best, so I did. Although I grant that, in my O-levels, I failed History and only just passed English Literature even though I could (and still can) quote from memory Et tu Brute? and Let me have men about me who are fat... yond Cassius has a lean and hungry look... such men are dangerous. My English teacher had said quotes were like the plums in the pudding.

I excelled at college too, leaving with a First Class Honours degree. And did pretty well in my first job working in the prestigious BBC Research Department during which I was granted MIET and CEng which title I have retained (by paying an annual subscription) until recently.

After a few years doing odd jobbing building work while playing at radical church, I started my own electronics design business and completed a number of projects for various customers. To facilitate this work I have a home office cum workshop and have taught myself how to hand solder down to 0.4mm pitch, how to program embedded devices in assembler or 'C' and some PC programming as well.

And then, all of a sudden I retired and electronics work dried up. True, I continue to provide occasional technical support for that one active project, but otherwise my office and its equipment and stock of components has become largely redundant.

I had wondered about teaching - trying to pass on the skills I have learned, for the benefit of the next generation. But so far no one appears to be interested. The parents of young children in the community here have decided to quit the assisted home schooling we have assumed to be the norm for oh so many years, so it looks like there will be no need for my usual maths and physics teaching here. So instead I am helping my son doing some building renovation work here, and stoke the wood-burning boiler, weed the drive and mend things around the place that others have broken. Come the summer (if we haven't already missed it) I may take a day or two to go exploring now that I have a Senior Citizen free travel pass. But otherwise it is a strange feeling, this being retired is. I have always considered myself as being highly motivated and never, dare I even utter the word, bored. No, I'm not bored, really I'm not, but sometimes I'm not sure that I am fully motivated and I wonder what life is all about. We come and go like a ripple on a stream.

Günter Wand

I don't listen to Buckner symphonies very often for fear of them becoming too familiar. Like - too much of a good thing.  Also it's hard to justify a time slot long enough to listen to a complete symphony so I tend to listen a movement at a time. Tonight it was Günter Wand's rendition of Buckner's final masterpiece and it was truly awesome. I say all this because it seems wrong that others should not get to enjoy it, either because of ignorance, claimed distaste or having "more important" things to do.

My link takes you to the 3rd movement but, if you have time, you really ought to rewind to the beginning.

 

Spring Lambs

Every year I have to see if I can still manage to complete the Church Mountain route. Because I am not getting any younger. I won't claim that I ran all the way, but I did make it there and back, barefoot of course. Nothing new about the route but still delightful there, up and down, apart from the drudgery of the return along minor roads some with loose chippings (ouch!): 14.7 miles, average speed moving 3.8mph, elevation gain 561m, total time taken 3:50, and made it back in just enough time for a quick shower before dinner. Oh, and I stopped at the summit for no more than a minute or so, long enough only to exchange pleasantries with a young couple there.

My track

Here are some photos including one of spring lambs!

Pitch magnet

I have mentioned that I suffer from tinnitus. It manifests as white noise in the upper register and is always present but most of the time I can ignore it. It is not so annoying as to prevent me carrying on a normal life, except when my surroundings are quiet or when I want to listen to a quietly spoken voice or music. Additionally, but related, is the discomfort I feel in a noisy environment such as at meal-time or the cacophony in praise-time in church.

I enjoy listening to music (my tastes are mostly classical) and playing the piano (though not well). One effect, doubtless caused by the tinnitus, that I have recently noticed is that I am unable, or at least find it difficult, to detect the pitch of a quiet note, particularly if it is in the lower register. For example, when sight reading music I know when I have played a wrong note - unless I am playing it very quietly. And then I am at least aware of the sound but I cannot be sure that it is the right pitch. Probably this is because the volume of the tinnitus is partially obscuring the note. I like to harmonise when singing in church but, again, I can be unsure that I am singing the correct pitch. 

For someone who loves listening to and making music this is kind of scary. Like, where will it end?  Am I to share Beethoven's destiny (though without the musical acumen)?

