Strongly Symmetric Spectral Convex Sets are Jordan Algebra State Spaces

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The title of this post is also the title of my most recent paper on the arXiv, from 2019, with Joachim Hilgert of the University of Paderborn. The published version is titled Spectral Properties of Convex Bodies, Journal of Lie Theory 30 (2020) 315-355.

Here's a preprint version of the J Lie Theory article:

BarnumHilgertSpectralPropertiesOfConvexBodiesPreprintVersion2Download

Compared to the arXiv version, the J Lie Theory version (and the above-linked preprint) has less detail about the background results by other authors (mainly Jiri Dadok's theory of polar representations of compact Lie groups, and the Madden-Robertson theory of regular convex bodies) which we use, and a bit more detail in the proof of our main result. It also has a more extensive discussion of infinite-dimensional Jordan algebraic systems, in the context of discussion of ways in which the Jordan algebraic systems can be narrowed down to the complex quantum ones. I like the title of the arXiv version better, since it states the main result of the paper, but Joachim was scheduled to give a talk at the celebration of Jimmie Lawson's 75th birthday in 2018, while we were writing up the main result, so he gave a talk on our work titled Spectral Properties…, and we decided to publish the paper in the proceedings, which are a special issue of J Lie Theory, so it ended up with the same title as the talk.

Here are slides from a talk on the result I gave to an audience of mathematicians and mathematical physicists:

MadridOperatorAlgebras2019

MadridOperatorAlgebras2019Download

Although the paper's main theorem is a result in pure mathematics, and, I think, interesting even purely from that point of view, it is also a result in the generalized probabilistic theories (GPT) framework for formulating physical theories from a very general point of view, which describes physical systems in terms of the probabilities of the various results of all possible ways of observing (we often say "measuring") those systems. The state in which a system has been prepared (whether by an experimenter or by some natural process) is taken to be defined by specifying these probabilities of measurement-results, and it is then very natural to take the set of all possible states in which a system can be prepared to be a compact convex set. Such sets are usually taken to live in some real affine space, for instance the three-dimensional one of familiar Euclidean geometry, which may be taken to host the qubit, whose state space is a solid ball, sometimes called the Bloch ball. In this framework, measurement outcomes are associated with affine functionals on the set taking real values---in fact, values between 0 and 1 --- probabilities, and measurements are associated with lists of such functionals, which add up to the unit functional---the constant functional taking the value 1 on all states of the system. (This ensures that whatever state of the system is prepared, the probabilities of outcomes of a measurement add up to 1.) This allows an extremely wide variety of convex sets as state spaces, most of which are neither the state spaces of quantum systems nor classical systems. An important part of the research program of those of us who spend some of our time working in the GPT framework is to characterize the state spaces of quantum systems by giving mathematically natural axioms, or axioms concerning the physical properties exhibited by, or the information-processing protocols we can implement using, such systems, such that all systems having these properties are quantum systems. To take just a few examples of the type of properties we might ask about: can we clone states of such systems? Do we have what Schroedinger called "steering" using entangled states of a pair of such systems? Can we define a notion of entropy in a way similar to the way we define the von Neumann entropy of a quantum system, and if so, are there thermodynamic protocols or processes similar to those possible with quantum systems, in which the entropy plays a similar role? Are there analogues of the spectral theorem for quantum states (density matrices), of the projection postulate of quantum theory, of the plethora of invertible transformations of the state space that are described, in the quantum case, by unitary operators? We often limit ourselves (as Joachim and I did in our paper) to finite-dimensional GPT systems to make the mathematics easier while still allowing most of the relevant conceptual points to become clear.

This paper with Joachim builds on work by me, Markus Mueller and Cozmin Ududec, who showed that three principles characterize irreducible finite-dimensional Jordan-algebraic systems (plus finite-dimensional classical state spaces). Since these systems were shown (by Jordan, von Neumann, and Wigner in the 1930s, shortly after Jordan defined the algebras named after him) to be just the finite-dimensional quantum systems over the real, complex, and quaternionic numbers, plus systems whose state space is a ball (of any finite dimension), plus three-dimensional quantum theory over the octonions (associated with the so-called exceptional Jordan algebra), this already gets us very close to a characterization of the usual complex quantum state space (of density matrices) and the associated measurement theory described by positive operators. The principles are (1) A generalized spectral decomposition: every state is a convex combination of perfectly distinguishable pure states, (2) Strong Symmetry: every set of perfectly distinguishable pure states may be taken to any other such set (of the same size) by a symmetry of the state space, and (3) that there is no irreducible three (or more) path interference. Joachim and I characterized the same class of systems using only (1) and (2). In order for you to understand these properties, I need to explain some terms used in them: pure states are defined as states that cannot be viewed as convex combinations of any other states---that is, there is no "noise" involved in their preparation---they are sometimes called "states of maximal information". The states in a given list of states are "perfectly distinguishable" from each other if, when we are guaranteed that the state of a system is one of those in the list, there is a single measurement that can tell us which state it is. The measurement that does the distinguishing may, of course, depend on which list it is. Indeed one can take it as a definition of classical system, at least in this finite-dimensional context, that there is a single measurement that is capable of distinguishing the states in any list of distinct pure states of the system.

If one wants to narrow things down further from the Jordan-algebraic systems to the complex quantum systems, there are known principles that will do it: for instance, energy observability (from the Barnum, Mueller, Ududec paper linked above, although it should be noted that it's closely related to concepts of Alfsen and Shultz ("dynamical correspondence") and of Connes ("orientation")): that the generators of continuous symmetries of the state space are also observables, and are conserved by the dynamics that they generate, a requirement very reminiscent of Noether's theorem on conserved generators of symmetries. Mathematically speaking, we formulate this as a requirement that the Lie algebra of the symmetry group of the state space embeds, injectively and linearly, into the space of observables (which we take to be the ambient real vector space spanned by the measurement outcomes) of the system, in such a way that the embedded image of a Lie algebra generator is conserved by the dynamics it generates. In the quantum case, this is just the fact that the Lie algebra su(n) of an n-dimensional quantum system's symmetry group is the real vector space of anti-Hermitian matrices, which embeds linearly (over the reals) and injectively into the Hermitian matrices (indeed, bijectively onto the traceless Hermitian matrices), which are of course the observables of a finite-dimensional quantum system. This embedding is so familiar to physicists that they usually just consider the generators of the symmetry group to be Hermitian matrices ("Hamiltonians"), and map them back to the antiHermitian generators by considering multiplication by i (that's the square root of -1) as part of the "generation" of unitary evolution. This is discussed in the arXiv version, but the Journal of Lie Theory version discusses it more extensively, and along the way indicates some results on infinite-dimensional Jordan algebraic systems since Alfsen and Shultz, and Connes, worked in frameworks allowing some infinite-dimensional systems. See also John Baez' excellent recent paper, Getting to the Bottom of Noether's Theorem. One can also narrow things down to complex quantum systems by requiring that systems compose in a "tomographically local" way, which means that there is a notion of composite system, made up of two distinct systems, such that all states of the composite system, even the entangled ones (a notion which makes sense in this general probabilistic context, not only in quantum theory), are determined by the probabilities they give to pairs of local meausurement outcomes (i.e. the way in which they correlate (or fail to correlate) these outcomes).

