[MEI-L] graceful beams

Byrd, Donald A. donbyrd at indiana.edu
Sun Apr 14 15:32:02 CEST 2013

Whew; I'll try to catch up this flurry of activity before it's too late :-) .

First, I agree almost 100% with Perry's analysis of the Chopin example, 
that it's really a (separate) grace note superimposed on the normal 
note; in fact, I was thinking of saying that, but I'm glad I didn't so 
it's clear arrived at the same conclusion independently. I seem to have 
deleted Maja's original message plus the Mozart example she attached; 
Johannes or Perry, would you mind resending it? -- but I'm sure Perry 
is correct about it too. This notational unicorn might exist; I'll keep 
my eyes peeled for it, but it's clearly SO rare, I don't think it's 
worth worry about.

And Frank Litterscheid's example is an interesting one! But small notes 
that clearlyt aren't grace notes in the normal sense aren't that 
unusual, especially in Chopin :-) . Attached is the latest version of 
my "More Counterexamples in Conventional Music Notation"; section 3a 
lists about ten examples.


On Sun, 14 Apr 2013 14:45:54 +0200, Johannes Kepper <kepper at edirom.de> wrote:
> Hi Frank,
> there is an attribute @size on <note/>, which can be used
> independently from the @grace attribute. In other words, you don't
> have to call a note a grace if all you want is to change the size...
> Interesting example, though ;-)
> Schönen Sonntag,
> Johannes
> Am 14.04.2013 um 14:31 schrieb <litterscheid at notensatz.biz>:
>> Because I have no idea how the size of a note is coded in MEI, I
>> want t ask a question.
>> In the attached file there is a small note (in this edition
>> editorial addings are engraved as small notes) which HAS to be
>> connected the the *normal* beam. I would no call that small note a
>> grace note, but if the term *grace note* is the only way of encoding
>> small notes, it would be good to be able to connect them to *normal*
>> beams.
>> Only a thought of an unknowing engraver J
>> Frank
>> ---
>> Frank Litterscheid
>> Am Kuhkamp 7
>> 37619 Hehlen
>> Tel 05533 - 979733
>> Fax 05533 - 979732
>> litterscheid at notensatz.biz
>> Von: mei-l-bounces at lists.uni-paderborn.de
>> [mailto:mei-l-bounces at lists.uni-paderborn.de] Im Auftrag von TW
>> Gesendet: Sonntag, 14. April 2013 12:52
>> An: Music Encoding Initiative
>> Betreff: Re: [MEI-L] graceful beams
>> So, to what conclusion do we come?  I think MEI doesn't lack any
>> features here, it should just be made clear at a more prominent
>> place in the specification/documented that grace notes will
>> graphically not be part of a beam, even if they occur within the
>> <beam> element.  If you *really* want grace notes to be part of the
>> regular beam, you can still achieve this using existing means.
>> Is this a valid summary of the discussion?
>> Thomas
>> 2013/4/14 Roland, Perry (pdr4h) <pdr4h at eservices.virginia.edu>
>> Hi Don,
>> Thanks for joining the discussion.
>> I should've been wary of using the word "never".  That's a dangerous
>> word when it comes to music notation. (Note to self:  Always avoid
>> the words "always" and "never".  Never use them.)  Chopin's notation
>> is usually pretty "slippery", so I'm not surprised you found
>> evidence there to trip up the unsuspecting.
>> However, in both the Mozart and Chopin examples, the notes in
>> question are clearly not part of the beamed group of "principal"
>> notes.  Stem direction is the best evidence.  The different stem
>> directions leading to the beams attached to the A# in the
>> penultimate measure of the Chopin clearly indicate that there are
>> two "layers/parts/streams/voices" here.  There isn't just one A#,
>> but two which occupy the same visual space. The big A# just obscures
>> the little one.  The grace note A# belongs to the upper layer while
>> the regular note A# goes with the lower one.  The same thing occurs
>> on the B natural in the last measure.
>> Now that the part writing has been disentangled, what is most
>> interesting is the *meaning* of this particular vertical alignment,
>> the collision really, of a "principal" note and a "grace" note.
>> What is Frederic trying to say?  I believe he's indicating that the
>> grace note arpeggio begins *with* the A#, not *after* it (this
>> comports with Gould) and that the performer shouldn't rush getting
>> to the A# at the top of the arpeggio.  (By the way, I believe the
>> sonic effect would've been the same if he'd simply written a wavy
>> line in front of A#-C#-F#-A# in the right hand, just like what's in
>> the left hand. But he made his choice and we have to live with it.)
>> There's an instance in the 3rd measure of the Chopin example that's
>> more closely analogous to the situation in the Mozart that started
>> the discussion: the grace notes between beat 2 and its second half
>> (assuming this notation is counted in 2/4) lie under the beam
>> connecting the G#-A-G# sequence, but they're not touching it.  In
>> addition, they're part of their own little beamed group.  They are
>> *logically excluded* from participating in the "big beam group" in
>> spite of occurring between its participating notes, just like the
>> grace notes in the Mozart example.
>> So, I stand by my assertion that grace notes are never (um,
>> "extremely rarely") beamed with "regular" notes, where "beamed with"
>> means "part of the same horizontal sequence as" normal-sized notes.
>> Granted, I haven't seen the entire universe of music notation, but
>> mixed grace- and normal-note beams are like unicorns -- I've heard
>> talk of them, but as yet I haven't seen one. :-)