Apparently this is a known effect as in this site which suggests that "tinnitus acts as something of a pitch magnet, drawing the voice or instrument to inaccurate notes."

Mullaghcleevaun

 First proper foray of 2022. The occasion being the first decent weather this year.

Hiking part 9.1 miles, elevation gain 787m

Bike to Pound Lane, Lacken, then hike over Black Hill to Mullaghcleevan then back via beautiful Cleevan Lough. Then bike back via Blessington. Fuel: one creme egg plus one granola bar.

 

Two Rock Mountain

I had taken N to the Beacon Hospital and had a spare few hours, so why not climb the nearest mountain. Two Rock Mountain is the highest in the Dublin Mountains range at 536m. I parked in the Blue Light car park. There are numerous trails to choose from. Storm Dudley was brewing - the forecast suggested I had to be done by midday, but already there was a tidy wind and wetness in the air so when I got back to the car I was considerably wet even if not quite soaking. The summit cairn is thought to cover a burial chamber and is known locally as the Fairy Castle. I saw no fairies though, nor the two rocks, nor any view. The wind made it difficult to walk and, having circumvented the cairn once, I made a hasty return trip to avoid hypothermia.

My track: 3.6 miles, 366m elevation gain

Terribly good

In our meeting the other evening we sang the song "King of My Heart" by Bethel Music.  The chorus (which we repeated ad nauseam) goes:

'Cause You are good, You are good, oh oh
You are good, You are good, oh oh
You are good, You are good, oh oh
You are good, You are good, oh oh

reminiscent of Gerald's "Peace will come..." in Adrian Plass' Sacred Diary. It set me thinking... The endless repetition should, I suppose, be excused as a literary device denoting emphasis.  The song argues "You're never gonna to let me down" (also repeated) because "You are good". What, I wondered, goes through people's mind when they sing this? Is it good like chocolate? A gooey sort of goodness that makes me feel... well... good?  I think not.

God, as portrayed in the Bible, is more like "terribly good" or "awfully good" - in each case employing the proper meaning of the adverbs, as in "It is a fearful thing to fall into the hands of the living God. " and "let all the inhabitants of the world stand in awe of him".

The children's introduction to Aslan (in the Lion, the Witch and the Wardrobe) illustrates this well:

"Then he isn't safe?" said Lucy.

"Safe?" said Mr Beaver; "don't you hear what Mrs Beaver tells you? Who said anything about safe? 'Course he isn't safe. But he's good. He's the King, I tell you."

And later on Mr Beaver tells the children: "He's wild, you know. Not like a tame lion."

You won't find many other Bible references to God being good. Here's one where Jesus quips "Why do you call me good? No one is good except God alone." According to Strongs, the Greek word used means "good (in any sense)" and the Hebrew word used in the OT means "good in the widest sense". Maybe this is more helpful than at first meets the eye. Whereas we consider "good" as a description of God as in "God is good", I suggest that we have it upside down and that it would be better to say "good is God", i.e. that God is the definition of true goodness. We know a thing to be truly good if it is like God. Which rules out the chocolate argument.

This goodness of which we speak is not a license for our lazy behaviour. Paul sums it up by "What then? shall we sin, because we are not under the law, but under grace? God forbid."

A momentary friend

Yesterday morning we parked at Tallaght in order to take the Luas into Dublin. Whilst waiting we exchanged pleasantries with a mother and her two boys possibly between four and six years in age, each with a three-wheeled scooter. One was messing about close enough to the edge of the platform to demand my attention. Just as the tram was coming in he stumbled and lurched towards the line. Jolted by an  adrenalin rush I jumped off my seat to help his mother pull him away. 

What could have happened had she, had I not reacted fast enough... well, such thoughts troubled my mind all the way into Dublin. This boy, hitherto unknown to me, suddenly had became someone I dearly cared for. It was almost as if I had become part of his family. When we alighted we waved goodbye and he waved back, momentarily friends. And this struck me as odd as it is extremely unlikely that I will ever meet him again or recognise him if I did. 

