User:Double sharp/sandbox

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.131.152501 new Ta-180m decay limit

https://onlinelibrary.wiley.com/doi/10.1002/anie.201407561 issues re oxidation states: not everything needs to have an OS (e.g. intermetallics' difficulties), and probably low OS like Ir(I) in Vaska's complex should be treated as formal only. Also read https://pubs.acs.org/doi/10.1021/ic052110i from the OS list

https://philpapers.org/archive/SCEWIA.pdf connect with three chemical revolutions

10.1021/acs.inorgchem.1c00662 (for Housecroft and Sharpe lanthanide polymerisation), https://pubs.aip.org/aip/apl/article-abstract/53/15/1405/54232/Measurements-of-3d-state-occupancy-in-transition?redirectedFrom=fulltext (3d and 4d metal occupancies do not match the block position in condensed phase, because that's not what it is about)

https://journals.aps.org/prb/abstract/10.1103/PhysRevB.105.174104 https://pubmed.ncbi.nlm.nih.gov/35172288/ https://era.ed.ac.uk/handle/1842/28881 - lanthanoids high pressure

JINR popular lectures on superheavies

There is no Lu 4f bonding https://www.sciencedirect.com/science/article/abs/pii/S0009261408016503

https://www.dora.lib4ri.ch/psi/islandora/object/psi%3A26126/datastream/PDF/Eichler-2019-The_periodic_table_%E2%80%93_an-%28published_version%29.pdf

Translate: Vitalii Goldanski from ru.wp, Marcelo Tupinambá from pt.wp

cool demonstration of sonorousness changing with temperature: https://sciencedemonstrations.fas.harvard.edu/presentations/lead-bell

Orbital radii:

The only stable Sb allotrope is the metallic one: 10.1134/s0020168513070017

https://isotoxals.github.io/index.html

Papers to read: https://arxiv.org/pdf/2301.02553.pdf https://link.springer.com/article/10.1140/epja/s10050-023-00939-3 https://link.springer.com/article/10.1140/epja/s10050-023-00919-7

https://www.jstor.org/stable/44511246 - Chinese history

https://onlinelibrary.wiley.com/doi/epdf/10.1111/1600-0498.12328 - transfermium history

https://iopscience.iop.org/article/10.1088/1538-3873/ab8eb9 (Solar System)

learn more about history of La 4f superconductivity - it was first proposed, some findings on Y seemed to discredit it in early 1970s, but after that people continued advocating it, so look at what happened between this and 1978 when it's still proposed (I'm convinced it must be right by periodicity and that it was prematurely discredited; Wittig was against it before he became for it). Seems another early one was the late Jun Kondō in 1963.

For investigating Cs 5d: 10.1088/0953-4075/33/17/323 (basically, looking at periodicity under pressure with the collapses)

https://journals.aps.org/rmp/pdf/10.1103/RevModPhys.84.1607 H and He at high pressure

Persian planet names: https://dsal.uchicago.edu/dictionaries/hayyim/ and the other book I just got

https://core.ac.uk/download/pdf/220129765.pdf dissertation to read on PT

Ion configurations from NIST https://physics.nist.gov/cgi-bin/ASD/ie.pl?spectra=Pu&submit=Retrieve+Data&units=1&format=0&order=0&at_num_out=on&ion_charge_out=on&el_name_out=on&shells_out=on&conf_out=on&ion_conf_out=on&e_out=0&unc_out=on&biblio=on (example: plutonium)

R Bruce King hybridisation https://www.mdpi.com/1420-3049/25/14/3113

History of Madelung derivations https://www.cs.utep.edu/vladik/1998/tr98-5b.pdf

More Ostrovsky https://nyaspubs.onlinelibrary.wiley.com/doi/full/10.1111/j.1749-6632.2003.tb06097.x

Wulfsberg https://archive.org/details/principlesofdesc0000wulf

https://pubs.acs.org/doi/pdf/10.1021/ic50224a038

More Jorgensen to read: https://link.springer.com/chapter/10.1007/BFb0111259

4f in LaIr: 10.1002/chem.201500902 (also more weird oxidation states)

Planetary-mass moons
The following table lists the data for the planetary-mass moons. As all of them are in synchronous rotation, their rotation periods equal their orbital periods.