Donald Byrd
Woodrow Wilson Indiana Teaching Fellow
Adjunct Associate Professor of Informatics
Visiting Scientist, Research Technologies
Indiana University Bloomington
-------------- next part --------------
by Donald Byrd, Indiana University, Bloomington
Revised mid April 2013

This is a supplement to the list of "counterexamples" in Sec. 2.5 of my dissertation,
Music Notation by Computer (Byrd, 1984). (The term "counterexample" is borrowed from
mathematics and mathematical logic.) As that section states, these are "examples of
published music...intended to counter the view that CMN, while it may have many complex
details, is in principle easily mechanizable". I restrict CMN to the period from about
1700 to 1935. These examples are virtually all from music published by respectable
publishers, and the vast majority are by well-known, mainstream composers. They cast
doubt on the idea that CMN can be easily mechanized by breaking many of the supposed
rules of music notation, including some that (in my experience) few musicians would
expect to see _any_ exceptions to, at least in publications like these.

My dissertation comments that "this collection is far from exhaustive: it is based on an
examination of a minute fraction of the relevant musical literature." The same statement
applies to this supplement.

A handful of these counterexamples are discussed in Byrd (1994).

A related collection of examples of unusual music notation appears in Byrd (2012). That
collection concentrates not on rule-breaking notation but on extreme usage of notation
wtihin the rules, e.g., shortest note duration, most independent voices on a staff.
However, the dividing line between extremes and rule-breaking isn't always clear.

See also Byrd (2010) and my unpublished list of Music Without Barlines (2010).

Thanks to Edward Auer, Lana Bode, Myke Cuthbert, Noam Elkies, Jay Hook, Thomas Loewenheim,
David Meredith, and Gabi Teodoru for their contributions (noted below).


The list below is organized into top-level categories named and numbered as in the list in
my dissertation. It uses the following conventions:

Asterisk ("*") preceding an item indicates those I haven't seen personally.

"B&I 7.5" (and similar) means this notation is item 7.5 in Byrd & Isaacson (2005).
"B & M, 1948" means the notation is visible in Barlow & Morgenstern (1948).
For edition, "Bo+H" = Boosey & Hawkes; "Br+H" = Breitkopf & Haertel.

The term "chord" herein means a collection of notes on a single stem.

(1) Collisions.

	Ravel: Gaspard de la Nuit (Durand ed.) (almost simultaneous intersections of two beams,
		two slurs, and hairpin)
	Scriabin: Piano Sonata no. 3 (Dover ed.), I, p. 49, top staff (double-dotted notes with
		a stem belonging to a note in another voice between the dots. I'm not sure if this
		is a perceptual collision as defined in my dissertation; it's more like a "perceptual

(2) Linear Symbols Interrupted By Other Symbols.

	Bartok: 3 Burlesques, Op. 8C, I (barline and staff interrupted by clef)
	Chopin: Prelude in f, Op. 28 no. 18 (?? ed.) (beam interrupted by clef) (B&I 12.6?)
	Strauss: An Alpine Symphony, Op. 64, after RM 69 (barline and staff interrupted by clef)