It never rains but it pours

We had to go back to the UK at short notice to care for Ali's mother who is deteriorating faster than expected... so now helping her through her last days... a carer comes in twice daily, one of us is called upon to assist turning mother on her side so that the carer can do what carers do, God bless them... unknown to us at the time one carer has a husband who has tested positive... Ali and I take turns reading to mother - they say hearing is the last sense to go... finally mother breaths her last and we also breath a sigh of relief - whatever your beliefs she is now in a better place, no more pain... and then the inevitable: first Ali then I contract the dreaded Covid... ten days of isolation (plus day zero, which makes eleven by my arithmetic) is a long time when you are not allowed off your property. At least we have a garden to walk around in circles, although to start with we do not feel like doing anything let alone walking. Must be hard for folk who live in a high-rise. But eventually the time passes and I am officially out of isolation at midnight tonight. Mind you, I'm not sure if I have the energy to avail of an instantly larger playground. 

Tomorrow J, C and S arrive for the funeral later this week. We've decided to do the catering ourselves (this decision was made before we succumbed) so there's been much cake baking and more to come. Eventually the dust will settle and I suppose we'll go back home. But where is home?

Can you know for sure 3 ?

The Truman Show

The film stars Jim Carrey as Truman Burbank, a man who grew up living an ordinary life that, unbeknownst to him, takes place on a large set populated by actors for a reality television show about him... 

As the show approaches its 30th anniversary, Truman begins discovering unusual elements such as a spotlight falling out of the sky in front of his house and a radio channel that precisely describes his movements... [and attempts to escape] Truman continues to sail until his boat pierces the wall of the dome. Initially horrified, Truman discovers a nearby staircase leading to an exit door. As Truman contemplates leaving his world, the Truman Show director Christof speaks directly to Truman through a speaker system and tries to persuade him to stay, claiming that there is no more truth in the real world than in his artificial one, where he would have nothing to fear. 

Which raises philosophical questions like: are all of us actually only living in a setup, an experiment run by some superior being or beings? After all, haven't we discovered some "unusual elements" like Modern Physics or even in Mathematics, which most of us figured was pure almost by definition, until the advent of Gödel's Incompleteness Theorems where undecidable questions have even arisen in physics, suggesting that Gödelian incompleteness afflicts not just math, but... in some ill-understood way... reality.

What some interpret as conspiracy others claim as die-hard truth. Take, for example:

Horatio Spafford: Not Well With His Soul

The very well presented Hugh Bonneville narration, and the oft congregational singing of "When peace like a river", leave out what for many are the more questionable aspects of Horatio Spafford's life. I quote: 

Like the false prophet Harold Camping [who predicted that the rapture and Judgment Day would take place on May 21, 2011 and that the end of the world would take place five months later], from his “bad experience” in an instituted church (brought about by his own egregious sin), Spafford proceeded to write off not just his own local church but all churches. Horatio repeatedly claimed, “God has showed us that ‘the Church’ in all its parts… is destitute of spiritual power… Theirs are false teachings”. Horatio, his wife Anna and their followers viewed the visible churches with “contempt”, calling them “Babylon” and that "God had chosen [us] instead of the organized church as the new ‘holy and peculiar people’ to be ‘the Bride made one with Him and one another'”

There are some noticeable resonances here with doctrine that I have described elsewhere in regard to my own loose connection with the Move although it is not my intention to equate them. Such movements are often driven by a singular personality and that attribute ought to be enough to warn the rest of us. But the opposite of singular is "all we like sheep" and anyway wasn't Jesus decidedly singular? The world might think Spafford a heretic but what would we have done, had we been around him? It's too easy to see the wool after the event. The trouble is, there is likely a degree of truth in the thinking of the Move, Spafford, and many present day "conspiracy" theories, and isn't it also easy to pick holes in the strange activities of the institutionalised "church"?

All of which does not help a chap in his quest for truth.

Go back to Part 2

In search for Birds Instant Whip

 

Knowing my childhood infatuations, my beloved snapped this up from a Lidl store. From the name it looks more like an Angel Delight look-a-like, but we tried it out anyway on her mother and myself. Did it satisfy? Well, kind of. She didn't comment, but ate it all, and for me it didn't quite resonate with my childhood memories but perhaps my tastes have changed over the years. In fact I am sure they have for I used to love roes on toast...

