1          Our Grouping of Publications on Musical Notation
2          Short Survey on the Non-Encyclopedic Works
2.1          Traditional Notation and Computers
2.2          Extended and Advanced Contemporary Notation
3          Synopsis of the Major Encyclopedias on Traditional Music Notation
3.1          The Books Considered
3.2          Publications Not (Yet) Considered Herein
3.3          Structure of the Tables
3.4          Table of General Topics
3.5          Table of Topics Specific for Families of Instruments or Types of Notation
4          References

^{^Inh} 1 Our Grouping of Publications on Musical Notation

This article gives a comparison of works on traditional western musical notation.
This method of writing down music is also called "common Western notation", "conventional Western notation", "CWN" / "bar based notation" [German "taktbasierte Notation"], "orthochronic notation" (Chailley, according to [gieseking, , pg. 20]). It had been started in Western Europe in the seventeenth century, by enhancing the medieval "mensural notation" by bar lines and ties ([readNotation, , pgs. 110,183] )
(Up to then, the only means for calculating durations had been divisions, the nesting of which had reached an incredible level of complexity. The new "tie" symbol introduced the operation of free addition, allowing to notate every thinkable duration. Thus bar lines became necessary as the new fundamental orientation mark in the now possible sequences of "arbitrarily long" note events.)

Today CWN includes all those extensions developed during the last centuries, in classical and romantic Western composition, up to contemporary avantgarde and electro-acoustic music.
For sake of shortness, this whole area will simply be called "music notation" in the following.

Here we look at published books which want to pre-scribe the rules for correct music notation, partly restricted to hand-writing, partly to engraving, but in most cases related to both.

We found the following grouping of the related publications sensible:

1. Works with encyclopedic claim, trying to cover all possible questions on notation in a systematic way.
   Since they all claim to treat the totatlity of all relevant questions, ideally, their "tables of contents" could be expected to be mere mutual permutations, and the answers they give to be widely identical. So these works are natural candidates for a synopsis, and that is the main contents of this article.
2. Books dealing with computer-based solutions of notational problems.
3. Books presenting extensions and alternatives to traditional notation.
4. Books on the fundamental philosophy of notation.

The first group is, as said, the main topic of this article.
But before we come to this central section, some books of the groups 2 and 3 will be presented briefly.
Group 4, the fundamental philosophy of notation, is spared for a dedicated later article.

^{^Inh} 2 Short Survey on the Non-Encyclopedic Works

^{^Inh} 2.1 Traditional Notation and Computers

Astonishingly few books deal with computer-based solutions of notational problems.
We found [byrd] , [gieseking] and [grover] .

(Please note that we treat [wanske] as an encyclopedic work, but not in this group, because the computer related parts of this valuable book are almost completely out-dated.)

The dissertation "Music Notation by Computer by Donald Alvin Byrd, [byrd], describes the author's computer notation system "SMUT", into which he invested fifteen years of research and programming labour. It had been part of a collection of software used by his university, but probably has vanished nowadays. This would be a pity, because the output examples look very convinving.
The book as such is valuable for the introduction, which tries the hard job of explaining musical notation to non-musicians, and which contains carefully selected examples which prove, that "FAHQMN", "fully automatic high quality music notation" can never be achieved.
In the algorithmic part esp. the treatment of "correct notation of rhythms w.r.t. a metric" is of general value. The work [gieseking] refers to this part, and both works will be the basis for our own contribution to this topic in senza tempo 2012 10 27 00 --- Metrisch korrekte Notation von Rhythmen,

The title of "A Computer Oriented Description of Music Notation" by John Grover [grover] does promise much more than the contents keep: It is a technical report which presents two algorithms as solutions to two very specific problems: (1) the placement of noteheads and augmentation dots which belong to multi-note chords, in the case of two-stemmed notation in one single stave, and (2) the arrangement of accidentals preceding such chords.
The work comes in three volumes, together about 280 pages, and is, in its limited scope, a very valuable contribution.
(We wonder whether these solutions have been implemented in any commercial product ?-)

The work of Gieseking is in German language, it deals, as it title says, with automated generation of music notation for interactive educational computer programs.