(3) Symbols With Highly Nonstandard Shapes Or Positions (but minimal or no unusual semantics)

a. Small notes with rhythmic values more-or-less like normal notes, excluding cadenza-like passages
entirely in small notes:
	Bartok: Dance in Bulgarian Rhythm no. 1, in Mikrokosmos (1926-39; Boosey & Hawkes ed.) Book 6,
		throughout, right hand (triplet of 3 16ths, the first full-size & the others small)
	Chopin: Prelude in f#, Op. 28 no. 8  (Br+H ed.), throughout, right hand (small 32nd notes
		regularly double-stemmed with longer normal notes when they coincide)
	Chopin: Prelude in d, Op. 28 no. 24  (Br+H, Paderewski eds.), several places (strings of
		beamed small eighth notes, sometimes starting with a full-size note)
	Chopin: Etude in A-flat, Op. 25 no. 1 ("Harp") (Paderewski ed.), throughout, right hand
		(beamed six-note groups of triplet 16th notes, the first full-size and the others small)
	Chopin: Scherzo in b-flat, Op. 31  (Br+H ed.), several places, right hand (passages of a couple
		of measures of all small notes)
	Debussy: Pour le Piano, I, mm. 148-156?? (small notes in a cadenza-like passage that seem
		to act like normal notes, interspersed with normal notes filling each measure's duration)
	Ives: Three Places in New England (Mercury Music ed.), I, p. 6, piano (psuedo-arpeggio of
		eighth-note dyads with upper note of each normal size, lower note small)
	Schumann: Carnaval (Kalmus/Clara Schumann ed.), Op. 9, no. 19 (Promenade), mm. 3-4, 11-12,
		etc. (small notes with simultaneous full-size rests on the same staff notes, but clearly
		intended to be played like normal notes, as if "cue" notes but for the same performer)
	Scriabin: Sonata no. 1, IV, beginning 52 mm. from the end (small notes that act just like
		normal notes)

b. Miscellaneous (NB: slurs with many inflection points were formerly listed here, but are now
in my CMN Extremes list):
	Bartok: Two Rumanian Dances, Op. 8A no. 2 (compound beam)
	Beethoven: Violin Concerto (Br+H ed.), II, last measure (very wide fermata over a series of
	Berg: Violin Concerto (Universal ed.), p. 47 (one-to-many, many-to-one slurs jumping staves
		and parts, e.g., clarinet to bass clarinet or bassoon, celli to violins & violas(?))
		(B&I 17.6 EXTENDED)
	*Berio: Don{de} from Pli selon Pli, p. 15 (slur jumping from clarinet to bass clarinet,
		to play an out-of-range note) (NB: after 1935) (B&I 17.6 EXTENDED) [contrib. by Cuthbert]
	Brahms: Capriccio, Op. 76 no. 5 (International ed.), mm. 7-8 (stem only one space long)
	Chopin: Berceuse, Op. 57, p.1 (split-stem grace notes, for augmented unison??) (B&I 5.25)
	Chopin: Nocturne, Op. 27 no. 2 (augmented unison in 2-stem notation ??SPLIT STEM OR 2 VOICE?)
	Bizet: Jeux d'Enfants, p. ?? (slur with 5 inflection points) ??IS THIS REAL?
	Debussy: Prelude a l'apres-midi d'un faune, piano arrangement by Leonard Borwick, m. 100
		(in a 3-staff system, arpeggio sign with notes on the top & bottom staves but not the
		middle one)
	Haydn: Piano Sonata in E minor, Hoboken XVI, I (fermata over nothing, halfway between 2 rests)
	Verdi: Falstaff (publ.?), p. 203 (accents marks _obviously_ moved to avoid accessory numerals)
	Ravel: Gaspard de la Nuit (Durand ed.), Scarbo, p. 41 (slur with 3 inflection points)
		(B&I 17.17)
	Ravel: Gaspard de la Nuit (Durand ed.), Ondine, next-to-last page (slur backing up in the
		middle) (B&I 17.17)

(4) Rhythm Notation.

a. Chord with notes of different durations (B&I 4.28):
	Bartok: Sonata for Solo Violin (Boosey & Hawkes ed.), I (double-dotted quarters on same
		stem as undotted quarters)
	Brahms: Symphony no. 1 (Henle), I, 4th m. of Allegro, violin 1 (dotted quarters on same
		stem as undotted quarters)
	Brahms: Symphony no. 4 (Eulenberg ed.), IV, last chord, violins & violas (dotted halfs
		on same stem as undotted quarters)
	Chopin: Scherzo in B minor, Op. 20 (Br+H ed.) (half head on same stem as quarter; occurs
		several times)
	Chopin: Prelude in Db, Op. 28 no. 15 (Paderewski, Universal, Br+H eds.) (dotted-half head on
		same stem as dotted-8th)
	*Dohnanyi: Violin Sonata, piano part (chords with quarter and half heads on same stem)
		[contrib. by Hook]
	Mozart: Violin Concerto no. 3 in G, K.216 (Schirmer/Franko ed.), I, m.42, solo violin
		(half head on same stem as 2 quarters)
	Mozart: Piano Sonata no. 6 in D major, K. 284  (Alte Mozart-Ausgabe), III, variation 4
		(half head on same stem as quarter heads)
	Tchaikovsky: Symphony no. 2 (Eulenberg ed.), IV, mm. 3-4, violins, violas, celli (halfs
		on same stem as quarters)

