Differentiating f(x)^g(x)

Black Pixel Red Pixel

My favourite mathematical "YouTutor" is Steve Chow, the guy behind the superlative blackpenredpen collection of mathematics videos on YouTube. Steve has developed a way of explaining proofs using two or more pen colours, hence the name of his YouTube channel. He holds multiple marker pens in one hand while writing on a whiteboard, deftly switching colours so as to highlight the essential differences between each pair of lines in the mathematical exposition. It's a very effective expository technique.

Until recently, my number one blackpenredpen video was this one, where Steve uses logarithmic differentiation and the chain rule to prove the power, product, and quotient rules of derivatives. The reason it's so high on my list is because of the additional bonus content at the end, kind of a "hidden track" type deal, where he goes on to solve for the derivative of a function raised to the power of another function.



Just recently Steve, a keen runner of physical marathons, published a truly marathon mathematical video - my new favourite - in which he performs a hundred and one integration proofs in a single take. I'll let you search for that 6 hour video yourself, and if you feel like sitting through it, may I suggest you limit your accompanying playlist to just these three songs: Steely Dan's "My Old School", Supertramp's "School", and Bowling For Soup's "High School Never Ends". This will help you digest the integration marathon in healthy 15 minute chunks.

Getting back to the bonus differentiation, I remember thinking, this procedure has the effect of subtracting one from the power of one of the functions. Yet it doesn't use the power rule in its own derivation. Aha, I bet this could be used to derive the power rule itself! And since I was looking for a suitable subject for my first foray into maths typesetting, using LaTeX in the Overleaf environment, that became my target.

Here is the resultant PDF. You'll notice the homage to blackpenredpen in some of the text colouring.



The actual Overleaf project which produced this PDF can be viewed here, if you're interested in examining the source (LaTeX is a markup language, just as HTML is a markup language).

This is the first in a series of articles looking at aspects of differentiation. Next time I'll be presenting a neat & simple differentiator, utilising the Expression Trees feature of Microsoft C#.

Kedgeree

My Curry Here

Smoked haddock kedgeree, with added petits pois and raisins why. Because they seem to go nicely. This recipe has been refined for more than a quarter century (I made it once in 1993, then suddenly again today). Wife says it's terrific, and she's a fantastic cook, so there's always that.

Preparation time: 15 minutes.
Cook time: 40 minutes.
Serves 4.
Main Ingredients:

• 300g smoked fillet of haddock
• 4 eggs
• 100g frozen petits pois
• 300 ml milk
• bunch of coriander
• 2 bay leaves

Rice Ingredients:

• 300g long grain easy cook rice (well rinsed)
• 1 large onion (finely chopped)
• 30g raisins
• 1 tsp ground coriander
• 1 tsp ground turmeric
• 2 tsp roasted curry powder
• 1 chicken or vegetable stock cube
• 2 tbsp rapeseed oil

Method:

1. Very important: partition your ingredients into rice and non-rice work areas!

2. Fry the onion in rapeseed oil until translucent (about 5 minutes).

3. Add the spices & salt seasoning; stir and continue frying for a couple of minutes.
4. Add the rice, raisins, crumbled stock cube, and 300ml of water.
5. Cover and simmer for 5 minutes, while...
6. ...poaching the haddock and bay in 300ml of milk, until flaky.

7. Drain the milk from the fish pan into the rice, then roughly flake the fish.
8. Cover the rice pan and remove from the heat.
9. Add the petits pois to the fish (they'll defrost almost instantly).
10. Boil the eggs for 4½ minutes, then plunge them into cold water.
11. After 5 minutes, peel and quarter the eggs, then add to the fish along with the rice and coriander.

12. Mix gently, season with black pepper, then serve with any additional herbage
(e.g. parsley, if you like that sort of thing).

Smiddy Shank Soup

A Photo Essay

A very hearty and rustic Ham Hough Red Lentil Soup. Seriously, if they had this recipe in Zelda: Breath of the Wild, it would break the cookery system. It brings health, stamina, attack and defence boosts, while simultaneously providing resistance to heat, cold and electricity. One plate of it would fetch at least two hundred and eighty rupees. Pro tip: for an additional speed boost, replace the carrots with "swift carrots".