Both parts of the book are valuable:
First there is an introductory part about the historic evolution of music printing, type setting and engraving, and on the most successful computer programs in this field.

The special part is much larger and presents algorithms for the most basic problems:

1. arrangement of multi-note chords in double-stemmed writing,
2. positioning of accidentals and duration dots,
3. break-down of note values ...
4. and of beams according to meters,
5. line breaking and horizontal spacing,
6. slur construction.

For the line break problem the author refers a standard solution (Hegazy and Gourlay, 1987), and for the rhythmic notation w.r.t. a metric he continues the work of [byrd] . The other algorithms are very lean and mostly elegant original contributions.

^{^Inh} 2.2 Extended and Advanced Contemporary Notation

The books in this group are about alternatives and extensions to musical notation.

"Pictographic Score Notation" by Gardner Read [readPicto] restricts itself nearly completely to symbols for instruments, and plans for the placement of instruments. It is not so very exciting.

"20th-century Microtonal Notation" [readMicro] by the same author: The title is misleading, the book also speaks about the origins of micro tonal music in the seventeenths century, and it is not only about notation, but touches also the fundamentals of micro tonal composition, calculation, physiologics, reception, etc. It seems a valuable book for experts in this area, -- we are not!

"Source Book of Proposed Music Notation Reforms" by the same author is an overwhelming compilation of threehundred-ninety-one(391) proposals for new notational systems from the last threehundred years.
The deeper reasons, why hardly one of them survived, and why the conventional system is, despite its deficiencies, still unbeatable, is discussed thoroughly in the introductory chapters, and in the literature quoted therein.
Then the proposals are presented in short, sorted by basic strategy, and chronologically.
It is funny reading!
But it is also relevant for serious research on notation: Many of the system, in spite of having failed historically, offer interesting insight into the structure of notation in general, and even into the qualities of the critizised conventional system they want to replace.

(One really annoying aspect coming with most of these "improvements" and with their presentation by Mr. Read is discussed separately in senza tempo 20120822 00 , in German language.)

An important collection is "Darmstädter Beiträge zur Neuen Musik, Volume IX, Notation", [darmstadt65] .
With [dahlhaus_notenschrift] and [ligeti_notation] it contains two fundamental articles about the philosophy of notation, followed by articles by famous performers on notation issues special for their instrument (string, piano, percussion).

^{^Inh} 3 Synopsis of the Major Encyclopedias on Traditional Music Notation

^{^Inh} 3.1 The Books Considered

Main subject of this article are the books on CWN which try to be comprehensive, i.e. to cover all aspects of notation. The works considered here, in chronological order, are [readNotation] , [stone] , [wanske] , [vinci] and [gould] . They all claim to be encyclopedic! The newest of them even calls itself "the definitive guide" in its title!

Most of them consist of a first general part, and a second with rules specific for certain families of instruments, incl. the human voice and electro-acoustics, or certain ensembles, etc.

Some, but not all of them operate with real examples from musical history and existing engravings.

Some of them appeared in recent times, some are already forty years old.
All of them are nice to read, but in the end, all these books will (mostly) tell you the same! This motivated us to write this synopsis article, comparing the major works in this area.

There are only a few questions for which different books give contradictory rules. One can assume that these questions are the real interesting ones !-)
Astonishingly, there are still relevant details covered only by one of them! So far with "definitive" and "encyclopedic" !

As you can see in the bibliograhy, all books are in the English language, except [vinci] , which we read in a German translation, and [wanske] , which is written in German and has (as far as we know) never been translated.

Here a short characterization of these works, in reverse historical order, as they appear in the synopsis table:

Most recent is the book by Gould [gould] . It has more than sixhundred pages, treating engraving of music. The first half deals with notation in general. The second part treats rules and symbols special for different families of instruments.