Joe Jackson

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Joe Jackson was initially associated with the ``New Wave" of pop/rock music of the late 1970s and early 1980s (Blondie, the B52s, Elvis Costello, Siouxsie and the Banshees, etc…) that followed quickly on, and was often influenced by, the 1970s onslaught of punk, but he's quite eclectic in style, even drawing from experience in jazz and classical music from the outset of his career. I'd neglected him somewhat in my listening until recently, although like most people alive (at least in the USA) in the early 1980s I was familiar with the hit ``Is She Really Going Out With Him?" even if not its author and performer. I quite enjoyed a vinyl copy of his album Body and Soul, which features a largeish band and often-jazzy or musical-theater influenced arrangements, especially first track `The Verdict', which opens with a slick brass-and-reeds fanfare. On more recent listening (streaming in HD), I still liked it, although I don't recall much detail past The Verdict. I haven't listened to his entire output, but will here log the current state of my investigations.

My favorite album of his so far is Volume 4, credited to the Joe Jackson Band. I'd say it's a minor masterpiece. I tend to lean towards catchy melody and relatively emotionally involved lyrics; keeping that in mind, my favorite songs on the album are `Still Alive ' `Chrome', and `My Blue Flame'. Still Alive opens with a chiming guitar figure (5 1 4 1 3 1 4 1 2 1 4 1 4 3 2 1 in major --- or if you prefer solfege, Pa Sa Ma Sa Ga Sa Ma Sa Ga Sa Ma Sa Ma Ga Re Sa) that perfectly conjures up a certain 60s pop-rock guitar feel, and the vocal reprises this figure but then goes in a rather different musical direction... then, typically for Jackson, a denouement, or at least change of tone, in the lyrics is accompanied by a catchy-as-hell change of harmony and descending melody, with `I know I said I couldn't live without you but I'm still alive". As often with Joe, there may be points where the lyrics get a tad too cute, but still this song---like the other two I singled out---is candy. `Chrome' seems to concern a crush who has become a star... after a somewhat pensive verse, a sudden and faster (the backing tempo stays constant) "Guess I was wrong" (and come to notice it, on the same dramatic descending notes (4321, in major) as "I'm still alive" (4 4 3 2-1) from Still Alive) introduces the chorus: "Now you shine like chrome / You're a star and bold like chrome / And from Tokyo to Rome / We're all aware of you", which is repeated with the last couplet changed to "And I'd like to take you home / But I'm scared of you." I perceived all three of these songs (and many of the others on the album, especially Love at First Light, and Little Bit Stupid ("You know what they say about Cupid") and perhaps even "Awkward Age") as addressed to the same person. My Blue Flame similarly involves an ex-lover, or maybe just crush, who is cold but again there is a change in mood to a somewhat anthemic chorus: "There's a blue flame inside of you so beautiful and rare ... You'd be so hard to love if love was not just there." Pretty sentimental but it works. If you're cold to these three songs, you probably don't like Puccini either, and that's fine, I guess. To make another classical vocal analogy, I'll liken some of Jackson's writing to the songs of Richard Strauss, which often used some pretty purple poetry, often not quite of the first rank, and could be extremely sentimental. "Morgen", "Allerseelen", or in fact almost all the songs I'm familiar with are quite sentimental , but also extremely effective and dramatic as songs, with striking and sometimes somewhat lush harmonic effects. There is apparently a body of more humorous songs by Strauss that are not much sung---if one is to trust the great accompanist, pianist Gerald Moore, it's because they're not very good. Here too there might be a bit of an analogy with Jackson...his humorous songs seem to me a bit weaker than his romantic ones---although I would not deprecate them as Moore does Strauss' humorous songs, and indeed one should note that there's quite a bit of ironic humor leavening the sentimentality in most of Jackson's romantic songs.

Not that the other songs on Volume 4 aren't mostly excellent too. The opening `Take it Like a Man" works quite well musically, hard-hitting bright medium-uptempo piano-driven new wave, but I find the lyrics a bit inscrutable and the line "take it like a man" a bit offputting (and the "ah-ooo" a little too cute...like it was pinched from Warren Zevon's `Werewolves of London') though maybe I'm just not getting the point. `Awkward Age' is bouncy and uptempo, and relatively sunny-sounding, the most reminiscent of relatively mainstream 1980s New Wave sound perhaps, Love at First Light seems to be about the possibility of something more significant growing out of a one-night stand...a nice song but melodically perhaps less distinctive than Alive, Chrome, or Flame, with a mellower and sunnier, more lullaby-like feel, at a medium tempo... also excellent. `Fairy Dust' is an uptempo rocker that seems to be a bit of a dig at people trying to be hip by engaging superficially with gayness (Jackson identifies as bi, I believe). Dirty Martini is a rocker, somewhat slight perhaps but maybe fitting into the overall picture by depicting a reaction to romantic disappointment ("too many olives and too much gin"). Thugz'r'Us is a catchy, perhaps somewhat cheap shot at (probably) white wannabe B-boyz ("Thuz 'r Us, Thugz 'r Us, wearing hoods and baggy trousers on the bus"), and doesn't much fit into an overall theme for the album although I guess it's something of a pair with Fairy Dust in a way. 'Bright Grey' is an uptempo, slighty thrash-y song about he/she dissonance, with some dissonant chords thrown in for subtlety, and an uptempo backbeat (snare hits on 2 and 4) you'll recognize from countless alt-pop-rock songs of the 00's and later. It's also quite good.

My other current favorite album by Jackson is his 1979 debut, Look Sharp. `One More Time' is sharp and punchy if lyrically bitter new wave, `Sunday Papers' is a bit nasty and trite in spots, but extremely catchy, its reggae or ska reminiscent, slightly herky-jerky backbeat. `Is She Really Going Out With Him' deserved its hit status. The hook in the chorus of `Happy Loving Couples' ("Happy loving couples make it look so easy") seems to me nearly identical with the melody to the words "They say you better listen to the voice of reason" (and "They don't give you any choice 'cause they say that it's treason") from Elvis Costello's `Radio Radio', which hit in 1978 in Britain and was written and already performed in 1977, and parts of the verse sound like they're from a Costello song too, but it's a pretty good song with its own identity nevertheless. As the reminders of early Costello might suggest, this record has the most consistent new wave rock feel of Jackson's work among the albums I've checked out. The song quality is consistently very high, and it's strongly recommended.

The follow-up I'm The Man, also from 1979, just didn't move me on first listen; the melodies just didn't seem as distinctive as on Look Sharp or Volume 4. I may give it another try but for now it's not on my recommended list. I had a similar reaction to Night and Day but again am not sure I've given it a fair chance. Both of these albums are highly lauded by some. Beat Crazy didn't move me overall either, since I found it too melodically weak overall, despite being the most ska and reggae influenced of his albums, although a few of the songs are catchy...`Battleground ' with its Linton Kwesi Johnson influenced dub poetry style, for instance, though you might find the lyrics (another song about black-culture-appropriating wannabes) a bit trite, and also not dig the use of the N-word.

As far as more recent Jackson goes, I found 2019's Fool pretty good on a first listen, though not of the high caliber of Look Sharp and Volume 4. Dips into each of the 2015 Fast Forward and the live 1986 Big World also seem promising.