Preparation time: 20 minutes.
Cook time: 3 hours 15 minutes.
Serves 8.
Ingredients:

• 800g Blair Drummond Smiddy smoked ham hough (shank)
• 2 baking potatoes
• 1 large onion
• 3 celery stalks with leaves
• 6 carrots
• 250g red split lentils (well rinsed)
• 4 garlic cloves
• 2 stock cubes (vegetable or chicken)
• 6-8 black peppercorns
• 1 teaspoon dried oregano
• 1 bouquet garni
• 2-3 bay leaves

Method:

1. To 3 litres of boiling water in a pot, add the ham, bouquet garni, peppercorns and bay.

2. Boil for 2½ hours.

3. Meanwhile, back at the vegetable station...

...peel the potatoes, onion, celery, carrots & garlic.

4. Dice the potatoes, onion, celery, and four of the carrots.

5.Crush the garlic and grate the remaining two carrots.

6. At the 2½ hour mark, remove the ham from the pot.

7. Skim the water, then add the potatoes...

...the chopped carrots...

...the celery...

...the onion...

...the grated carrots...

...the crushed garlic...

...the oregano and stock cubes...

...and finally the rinsed lentils. Simmer for 45 minutes.

8. Strip the ham off the shank and add back into the soup before serving.

9. It sticks tae yer ribs. Serve with a twist of pepper.

Acknowledgements

I am gratefully indebted to my beautiful assistant and arm model @catsjamas for her help with the visual production aspects of this project.

Japanese Numbers

The New Job

Nowadays I'm working in medical research. One recent task was to internationalise some UI, then localise it into Japanese. With little in the way of a clue how to do this, but having built up some Audible audiobook credits over the spring months, I decided to take advantage of my three hour daily commute to learn a little about the Japanese language and culture. After all, there's every chance I'll soon have the opportunity to visit Japan on the company ticket, and I'd like to be able to speak to people in their first language, without causing humongous offence. So I bought a couple of Teach Yourself Japanese audiobooks.

Linguistic Regularity

Boy, did they do a job on me. You would never think, looking at the Japanese writing system, reputedly one of the most horrendously complex in the world, that this language could be a clean and tidy, logically lovable, stone fox. But I was soon smitten. I mean, just look at some of these features. There are no singular or plural nouns, there's just the noun. The verb to be, one of the most irregular in my native tongue, doesn't conjugate at all; it's just like I be, you be, he she or it be. Month names are like first month, second month, and so on. Dates are in perfect ANSI order: the greater subdivision always comes first, so it's year-month-day, or yyyy-mm-dd. Ideal for sorting by computer! There are only 47 syllables in the language, and every vowel is always pronounced the same.

Of course that's just the first flush of romance; eventually reality and entropy make themselves heard. There might indeed be so many welcome regularities in Japanese, but then they go and spoil it all by saying something stupid like "there are three levels of formality for every sentence", or "men and women speak with subtly different inflections." This last, together with the fact that most teachers of Japanese are female, has the interesting consequence that male learners usually, unwittingly, start off sounding quite effeminate.

Numeric Logicality

But then there are the numbers. The Japanese counting system is beautifully simple and regular, with very few exceptions in structure and pronunciation. Again, the first idealistic impression is somewhat spoiled by reality, this time by the introduction of "counters". These are little particles which must be appended to numbers, when counting objects. Surprisingly, the particular counter used is often based upon the physical appearance of the thing being counted. Then again, certain numbers cannot be used in counting certain types of thing, but must be substituted with other special purpose counters...

Still, the basic counting system is quite easy to learn, interesting too, and if nothing else can at least be used while you count through the steps of kata in your chosen martial art (mine is press-ups-do). I considered it potentially a big win, both mathematically and scientifically, to count as high as I possibly could using this system. As a study aid I made a little text file, delighted to realise that all the kanji characters and superscript numerals available in unicode were supported in Notepad. Printed out and laminated in A6, it became a pocket reference card. Later in A4 format, it would become a placemat suitable, used in conjunction with a transparent plate, for learning your ichi-ni-san while eating your sushi.