In both parts, most rules are about the optical appearance of the notation text. But with many rules, the author gives reasons for the rules, nearly always coming out of execution pragmatics. Partly, these reasons reach into areas which could be called semantics of notation.

The work contains also a chapter dedicated to electro-acoustic music. Since the other works are significantly older, and the last decades brought revolutionary changes, comparison is not sensible w.r.t this special topic.

The large chapter on vocal text presentation (pg. 437 pp.) is unique and left out in this article, esp. because it is limited to English lyrics (which no-one really wants to hear outside pop music !-)

The book by Vinci [vinci] is comparatively small, also quite recent, and focused on hand-writing of music. Nevertheless, the topics (and even partly their sequential order) are the same as in the much larger, preceding one.

The work by Wanske [wanske] again treats engraving. It is a historic attempt to prepare for a note engraving computer software. While the technological aspects are totally outdated, the book is still relevant in different respects:
First, the author has led interviews with engravers from big publishing companies, to collect, publish and thus preserve their professional knowledge.
Second, aiming at a software solution, the author tries a first systematic approach:
(a) the basic symbols are grouped according to different aspects (internal graphical syntax, constant vs. variable geometry, category w.r.t. meaning).
(b) the rules for combining these basic symbols are also tried to systematise by introducing a notion of "chaining" [dt. "Verkettung"]. This is without any doubt an adequate approach.
Thirdly, the author gives mathematical models for selected details, like matrices and derivation rules for basic symbols, possible relations of note heads, calculation of beam angle, calculation of slur contour, etc.

Therefore this book is still a paradigmatic approach to the very complex problem of musical notation.
This book is not organized along the different parameters of music, like most others, and like our synopsis table, but the logic of combination and position calculation. Therefore the page references in the table below appear rather scattered.

The book by Stone [stone] is special because it explicitly covers hand-writing and engraving, and lists differences explicitly.
It also consists of a first general part, and a second part specific to families of instruments. Its main focus is on modern techniques, but of course the basic is still CWN, as defined above.
The structure is confusing: The second level are chapters, related to major fields like "Pitch", "Rhythm", "Scores". But the organization one level below follows the names of concepts in alphabetical order.

Very welcome and unique are some sections with more fundamental discussions from strategical and philosophical view point: About the different possible relations of new music's time organization and traditional metric notation (pg. 81 pp.), about different strategies for using beaming (pg. 114), etc.

The chapter on the harp is much more detailed than the rest of the book, it can serve as a hand-book for modern harp playing techniques! Since it is unique, we have ignored it for the purpose of this synopsis.
The same applies to the (valuable) chapter on keyboard reduction [dt. Klavierauszug].

The work by Read [readNotation] starts with a short survey on the history of notation, but in its main part again tries to establish a systematic linear order.
It covers hand-writing (as opposed to the rules for engraving) in a dedicated chapter.
It is the only one of all the books which comes with practical notation excercises at the end of each chapter.

The author is more a composer than a philosopher or mathematician. See e.g. the remark about the graphic appearance of second intervals in a chord on pg. 71:
"Observe that the "adjacent" tone (which creates the interval of the second) is placed to the right of the chord when ..."
This is of course pure non-sense! How can one single note ever "create an interval"?

In spite of flaws like this, it is a very valuable and famous book and covers many aspects which got lost by its successors, as it is clearly shown by the lines in the following tables which have only one single entry!

^{^Inh} 3.2 Publications Not (Yet) Considered Herein

The author of [wanske] frequently refers to [hader] as an important preceding standard publication.
In a similar way [gould] and [stone] frequently refer to [ross] .

We have not yet been able to get hold of these two books, but perhaps they are so good that they will require a future extension of this article.

The book [heussenstamm] by George Heussenstamm is lovely to read! He talks exclusively about calligraphic hand-writing and extensively about choosing the right ink and the fitting eraser.
In our context the diagrams are valuable which give a survey over many different topics at one glance, very compressed in space.