Margaret Bonds: pianist composer, and teacher

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Margaret Bonds (1913-1972) was a pianist, composer, and teacher of music. I probably first became aware of her as a teenager, through some of her arrangements of spirituals for "classical" voice, especially as sung by Leontyne Price (e.g. He's Got The Whole World In His Hand, which Price commissioned from Bonds in the early 1960s) but have only recently delved more deeply into her work, and realized that many of her compositions --- the classical songs and some piano pieces are what I've really gotten into so far--- should be considered classics of 20th century American music. I expect they will become---indeed, hopefully, many of them already are---a permanent part of the classical music repertoire.

Most recently, I was reminded of Bonds by an excellent essay by pianist and composer Ethan Iverson, whose blog Do the M@th is essential reading for those interested in jazz and/or classical music. "Black music teachers in the age of segregation" emphasizes their contribution to the musical development of jazz musicians, both by teaching European techniques and theory, and leading ensembles often covering a wide range of music styles, sometimes integrating African-derived and African-American-developed elements and procedures. Iverson doesn't mention Bonds in his essay, but she is yet another example of a black musician whose role as teacher was important in American music---although her compositions and (sadly, probably under-documented) live performances are equally important contributions.

Bonds as teacher, as well as performer and composer, figures prominently in the diaries and essays of Ned Rorem---she was one of his childhood piano teachers in Chicago, and helped him with his first forays into notated composition. Rorem's discussion of his time with her, as well as with other childhood teachers, in the essay "The Piano in My Life" from Setting the Tone: Essays and a Diary is engrossing.

It was time for a real teacher... Margaret Bonds .... at twenty-two was a middle-western "personality", having played Carpenter's Concertino with the Chicago Symphony under the composer's direction, and being herself a composer of mainly spiritual arrangements and of original songs in collaboration with Langston Hughes. ... At our first lesson, she played me some ear-openers, The White Peacock by Griffes, and Carpenter's American Tango. Had I ever heard American music before? ...

Margaret Bonds played with the authority of a professional, an authority I'd never heard in a living room, an authority stemming from the fact that she herself was a composer and thus approached all music from the inside out, an authority that was contagious. [...]

The first piece I wrote down, "The Glass Cloud," was influenced by Margaret's other prize pupil, Gerald Cook. [...] In the years to come his identity with Margaret would shift from student to colleague as the two-piano team, Bonds and Cook, became a glamorous enterprise at Cerutti's in New York, and at Spivy's Roof. When Margaret went her separate way to marriage, motherhood, documentation of Negro song, opera writing, and death, Gerald turned into the greatest living accompanist of the Blues, working first with the lamented Libby Holman, then--and still--with Alberta Hunter.

Did I outgrow Margaret Bonds? Why were lessons discontinued? If there was an objection to a seeming glib jazziness chez elle, Margaret thought of herself as classical and deep. (Conversely, I feel as influenced by prewar jazz as by "serious" music. Not the tune itself but Billie Holiday's way with a tune taught me to knead a vocal phrase, just as Count Basie's piano playing still shapes my piano composing.) In any case Margaret and I lost track of each other until we had all moved East during the war. Then we remained close friends until she died.

The whole essay is a great read, simultaneously sketching with vivid strokes aspects of an era in American music and American life, and of Rorem's musical development.

There is much more about Bonds at the pages for the 2016-2017 exhibitions "Margaret Bonds: Composer and Activist" and "Margaret Bonds and Langston Hughes: A Musical Friendship" at the Georgetown University Library (where some of her papers are held) including music manuscripts, photographs, concert programs, and correspondence from, among others, Rorem, Hughes, and Andy Razaf (whose stationery sports a sidebar listing songs he composed and/or wrote the lyrics to). Directly relevant to the matter of Black teachers and the institutions they worked in as a crucial resource in the development of American music is this from the exhibition text:

Throughout the 1950s, Bonds continued her work as a composer, performer and teacher. In addition to private lessons, she joined the staff of East Side House Settlement, a non-profit social services organization committed to serving New York’s underprivileged youth. At East Side House she taught weekly music classes, hosted performances featuring African-American composers, and served as music director for the annual spring musical.

There may be a lot to rediscover about her influence, as a teacher, on jazz and classical musicians, especially African-American ones, during this period in New York. East Side House Settlement is still active.

As far as her work as composer is concerned, from what is available on disc or digital streaming I'm particularly partial to her pieces for solo piano, and her songs. What is available in these genres is extremely good, and should find a permanent place in the repertoire of pianists and singers. Although the list of works in her Wikipedia entry is not lengthy, there is much that looks promising that does not appear to available in recordings or online performances; one hopes that will change.

 The Bells, based on the spiritual Peter Go Ring Dem Bells, from her Spiritual Suite for Piano, beautifully melds influences from European and American classical music (especially Debussy, Ravel, and perhaps Americans like Charles Tomlinson Griffes (who crops up in the Rorem quote above)) with African-American spirituals and pianistic touches reminiscent of jazz or perhaps the popular music of the time. Here it is played by Thomas Otten as part of a 2013 symposium on Bonds' work:

The other two movements, Dry Bones and Troubled Water, are also on youtube played by Otten at this symposium; below, Troubled Water, based on the spiritual Wade in the Water, is played by Samantha Ege:

The Youtube listing for Ege's performance gives the date of Troubled Water as 1967, but Randye Jones' online biography (which also displays the abovementioned concert program) also lists it as part of the Spirituals Suite, which it dates to the 1940s or early 1950s.

Bonds' setting, published in 1959, of Three Dream Portraits by Langston Hughes is superbly done. The only version for low male voice with piano that I've found on Youtube in acceptable sound is an excellent one by baritone Thomas Hampson with Kuang-Hao Wang on piano:

(Dorian Hall deserves mention for a superb performance with Dr. Timothy Cheek on piano, but there is unfortunately a lot of distortion in the recording---this would appear to be a casually recorded, though musically top-notch, recital.) There are several female voice versions on Youtube in good sound, for example one sung by Bonnie Pomfret with Laura Gordy on piano; another by Icy Simpson with Artina McCain on piano and one by an unidentified singer and the Ritz Chamber Players. The live recital recording of no. 1 in the series, Minstrel Man, by Nicole Taylor with Joan Sasaki on piano, is also worth mentioning, though the recorded sound quality is not perfect. Yolanda Rhodes and Josefina Gandolfi also do an excellent job with this song.

The settings of Hughes' Songs of the Seasons are also excellent. Below, an excellent live performance (the vocalist is Louise Toppin) of Summer Storm from a valuable 2013 symposium on Bonds, available as a sequence of youtube videos, that includes lectures as well as performances of works by Bonds and by her teacher, Florence Price (e.g. Price's Night, beautifully sung by the extraordinary countertenor Darryl Taylor).

In this symposium Toppin also performs several excellent songs that are not listed in the Wikipedia entry on Bonds. Stopping by Woods and The Pasture, from 1958, are on texts by Robert Frost; Feast, on a text of Edna St. Vincent Millay. Winter Moon, another of the four Songs of the Seasons, is available in a studio recording by Toppin with John B. O'Brien on piano. Bonds' songs also work beautifully sung by baritone Malcolm Merriweather with Ashley Jackson on harp rather than piano: Winter Moon from Seasons, To A Brown Girl, Dead (1933) on a text by Countee Cullen, and the Three Dream Portraits appear on a CD along with Bonds' Christmas cantata, Ballad of the Brown King, to words of Langston Hughes. Little David is an example of Bonds' setting a traditional African-American spiritual melody and text:

Here, as in many of Bonds' arrangements of spirituals, the piano part doesn't provide a conventional chordal background, nor does it double the voice---it is new musical material that is entirely Bonds', and contrasts with the vocal line while being absolutely appropriate to it.