Original Text Version

The version below can be copied to the clipboard as text, then saved in Notepad. Just remember to select one of the Unicode options, such as UTF-8, from the Encoding drop-down list.

0  〇/零  zero/rei  JAPANESE NUMBERS REFERENCE CARD  * Learn these exceptions!

       1            10               100              1,000           10,000

1   一 ichi       十 jū            百 hyaku         千 sen        一万 ichi-man
2   二 ni       二十 ni-jū       二百 ni-hyaku     二千 ni-sen     二万 ni-man
3   三 san      三十 san-jū      三百 san-byaku *  三千 san-zen *  三万 san-man
4   四 yon      四十 yon-jū      四百 yon-hyaku    四千 yon-sen    四万 yon-man
5   五 go       五十 go-jū       五百 go-hyaku     五千 go-sen     五万 go-man
6   六 roku     六十 roku-jū     六百 ro-ppyaku *  六千 roku-sen   六万 roku-man
7   七 nana     七十 nana-jū     七百 nana-hyaku   七千 nana-sen   七万 nana-man
8   八 hachi    八十 hachi-jū    八百 ha-ppyaku *  八千 ha-ssen *  八万 hachi-man
9   九 kyū      九十 kyū-jū      九百 kyū-hyaku    九千 kyū-sen    九万 kyū-man

10⁵ 十万 jū-man       10⁶ 百万 hyaku-man       10⁷ 千万 sen-man

10⁸    10¹²   10¹⁶   10²⁰   10²⁴     10²⁸   10³²   10³⁶   10⁴⁰   10⁴⁴   10⁴⁸
億     兆     京      垓     𥝱/秭    穣     溝      澗     正     載     極
oku    chō    kei    gai    jo/shi   jō     kō     kan    sei    sai   goku

10¹² 一兆 itchō      8x10¹² 八兆 hatchō        10¹³ 十兆 jutchō †
10¹⁶ 一京 ikkei      6x10¹⁶ 六京 rokkei      8x10¹⁶ 八京 hakkei

10¹⁷ 十京 jukkei †     † Multiples of 10:  change -jū to -jutchō or -jukkei
10¹⁸ 百京 hyakkei ‡    ‡ Multiples of 100: change -ku to -kkei

10⁵²⸍⁵⁶       10⁵⁶⸍⁶⁴       10⁶⁰⸍⁷²       10⁶⁴⸍⁸⁰       10⁶⁸⸍⁸⁸
恒河沙         阿僧祇     那由他/那由多     不可思議      無量大数
gōgasha       asōgi        nayuta        fukashigi    muryōtaisū

How It Works

The first thing to do is memorise the top left column, digits 1 to 9, and 10: ichi, ni, san, yon, go, roku, nana, hachi, kyū, jū. Note that the horizontal bar along the top of a vowel just makes it sound "long" - some guides use double vowels for this purpose.

Next, to form the numbers 11 to 19, just use literally ten-one, ten-two, ten-three, etc. So that's jū-ichi, jū-ni, jū-san, etc.

Multiples of ten up to ninety are found in the second column: ni-jū (20) is literally two tens, san-jū (30) three tens, and so on. Intermediate numbers are simply concatenated or added together, so 42 is "four tens two", or yon-jū-ni.

It's a similar story for multiples of 100, found in the third column, although there are three little exceptions to be aware of - more or less subtle variations in pronunciation. I've marked these with asterisks. So although 3 is san and 100 is hyaku, 300 is not san-hyaku but san-byaku; note the hard 'b' sound here, and also the hard 'pp' in 600 (ro-ppyaku instead of roku-hyaku) and 800 (ha-ppyaku rather than hachi-hyaku).

Multiples of 1,000, as seen in the fourth column, also have exceptions marked at 3,000 and 8,000, although there isn't an exception for 6,000, which is just business as usual: roku-sen.

Chinese Roots

Reaching 10,000 there's another little surprise in store, and quite an important one. It might help a bit to think first about English powers of 10. Notice that 100 (one hundred) and 1,000 (one thousand) both begin with the word "one", whereas 10 (ten) and 10,000 (ten thousand) don't. But actually, there is an old English number "myriad", one of whose older meanings is literally ten thousand. We might therefore think of 10,000 as "one myriad", and in fact that's similar to what the Japanese, following on from Chinese tradition, actually do. Ten thousand is best translated into Japanese via "one myriad", hence ichi-man.