b. Note with duration apparently extending across the following barline (cf. "impossible rhythm").
Many of these involve dotted notes where the dotted part of the duration is after the barline:
	Barber: Piano Sonata, I, p. 7 (notehead and double dots together before barline)  [contrib.
		by Meredith]
	Bartok: Violin Sonata no. 1 (Universal ed.), I (notehead before but dot after barline)
	Brahms: Symphony no. 1 (Eulenberg ed.), IV (notehead before but dot after barline)
	Chopin: Etude in A-flat, Op. 10 no. 10 (Paderewski, Henle eds.), beginning (it's in 12/8; the
		left hand plays continuous 8th notes, but the 4th and 10th of several mm. have half-note
		heads; in the Paderwski ed., they're also stemmed separately with augmentation dots)
		[contrib. by Hook]
	Chopin: Prelude in D, Op. 28 no. 5 (Paderewski, Universal, Br+H eds.), mm. 1-3, etc. (the last
		16th of the measure is double-stemmed as an 8th)
	Mozart: Piano Sonata in Eb, K.282 (Presser/Broder), III, mm. 48-54, right hand (notehead before
		but dot after barline)
	Mozart: String Quartet, K.465 (Br+H ed.), IV, last page (notehead before but dot after barline)
c. Note with duration arguably shorter than it appears. Usually this is because it otherwise extends
across the following barline but following events in the score indicate it should not be held for
the full notated duration (a type of "impossible rhythm"):
	Brahms: Variations on a Theme of Haydn, Op. 56, theme (breve in 2/4 time)
	Brahms: Capriccio, Op. 76 no. 1. m. 26, 30 (dotted half in 6/8 time starting a 16th after the
		downbeat, and tied to a note on the downbeat of the next measure; clearly it's intended to
		last only 11 16ths instead of 12)
	Franck: Prelude, Chorale, & Fugue, Prelude, m. 48 (quarter notes overlapping with 32nd rests
		in the same voice; clearly the "quarter notes" are intended to last only 7 32nds instead of
		8) [contrib. by Hook]
	Verdi: Falstaff (Ricordi), last m. of Act I (breve in 6/8 time)
	Verdi: Falstaff (Ricordi), last m. of Act II (breve in 2/4 time)
	Verdi: Requiem (Dover), last page (breve in cut -- here unequivocally 2/2 -- time)
d. Time signature change in middle of measure (B&I 10.8):
	Anonymous (folk song): Wassail Song (typically notated as 6/8 to C or 4/4, but 6/8 to
		Cut would make more sense: tempo is dotted-qtr = half)
	Beethoven: Piano Sonata, Op. 109, I & III 
	Beethoven: Piano Sonata, Op. 110, III (four times; the passage also has multiple mid-measure
		key changes)
	Beethoven: Piano Sonata, Op. 111, II (occurs at least twice)
	Handel: Keyboard suite no 5 in E major, last mvmt (a.k.a. "The Harmonious Blacksmith") (at
		join between Var. 2 and 3, right hand switches from C to 24/16 in mid-bar, left hand staying
		in C; between Var. 3 and 4, the hands switch time signatures in mid-bar; and between Var.
		4 and 5, left hand joins right hand's C in mid-bar) [contrib. by Elkies]
	Verdi: Falstaff (Ricordi), p. 71 (12/8 to C)

e. Time signature with ambiguous measure duration
	Bach: Well-Tempered Clavier, Book II, Prelude in D ("C 12/8" for simple vs. compound
	Brahms: Piano Trio, Op. 101, III ("3/4 2/4", meaning each measure is one or the other; later,
		"9/8 6/8", with the same meaning)
	Debussy: Preludes, Book 1: Les collines d'Anacapri (State Music Pub. House/Sorokin ed., Dover
		reprint) ("12/16 = 2/4" for simple vs. compound equivalents)
	Rimsky-Korsakov: Scheherazade, Op. 35 (Belaieff/Dover ed.), IV, m. 30ff. ("2/8 (6/16 3/8)")
	Ysaye: Solo Vn Sonata, Op. 27 No. 2 (Ysaye/Schirmer ed.), III ("3/4 = 5/4": the vast majority
		of measures are in 3/4, but a few are in 5/4, one in 4/4, and one, marked "-2-", in 2/4)
	Ysaye: Solo Vn Sonata, Op. 27 No. 2 (Ysaye/Schirmer ed.), IV ("2/4 3/4": each measures is one
		or the other)

