The preceding post examined the first system put forward in the USA for writing music without the graphic complexity of conventional staff notation, published in 1785. It used letters numbers and a few common typographical symbols. The present post takes a look at a method with the same purpose, based solely on the numerical representation of notes. It was published in London in 1638, with a claim of having been devised ca. 20 years earlier.
William Braythwait presented it in a compendium of 27 sacred pieces he culled from a larger collection published by Georg Victorinus in Munich, in 1622 (1st ed. 1616), both titled Siren coelestis (Celestial Siren). The upper half of the earlier title page is reproduced on that of the compendium, which is advertised further as “the easiest method of teaching and learning music by far.” (All translations in this post are my own.)
Braythwait explained this method and the rationale behind it in a narrative adjunct to the music, adding further detail in 1639 (also changing the spelling of his name to Braithwaite). He represented the seven notes of a diatonic scale with the Arabic numerals 1–7 and the octave with diacritical marks. This was also a basic feature of an earlier Spanish tablature that first appeared in a text titled Libro de cifra nueva para tecla, harpa, y vihuela (Book of new numbers for keyboard, harp and vihuela) published by Venegas de Henestrosa, in Madrid, in 1557 (to be discussed further in a separate post).
It is not know if Braithwaite was familiar with the Spanish approach but he appears to have been firmly on his own territory with an idiosyncratic scheme for indicating the duration of notes with font variation. He also permitted the alternate use of Roman numerals and articulated the far-reaching purpose of ensuring that:
…melodies and songs conceived in their native land can be transmitted to other peoples. For to what nation and race are these [numerical] symbols not obvious and familiar when used for notes?
Braithwaite claimed additional benefits to a hyperbolical extent that was seldom outdone by similarly inclined authors of other notation schemes. The hobbyhorse example on this blog thus far has been a system devised over two and a half centuries later by C. F. Zimmermann. He also used the Arabic numerals 1 through 7 to represent the notes in a C major diatonic scale, and differentiated between those notes and the chromatic semitones above them by printing the same number in a hollow or otherwise lighter font. (Autoharps and other fretless zithers marked with this notation are still in circulation and use.)
Braithwaite embedded the explanation for his system in transcriptions of the upper and lower voices of settings taken from the Victorinus collection (online here). The original part books include staff notation with text underlay except for the lowest one, which presents an untexted single figured bass line for an organ. In his compendium (online here), Braithwaite replaced all staff notation with his own unlined numerical notation.
It includes elements not detailed in the text. However, most can be clarified by comparison with the original 1622 edition (an option presumably unavailable to most contemporary readers of the compendium). The terse introduction to the first of the tutorial statements is quoted above and the second presents it as:
A new way of teaching and learning old (if I may say so) music; its novelty will be surpassed by ease, its ease by delight, that delight by usefulness; conceived and invented twenty years ago (thanks to God) by William Braithwaite; an Englishman, a servant of Jesus Christ, formerly a fellow of St. John’s College, Cambridge.
His lengthier presentation of the rationale behind the method is appended to this post. Its core typographic components are detailed in a table:
The note names that are its point of departure appear underneath the columns of numbers that replace them. Each name starts with a letter from A to G, followed by the re-mi-fa-sol-la syllables familiar from modern solfège, and “ut” is synonymous with the “do” that subsequently replaced it. There was as yet no seventh syllable in that sequence (later provided by an ever more widespread “si” that finally changed to “ti” in anglophone usage).
Braithwaite divided the table into two parts. The upper half shows an untransposed regular musical scale for use in the “hard” system — cantus durus. The lower half shows a transposed musical scale for cantus mollis (the “soft” system) formed in staff notation by the addition of a key signature with a single flat sign. In addition to indicating transposition in the current sense of the term, this also transformed the hard B —♮— to a soft B —♭.
The musical note or sound C fa ut of the regular system (in ordinary discourse about singing in the hard mode [cantu duro] for ut or fa, is pronounced “one” in English and written with musical arithmetic characters as 1; D sol re is pronounced “Two” and is likewise notated 2 right on the same line as just started; E la mi is heard as “Three” and thus signed 3; F fa ut “Fower”, similarly numbered and signed 4; G sol re sounds “Five” and is notated 5; A la mi re “Sax”, in the Scottish dialect, and written 6; b fa b mi “Siven” as pronounced in the Palatine dialect, is drawn 7. Again c sol fa ut [starting the next octave] is pronounced “one” and written `1 with a straight acute accent…
Transposed to F fa ut, or (as others please) sung in the soft mode [cantu molli], the musical syllable is pronounced “one” and drawn 1, as before; in G sol re the note will be called “two” and will be formed 2; in a la mi re “three” 3; in b fa b mi “fower” 4; in cc sol fa “five” 5; in d la sol re “sax” 6; in e la mi “siven” 7; in f fa ut `1…
The regular middle octave (in mediis) begins with what we often call “the C below middle C” and abbreviate in standard pitch notation as C3. The next higher octave is indicated by an accent drawn upward from its point of attachment to the base numeral, angled either to the left or the right. The curved accents that mark the octave beyond that also ascend in either direction from the point of attachment. The octave below the middle octave is similarly indicated with a descending accent.