An interesting early speculation on noble gas electronegativity 10.1021/j100886a039 confirms He with much less EN than Ne

other symbols
pedal heel/toe?

Superheavies
https://link.springer.com/article/10.1007/s12210-022-01057-w

Space colonisation
Gravity: https://pubmed.ncbi.nlm.nih.gov/23889757/ https://pubmed.ncbi.nlm.nih.gov/22999922/ https://pubmed.ncbi.nlm.nih.gov/25184481/

DPs

 * Firstly, I think the text I wrote earlier (start of Characteristics) probably would better link in to History, no? Because you can't really have much of an understanding of geophysical planethood until, well, the smaller bodies of the Solar System started revealing themselves.
 * I think the idea of the current history section is not bad, it just needs trimming. Maybe something like

Starting in 1801, astronomers discovered Ceres and other bodies between Mars and Jupiter that for decades were considered to be planets. Between then and around 1851, when the number of planets had reached 23, astronomers started using the word asteroid for the smaller bodies and then stopped naming or classifying them as planets, as it was clear that these bodies formed an asteroid belt and did not gravitationally dominate their neighbourhood.

Pluto was discovered in 1930, and was considered by astronomers to be the ninth planet. For 50 years it was thought to be larger than Mercury, with the discovery in 1978 of Pluto's moon Charon, it became possible to measure Pluto's mass accurately and to determine that it was much smaller than initial estimates: it turned out to be about 1/450 the mass of Earth, making it by far the smallest planet. Its large orbital eccentricity and high orbital inclination also made it evident that it was a different kind of body from any of the other planets. Matters began to come to a head in the 1990s, when more bodies in Pluto-like orbits were discovered, and it became clear that Pluto orbits in an asteroid belt as well (the Kuiper belt) and is not a dominant body. Logically, either the larger of these bodies would also have to be classified as planets, or Pluto would have to be reclassified.

[Then something about how the geophysical distinction came about, so we knew Ceres and Pluto were round] This led to two differing conceptions of what a "planet" should be. Dynamicists usually prefer using gravitational dominance as the threshold for planethood, because from their perspective smaller bodies are better grouped with their neighbours, e.g. Ceres as simply a large asteroid and Pluto as a large Kuiper belt object.[44][45] However, geoscientists usually prefer roundness as the threshold, because from their perspective the internally driven geology of a body like Ceres makes it more similar to a classical planet like Mars, than to a small asteroid that lacks internally driven geology. [And then maybe Alan Stern giving the name dwarf planet here]

The discovery of Eris, then thought to be slightly larger than Pluto, forced the hand of the International Astronomical Union (IAU). The issue of planethood thus became a matter of intense debate during the IAU General Assembly in August 2006.[18] The IAU's initial draft proposal was based on geophysical concerns, and included Pluto, Eris, and Ceres in the list of planets; it also included Charon. [should we maybe have a note about why it did that? and wasn't there some dispute precisely about that point?] After many astronomers objected to this proposal, an alternative was drawn up by the Uruguayan astronomers Julio Ángel Fernández and Gonzalo Tancredi: they proposed a dynamical definition with only the eight dominant bodies considered planet (Mercury through Neptune), but with an intermediate category for objects large enough to be round but which had not cleared their orbits of planetesimals. This became the category of dwarf planets, which despite their name were not to be considered planets. Although concerns were raised about the classification of planets orbiting other stars,[28] the issue was not resolved; it was proposed instead to decide this only when dwarf-planet-size objects start to be observed.[19] This definition was accepted, and is now generally used among astronomers, though some geophysicists still object and advocate a geophysical definition of planet that would include dwarf planets (among other objects).