^{^Inh} 3.3 Structure of the Tables

The following tables try to list fine-granular questions/topics, and refer to the pages where these are answered/treated in the different books. As a reference we give the number of the page where the explanation starts. This number refers to the edition from the bibliographic list below, but different editions should not vary suprisingly.

The list basically follows the sequential arrangement of topics from [gould] , because it is the latest publication with the most differentiated structure. This inspite of some minor objections we do have (e.g. the topics concerning the general score layout are rather late, "freedom and choice" is extracted from the general discussion of time and tempo, some topics are doubled at different places, and not always in a consistent way.). Nevertheless we decided that it should not be the function of such a synopsis article to establish a new and different linear view. Some minor of these dislocations have been silently corrected, partly by doubling, as can be seen easily in the first column of page numbers in the tables below.

Indeed, a really adequate index would have to be multi-dimensional, because most questions arise from a combination of different topics, eg. accidentals with horizontal alignment, overlapping parts with articulation, tuplets with changing metrics, etc.
To create such an indexing system would require substantial effort, because a simple two-dimensional matrix does not suffice:

First, the conflicting entities may reside in very different realms: e.g. concrete graphems with concrete geometries may be combined or collide with semantic concepts, valid only in certain periods of style and history (like in the rule "accidentals for two notes in a chord in different octaves but with the same note name [dt. Stammton] must align.").

Second, in many cases the combination of more than just two(>2) concepts (may they be graphical, semantical, ergonimical etc.) create the interesting question ("tied notes with accidentals together with clef change and line break in the middle of the bar").

Third, the meta-classification of the kinds of questions and rules has significant impact on the meta-rules for combining and priorizing the rules. Questions like "How are the graphems arranged geometrically to realize this specific notation variant?" and "Is it advisable to choose this notation variant for an oboist?" are of very different nature! The questions of these various classes are considered or not left out in the various books following very different strategies!

So the problem is in deed too complicated to be solved by simple two-dimensional tables, as we present herein. Nevertheless, these tables may serve well two purposes:
First, they may be valuable indexes for finding the answers for given questions when using one or more of these books, and
secondly, they show at one glance gaps and special merits.

So for every question involving more than one concept (and that will be the majority) the reader has to search at all the different places.

The wording and spelling of notions, questions and topics have been taken from the book coming first in the list. Eg., [gould] says "stave" and "staves", not "staff", and so we overtook this spelling. [gould] again says "ledger lines", vs. [stone] "leger lines", [gould] says "tails", vs.[readNotation] "flags".

More substantial, [gould] takes the word "bar" for the time duration between two "bar lines" (c.f. pg. 41), while [readNotation] insists that the only correct word for this time section is "measure", while "bar" is just a synonym for "bar line" (pg. 184).

But with the naming of duration values we insist on the logical way, using whole, half and quarter, and do not follow [gould] with "semi-quaver", "crotchet" and all this medieval crypticism.

We tried to cover the first and general parts of all books completely, while aiming at a sensible level of granularity, having in mind that the "problem of an adequate index", as sketched above, cannot be solved in a short article like this.
Contrarily, in the second, specific parts we were very selective and considered only the topics of general interest. We completely left out the chapters on piano reduction and on lyrics in vocal music.

^{^Inh} 3.4 Table of General Topics

This first table refers to the general topics.
We tried to be exhaustive, with a reasonable level of granularity.

^{^Inh} 3.5 Table of Topics Specific for Families of Instruments or Types of Notation

The following table refers to the topics specific for certain families of instruments or types of notation documents. Again, we follow the order of [gould] .

In contrast to the class of general topics in the preceding section, here we do not include the topics which are too specific to be of general interest (e.g. different stopping techniques for brass or different ways of knocking on the corpus of a harp !-). We collect only those topics which are also of general interest, which is at about the half of all material.

^{^Inh} 4 References

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