f. One notehead for notes of different duration ending at the same time, and therefore beginning
at different times. This is the principal "impossible rhythm" situation of Hook (2008), which
gives dozens of examples besides those listed here:
	Brahms: Variations on an Original Theme, Op. 21 no. 1 (Br+H ed.), Variation 5 (one
		notehead for normal 16th and triplet 16th => 1/2 = 2/3; occurs many times) [contrib. by
	Brahms: Intermezzo, Op. 119 no. 1 (1893; International ed.), 12 m. before the end (one
		notehead for normal and triplet 8ths ending at the same time => 1/2 = 2/3)
	Chopin: Ballade in f, Op. 52 (Br+H ed.), mm.?? (one notehead for normal and triplet
		16ths ending at the same time => 1/2 = 2/3; occurs several times)
	Chopin: Concerto in F minor, Op. 21 (Br+H ed.), III, mm. 335-36 (one notehead for normal and
		triplet 8ths ending at the same time => 1/2 = 2/3) [contrib. by Hook]
	Chopin: Mazurka in A minor, Op. 17 no. 4.
	Chopin: Prelude in C, Op. 28 no. 1 (1836?; Paderewski ed.) (one notehead for normal and
		triplet 16ths ending at the same time; occurs >20 times) [contrib. by Hook]
	Chopin: Prelude in C, Op. 28 no. 1 (1836?; Paderewski ed.) (one notehead for normal and
		quintuplet 16ths ending at the same time; occurs 6 times) [contrib. by Hook]
	Chopin: Sonata no. 1 (1828?; Schirmer-Mikuli ed.), III (one notehead for normal and
		quintuplet 16ths ending at the same time; occurs 3 times)
	Ravel: Sonatine (1903-05; Durand/Dover ed.), III (one notehead for normal and triplet
		8ths ending at the same time; occurs 4 times)
	Schumann: Bunte Blatter, Op. 99 no. 2 ("StŸcklein II") (one notehead for normal 32nd and
		triplet 8th => 1/3 = 3/8 & 2/3 = 5/8; occurs 4 times) [contrib. by Hook]
	Scriabin: Prelude in C, Op. 11 no. 1 (Muzyka (State Music Pub. House) ed.)
		(various conflicts??) [contrib. by Hook]
	Scriabin: Sonata no. 7 (Muzyka (State Music Pub. House) ed., Dover reprint), p. 148
		(one notehead for normal 8th and triplet 8th ending at the same time)

g. Half notehead with beam(s):
	Brahms: Rhapsody in G minor, Op. 79 no. 1 (Peters/Sauer, International eds.) (dotted-half
		head; occurs many times)
	Chopin: Prelude in Db, Op. 28 no. 15 (Paderewski, Universal, Br+H eds.) (half head and
		dotted-half head in beamed group of 8th notes; each occurs several times, sometimes
		in the middle of the group)
	Debussy: Arabesque no. 1 (Durand ed.) (double-stemmed half head in beamed group of 8th
		notes; occurs many times)
 	FaurŽ: Dolly Suite, Op. 56 (Dover reprint of Hamelle et Cie ed.), Berceuse, Seconda part
		(half head beamed to 8th; occurs many times)

h. Non-aligned barlines (these seem to be less common than one would expect; but they're surely
		more common than these few examples suggest, even up to 1935!) (B&I 7.5):
	Bartok: String Quartet #2 (Boosey & Hawkes ed.), I, rehearsal mark 8 (polymeter: 6/8 vs.
	(3+4)/8, 9/8, etc. with 8th = 8th)
	Chopin: "Minute" Waltz, Op. 64 no. 1 (Paderewski ed.), last 3 measures (barlines omitted on
		one staff)
	Chopin: Ballade no. 1 in g, Op. 23 (Br+H ed.), last page (barlines omitted on one staff)
	Ives: The Unanswered Question (1908; Southern Music)
	Ives: Three Places in New England (1903-14; Mercury ed.), II. Putnam's Camp (polymeter)
	Ives: Symphony no. 4, I, p. 3 (1910-16) (polymeter)
	Mozart: Don Giovanni (1787; all eds.), Act I Finale (no. 13; ballroom scene) (polymeter:
		3/8, 2/4, 3/4. 2/4 quarter = 3/4 quarter; 3/8 dotted quarter = 2/4 or 3/4 quarter)
	*Wagner: Gotterdammerung (Eulenberg), end of Act III, pp. 1337-57 (3 mm. of 6/8 vs. one
		of 3/2; 2 mm. of 6/8 vs. one of 2/2)