Last but not least, perhaps Bonds' best known song is her setting of Langston Hughes' The Negro Speaks of Rivers, composed around 1936 and first published in 1944. Bonds spoke of the great personal significance of this poem to her, in an interview with James Hatch quoted in Jones' online biography:

I was in this prejudiced university [Northwestern, where she matriculated in 1929 and where, according to Jones, "she was allowed to study but not to live or use their facilities"], this terribly prejudiced place–I was looking in the basement of the Evanston Public Library where they had the poetry. I came in contact with this wonderful poem, “The Negro Speaks of Rivers,” and I’m sure it helped my feelings of security. Because in that poem he [Langston Hughes] tells how great the black man is: And if I had any misgivings, which I would have to have–here you are in a setup where the restaurants won’t serve you and you’re going to college, you’re sacrificing, trying to get through school–and I know that poem helped save me.

A favorite performance of mine is Gerald Blanchard's, from his CD on Blue Griffin:

Thomas Hampson gives a mellower, less urgent reading, but beautifully phrased and recorded, and making the text exceptionally intelligible:

One can also find on youtube a mixed-chorus SATB arrangement of this setting---it is not clear to me whether the arrangement is by Bonds herself or not, though I suspect it is---which would be well worth tracking down by interested choirs.

There's much more to be said, and investigated, about Bonds and her work; some of the links above, especially the Kilgore dissertation and the brief online Randye Jones biography, are good starting points, as is the Song of America page on Bonds. I have a copy of Mildred Denby Green's Black Women Composers: A Genesis, which has more on Bonds, her teacher Florence Price and others, on the way, as well as an Anthology of Art Songs by Black American Composers, edited by Willis Patterson (published by Hal Leonard Corp.) that includes the score of Three Dream Portraits. I'm looking forward to seeing what I discover in this anthology, although I'll probably be studying the musical content of, rather than singing, the Dream Portraits, while searching for scores for the Songs of the Seasons and the Frost and Millay settings, which are not included in that anthology. But I'll stop here for now, and leave you to enjoy her music.

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What's wrong---and what's right---about quantum parallelism as an explanation for quantum speedup

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I couldn't help crying "Nooo!!!!" on Twitter to the following statement by Pierre Pariente, "Strategic Analyst chez L’Atelier BNP Paribas," from a 2015 article "Quantum Computing Set to Revolutionize the Health Sector"

L’Atelier's more mathematically-inclined readers will recognise the general rule that with n qbits, a quantum computer may be in a quantum superposition of 2^n states and will thus possess the capacity to solve that number of problems simultaneously.

In the interest of not just being negative, I should explain what's wrong with this statement---and why it does capture something relevant to many examples of what most quantum computation theorists believe to be theoretical speed advantages of quantum algorithms over classical algorithms.  I'll give the short version first, and maybe in another post I'll explain a bit (groan) more.

What's wrong with quantum parallelism?

If you want, you can run a quantum version of a classical algorithm for solving some problem---say, computing a function on an n-bit long input string---on a superposition of all 2^n states representing different input strings.  This is often called "quantum parallelism".  If we consider computing the value of some function, F, on each input x to be "solving a different problem", then in some very weak sense we might think of this as "solving 2^n different problems simultaneously".  However, the drug designers, or radiotherapists, or whoever one is going to be selling one's quantum computers and software to, are presumably going to want to know the answers to the problems.  But you cannot read out of a quantum computer that has run such a "quantum parallel" computation  the answer to all of these problems (the value of the function on all inputs).  In fact, you can read out the answer to only one of the problems (the value, F(x), of F on a particular input x).  If you have run in superposition and you measure the register in which the algorithm writes the value F(x), you'll get the answer on a randomly drawn input (the famous randomness of quantum theory), and if you measure a part of the computer where the input string was stored, you'll also get the value of said randomly drawn input. There is absolutely no advantage here over just running the classical algorithm on a randomly chosen input.

What's right with quantum parallelism

So how can this quantum parallelism nevertheless be useful?  The reason for this is essentially the existence of many mutually incompatible observables in quantum theory (position and momentum being the most famous example of a pair of incompatible observables, though they are not the ones usually used in proposals for quantum computation).  In particular, quantum theory allows such a superposition state to be effectively (and often efficiently) measured in ways other than reading out the value of F and the input that gave rise to it---ways incompatible with that readout.  This can tell us certain things about the function F other than its values on specific inputs, and these things may even depend on its values on exponentially many inputs.  The incompatibility of these measurements with the one that reads out the input and the function value, implies that once the global information is obtained, the information about inputs and function values is no longer available---an example of the well-known fact that  "measurement disturbs the state" of a quantum system.

Why do we care?

Many problems of practical interest take this form:  we have a program (say, a classical circuit---from which we can always construct a quantum circuit) for computing a function F, but we want to know something about the function that we don't know how to just read off from the information we used to construct the circuit. For example, if F takes values in an ordered set (like the real numbers, to some precision) we might want to know its maximum value, and probably also an input on which it takes this maximum. (This application, "optimization", is mentioned in the article.)  Or, we might know because of the way the circuit for computing the function is constructed that it is periodic (we will need for the set of inputs to have some structure some that allows us to define periodicity, of course---maybe they are interpreted as binary notation for integers, for example), but we might not know---and might want to know---the period.  To oversimplify a bit, solving this problem is the key ingredient in Shor's algorithm for factoring large integers using quantum computation---the one that breaks currently used public-key cryptography protocols.  If we could compute and read out the values of the function on all inputs, of course we could figure out about anything we want about it---but since there are 2^n inputs, doing things this way is going to take exponential (in n) resources---e.g., 2^n calculations of the function.  To repeat, it is the fact that quantum computing allows such a superposition state to be effectively measured in ways other than reading out the value of F, that  nevertheless gives us potential access, after just one function evaluation, to a certain amount of information about "global" aspects of the function, like its period, that depend on many values.   We are still very limited as to how much information we can get about the function in one run of a "quantum parallel" function evaluation---certainly, it is only polynomially much, not the exponentially much one could get by reading out its value on all inputs.  But in some cases, we can get significant information about some global aspect of the function that we care about, with a number of quantum-parallel function evaluations that, if they were mere classical function evaluations, would leave us with the ability to get far less information, or even no information, about that global aspect of the function.  How significant this speedup is may depend on what global information we want to know about the function, and what we know about it  ahead of time.  If we know it is periodic, then in good cases, we can use polynomially many evaluations to get the period in situations where it's thought we'd need exponentially many classical evaluations.  This is the basis of the "near-exponential"  speedup of factoring by Shor's algorithm (it is not quite exponential, presumably because the best classical algorithm is not just to try to brute-force find the period that is found in the quantum algorithm, but is more sophisticated).   For relatively unstructured optimization problems, quantum algorithms usually make use of Grover's algorithm, which, again, does use quantum parallelism, and can find the optimum to high precision with roughly the *square root* of the number of function evaluations needed classically.  If the classical algorithm needs (some constant times) 2^n evaluations, in other words, the quantum one will need roughly (some constant times) 2^{n/2}---still exponential, though with half the exponent; an advantage which could still be useful if the large constant cost factor that comes from doing quantum operations instead of classical ones does not swamp it.