[Maybe move the stuff about what objects are dwarf planets to the start of "Population of dwarf planets"]

Stuff
https://www.japanpolicyforum.jp/science/pt20171226201728.html nihonium

https://www.nishina-mf.or.jp/wp/wp-content/uploads/2019/12/2016Lec.pdf


 * how Auer von Welsbach was posthumously robbed of cassiopeium just because the name was only used in German and Dutch and was supposedly difficult to adapt to other languages (LOL, lawrencium)

Post at ELEM https://arxiv.org/abs/2102.08793 https://link.springer.com/article/10.1140/epja/i2017-12307-5

Transfermium history 10.1111/1600-0498.12328

Nobelium 10.1524/ract.1992.56.3.125

Try to find G. V. Ionova, V. G. Pershina, and V. I. Spitsin, Zh. Neorg. Khim., 28, No. 12, 3107 (1983) - is ok, i have a pdf now

To read: https://onlinelibrary.wiley.com/doi/pdf/10.1002/zaac.19865400912

http://web.archive.org/web/20160305034205/http://www.primefan.ru/stuff/chem/ptable/ptable.html

https://en.wikipedia.org/w/index.php?title=Periodic_table&oldid=995192171

The Heaviest Metals: Science and Technology of the Actinides and Beyond

5g 2.48 eV 121 https://journals.jps.jp/doi/pdf/10.1143/JPSJ.65.3175

TO READ WHEN FREER

Wojciech Grochala, generalised maximum hardness principle (10.1039/c7cp03101g and 10.1039/C7CP05027E)

--- Yet another explanation of the 3d vs 4s thing (seriously, it is standard)

https://journals.sagepub.com/doi/pdf/10.3184/003685018X15173976099750 yet another Og

The autograph of 3 masters (Beethoven, Schubert, Brahms)

Useful links to understand policy

 * WP:NOR
 * WP:ORNOT (especially section "Conflict between sources")
 * WP:LIKELY
 * WP:SYNTH
 * WP:CONTEXTMATTERS
 * WP:NOTNEO

Random links
10.1109/T-C.1971.223307 (octal)

https://inis.iaea.org/collection/NCLCollectionStore/_Public/31/047/31047604.pdf

An early ffff appears in: Alkan, Op. 76 No. 1 (1838–40)

http://cisdur.de/e_index.html keys with seven accidentals (missing: Alkan Op. 21/ii, L'Enfer, C-sharp major; Stevenson Le festin d'Alkan, III, much A-flat minor at the beginning)

10.1103/PhysRevA.53.3926 update Nh

10.1002/ejic.201600146 update Cn and Fl

H. 49 sonata (IV = VII/V = It.6)

https://www.degruyter.com/view/j/ract.2019.107.issue-7/ract-2019-0012/ract-2019-0012.xml https://www.sciencedirect.com/science/article/pii/S095994361830124X https://search.proquest.com/openview/bc98ac375ecbc986c51b47fe823ff5f0/1?pq-origsite=gscholar&cbl=2028809

https://www.ncbi.nlm.nih.gov/pubmed/24995984

https://link.springer.com/article/10.1007/s10967-018-6270-x https://www.sciencedirect.com/science/article/abs/pii/S0009261417310242 (Nh)

https://www.osti.gov/pages/servlets/purl/1524727 https://link.springer.com/article/10.1007/s10967-018-6207-4 (Fl)

tertiary subdominant IV of IV of IV end of Gloria in Beethoven Mass in C

Why on Earth is David C. F. Wright even ever cited on Wikipedia? (Live sighting from April 2020!!) (If you don't know about his writings already, you are lucky...)

Megaposting for Basemetal
OK, here's a start. I find I lack the time currently for megaposting, so I'll try to serialise this instead.

[talk about the Phrygian chord here] ♭vii as N substitute appears in Grand Duo - start of development. better example in Les Adieux (near the end of the 2nd movement)

IV to #iv (start of Haydn Op 76 No 4); IV to #IV (end of that chorus to toil in Haydn's Seasons)

I think that for the Viennese classics the augmented sixth may really have been just like a seventh chord (Mozart quartets have many examples, e.g. KV 499 retransition IIRC where it is arpeggiated). Certainly Alkan in Fa makes it a ninth chord too!

N to ii huge transition Schubert Mass No. 5 Quoniam tu solus

flipping to n Beethoven Op 86 Sanctus

iv of iv Liszt Hungarian Rhapsody 2 opening, of course. n, end of Liszt Hungarian Rhapsody 5

Schubert D 87/ii, ending, V of VI resolving to IV (like a mediant)

It should be noted that I do not propose to throw out everything about theoretical functions. Indeed, it is perfectly obvious that there are certain features common to multiple chords that unite them. For instance, we can think of "sharp-side" and "flat-side" chords as enhanced dominants and subdominants; we can think of a superset of "mediants" that includes chords related to the tonic through one (or a series of) semitonal changes; and so on.