i. Multibar rest not in a part of an ensemble piece:
	Beethoven: Piano Sonata no. 31, Op. 110, II (in music for a solo instrument)
	Kodaly: Hary Janos Suite (Universal ed.), I, m. 75 (in the score of an ensemble piece)
	Ravel: Gaspard de la Nuit (Durand ed.), Scarbo, mm. 30-31 (in music for a solo instrument)

j. Grace-note phenomena:
	Chopin: Nocturne, Op. 15 no. 2, mm.8 & 9 (ordinary notehead with one stem and beam to an
		ordinary note, and one stem and beam to grace -- not just small -- notes)
	Debussy: Estampes: Jardins sous la pluie (Durand, 1903) (series of 9 small-note 32nds
		marked "9": judging from the rhythmic context, apparently grace notes) (B&I 11.14)
	Debussy: Preludes, Book 1: La Puerta del Vino; La Terrasse Des Audiences Du Clair De Lune
		(Muzyka (State Music Pub. House)/Sorokin ed.) (normal notes beamed to grace notes)
	Ives: from "Lincoln, the Great Commoner", no. 11 in 114 Songs (grace-note beam whose last
		note is a normal note in the middle of a beamed group)
	Rachmaninoff: Prelude, Op. 32 no. 3 (Muzgiz ed.), mm. 23 & 24 (series of 5 small-note eighths
		marked "5": judging from the rhythmic context, apparently grace notes) (B&I 11.14)
k. Other:
	Tchaikovsky: Piano Concerto no. 1 (Billaudot), I, p. 25 (measure of two duplet quarters
		followed by three triplet quarters in C time)

	Chopin: Nocturne, Op. 27 no. 2 (6:4 groupets in 6/8 meter) [??IS THIS INTERESTING ENOUGH
	Chopin: Prelude in Db, Op. 28 no. 15  (Paderewski, Universal, Br+H eds.) (7 8ths in the time
		of 2)
	F. Couperin: Passacaille from Pieces de Clavecin, Ordre VIII (pub. 1717) (numerous groups of
		three 128ths that should be triplet 32nds, and of two 64ths that should be 32nds)

	Bach: Brandenburg Concerto no. 4, III, solo violin ("tuplets" that are unambiguous but
		seem pointless because they're just ordinary notes: 8 16th notes in the time of 8, and
		16 16th notes in the time of 16)

	Bach: Jesu, Joy of Man's Desiring, arr. for piano by Myra Hess (Oxford) (single notes --
		not part of a chord -- on "wrong" side of stem, to show three voices on one staff)

	Elgar: Enigma Variations, no. 7 (Eulenberg ed.): time signature of "1", i.e., no denominator
		(NB: fairly common in early music, even Bach, but extremely rare since) (B&I 10.2)

	Hummel: Prelude in B major, Op. 67 no. 1 (Universal/Dover ed.) (tuplet of 8 16th notes in an
		amount of time that's part of a cadenza-like passage and impossible to define)
	Schumann: Carnaval, Op. 9 (Kalmus/Clara Schumann ed. & an an unidentified edition on the Web,
		http://imslp.org/wiki/File:Schumann_-_Carnaval,_Op_9.pdf), no. 6 (Florestan), last 4 mm.
		(change of meter without notice: the movement has a time signature of 3/4, and it really
		is in 3/4 until the last 4 measures, each of which has a duration of 2/4)

	Schumann: Carnaval, Op. 9 (Dover ed.), no. 1, mm ??, right hand: "hugely ambiguous" double-
		stemmed double-dotted quarters [contrib. by Cuthbert]

(5) Miscellaneous.