Quantum algorithms beyond quantum-parallelism

There are of course other scenarios in which quantum computing may be useful, that are not well described as "finding out unknown properties of a function by running a circuit for it"---especially those where the problem itself comes from quantum physics, or happens to have a mathematical structure similar to that of quantum physics.   Typically these have the property that one is still "finding out unknown properties of a quantum circuit by running it", but the circuit is not necessarily a quantum version of a classical function evaluation, but rather represents some mathematical structure, or physical evolution, that is well-described by a quantum circuit.  The most obvious example is of course the evolution of some quantum physical system!  Some of these kinds of problems---like quantum chemistry applications---are among those potentially relevant to the health applications that are the topic of the BNP article.

The greatness of Cecil Taylor (1929-2018)

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Cecil Taylor, one of the most important musicians of our time, and one of the pioneers of what is roughly called "free" or avant-garde jazz, died on April 5, 2018, at 89 years old.  Ben Ratliff has written an obituary at the New York Times, and Ethan Iverson has written an appreciation at his blog Do The Math.

I'm not going to write extensively about his music or life here; I'm just going to give links to a few of my favorite Taylor works, mostly ones that I am intimately familiar with.  (Well, I ended up writing a fair bit about some of them.)  They're chosen primarily for their intrinsic greatness, but with the main purpose of getting people who may not be familiar with Taylor in touch with his music, so the choice may be biased a little bit towards more "accessible" pieces.  I've been toying with the idea of a post, perhaps titled "Canon and Playlist," which would include a personal canon of the music commonly referred to as "jazz".  One idea would be to include just "masterpieces of the highest order" --- you know, stuff on the level of the late Beethoven piano sonatas, Janacek's "On an Overgrown Path", etc.  (So in jazz, e.g. "Parker's Mood" (Charles Parker), the album "Saxophone Colossus" (Sonny Rollins), Lester Young's greatest performances with the Count Basie Orchestra and with smaller groups in the 1930s---that sort of thing.)  The first two or three pieces I'll link here were would be my top Cecil choices for such a list (where they definitely belong). Anyone seriously interested in music owes it to themselves to listen to these pieces, several times if you don't connect the first time. You will probably find yourself richly rewarded. "Straight masterpieces", as someone said in a different context. If it weren't for the fact that Taylor grew up in Queens and settled in Brooklyn, I'd be tempted to refer to it as real Uptown Funk as well.

1. "Bulbs" from "Into the Hot", one side of a 1962 LP issued under the name of Gil Evans, but with the "Into the Hot" side composed and performed by Taylor and his group (the other, much less consequential, side, "Out of the Cool", was by Johnny Carisi). Evans was a great arranger, known especially for his work with Miles Davis, but I think he's generally considered to have acted merely as producer for this session. By turns, and often simultaneously, funky, sardonic, spooky, transcendently beautiful. Make sure and listen all the way to the end...where some amazingly beautiful things happen involving lines made of hierarchies of ascending arpeggios, calling to or layered over each other, decelerating into some calm after the high-energy drive of the central portion of the piece, then crystallizing into a hard-to-describe, somewhat raunchy, sardonic, and joyously dancing bit of riffishness, expanding again into transcendence as the arpeggiated lines layer over the cyclic riffing, then come apart centrifugally into jagged notes and long tones relaxing toward silence as they ascend, fading, into the empyrean.  Or whatever. Just don't miss it.

Cecil Taylor, piano; Jimmy Lyons, alto sax; Archie Shepp, tenor sax; Henry Grimes, bass; Sunny Murray, drums.

Like many people, probably, I was turned on to "Bulbs" long ago by a piece collected in Amiri Baraka (then writing as Leroi Jones)'s book "Black Music" (at Barnes and Noble; at Amazon) which reviewed the whole Taylor side of "Into the Hot/Out of the Cool" and singled out "Bulbs" especially. I picked it up as a teenager as part of a three-LP Impulse sampler, "Energy Essentials", being sold as a cutout, which also featured things like a 10-15 minute sampler from the alternate take of Coltrane's "Ascension", and various pieces by Albert Ayler, Archie Shepp, and such. I also highly recommend the other "Into the Hot" pieces. Some motives or melodic moves from "Bulbs" also appear in the other pieces. Because it is more of a contrast with "Bulbs", I recommend starting with "Mixed", where the embedded video below will take you on first click, and then replaying the video from the beginning if you want to hear "Pots" as well. "Mixed" adds Ted Curson on trumpet and Roswell Rudd on trombone, and starts in a low-key, slow, out-of-tempo vein, with muted trumpet as well as Rudd's tromobone in the mix, spacious textures and much attention to varieties of timbre, slightly reminiscent of certain veins of 20th century classical music, then morphs into a very pretty ballad episode (I hear a slight suggestion of "All the Things You Are" in places, but would be interested to know if there are any more clearly recognizable standards being alluded to here), then is taken over by a repeating, somewhat sardonic riff, which alternates with a three-note ascending chromatic line (this is one reference to the "Bulbs" material, where the line is one note longer, a chromatic 1-2-3-2), develops more complexity and segues into a superbly improvised piano-and sax duet. Great stuff from Archie Shepp on tenor. And on and on... I would class "Mixed" as a masterpiece also.

2. The second unmissable masterpiece (well, let's count "Mixed" and call it the third) I'm going to recommend is "Indent", a solo piano performance recorded in concert at Antioch College in Ohio in 1973. It starts out with incredibly funky pentatonic motives, layered, developed, combined with a more chordal "second theme" (perhaps, and with variants), and these and other materials that are introduced are built up into an increasingly complex structure which ends up spinning into intense and dissonant flurries of note-clusters. This kind of cycle is repeated a few times in the piece, with different thematic material, and also with recurrences of earlier material. A masterful composed-and-improvised sonata. If the dissonant flurries put you off at first (which won't necessarily be the case!), just hope that they will make more sense on repeated listenings, and know that there are calmer and more consonant passages, often of great harmonic and melodic beauty, on the way.

For more solo piano of this sort, Silent Tongues (Live at Montreux) was in heavy rotation (on the sorts of stations that played this stuff at all, i.e. WEMU (Eastern Michigan University) and WUOM (University of Michigan)) when I was first getting into Taylor's music.  I recommend repeated listening to one of his solo records until it is fully appreciated, though, rather than skipping around; Indent was the one that got me into it and is still my favorite.  Once you dig it, there are many more to explore...

Now, for further listening, I'll embed a few more things that I'm familiar with and love.

3. To represent early (i.e. late 1950s) Cecil, here's a 1959 take on Cole Porter's Love for Sale with Buell Neidlinger on bass and Denis Charles on drums. I wonder if anyone bought this for the hilarious (in context) noirsploitation cover expecting some smoky late-night make-out music to play when bringing a date back to their pad...I hope so. The introduction is remarkably prescient of the kind of playing Taylor was to do in later work such as Indent that makes no reference to standards, but the fusion of this with subtly-transformed but recognizable standards-and-bebop style and material is a beautiful thing. (It is further advanced in that direction than on some of his records from a few years earlier.)