With that in mind, column five otherwise proceeds much as before: 20,000 is ni-man (two myriad), 30,000 is san-man, and so on without further exceptions. But we have just passed an important milestone here. Just as our big numbers tend to group themselves into powers of 1,000 such as thousands, millions, billions, trillions, and so on, each time multiplying by 10³ and adding another comma, so the oriental tradition is to partition into powers of 10,000, and groups of four digits. The importance of this structure is reflected in the use of the ichi (one) prefix for 10,000: not just man (myriad), but ichi-man (one myriad).

The same caveat will apply to all subsequent powers of 10,000. But before getting to those, look at the next few powers which are not multiples of 4, and don't need the ichi prefix. As shown immediately below the main table, we already knew how to construct:

• one hundred thousand (100,000  = 10⁵ = ten myriad = jū-man),
• one million (1,000,000 = 10⁶ = hundred myriad = hyaku-man), and
• ten million (10,000,000 = 10⁷ = thousand myriad = sen-man).

Next, we shall alight upon the Big Sequence, the powers of 10⁴ spanning 10⁸ to 10⁴⁸ (one quindecillion!), listed in the second horizontal table.

To Infinity And Beyond (almost)

So, now we avail ourselves of the long line of Powers of Myriad (that's definitely the name of my next witching and wizarding trilogy, watch out JK). We have reached 10⁸ which is labelled oku, but since 8 is a multiple of 4, we have to prepend this with ichi. Thus, 10⁸, or a hundred million, becomes ichi-oku. Two hundred million is ni-oku. And so on.

Things chug along quite nicely until we reach one trillion, or 10¹². Everything we've covered so far leads to the expectation ichi-chō, until we stop and consider the clumsiness of that utterance. Surely that is the reason the wise Japanese have decided to contract it to itchō. Similarly, eight trillion becomes not hachi-chō but hatchō, while ten trillion is not jū-chō but jutchō (with the shorter u).

Similar exceptions apply to the next big multiplier, 10¹⁶ (which becomes not ichi-kei but ikkei), as well as multiples of this by 6, 8, 10 and 100. There is a pattern to the modifications in these cases, codified by the daggered comments in the bottom half of the reference card (or placemat).

Finally, we reach the bottom 3 rows of the card, where the only reliable historical sources contradict each other. In a denouement reminiscent of the war between American and British billions (see Wikipedia for details, https://en.wikipedia.org/wiki/Names_of_large_numbers), there's a forking schism in which the same terms are used to count, simultaneously and incompatibly, using multiples of 10⁴ and/or 10⁸, into an uncaring infinity. Of limited scientific use admittedly, but why not take advantage of the Creative Commons licence, and print out and laminate your own set of Japanese Numbers placemats?

My Collie Here

Meet our Archie

Every cat needs a collie, and this is Cleo's new wee brother, Archie.

"Wee" brother is right. Although he's grown to double her size, in the 4½ weeks he's been with us - compare the picture on the right with the one below, taken 4½ weeks later - he still gets "Wee Archie" due to his determination to cover the whole house in a uniform coat of wee!

Actually, that's a bit unfair. When he came to us at exactly 8 weeks old, he was already trained to go on the puppy training pads, and had more or less a 100% record on those. But that was only for wee; anything more demanding would be deposited instantly and immediately, just wherever he happened to be, as the mood took him. Now that we've started trying to take away the training pads, the result - with apologies to Kevin Bacon - has been a return to Everything Everywhere.

End of the Tunnel

Yesterday he attended his first puppy socialising class at The Dogs Trust, where he did us proud with his precocious knowledge of the Sit, Stay, and Down commands. All credit to Linda there, for her decades of experience training very intelligent border collies.

Socialising per se was less successful. Archie has had to be kept away from other dogs for longer than is usual, because his breeder failed to immunise him against deadly diseases such as Parvovirus. We didn't find out about this until we took Archie to our own vet, for what we thought would be his second and final inoculation, but which turned out to be a complete restart at day one.