a. Simultaneous notes in two clefs on one staff (B&I 8.4)**:
	Brahms: Piano Sonata, Op. 5 (Br+H ed.), I [contrib. by Auer]
	Debussy: Preludes, Book 1: La Cathedrale Engloutie (Durand ed., 1910); occurs 3 times
	Debussy: Preludes, Book 1: Voiles (State Music Pub. House/Sorokin ed., Dover reprint);
		occurs 3 times (with clef in mid-air in front of note on ledger lines)
	*Dvorak: Humoresque in F Major, Op. 101 no. 4 (Simrock ed., Dover reprint), near end
		[contrib. by Hook]
	Poulenc: Concert Champetre (orch. reduction, Editions Salabert, 1929), I, p.24 (in an
		extended passage)
	Puccini: Turandot (piano/vocal score, Ricordi), pp. 374, 375, 376, & 377
	Rachmaninoff: Prelude, Op. 23 no. 1, 2, 3, 7, 8 (International) (overlapping notes in two
		clefs on one staff)
	Rachmaninoff: Prelude, Op. 23 no. 3 (International ed.)
	Ravel: Gaspard de la Nuit (Durand ed.), Scarbo, several places (note(s) on downbeat in
		one clef, clef change, then note(s) that must also be on the downbeat)
	Szymanowski: Piesni Muezina Szalonego, Op. 42 (1918) (ex. in Hewlett & Selfridge-Field,
		1994), no. 4 (with clef in mid-air in front of notes on ledger lines)

b. One clef for two staves:
	Pozzoli: [solfeggio book; but NB probably published after 1935, and arguably not CMN]

c. Movement starting/ending with whole measures of rests:
	*Ligeti: Lux aeterna (movement ending with 7 measures of rest) (NB: after 1935) [contrib. by Hook]
	Liszt: Mephisto Waltz no. 1 (movement starting with a measure of rest) [contrib. by Auer]
	Messiaen: Oiseaux Exotiques, last movement (NB: after 1935) (movement ending with a measure
		of rest)
	Mozart: Piano Sonata in G, K. 283, last movement (movement ending with a measure of rest)

d. Non-numeric measure numbers (B&I 7.12) or page numbers:
	Schubert: Impromptu, Op. 142 #1 (non-numeric measure numbers. The last measure before the two
		one-measure endings of a repeated section is 81; in one edition, the 1st ending is
		labelled "81a", and in another, the 2nd ending is labelled "82b"; in both, the measure
		after the endings is 83.)
	R. Strauss: Ariadne auf Naxos (Fuerstner/Dover ed., 1916), pp. 88a, 88b, 88c (non-numeric
		page numbers. The next page, numbered 89, starts a new scene)
	Puccini: La fanciulla del West, vocal score (Well-Tempered Press), pp. 190a-190b
		(non-numeric page numbers)

e. Non-standard key signatures (B&I 9.1):
	Bach: Well-Tempered Clavier, Book I, Prelude in G (sharps or flats not in their usual octaves)
	Bartok: Mikrokosmos, nos. 76, 79, 82, 93 (sharps or flats not in their usual octaves)
	Bartok: Mikrokosmos, no. 99 (non-standard key signatures: unusual combinations of sharps
		or flats)
f. Tied notes with spelling change (B&I 17.1):
	Bartok: String Quartet #2 (Boosey & Hawkes ed.), I, mm. 3-4, violin 1 (B-flat tied to A-sharp)
		(in B & M, 1948).
	Beethoven: Piano Sonata in e (Dover/Schenker, *Henle, Ricordi/Casella eds.), Op. 90, II,
		m. 216 (tied notes in dyad with spelling change on each) [contrib. by Teodoru]. NB:
		in the Casella edition, this occurs a beat later than in the Schenker & Henle,
		probably to avoid a diminished 2nd in another voice. But how did Beethoven write it?
	Chopin: Sonata no. 3, Op. 58 (Mikuli, Paderewski eds.), mm. 95ff [contrib. by Hook]
	Chopin: Scherzo no. 4 in E, Op. 54 (Br+H ed.), m. ??  (chord of D#, Fx, C#, D# tied across key
		signature change to Eb, G, Db, Eb) [contrib. by Bode]
	FaurŽ: Dolly Suite, Op. 56 (Dover reprint of Hamelle et Cie ed.), III (Le jardin de Dolly),
		Seconda, mm. 14-15 (C-flat tied across barline to B)
	FaurŽ: song cycle "La Chanson d'Eve" (Heugel & Co. ed., Paris, 1907), Song 1, mm. 94-95
		(C-flat tied to B-natural, in piano RH) [contrib. by Hook]
	FaurŽ: " " , Song 10, m. 15 (C-flat tied to B-natural, in piano RH) [contrib. by Hook]
	*Franck: Piano Quintet in F Minor (Peters ed.), I, about midway between rehearsal letters K
		& L, piano (the left hand has octave D-sharp tied across a barline to octave E-flat. (At
		the same time, the cello has E-flat tied to E-flat.)) [contrib. by Hook]
	Ravel: String Quartet (International ed.), III, rehearsal mark K, viola (Gb tied across
		barline to F#)
	Ravel: Gaspard de la Nuit (Durand/Dover ed.), II (Le Gibet), mm. 27-31  (a series of A-sharp
		octaves is followed by one of B-flat octaves, then back to A-sharps, then to B-flats; the
		last of the 1st three series is tied to the first of the next series)
	Strauss: Also Sprach Zarathustra, in the fugue section titled "Von der Wissenschaft" (occurs
		at least four times at different pitch levels) [contrib. by Hook]