4. In the abovementioned appreciation, Ethan Iverson is of course right to cite the 1960 This Nearly Was Mine, also with the Neidlinger/Charles rhythm team, as a supreme Cecil achievement in the realm of reimagined standards.  Definitely another unmissable masterpiece.  Mosaic Records reissued most of the Candid sessions with Neidlinger, Charles, and Taylor (and often Archie Shepp on tenor and Lyons on alto), including this performance, and this set is a highly recommended collection, once you have Into the Hot and Indent, for getting further into still relatively accessible Taylor.  Unfortunately, although I bought the CD version when it came out, it is now out of print and used copies seem to be very expensive, so getting the individual Candid albums seems to be the way to go now.  The World of Cecil Taylor, Air, Cell Walk For Celeste, Jumpin' Punkins, New York City R&B.  (There also appear to be some multi-album sets but I am afraid these might be fly-by-night European ripoff editions.)

5. For more great ensemble Taylor, still relatively accessible, I recommend as the next step after Into the Hot, the 1966 Blue Note album Conquistador, specifically the title piece. A long form, well-structured and full of variety, with lots of beautiful episodes and material, and great improvisation. Early in the piece there is one of my favorite Jimmy Lyons alto solos. Lyons often brings beboppish lines into Cecil's free framework, often to great effect, but sometimes (not in anything I've linked above, I think!) I can find them a bit repetitive or unimaginative (as standard bebop lines can also become on occasion). I love the transition from an episode of long, pretty trumpet (or is it fluegelhorn?) lines by Bill Dixon (at 5'37 he seems to begin to quote Miles Davis on the Davis/Gil Evans Sketches of Spain, but takes the line elsewhere!), to funky vamps beginning at 7'20 or so, behind an appealing rising melody, aimed at gradually bringing the energy back up, and ultimately taking it into a top-notch Taylor solo. This solo is pretty intense, with a lot of the lines that sound like flurries of note-clusters, but interspersed on fairly short time-scales with short bits of other material...and the control and variety of structure in the intense fast lines is great. The beautiful rising melody-over-vamp recurs momentarily to mark the end of this solo, and things go on from there.

The other long track, With(Exit) is also superb. I have had this on LP, again since teenage years, but this remastered version sounds pretty great even on Youtube... I may have to buy the CD.

The other ensemble Blue Note recording of the era, Unit Structures, is also excellent.  It seems to have gotten more attention for a while.  For instance, Martin Williams included Enter Evening (Soft Line Structure) to represent Taylor in the Smithsonian Collection of Classic Jazz that he edited, a sort of gesture toward establishing a jazz canon, back in 1973.  That piece (the second track on Unit Structures) is mostly slow-paced and out of strict tempo, mellower and more reminiscent of European-rooted avant-garde classical music and atonality, than much of what Taylor was doing at the time (though I don't mean to suggest that avant-garde "classical" music was its primary inspiration or that that whiff of it is very strong, or that it is strictly atonal).  The first piece, "Steps", on the other hand, gets into an intense alto improvisation (I am not sure at the moment whether it is Lyons or Ken McIntyre) that might remind one at places of Albert Ayler, and reminds me of Joseph Jarman's intense sax work on the Art Ensemble of Chicago's masterpiece Fanfare for the Warriors (also the name of the album, which as a whole is also a masterpiece).  The solo on "Steps" is somewhat in the "screaming" vein of free jazz...not really something I would recommend as accessible to someone new to Taylor and avant-garde jazz although you never know.  (Ditto for the sax work on Fanfare.)  I am enjoying Unit Structures a lot and will put it into heavier listening rotation if I find time to.  (As I write this, around the 30 minute mark of the whole-LP Youtube video of Unit Strucures, Jimmy Lyons is combining is free boppish lines with more avant-garde stuff in a great, melodically inventive vein.)  But for those new to Taylor I recommend sticking to Conquistador at first.

6.  Finally, if you really want to sample a full-bore, hour-long exorcism and communal communion with the spirit world, Streams and Chorus of Seed, the only track on the live album Dark To Themselves (recorded at the Ljublana Jazz Festival on June 18, 1976) is your ticket. If you are just trying to learn to dig Taylor for the first time, you might want to skip this, but not to go here or somewhere similar is not to give a full picture of Taylor. Besides Taylor on piano it features most prominently the tenor sax of David S. Ware, as well as Jimmy Lyons on alto, Raphe Malik on trumpet, and Marc Edwards on drums. You will probably want headphones for this one---use good ones, as I doubt cheap earbuds will be up to reproducing these sounds accurately enough. Watch the volume, though. The screaming sax of David Ware, especially, on this can be a bit hard to take particularly since it goes on for a long time---but it is a powerful statement (or at any rate, powerful--I am not sure "statement" is the right word) and there is simultaneously often a lot of interest going on in Cecil's piano to focus on. The LP that was the initially-issued version was a heavily cut version of this---the whole thing could have been issued on a two-LP set but perhaps it was thought it would be too much for people. Indeed I am having to take a break from this at the 37 minute mark or so. The CD edition I'm linking to the Youtube upload of includes, I think, the whole performance and has much better sound than the LP. I am still not quite sure what to make of this performance overall, but it has much to offer and is definitely pure, uncompromising Taylor. But I'm sure what to make of Taylor overall: a first-rank master whose creations will be with us, I hope, for as long as humans exist and love music.

De Guise-Langlois & Morgenstern Trio in Messiaen's Quartet for the End of Time, and Dover String Quartet in Mendelssohn Op. 80, at the Tucson Winter Chamber Music Festival

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On Wednesday, March 7, 2018, at the Leo Rich theater in the Tucson Convention Center, I heard two of the best chamber music performances I've ever heard.  As part of the 25th Tucson Winter Chamber Music Festival, clarinetist Romie de Guise-Langlois and the Morgenstern Trio performed Olivier Messiaen's Quatuor pour la fin du temps (Quartet for the end of time), for a standard piano trio (piano, violin, cello) plus clarinet, and the Dover Quartet performed Mendelssohn's String Quartet in F minor, Opus 80.  You may find in my reviews that I tend to emphasize the positive, and not belabor it when a performance could have been better, instead concentrating on how much I have gotten out of the performance that was actually given.  So let me emphasize that that is not the case here: one could imagine performing these works a little differently, perhaps, but not better than was done here.  This was an extraordinary, unforgettable evening of music.

Program for the first performance of Quatuor Pour la Fin du Temps

The Messiaen is a piece I have valued for decades; I know it to the point of recognizing many of the themes when played in concert, but (unlike some other works) I have not internalized it to the extent of being able to replay significant parts of it in my head.  I have long considered it one of the most significant pieces of twentieth century chamber music; the performance by de Guise-Langlois and the Morgenstern made it clear that it is one of the pinnacles of music of any time or place.  It is inspired by the biblical book of Revelations, and deeply informed, as was all of Messiaen's music, by the composer's intense and very personal form of Catholic faith, and while it should be experienced in this light, with the aid of Messiaen's own program notes (and the obvious signposts provided by the movement titles), it is of universal value and appeal regardless of the auditor's faith or lack of faith.    A translation of Messiaen's notes is included in the Wikipedia article on the piece.  (References like "blue and orange chords" evince Messiaen's synaesthesia, in which harmonies evoked experiences of color.)  I won't try much to describe the significance of the music or the experience of listening to it, since Messiaen's notes give a pretty good idea of what's in store.  In this regard I'll just say that he is strikingly successful at achieving---roughly speaking, as the color experiences will not be available to most of us and the specific religious references are more inspiration or metaphor than something reproducible or verifiable---what he describes in the notes:  the music is powerful, beautiful, glorious.