The functions of N etc. (what are the roots of the augmented sixths?) First cover all those semitonal resolutions

Difference between diatonic and chromatic semitone usages – the former changes the degree of the scale, the latter does not. Indeed the latter is akin to modal mixture – you go from C major to C minor by adding accidentals, as it's an E-flat and not a D-sharp as the third. Hence we may indeed consider altered tonics as such?! That means that the "minor Neapolitan" may indeed not only be the Neapolitan

Liszt sonata contains a lot of good examples; it even ends in that "plagal cadence" ♯IV–I (there's also another wandering-harmony passage in the "slow movement"). It's kind of a plagal Neapolitan (C♮ in the bass line as an upper leading tone). IV of N, N, IV of VII (maj), VII (maj) (sequence by whole tones), IV of VI, VI, II, V, I (closing formula) [ from memory ]

At some point we must get to colouristic harmony (otherwise you are free to try analysing Berg tonally). But to some extent mediants are already this (look at Kerner Lieder no. 6). No. 7 also has a mediant shift that then gets explained as a chain of dominants. Actually No. 8 has a good example where I$6 4$ could be considered its own chord for harmonic rhythm; but No. 9 suspensions are also a good argument otherwise. (Mozart's Lacrymosa is clearer)

the sound of mediants, like n and L is kind of enharmonic

Does the makeup of a chord define its root?
Now, it must be noted that despite my support for the Stufentheorie, we should not use it blindly. In particular, we cannot simply make up a list of chords and say that they will always have a certain function: LQELQV has already made it clear with the example of the half-diminished seventh chord, which may be labelled V (as viiø7) or as II (as iiø7) depending on context. Indeed, without the possibility of a chord with two meanings, we should never be able to have a simple pivot-chord modulation; nor could we have the diatonic analogue of one, in which a chord is approached with a certain function and quitted with another (I use LQELQV's example below):

[Schubert D 664]

But there are further difficulties as well, as there are some chords for which we are quite hard-pressed to decide what the root even is. Chief among these are the augmented sixth chords.

It's not just them for which the root argument is inconclusive: consider the occasional production of ♯iv°7 from raising the root of an already present IV♭7. It would be madness to analyse this as really a IV chord, wouldn't it? It has the raised fourth common to V of V. What we have here must be another expression of the near-interchangeability of mediant-related triads: II and IV are pleonastic, as LQELQV correctly states, but to some extent so are all 3rd-related pairs. This is how we can think of T, D, S, and M as functional directions even so.

TLDR

Basically the functions exist, but we cannot be pedantic and list down what chords belong to them. I'm not sure if Riemann is free from such pedanticism (honestly given his idea of major-minor dualism he probably isn't); it must be admitted that it doesn't help matters to call II always the subdominant parallel because as demonstrated above it can be otherwise.

it's also true that when harmonies are used without their usual character it creates a sapping of all harmonic energy, e.g. V of V (supertonic major triad) being robbed of its power in the Eroica and in Schubert's D 960. (Hence also what happens to V without its leading tone.) So the fact that the augmented sixth feels fine as a VI substitute in a sort of interrupted cadence illustrates adequately that this is not in contradiction to its usual use as V of V [e.g. Mozart KV 219/i]

we also can't just speak of the sound of a harmony – yes, mediants sound different from subdominants, but so does the Neapolitan, so does the supertonic

[mediant-like linkages between m.m. – e.g. N and II, III m.m. and III and so forth; thus you have a different sense of sharp 1 from flat 2]

[functional modal harmony]

great examples: Liszt Funérailles: (es-moll) V of II → N [substituting II] → V → I; Schumann Humoresk V of IV → IV (m.m.) with enharmonic #5 = b6; also it has near the end such wonderful cadences as ♭VII7→I obviously acting as a perfect cadence because of ♭6 as an upper leading tone. Is that a dominant? Well maybe it is both "V of III m.m." in a sequence and "V (mediant substitute)", but if there is no leading tone I want everything else to be accepted to the letter...