The duration of a note is shown by font variation. Whole notes are set in a solid font. The next two longer values (double whole note and longa) are indicated by flourishes extending from the number on the side opposite any accent. The longest value (maxima) is set in a hollow font. The four shorter values (half, quarter, eighth, sixteenth) are marked by broken fonts. The penultimate column in the top half of the table shows the duration in staff notation with the corresponding rests in the final column. A dot following a number or rest increases its nominal duration by half.
Among the unexplained details in Braithwaite’s transcriptions are the marking of a sharp with an a before the number and a flat by an o, but this was a common notational convention. The time signature appears as an inverted number at the start of the first line. Here is the beginning of the upper voice in the second piece, followed by the 1622 staff notation. There is no key signature but it is in G major, with each sharp written in place. This also pertains to the bass voice, seen in this post’s banner image.
Combining the two representations of the first phrase of the melody in modern staff notation gives:
The regular scale in Braithwaite’s table correlates to present day C major and is characterized by the lack of accidentals. The G major scale in the preceding piece is not accounted for separately in Braithwaite’s table. However, its use of a hard B makes it a hard system, and therefore follows the upper half of the table. The number 1 designates the C in it, and its keynote G is a 5.
The transposed scale in the lower half of the table is for soft systems, characterized by a B flat in the key signature. The numerical sequence then shifts to begin on F, representing it with 1 and C with 5. The practical application of this can be seen by comparing, as before, the first of Braithwaite’s transcriptions with the original staff notation. It is in the key of F major and the requisite B flat also appears at the outset of the bass voice.
Combining the two and adding the bass line as it appears in both sources:
The reasons for the different treatments of hard and soft scales are inherent in what by Braithwaite’s day had become a complex and inconsistent theory of modes and scales. The upshot for present purposes is that his system pointed forward to what was to become an established (and contentious) dichotomy between “fixed” and “moveable” references to the starting point of a scale. With the first, the number 1 or syllable do (initially ut) is always C regardless of the key the piece is in. With the second, 1 or do designates the keynote of the piece.
Here is William Braithwaite’s statement of the rationale behind his method:
To the patrons, supporters, and admirers of music
W.B: I wish you ever manner of joy.
Music is the relish and relief of all knowledge, study, and action, both divine and human. It has long been encumbered with superfluities for mortal man, weighed down by more than twenty-two hexachords, mutations, and substitutions of musical voices; bearing the weight of regular and transposed systems, of useless multiple divisions of tempo, descriptors, ligatures, and further baggage; parallel lines, spaces, and other swollen impediments.
I have done what I can to relieve the student of music who is gasping for air under this burden and prepared this compendium. Through it, the mysteries of the Greeks and Romans, and perhaps even the Hebrews, may be understood more certainly, more quickly, and lead more deeply into the theory and practice of music. Hereby, musical intervals and their rationale are clearly understood and the manifold variety of systems and scales is reduced to a single essence. This permits reference to the mode of any song (since modes are not defined by keys but by voices) that any student of music can comprehend, and musical instruments are more efficiently come to terms with and played.
If alphabetical descriptors are fashioned in accordance with this musical arithmetic, the duration and rhythm of the musical tones will be understood simultaneously with the character of the piece, also qualitatively and quantitatively clarifying the duration and pitch of any musical sound. It additionally leaves the semitone between mi and fa undisturbed, around which the ancients said that all music revolves.
In this way the entirety of music can be presented in lines of numbers and spaces, to the eye, to the ear, to the touch. The names of notes appear at a first glance in the most rapid movement, without further discussion. By this, monodic melodies and harmonies, (I could almost say) all melodies and songs conceived in their native land can be transmitted to other peoples. For to what nation and race are these symbols not obvious and familiar when used for notes? They are very well known even to farmers and shepherds, and can therefore be called universal elements of music.
Finally, using a certain admirable compendium, anyone born to the more pleasant muses, will make greater progress in the art of melody, with much less effort (than has ever been done before). Since the advantages of this method are so many, so great, so remarkable, for whom will it not make joys more delightful? Pains lighter and shorter? A more cheerful conversation? A more pleasant life? Diseases more bearable? Even a death less bitter, if not much sweeter. I have given these few foretastes. In the meanwhile, I look forward to the liking of those who judge it candidly.