So yesterday, two weeks later than he should have, he finally got to meet other pups. He was timid and reluctant, and basically failed to do so. However the instructor expressed his confidence that this delayed development can be put right over the coming month.

Archie and Cleo, everybody!

FLAC Forensics

Frequency Fingerprints

I was asked by a friend if it was possible to check whether some downloaded files were actually faithful to the original WAV format entities, or whether they had in fact been rehydrated from an unfortunate, lossy intermediate MP3 excursion. The files in question were FLAC compressions of the original 3½ hour, 42 track Analord series of electronic pieces by Richard D. James, most of which were only ever issued on 12" vinyl by the artist's now defunct Rephlex Records outlet.

Update: My personal RD James expert informs me that these original 42 tracks were also released in lossless digital format on Rephlex, and that some (or all?) of the subsequently released additional, digital-only tracks were also added to these by Rephlex.

I loaded the first of these files, SteppingFilter 101, into Audacity, and took a look at the frequency domain graph (Analyze|Plot Spectrum...). After a brief complaint about only being able to analyze 237.8 seconds of audio at a time, the result was this:

Notice the slight uptick at the extreme right (high frequency) end, around 22kHz. This represents extraneous noise generated by the digital sampling process, which in this case appears to have been set naturally enough to the CD standard stereo setting of 44.1kHz. This effect will be present in any rip, at some frequency or other, and is of a different kind from the artefacts introduced by MP3 processing.

Next, I used FooBar2000/LAME to convert this file to MP3 format, using the highest available quality, Constant Bit Rate standard preset, namely 320kbps CBR (actually LAME can handle non-ISO bit rates of up to 640kbps via its freeformat option, but very few MP3 players can handle such files).

The result of this 320kbps conversion has a very obvious steep cutoff at about 20kHz:

Any attempt to convert this back to the WAV format will preserve this telltale high frequency cutoff. Does this mean we can be confident that the source file represents a good, high quality, uncompressed rip from the original vinyl? I would say confident, yes; certain, well, that's another bottle of kippers. We haven't ruled out nonstandard MP3 or other shenanigans with this test alone, but those compression antics are at worst extremely unlikely.

Sundry Surround Sound Recordings

Planned Obsolescence

At the time of purchase in May 2015, my current universal (DTS/SACD/DVD-A/Blu-ray) player, a Pioneer BDP450, cost me a featherweight £159. Just over a year later it's "unavailable", unless I'm willing to settle for a refurbished model from Ebay. Reasonably priced multichannel DTS/SACD and DVD-Audio players are becoming really hard to find, even from the manufacturers who invented these formats. At present the best available options appear to be:

• PIONEER BDPLX58 (£449 at Richer Sounds)
• CAMBRIDGE CXU (£799.95)
• OPPO BDP105D (£1,099)
• PIONEER BDPLX88 (£1,099)

No wonder then that collectors of surround sound DVD-Audio recordings, and even more so those of multichannel DTS media or SACDs, are feeling increasingly under siege these days. For how much longer will we be able to play these purchases? How many more times will we be able to afford a new player, when the last one packs in and its perishing rubber wheels and belts and lasers can't be replaced?

This is a partial list of my surround sound recordings by format. It will let me sit and grieve as first DTS, then SACD, then DVD-A, and finally (sooner than you'd think!) Blu-ray playback become impossible. Then I will at least be able to see at a glance each month, exactly what fraction of my collection has now become permanently unavailable to me. It's also a work in progress, since I have no intention of losing the bad habit of buying these wonderful recordings; currently I'm looking forward to the much-delayed Steven Wilson remixes of the early Roxy Music albums.

Top 100+ Speciality Multichannel Studio Mixes

This first table lists recordings where a studio engineer (usually Steven Wilson or Jakko Jakszyk ;-) has carefully pored over the source material, and arranged things in space to produce a curated, meticulously arranged, surround sound experience.