g. Multiply-augmented or -diminished melodic intervals:
	Brahms: Clarinet Sonata in E-flat, Op. 120, No. 2 (Wiener Urtext ed.), m. 97: doubly augmented
		unison (bass line moves directly from F-sharp to F-flat) [contrib. by Hook]
	FaurŽ: song cycle "La Chanson d'Eve" (Heugel & Co. ed., Paris, 1907), Song 1, mm. ??:
		doubly diminished third (Cx to Eb) in LH in second system [contrib. by Hook]
	" Song 8, mm. 15-16: doubly augmented unison (G# to Gb) in first measure, RH [contrib. by Hook]

h. Other:	
	Chopin: Nocturne, Op. 15 no. 1 (Durand ed./Debussy), near end (grace note on grace note) (B&I 5.36)
	Mendelssohn: Spring Song, no. 30 of Songs without Words (?? ed.), m. ?? (grace note on grace note)
			(B&I 5.36)
	Tchaikovsky: Piano Concerto no. 1 (Eulenberg, Billaudot eds.; Schirmer/Joseffy 2-piano
		reduction), I, m. 6 - at least 14 (simultaneous 8va and non-8va notes on one staff)
	Ravel: Gaspard de la Nuit (Durand ed.), Scarbo, last page (one 8va sign for both staves)
	Haydn: "Farewell" Symphony, IV, Coda (heavy double bars in some staves, single bars in others)

	Strauss: Also Sprach Zarathustra (Eulenberg ed.) (system spanning two pages, sideways)
	Wagner: Die Meistersinger (old Schott miniature score) (system spanning two pages, sideways)
	Nancarrow: Study no. 35 for Player Piano (metronome marks qtr = 283-1/3, 141-2/3, etc.)
		[NB: this is relatively recent music, and probably not from a respected publisher!]
	Schumann: "Susser Freund, du blickest" in Frauenliebe und Leben, Op. 42 (grace chord with
		arpeggio sign) (B&I 5.28)
	Tchaikovsky: Symphony no. 2 (1873; Eulenberg ed.), I - II, timpani (invisible key signature,
		i.e., flats indicated by an accord only (in IV and perhaps III, accidentals appear on
		flatted notes); this is common in classical-period music, but not Tchaikovsky! B&I 3.1)

** My dissertation refers to "two clefs simultaneously active on one staff" instead of
"simultaneous notes in two clefs on one staff", but the former concept also includes the
much more common and _usually_ less interesting case of a long note written in one clef
continuing to sound as shorter notes, written on the same staff in a different clef, begin.
If a 2/4 measure on one staff begins in bass clef, with a half note in one voice and a
quarter rest in another, then changes to treble clef for some notes in the second voice,
that's not a big deal. But if the half note is replaced with two tied quarters, and the
second quarter appears in the same horizontal position as the first, it's much harder to
explain with conventional rules.

On the other hand, the "clef in mid-air" of La Danse de Puck and Voiles really _is_ "two clefs
simultaneously active" and not "simultaneous notes in two clefs"! It's interesting to
compare this bit of notation with a device that is not too unusual in cello music. E.g., in
the Kodaly Sonata for Solo Cello, Op. 8, there are several instances of a low note
appearing, preceded by a bass clef, on a very short staff segment below the (main) staff.
[contrib. by Loewenheim] This device is far easier to explain in terms of conventional
notation, but it does not save as much vertical space.


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Byrd, Donald (1984). Music Notation by Computer (doctoral dissertation, Computer Science
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Byrd, Donald (2012). Extremes of Conventional Music Notation. Retrieved June 20, 2012,
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