Alex Ross' 2004 New Yorker article (reviewing a book on the piece by Rebecca Rischin, and a performance by the Met Chamber ensemble) provides further valuable background and reaction to the piece, which he calls "the most ethereally beautiful music of the twentieth century".  It was composed primarily in 1940-41 while Messiaen was imprisoned in the German prisoner of war camp Stalag VIII, and first performed there in 1941.  Parts of it were apparently begun earlier (notably the third movement, Abîme des Oiseaux (Abyss of the Birds, for solo clarinet).  I am not sure how deeply the music was influenced by the conditions under which it was composed, since in style, content, and intensity it does not seem to me radically different from his work before and after the war.  It's possible that the composition of the work for a medium-size chamber group may be one of the most important effects of the quartet's origin in a POW camp---it may be my own ignorance, but most of the other great works I am aware of by Messiaen are either for piano (or piano and voice), or large groups like orchestra or orchestra with chorus.

Ross differs from Messiaen in how he describes the "Seven Trumpets" movement, writing:  "the gentlest apocalypse imaginable. The “seven trumpets” and other signs of doom aren’t roaring sound-masses...".  Whereas for Messiaen it is "Music of stone, formidable granite sound; irresistible movement of steel, huge blocks of purple rage, icy drunkenness. [...]terrible fortissimo[...]".  How one experiences it may depend on the performance, I guess, as well as the auditor.  Ross calls the "Trumpets" section "Second Coming jam sessions", and in connection with the piece overall (not necessarily this movement), my wife also mentioned a kinship with jazz.  This should be understood in light of the rather wide range of jazz my wife and I listen to --- not just bebop and swing masters like Bob Rockwell and colleagues, but avant-garde artists like Charles Gayle and Peter Broetzmann, and modern if not quite avant-garde groups like Kenny Werner's quartet, Charles Lloyd with Bill Frisell, and the Billy Hart Quartet, just to mention a few groups we have recently heard live.  Indeed, the Lloyd/Frisell combo and the Hart quartet (with Ethan Iverson on piano, Mark Turner on sax, and Ben Street on bass) are especially prone to episodes of Messiaenic intensity: continually evolving ecstatic/reflective grooves, carefully crafted harmonic coloration, dancing rhythmic complexities, calm serenities bringing to mind Baudelairean realms where "tout n'est qu'ordre et beauté, / Luxe, calme et volupté".

As I said above, the performance by de Guise-Langlois and the Morgenstern was one of the best things I've ever heard.  Clichés like "riveting", "stunning", etc...apply without reservation and quite literally:  my attention did not wander for a moment during the long performance, and the audience sat in the proverbial stunned silence for ten or twenty seconds after the musicians lowered their bows and instruments, before breaking into a standing ovation.  Of course, S.O.'s have become disconcertingly common these days (it especially annoys me when people stand and clap as a prelude to an early run for the exits), but this one was fully deserved. Ross' generally positive review of the performance he attended remarks that it "lacked the total unanimity that makes a great performance of the Quartet seem like a mind-reading séance".  This performance had no such lack, although our close vantage point in this relatively small auditorium disclosed that the mind-reading was taking place in the usual way, through ears and eyes, as they very actively looked at each other, nodded for cues, sometimes swaying to the music.  It was indeed a kind of séance.  De Guise-Langlois' clarinet playing is remarkable in its dynamic and expressive range and sensitivity to the other musicians; I got the impression (perhaps misguided) that her attention to the other musicians may have been the crucial ingredient binding them into a unit capable of such a sublime achievement.  She has a wide range of expressive timbre at her command, but overall I would say skewed toward clarity and purity of tone.  Catherine Klipfel's tone, on a Steinway D, was great for this piece, bell-like with just enough of a touch of hollowness and edge to add complexity and not to be icily pure.  Everyone played superbly and I will be on the lookout for the Morgenstern and de Guise-Langlois in other repertoire.  De Guise-Langlois seems to me clearly a rising superstar of the classical clarinet.  I didn't find any single link at Youtube that I felt gives an adequate idea of the full range of what she can do, in a sympathetic medium-size chamber context.  I did very much like a contemporary (though relatively conservative stylistically) duet with piano, composed by Kevin Puts.

The space above the stage in the Leo Rich auditorium was larded with microphones for this performance, and highlights of Tucson Chamber Music Festival are eventually broadcast on Classical KUAT-FM, 90.5/89.7 FM, so I recommend trying to find out when this will happen and streaming the broadcast over the web.  (It may be a long time from now, though.)  I would be thrilled if it eventuated in a full-fidelity digital recording---the Arizona Chamber Music Association does sell CDs of past festival highlights, so we can hope this performance will appear on such a disc in the future.

Ross recommends the 1975 recording by Tashi as "still unsurpassed" (at least in 2004).  I have long had this on LP, but have done most of my listening to this Deutsche Grammophon CD featuring Daniel Barenboim on piano (Youtube link here).  I also recall getting a lot out of an excellent performance at the Santa Fe Chamber Music festival in the 1990s, and a really wonderful performance of the solo clarinet movement at the Smithsonian American Art Museum's concert series a few years back.  I think it was part of a concert by the ensemble Eighth Blackbird.  I haven't revisited the recordings I own since the Tucson concert, because I don't want anything to displace it in my memory, although I think it is now time to start listening, as this is a piece of music I want to "git in my soul," as Charles Mingus might say.

I'm not sure if I'd heard of the Dover quartet before this performance of the Mendelssohn.   I quickly decided that the Dover is one of my favorite string quartets ever.  String quartets can sometimes sound strident---an effect that may depend partly on the type of strings they are using.  The Dover was anything but, with a warm, even at times mellow timbre that nevertheless had plenty of texture and was compatible with great intensity and drive where needed.    The F minor quartet, Opus 80, was composed in the shadow of the death of Mendelssohn's beloved sister Fanny; within a few months of its composition, Mendelssohn too was dead.  It is a masterpiece, and the Dover did it full justice.  The outer movements had plenty of intensity.  The slow movement had a bit more autumnal, meditative, mellow pastoral feel --- I had a sense that this movement, too, could have been given more intensity and a different, more anguished, emotional tone in places, but not the sense that such an interpretation would have been preferable, particularly in light of the Sturm und Drang that was often in evidence in the outer movements.  An outstanding performance, also fully deserving of the standing ovation that ensued.