Artist or Composer	Album Title	Year	Physical Media
			SACD	DVD‑A	Blu‑ray
Ian Anderson	Homo Erraticus	2014		✓
Bach	Bach Classics	17xx		✓
Bass Communion	Loss	2006		✓
The Beatles	Love	2006		✓
Beethoven	Beethoven Classics	18xx		✓
	Symphony No. 6 "Pastorale"	1808		✓
Blackfield	Blackfield V	2017			✓
David Bowie	The Rise and Fall of Ziggy Stardust...	1972	✓
Caravan	In the Land of Grey and Pink	1971		✓
Eagles	Hotel California	1976		✓
	Hell Freezes Over	1994	✓
ELP	Tarkus	1971		✓
	Trilogy	1972		✓
	Brain Salad Surgery	1973		✓
Flaming Lips	Yoshimi Battles the Pink Robots	2002		✓
Fleetwood Mac	Rumours	1977		✓
Genesis	Trespass	1970	✓	✓
	Nursery Cryme	1971	✓	✓
	Foxtrot	1972	✓	✓
	Selling England By The Pound	1973	✓	✓
	The Lamb Lies Down on Broadway	1974	✓	✓
	A Trick of the Tail	1976	✓	✓
	Wind & Wuthering		✓	✓
	...And Then There Were Three...	1978	✓	✓
	Duke	1980	✓	✓
	Abacab	1981	✓	✓
	Genesis	1983	✓	✓
	Invisible Touch	1986	✓	✓
	We Can't Dance	1991	✓	✓
Gentle Giant	Three Piece Suite	1970-2			✓
	Octopus	1972			✓
	The Power and the Glory	1974			✓
Handel	Handel's Water Garden	17xx		✓
Gavin Harrison	Cheating the Polygraph	2015		✓
Jethro Tull	Stand Up (The Elevated Edition)	1969		✓
	Benefit (A Collector's Edition)	1970		✓
	Aqualung	1971		✓
	Thick as a Brick	1972		✓
	A Passion Play	1973		✓
	War Child	1974		✓
	Minstrel in the Gallery	1975		✓
	Too Old to Rock'n'Roll: Too Young to Die!	1976		✓
	Songs from the Wood	1977		✓
	Heavy Horses	1978		✓
King Crimson	In the Court of the Crimson King	1969		✓
	In the Wake of Poseidon	1970		✓
	Lizard			✓
	Islands	1971		✓
	Larks' Tongues in Aspic	1973		✓
	Starless and Bible Black	1974		✓
	Red			✓
	Discipline	1981		✓
	Beat	1982		✓
	Three of a Perfect Pair	1984		✓
	THRAK	1995		✓
	Radical Action (To Unseat The Hold...)	2016			✓
Marillion	Misplaced Childhood	1985			✓
The Moody Blues	Days of Future Passed	1967	✓
	On the Threshold of a Dream	1969	✓
	To Our Children's Children's Children		✓
	Seventh Sojourn	1972	✓
Mozart	Mozart Classics	17xx		✓
Mike Oldfield	Tubular Bells	1973		✓
	Hergest Ridge	1974		✓
	Ommadawn	1975		✓
	Five Miles Out	1982		✓
Opeth	Still Life	1999		✓
	Deliverance & Damnation	2002/3		✓
	Watershed	2008		✓
	Heritage	2011		✓
Anthony Phillips	The Geese & the Ghost	1977		✓
	Wise After the Event	1978		✓
	Slow Dance	1990		✓
Pink Floyd	Atom Heart Mother (Devi/Ation, quad)	1970		✓	✓
	Echoes (Reverber/Ation, quad)	1971		✓	✓
	Meddle (Reverber/Ation, 5.1)	1971			✓
	The Dark Side of the Moon	1973		✓	✓
	Wish You Were Here	1975		✓	✓
Porcupine Tree	Stupid Dream	1999		✓
	Lightbulb Sun	2000		✓
	Deadwing (2 copies, 1 signed)	2005		✓
	Fear of a Blank Planet	2007		✓
	The Incident	2009		✓
Riverside	Love, Fear and the Time Machine	2015		✓
Roxy Music	Roxy Music	1972		✓
	Avalon	1982	✓
Schubert	Schubert Classics	18xx		✓
Simple Minds	New Gold Dream (81-82-83-84)	1982		✓
	Sparkle in the Rain	1984		✓
	Once Upon a Time	1985		✓
Steely Dan	Gaucho	1980	✓
	Everything Must Go	2003		✓
T. Rex	Electric Warrior	1971	✓
Tchaikovsky	Tchaikovsky Classics	18xx		✓
	The Nutcracker	1892		✓
Tears for Fears	Songs from the Big Chair	1985			✓
Trondheim Solistene	Divertimenti	2008	✓		✓
	In Folk Style	2010	✓		✓
Rick Wakeman	The Six Wives of Henry VIII	1973		✓
	The Myths and Legends of King Arthur...	1975		✓
The Who	Tommy	1969	✓
	Quadrophenia	1973			✓
Steven Wilson	Insurgentes	2009		✓
	Grace for Drowning	2011			✓
	The Raven that Refused to Sing	2013		✓	✓
	Drive Home				✓
	Hand. Cannot. Erase.	2015		✓	✓
	4½	2016			✓
	To The Bone	2017		✓	✓
XTC	Drums and Wires	1979			✓
	Skylarking	1986			✓
	Oranges & Lemons	1989			✓
	Nonsuch	1992			✓
Yes	The Yes Album	1971		✓	✓
	Fragile (2002 - Rhino)			✓
	Fragile (2015 - Panegyric)			✓	✓
	Close to the Edge	1972		✓	✓
	Tales from Topographic Oceans	1973		✓	✓
	Relayer	1974		✓	✓