Like most deserts Heavenly Delight was vastly improved by the addition of double-cream and a generous dollop of ice cream.

Memories: Part 2

Why do we like to delve into our past? Is it because we are at least partly a product of our memories? Or maybe our memories are an increasing treasure as we get older, and might even in some small way live on in our children's minds long after we die. 

We are at the moment caring for A's aged mother who has been diagnosed with cancer. Her short term memory gets worse but every so often she comes up with a memory of long ago. Memories are certainly of value to her, even if for us we have heard her speak of some of them rather too many times! So I'm not at all sure that any of any of my readers has the least interest in the memories I recall herewith but maybe they will resonate or at least make you chuckle. 

I was about 13 when my parents took me to see the newly released Sound of Music. I became infatuated not only with the music (which has become a part of me) but also with Julie Andrews as Maria - to the point that my father thought it necessary to warn me that it wasn't any good falling in love with a film star. I hadn't thought I had fallen in love, but I bookmarked his words.

My dad's LP record collection was about as limited as my own small pile of CD's. One of his favourites was Mediterranean Moonlight by Frank Chacksfield and this became, along with hymn tunes, my early musical bread and butter: example tracks here and here. This music still haunts me. Lady of Spain I adore you...

My best friend's musical taste was much more refined than mine - I suppose I was less mature and had not yet discovered the sort of music that I would end up loving for the rest of my life. Back then I listened to what might be described as light music. As opposed to "pop" which my parents disapproved of. I remember Cliff Richard's Congratulations when it first came out and feeling ashamed because, though 'pop', I rather liked it. Even to this day I do not allow myself to listen to pop music channels on the radio whether or not I like what is playing (generally I do not but there are exceptions). 

Of this "light music" two songs are still part of the rather limited repertoire of tunes that to this day still go persistently around and around in my head.

Things is a song which was written and recorded by Bobby Darin in 1962 and reached No.2 in the UK. One pertinent line goes Memories are all I have to cling to.

The other is For all we know, this may only be a dream. We come and go like a ripple on a stream. So love me tonight - Tomorrow was made for some - Tomorrow may never come - For all we know, which was written before my time but was performed here by Bobby Vinton in 1970. I found the analogy of a ripple very evocative.

These songs are all mixed up in my memories with my adolescent discovering an attraction to the opposite sex: puppy love I suppose, but at the time it was heart rending. 

I am almost ashamed that I had such shallow musical tastes and I guess my recent "music appreciation" classes that I have given to four youngsters in our community have been my attempt to make sure they at least have the opportunity to hear some genuine music. Whether or not they like it! Although I doubt if my attempt will be wholly successful.

But then by accident I discovered Bruckner and all of a sudden I started to grow up.

Can you know for sure 2?

My recent post proposed that, for mortal man, there cannot be any sure knowing of anything, much less of a divine omnipotent, omniscient eternal being about whom You ask me how I know He lives? He lives within my heart - which I quote because sentiments like this only make me less sure. If that's the only way that I can know He lives then it's decidedly shaky ground!

So it was with some interest that I read the article that Facebook presented to me this morning in its inimitable way. It's worth reading if only because it sums up what I was trying to say, but does it somewhat better than I did.

Earliest memories: Part 1

I wrote the following some while ago and thought I had published it, but either I hadn't or else I had accidentally unpublished it. So here it is, but as I now have more material I want to share it will have to be renamed with "Part 1" in the title.

Possibly my earliest memory is sharing a bath with my older sister and somehow slithering around so that I was face down in the water, at which I made such a commotion that I was quickly rescued. This occurred more than once so that taking a bath became a dangerous mission. For me to remember this at such an early age, it must have been very traumatic and may well be why I still easily panic when out of my depth in water.

I've noted elsewhere how I distinctly remember posing for this photo, feeling the coarse sand-dune grass scratching my body. I like to think the location was our favourite holiday haunt Brea Hill, Daymer Bay but I cannot be sure.