Ensembl Mitdvest: Muczynski, Bach, Birtwistle, and Dvorak at Kastelskirken, Copenhagen

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At Kastelskirken in the Kastellet fort in Copenhagen today (19.11.2017) a wind quintet drawn from the Danish Ensembl MidtVest played Robert Muczynski's woodwind quintet, opus 45; J. S. Bach's Partita in A minor for solo flute and basso continuo (bass clarinet); Harrison Birtwistle's Five Distances for Woodwind Quintet, and an arrangement by David Jolley of Antonin Dvorak's String Quartet # 10 in E minor, opus 51. With its white rectangular interior and tall mullioned windows with clear panes affording views of the 17th century buildings, with their steep tiled roofs, around the spacious raked-gravel courtyard inside the fort, and the Danish state flag with swallowtail streaming in the wind, as well as strollers and the occasional patrolling pair of soldiers on the grassy outer rampart, Kastelskirken was an atmospheric location for a concert on a blustery late-fall afternoon. The quintet is Charlotte Norholt, flute; Blanca Gleisner, oboe; Tommaso Longquich, clarinet; Niel Page, horn, and Yavor Petkov, bassoon.

I did not previously know American composer Robert Muczynski (1929-2010), and am delighted to have been introduced to him. The wind quintet is a super piece, in a melodic, more or less tonal style, with plenty of brio and humor at times, especially in the opening Allegro risoluto, but also beauty and seriousness, especially in the second movement (Andante). His style is personal rather than derivative, but to give a rough idea what to expect, one might cite some commonalities with impressionism, flecked with a little bluesiness in places (to my ear); Poulenc and other composers of that era; Rorem, William Schuman, and others of that ilk, even while I had a clear sense that he was aware of post-tonal developments and able to incorporate aspects of them where it made musical sense. A great pleasure to hear and I will seek out a recording and other chances to hear it again. An interview with Muczynski by classical DJ Bruce McDuffie is very much worth reading.

I thoroughly enjoyed the Bach also. Flutist Norholt used quite a bit more rubato than I'm used to in Bach, especially in the very familiar first movement of this piece, but it was not an impediment to enjoyment.

It's always good to finish off the first part of a program with a substantial, crowd-pleasing potboiler to send folks into intermission with, and the MidtVest did just that with Harrison Birtwistle's Five Distances. The English composer, born in 1934, is generally considered a pretty austere, uncompromising atonal composer, and this was no largo sweetota, but the piece has structure, recognizable recurring elements, variety and beauty. The MidtVests' performance seemed perhaps more expressive and intense, than the Boulez/Ensemble Intercontemporain performance I linked above, though it's hard to compare a live performance to a recording. The audience (which I estimate numbered around 70-90) seemed to have no trouble connecting with it, and it received a rousing round of applause.

After the break, an excellent performance of a familiar and well-loved Dvorak string quartet, arranged for wind quintet. At first I though it was missing something in the phrasing that could perhaps only be provided by the original strings, but fairly quickly settled in to enjoying a committed and successful performance.

An excellent concert all round, with the superb, and to me, unfamiliar, Muczynksi and Birtwistle pieces real standouts. Kudos to the MidtVest for top-notch playing and for succeeding with an adventurous program.

Harmaleighs at Fuller Lodge, Pretty Picture, Dirty Brush

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Great concert by indie folk/pop duo The Harmaleighs (Haley Grant, guitar & vocals; Kaylee Jasperson, bass & vocals) Halast night (Feb. 19) at Fuller Lodge in Los Alamos, accompanied by Mike (?) Baker on guitar and supporting vocals.   I bought their excellent album Pretty Picture, Dirty Brush at the show; it's also on Spotify and at itunes.  A new album will be out May 5th. Here's a live acoustic duo version of the first song, "Hesitate", on Pretty Picture:

I guess "Diamond Ring" might appear on the upcoming album. Here it is live with the addition of Baker:

A group of three girls from Los Alamos High, the Hopeless Distractions, did an excellent warm up set of three or four songs, covers although they told me they are working on a few things. They are in the same vein---indie/country/folk/pop, sweet and somewhat ethereal vocal harmonies.

Huge thanks to Los Alamos High history teacher John Lathrop for organizing the concert, and the Harmaleighs for playing this little burg! I'll update this post with a few photos soon...

Schumann: Papillons, Blumenstück, Novellette; Novaes, Arrau, Sokolov

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Since my last post involved some Schumann piano pieces, I thought I should link to some performances of them:

Papillons, Op. 2, Guiomar Novaes, piano:

Blumenstück, Opus 19 in Db major, Claudio Arrau, piano:

Novellette, Op. 18 No. 8 in F# minor.  Grigory Sokolov, piano:

Orion Weiss with the Salzburg Marionettes: Schumann, Debussy

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Not sure why this has been sitting around as a draft, but I'm belatedly posting it now; good music is always relevant:

Really glad I finally decided to go see and hear the Salzburg Marionette Theatre with pianist Orion Weiss play Los Alamos on Nov. 1 (2014), because Weiss' Schumann was a revelation, and his Debussy superb as well.  With relatively spare sets and costuming, the Marionettes accompanied Weiss in Schumann's Papillons, Opus 2, a succession of short dance movements bookended  by an introduction and finale.  The Marionettes' storyline seemed to involve a love, or at least flirtation, triangle.  Relatively lighthearted, as was the music (at least for Schumann).  The music was my main focus and it held my attention.  Superb music, superbly played.  Perhaps even better were the two longer pieces, played without Marionette action, the Blumenstück in Db, Op. 19, and the Novelette no. 8 in F# minor.  I'm no expert on Schumann's piano music, but I have the impression that many of Schumann's longer works in general can be difficult to interpret effectively---it is easy for them to appear unstructured, longwinded, and/or even a bit repetitive.  No such problem here.  Long developmental passages had a definite trajectory, and both on the level of phrases and the overall structure, Weiss penetrated to the musical meaning of the piece instead of just letting the notes unspool.   When I spoke with Orion after the concert he mentioned that it can be challenging to make the main theme in these pieces still meaningful, and bring something new to it, each time it recurs; he definitely succeeded.  I've sometimes felt like the Los Alamos Concert Association's Steinway D can sound not quite brilliant enough, and perhaps like the action is a bit heavy, slowing things down a bit.  Not so much recently, though.  I enjoy hearing how different that piano can sound each time a different artist plays it, and Weiss got a great tone out of it, balanced between brilliance and purity and warmth and complexity, and played with great facility though not in a technically showy manner.  (I suspect that just to sound at ease in these pieces is quite a technical challenge!).

Unfortunately although Weiss has quite a few CDs out, for example Scarlatti sonatas, and Rhapsody in Blue (on different CDs!) on Naxos, his Schumann is not available on disc.  If he ever puts out a disc of Schumann, I'll snap it up; in the meanwhile I'm going to investigate the piano music in more depth.

After intermission, we were treated to Debussy's relatively rarely performed La Boîte a Joujoux (The Toy Box).  This was explicitly composed as music for a marionette ballet, and the sets were much more elaborate and beautifully done, the music and action perfectly integrated.  The music, appropriately, is a tad less adventurous than the great piano-only works like the Preludes, with perhaps more standard sounding pentatonic and whole tone material, and a bit less complex and coloristic harmony, a bit more emphatic and regular rhythm at times (and explicit punctuation of the action), but still, very rewarding, and perfectly played.  Atogether a wonderful, transporting evening of music and stagecraft.

Addendum:  I found this Nov. 2 post by the piano technician for LACA--- if it refers to the previous night's concert, as the photo of the artist also suggests, then I join Orion in thanking him for a great job getting the piano ready.