Beethoven variations on "Ein Mädchen oder Weibchen" (some chromaticism in the last 3/4 variation)

sidesteps through modal mixture? (e.g. E-flat major resolving to A minor = V of VI m.m. to VI) This also explains a lot of weirdo mediants like (F major - A-flat minor) in Bénédiction de Dieu dans la solitude

♮VI7 as an augmented sixth: Paysage (Liszt transcendentals)

tt as IV of N (Berlioz Faust hell scene); but directly as voice leading (D 625/iii, Trio). And as VII of V: end of Credo in D 678

n: D 678, Sanctus; end of Credo has F-sharp 7 going to G7

the way we get to a key may be unclear (brouillage is on LQELQV); D 940/iii has one in the Trio; so why not have them be unclear going in and out like Chopin Op 56/3? Then the precise nature of the relationship is not the important thing, just harmonic exoticism in chains of relationships (e.g. Don Gayseros, Chopin Op 18, when the precise relation to the tonic is not important because the structure is additive and only relationships to the preceding section are important)

mediants and half steps are just generalised major/minor shifts

using instrumentation to mess with the bass (Choral Fantasy end timpani roll)

Strange sonata forms
What on Earth is going on with the key structure of Schumann's Op. 44/iv? (the Piano Quintet; check out the Quartet too if you have time)

We may well accept E♭ as the tonic only because iii was in that key?


 * Exposition: g → Es → d → B → G
 * Development: h (becoming H) → E → gis →
 * Recapitulation: gis (becoming dis quickly through changing VI to N; kind of parallel to how the big gesture with string triple stops makes us think at first that the off-tonic opening is in c, which is iv of iii) → H → ais = b → Ges → Es
 * Coda (paralleling development at first): g [is this jump why we accept this in hindsight? plus the very long focus on the tonic] → Es [with a new theme that recurs again, paralleling this] → fugato (some related minor keys e.g. g, c, d) → Es (the theme in E and then more stuff and then the return of the first movement)

Similarly literal recapitulations (many of which even starting in IV like this one) may easily be found in Schubert, of course...

more chromatic alterations:

is D#-F#-A-C also a subdominant? In a certain sense these and other common tone dim7's are

which means that C#(Db)-E-G-Bb in the Eroica might be both S of D (exposition) and D of S (recap)

also of course common-tone dim7's are their own chords, Chopin even uses one as a pivot in his First Concerto (near the end of the development)

The remote relationships in the Emperor Concerto first movement, are pretty amazing

a really common trope to get to the tritone-related key is to raise everything a half step (e.g. C minor to D-flat major chord as V of tt); Beethoven does it in Op. 10 No. 1, Liszt does it in Wilde Jagd, Brahms in the Violin Concerto (2nd movement). Or similarly (proving VII as the root) – we can take the tonic and build VII7/V on it (e.g. D major to A-flat minor in Op. 26; and the beautiful one at the end of Rosenkavalier)

actually the #1 reason why I cannot believe the aug6 is not a VI chord is because it can be arrived at by interrupted cadence – putting an A6 on top of a VI m.m. chord sounds exactly like adding a 7th or a 9th to an already existing triad or seventh chord respectively. Quick example in Op. 14 No. 1 of Beethoven because I played through it today, I could multiply dozens.

I can't believe also that a major and a minor chord on the same root must be analysed differently: even secondary dominants stay part on the circle of fifths in the right place. Even diminished II and VII chords count for their places in the circle of fifths as does the augmented V chord. Hence my analysis of mediants as mediants. Sure, you can do V of II → IV or something like that, II and IV have a mediant relationship, so do IV and VI, so you can substitute them for each other etc etc. {Perhaps also this is how the tritone couple got legitimised – we were all familiar with it already from N–V}

where's that example of VI7 → V? (not augmented 6th)

still haven't found it but I found bIII7 (augmented 6th) - V in Schumann Op 44/iv. Gb-Bb-Db-E would normally resolve to F-Bb-D-F indeed, but this can be a real 6/4 chord (not just cadential), so here a 4/3 is substituted