I remember, pre-school, standing, legs apart, on the dining room fireplace hearth and swaying from one foot to the other whilst enquiring of my older sister what was school like, and then years later asking her what senior school was like ("Physics" - 'what's that?', "oh ever so boring, all about light and speed and weight and stuff" - 'sounds very interesting to me!')

Pose for annual official photo at APS

Of course I remember my first day at Alresford Preparatory School ('APS', a dame school), at least I remember being introduced by my older sister. My older sister comes into many of these tales. I can remember not wanting this cheap toy telephone to be in my official photograph but being told to pose like this. Back then the government provided all pupils with a third pint bottle of milk every day and this we consumed via a straw. In the winter it was sometimes frozen and I remember the disgust I felt at the teacher saying it was "just like ice cream". Adults sometimes say ridiculous things to children and expect them not to be taken in. On one occasion I tried blowing instead of sucking through the straw, with disastrous results. But it was only an experiment - how else does one learn? 

My mother and me

That's my mother, just how I remember her: this picture still gives me a lump in my throat. Memory is so frustrating: I feel like I ought to be able to recall, oh, so much more but in fact I remember so little about my parents, good as they were. She loved flowers, that much I can remember - and her signature meal was roast lamb with all the trimmings (which would include Yorkshire pudding even with lamb).

We aggravate the world by first being born then, in order to stay alive, by consuming its bounty until we die and rot in our graves leaving behind no more than an aroma and a feint but gradually vanishing memory in the minds of those we came in contact with.  Such is life and what is achieved?  All is vanity!

I did it! Again!

This time the goal was to "do" the Granite Way, a dedicated cycle route from Okehampton to Lydford on the track bed of the former Dartmoor railway which originally ran all the way to Cornwall and follows the northern border of Dartmoor passing several of its Tors.

My track: 94.2 miles, 2045m elevation gain, average 10.3mph

The outward journey was the same as for the Tarka trail up to Crediton. To ring the changes my return journey started with a segment of A30 which is a major trunk dual carriageway with very fast traffic and then veered northwards at Whiddon Down crossing the mid-Devon aka Tarka branch line several times.

A carefully dosed administration of magnesium ions in the form of supplement tablets and, on returning home, an Epsom salts bath successfully warded off cramp which on former long bike rides has plagued me.

You can view my photos here. Some notes on the photos in order:

• The trail starts at Okehampton station which is currently being resurrected from 50 years of inactivity;
• The trail is initially adjacent to the still existing but disused railway track as far as and which served a quarry; 
• Beyond the quarry the trail goes over the Meldon steel girder viaduct, after which I deviated to view the nearby Meldon reservoir and dam from which the viaduct is visible;
• Later on it crossed a second smaller viaduct made of granite
• The trail terminates rather abruptly in Lydford, a charming village where everyone I met was very friendly;
• I went a bit further to check out Lydford castle and church;
• To return I retraced my steps, stopping to snap a lovely beech avenue, a sample of the short stretch of unpaved surface, and a view of the Sourton Tor on the skyline;
• Some more views of the Meldon viaduct and its inner workings;
• I left the trail just before its end to access the A30 as suggested by Google maps and to do so had to masquerade as an Emergency Vehicles Only;
• I've included a couple of views of where I crossed the mid Devon line.

Whilst 94 miles in one day seems like an achievement for me, it was nothing compared with the guts and stamina and tenacity we have witnessed in the 2020 Paralympics.

Can you know for sure?

Every science pupil knows about drawing a best-fit straight line by eye through a scatter plot of experimental data. But at college level I discovered something so much better in regression analysis. Better, because the resulting best-fit (trend) curve or line (polynomial) is mathematically deterministic and no longer depending on the vagaries of human judgement. Apt and questionable use of regression is well illustrated by...