Notice that most of the Yes titles are double entries (in fact Fragile is a triple): the DVD-Audio and Blu-ray editions of these are of course equally essential.

The Loneliness of the Long Interval Musicologist

The Year column is problematic. Every recording has its place on multiple chronologies; for example, the life and development of its composer, its conductor, and its performing artist(s). The difficulty is that different performances naturally emphasise disparate chronologies, and a single date field in a table or database struggles to accommodate these variations.

For the historical study of musical development, the time stamp of primary interest is the date of composition. Sadly this is not recorded in typical media metadata, such as the ID3 tags on MP3 files. The "Year" recorded there represents the release date - when the particular edition was issued. Now, for most "popular" music (in the strict Amazon.com sense of "anything non-classical"), this is close enough to the date of composition; but for all of the recordings listed here, without exception, the release date for the multichannel edition is many years later than that of first publication of the original material, and the problem is only worse in the case of classical works.

Generally I've tried to get as close as possible to the date of composition. That means for popular works using the year of first issue, and for classical, the historical year (or century, for compilations) of composition. Still there remain intractable inconsistencies. For example, all of the material on the Beatles' "Love" album was recorded and issued long before Cirque du Soleil went shopping for a soundtrack in 2006. Finally, there's Daniel Barenboim. When the focus of a classical recording is neither composer nor performer, but instead a famous conductor, then I use the performance date.

Live Surround Sound Music Videos

This second table lists live video recordings of musical performances that just happen to have a surround sound component, often limited to a feeling of ambience in the hall where the recording was made. These are the second class citizens of the surround sound community, and this collection listing will be incomplete.

Artist or Composer	Album Title	Year	Physical Media
			DVD	Blu‑ray
Ash	Tokyo Blitz	2001	✓
Daniel Barenboim	Knowledge is the Beginning / The Ramallah Concert	2008	✓
	Neujahrskoncert 2009	2009	✓
	Europakonzert 10	2010		✓
	Mahler Symphony No. 9		✓
	The Salzburg Concerts	2011		✓
Blackfield	NYC - Blackfield Live In New York City	2007	✓
Dream Theater	Live at Budokan	2004	✓
	Score	2006	✓
David Gilmour	Remember That Night	2007	✓
Led Zeppelin	The Song Remains the Same	1999	✓
	Led Zeppelin	2003	✓
Opeth	Lamentations	2006	✓
	The Roundhouse Tapes	2007	✓
	Live at the Royal Albert Hall	2010	✓
Orphaned Land	The Road to Or Shalem	2011	✓
Porcupine Tree	Arriving Somewhere...	2006	✓
	Anesthetize	2010	✓	✓
Steven Wilson	Get All You Deserve	2012	✓	✓
Yes	Symphonic Live	2002	✓
	YesSpeak	2003	✓
	Acoustic	2004	✓
	Live at Montreux 2003	2007	✓
Youssou N'Dour	Live at Montreux 1989	2005	✓