Das Lied von der Erde – whole tone turns into French sixth on tritone resolving to I (ending)

unharmonisable notes: D♭ in Op.110/i (start of development)

VII usually occurs sequentially leading up to I as the next step (e.g. Waldstein, Auf dem Flusse)

uses of bVII: D 575/ii, D 678 (end of Gloria, Tu solus altissimus)

Analogy
All this stuff - modal mixture, secondary chords - are really a sort of analogy: if it works in that key, it ought to be importable into this one, as a key is just an expanded chord. Similarly, N-V then serves as an analogy for tt-I (it is like a sort of transposition that remains in the key, like all the Phrygian plagal harmony that happens at the end of Baroque pieces with long Picardy thirds that sounds like it is in IV, but has I as the tonic in the end). Functions are for sure another analogy: chords are united by common tones (if this chord with a leading tone works this way, so should this other one; if this chord with a flattened supertonic works this way, so should this other one; and so forth)

good example: D 850/iii (random F-sharp major chord in between D majors - obviously treating it as an analogy to VI-I64, but without tonicising F# major really)

for god's sake just analyse the Liebesnacht already!

Rosamunde 1. Act entr'acte: C-D-F#-A# resolve to B-D-F#-B (2nd subject, recap)

early septuple meter
Pensées des morts

fp and accent on same note in Schubert
D 804/iv

chem links
Electron affinity

https://pubs.rsc.org/en/Content/ArticleLanding/2011/CP/C0CP01785J#!divAbstract

Tolkien-related stuff
https://physics.stackexchange.com/questions/122785/could-legolas-actually-see-that-far

In the Round World Version, Venus existed prior to Eärendil's arrival. NoME, Part 3, Ch. I: Certain stars (no doubt those we call planets) and among them especially Venus, which they called Elmō (and later mythologically Eärendil), they early observed were “wayward” and altered their places with regard to the “far stars” (fixed stars). These they called companions of the Sun and thought them quite small heavenly bodies – derived from the Sun.

Amusingly, this suggests that Elves were Tychonians before reaching Valinor, since they called the planets "companions of the Sun". Well, if Elves can see Neptune by the naked eye, then they should be able to resolve the Galilean moons and, most importantly, the phases of Venus! In Valinor, they learned heliocentrism. (So their eyes are not so good that they can see stellar parallax without instruments, of course.)

No, I don't have a solid explanation of how Venus is supposed to work in the Round World version. But since the Sun could exist both with and without Eru's primeval light, perhaps it was just once again transferred from the recovered Silmaril to Venus, so that all of Earth could have it again. The Sun and Moon would be unsuitable since Melkor had already been doing too many extracurriculars there.

Regarding the eternal question of what mithril is: in fact, there actually do exist metals that would fit Gandalf's description. What you want is an element, less dense than steel, that is malleable by itself and yet acts as a hardener and anti-corrosive agent when alloyed with Fe. Aluminium and vanadium quite well fit this. The problem, rather, is that there is no such element that a medieval society could feasibly extract: both are famously difficult to reduce to the metal. So you more or less have two options: (1) call it magic, or (2) posit that there is some kind of weird geology going on in Moria alone (and in Númenor and Aman thanks to divine intervention) that creates an unusual native element deposit. As for what to use for fannish purposes, I personally prefer vanadium. I don't think we'll ever see aluminium with 19th-century eyes again. :)

(We're going to just stay away from the notes in "Elvish Reincarnation" where the Elves seem to know about atoms and radioactivity being transmutation. Although it's definitely an entertaining idea. I prefer to take the "Fate and Free Will" version where only hydrogen and oxygen are referred to, as that's actually plausible: it then amounts to Elvish chemistry guessing that combustion works the correct way around. Then they'd be a hypothetical medieval society with the right theory and making the right guesses when it comes to chemistry, so in terms of chemical knowledge they have pretty much reached 1800 while still being far from an actual industrial revolution.)

Galvorn is more plausibly just steel coated with some kind of black oxide. Tantalum is a fun option for fannish purposes, but realistically impossible. At the tech level even the 19th-century chemists had, it would be impossible to get it pure enough to determine its malleability.