The black dots represent experimental data, the same in all 12 graphs, and the various red lines are "best fit" attempts to determine the underlying theory that explains these data. In the simplest case the experimenter will massage the theory into an equation of a straight line, plot the data according to this equation and then using linear regression to fit the best straight line as in the first graph. The resulting gradient and y-intercept are the summary data and the correlation coefficient provides a measure of confidence level. 

Measured data is generally discrete as well as being subject to experimental error, whereas the theory is hoped to be exact and generally continuous. For example, with an experiment to verify the well known equation for the period of a simple pendulum:

the period T will be measured for discrete values of length L.  Squaring both sides of the theoretical equation shows that plotting T² against L should result in a straight line through the origin whose gradient will give a value for the acceleration of free fall g.

Whereas the period might have been measured for discrete lengths, regression will give us a value for the period at any length. Getting a value in this way within the experimental range is called "interpolation", or outside that range is called "extrapolation". The latter is often unreliable, as illustrated in the last graph above, especially for higher orders of the regression polynomial.

Valid or spurious?

But even interpolation can be tricky. Consider the experimental data depicted in the above graph. The "outlier" red point might be due to human measurement error or might describe some real but anomalous phenomenon. If in fact no measurement had been taken at this x-axis value any such phenomenon would have been missed. Of course the correct action in either case would be to take more measurements. But this freedom to re-measure is not always feasible, particularly if we are dealing with data measured historically or with apparatus that is no longer available or is too costly to set up.

We are talking about experimental data versus theory. Science is all about coming up with theories to explain observed phenomena. In physics the epitome would be to fulfil the quest for the so far illusive Theory of Everything. 

As you can see from the Curve Fitting Methods image, there might be more than one theory that fits the same experimental data, so which is the correct one? An example is the wave / particle duality of elementary particles. That light was observed to sometimes behave as a wave, and at other times as a stream of particles, birthed the start of what we now call Modern Physics. Back then these two theories seemed to be at odds but we now accept that they are different facets of the same truth. Enter the "greatest mistake" in Arago's spot. And we are similarly happy with the concept that what we call matter is not as tangibly solid as suggested by Thomas' "Unless I see in his hands the mark of the nails, and place my finger into the mark of the nails, and place my hand into his side, I will never believe" but rather is subject to the fuzzy laws of probability - or at least so quantum theory says.  But these are theories often beset with hard or costly to obtain data and of course we can neither directly "see" nor touch some of this stuff. Think Large Hadron Collider, the world's largest and highest-energy particle accelerator.

To the uninitiated the various "modern" theories such as General Relativity, String theory and the Standard Model with its quarks and more recent supposed anyons that can only exist in 2D appear whacky indeed and the only reason there are no large scale public demonstrations to either refute or endorse them is, I suppose, because the average member of the public doesn't have a clue about what they all mean or their relevance to every-day life.

But perhaps none of these currently accepted theories is in fact the best fit to the data, witness that a Theory of Everything has not yet been proposed. And perhaps a similar argument can be applied to other realms, for example climate change aka global warming and the role of CO2 where a lot depends on questionable extrapolation. Add to this the political agendas that seem so often to have the media promoting particular theories to their own end and you have such a mishmash that all the ordinary person is left to choose is whether to go with the flow or go against the flow, neither course being as strongly based on science or truth as we would like. 

Part 2

Pianist's bane

One of the many banes of a pianist's life is a squeaky sustain pedal. And the propensity for machines to get into a state where they squeak, chatter or vibrate seems to be a general issue of which the piano is but one instance.

To aide my sanity and make profitable use of my spare time whilst in Devon I have invested in an Alesis Recital Pro piano keyboard. I am generally very happy with this machine even if it is no match for a real piano, but as it came without stand or sustain pedal I have improvised on each and my pedal design is shown below on its side.

My foot presses the darker plywood pedal which is hinged to the base and operates a small microswitch. A helical compression spring is located in a hole drilled in the base, but there is no matching recess in the actuator. Yes, the microswitch clicks and this is annoying but, worse, the mechanism in general develops a squeak over time which could be caused by the spring, or the brass hinge, or the microswitch lever rubbing against the pedal. It's hard to know which because upon investigation the squeaking promptly stops. Short of a major redesign, my present recourse is to apply oil to all of the above. But I'm pretty sure that sideways motion in the pedal allowed by slack in the brass hinge puts the spring off centre and which then rubs when the pedal is depressed and causes the squeak. if so the solution would be to use a more precise hinge.

Oh, and in use it tends to walk across the carpet ending up abutting the piano stand and thus either not working or scraping the stand when depressed, so I have now affixed it to the stand to stop that happening.

Squeaking is caused by stiction when one surface rubs against another. The two surfaces stick to one another until the sheer force is strong enough to overcome stiction. The surfaces now slide until the force reduces below that of friction. This typically makes a "tick" sound, but if it repeats frequently enough it becomes a squeak. Related phenomena are vibration caused by imbalance or backlash in rotary mechanisms, and chattering in a very loose bearing. In each case there is unwanted movement, doubtless caused by excessive manufacturing tolerances. I can well imagine that my spring might wander in its locating hole or go out of plumb and thus slide across the ply actuator and generate the squeak. 

But what interests me here is that parts of a machine will move (if given liberty) until they find a position in which they squeak or vibrate, and then stay there. Why should this be? Is it the propensity and perversity of nature as in if a thing can possibly go wrong then it will and moreover will generally choose the most inconvenient time to do so. Or is it positive feedback which exacerbates the effect?

Playing about with the Recital Pro

Is my newly acquired Alesis Recital Pro digital piano keyboard out of tune or is my musical acumen failing with age?

First some facts. The Recital Pro is an 88 key keyboard so spans from lower A0 to upper C8 with an overall pitch range of just over 7 octaves. It boasts 12 basic voices with various additional functions. Some of the voices (namely "Clavi", "Acoustic bass" and "Fingered bass") sound an octave lower than normal giving effectively an overall range of just over 8 octaves, although this shift is tacitly cancelled when layering with a normal voice. Moreover the whole range can be "transposed" by up to 12 semitones up or down extending the effective range to about 10 octave but q.v.. 

In what follows the term "normal" will refer to the standard piano pitches with A4 (above middle C) having the frequency 440Hz (this being Concert Pitch by definition).

The keyboard extends downwards 4 octaves and upwards 3 and a bit octaves from A4 so we have:

C8    ~4186Hz      (highest normal note, all C frequencies per equal temperament)

A7     3520Hz

A6     1760Hz

A5      880Hz

A4      440Hz   (standard pitch)
C3     ~261.6Hz (middle C, 2ft open pipe e.g. flute)

A3      220Hz

A2      110Hz

A1       55Hz

C1      ~32.7Hz (16ft open pipe)

A0       27.5Hz (lowest normal note)

With voice "Fingered bass" selected the lowest note becomes C0 at 16.35Hz and the A below at 13.75Hz, and with decent headphones on (because the internal speakers have poor low frequency response) the sound is impressive and reminiscent of a real (acoustic) organ at 32ft register. The sound is a combination of deep bass and tangible throbbing (at 13.75 times per second). Of course, the listener is probably hearing the harmonics (or "partials") rather more than the fundamental, witness with the purer voice "Acoustic bass" for which the deep bass is hardly audible, but this fact hardly detracts from the experience because non-linearities themselves can create undertones giving the illusion of bass deeper than the equipment should be able to produce.

But one can go even lower in pitch with "Transpose" set to its minimum of "-12" i.e. 12 semitones lower. With this setting the lowest note to sound is C#0 which calculates as 8.66Hz and sounds little more than a throbbing, and this simulates the 64ft organ open pipe register.

Similarly with "Transpose" set to positive amounts one can explore the Recital Pro's upper register. In principle, by playing the top note, with the settings up to the maximum of "+12" one should get up to B8 at 7902.13Hz. In fact with the standard "Piano" voice there is already hardly any output at top C even without any transposing (as indeed with an acoustic piano).  Apart from obviously the voices that sound an octave below normal, the voice "Synth" perhaps does the best at top C. Then, as the "Transpose" setting is increased up to "+12" sampling alias artefacts become very evident and at "+12" the apparent pitch seems actually lower than with setting "00". Which suggests that, internally, the digital pitch engine is sampling maybe lower than the industry standard 44.1kHz or at least there is insufficient anti-aliasing filtering. All this is a bit academic because I have no call to be making noises at this high a frequency. But maybe younger players with better hearing might want to. 

Both effortless low frequency response and high frequency response plagued with aliasing are of course typical of any digital audio system.

But back to my opening gambit. I play mostly by ear so hit notes that my "ear" thinks are correct, rather than reading them from a music score. I have found with my Recital Pro that I not infrequently find myself playing notes in the lower register that are entirely incorrect and yet taking a while to notice it. Which I cannot remember doing on an acoustic piano. Or I find, even when the score confirms I am playing the correct note, it just doesn't sound right.

Now, as I've said this may be due to my ailing musical acumen or else it could be a real effect and I'd be interested to hear if my readers have any similar experiences or observations. If it is a real effect then I suspect it is related to the Railsback effect observed in acoustic pianos and thus possibly simulated in their digital counterparts.

The deal here is that real (acoustic) piano strings have thickness as well as length. Based on length alone (and thus assuming no effect of bending at either end), a string can vibrate with fundamental and harmonics. By definition the frequencies of the harmonics are integer multiples of that of the fundamental. But if the resistance to bending near the fulcrums is taken into account what were harmonics become mere overtones i.e. no longer having exact integer relationship with the fundamental indeed becoming "inharmonic". In a piano the lower pitch strings have to be made heavier than mere scale would demand in order that their length and thus the overall dimensions of the instrument should remain feasible for the average owner. Not only that but the lower the pitch, then more the "ear" is aware of the overtones over and above the fundamental because of the tail-off of low frequency response of the ear and of the piano's sounding board. To compensate the piano tuner favours the first few overtones over and above the fundamental and thus has to effectively detune the lower strings.

A similar effect applies to the higher strings where it becomes necessary for mechanical robustness to make the strings thicker than mere scale would demand, thus increasing inharmonicity.

The overall effect is the Railsback curve which sort of averages, I suppose, what piano tuners have been trained to do as part of their art. Which of course applies to acoustic pianos and contributes to their overall sound quality.

Enter the digital piano. Of course, when tuned, there is now no reason to copy the Railsback curve as far as mechanics are concerned as there are none. But what does persist is the piano players' expectations, and the article linked above suggests that digital pianos do regard Railsback and perhaps that is why the lower register of my Recital Pro sometimes seems over of tune to my ears.

Comments please!

Bampton

Today's bike route was Planned!  The key is to make the forward journey harder and the return easier. Which I failed to do with the Tarka trial expedition. Google maps gives the elevation profile which helps the planning. And the return journey was wonderful instead of being gruelling!

Outward journey to Bampton via main roads

Return journey via side roads, mostly downhill

My track 27 miles 476m elevation gain

A duck race?  

Why do we love music?

Following the US government’s recent report there has been a resurgence of interest in UFO's. Personally I retain an open but cautious mind on the subject. It feels not too dissimilar to the God argument, well pictured in Orual's "If that's all they mean, why do they wrap it up in so strange a fashion?" "Doubtless," said Arnom (and I could tell that he was yawning inside the mask, being worn out with his vigil), "doubtless to hide it from the vulgar."  If either entities exist, why do they dangle half truths so enticingly? Why not either totally hide or brazenly show themselves for what they are?

Imagine these supposed green men (or maybe there's only one who is extremely dextrous), sentient yet alien to human culture, discovering thousands of humans crowed into an enclosure (in this instance the one we call the Royal Albert Hall) in which a number of them are blowing into or otherwise stimulating convoluted sound making machines, and enduring for a significant period this experience with apparently very great pleasure?

Concerning this piece, the composer said "I gave everything to it I was able to give. What I have here accomplished, I will never achieve again". And I can believe it. And this is possibly the best recording I have heard and if it don't send shivers down your spine then I don't know what will. 

So, why do we humans love music?