Pitch nomenclature.

The naming and definition of a particular pitch or class of note. In Western tonal music 12 classes of note are distinguished and may be further defined by their octave. The following discussion describes the systems of pitch nomenclature currently used in Western music and traces their historical development. For systems used by non-Western cultures, see Notation, §II, 2–4; see also Greece, §I, 6.

The names most commonly used today are those based on the seven notes of the octave, further modified by the addition of accidentals. In English and German practice the letters of the alphabet form the basis of the nomenclature, A–G being used in the former and A–H in the latter. In French, Italian and Spanish the names are ultimately derived from the Guidonian hexachord (see below). In German, suffixes are added to the letter to denote sharp, double sharp, flat and double flat, whereas English, French, Italian and Spanish add the usual words for sharp, flat and so on to the basic name. See Table 1.

The origins of modern pitch nomenclature lie in the scale or gamut of Guido of Arezzo (c991–2; d after 1033), which is set out conveniently in a diagram in the first lesson of Thomas Morley’s Plaine and Easie Introduction to Practicall Musicke of 1597 (fig.1; see also Hexachord; Solmization). In this system notes of different octaves are in many cases distinguished by different names: for example D sol re and d la sol re. This terminology occurs not only in musical writings but (in the 17th and 18th centuries) also in the writings of the ‘natural philosophers’ who were Fellows of the Royal Society, such as John Wallis and Robert Smith (iii). In it may be sought the origin of the distinctions between notes of different octaves through the use of upper- and lower-case letters, duplicated letters and so forth, which occur in later, more extended pitch nomenclatures.

In this article (and this dictionary as a whole) italic letters are used exclusively with application to pitches as shown in ex.1 line (1). Except in the discussion of other pitch nomenclatures, non-italic capital letters denote pitch classes, not specific pitches.

In Morley’s diagram the letters in the left-hand column run by octaves from A to G and from a to g, and continue from aa. In this particular diagram they differ from the letters used in later systems, which run upwards by octaves from each C; yet the terminology of the gamut is the key to such systems of nomenclature, of which the seven most generally encountered in the 20th century are shown in ex.1. (There is one partial exception to this rule of octaves starting with C, in the bass notes of line (2) of ex.1 as applied to the earlier organs.) The first two have been the most important in Britain; the last two are technical methods of designating pitches for instruments tuned in equal temperament. The figures standing above or below each C on the staves at the head of the table in ex.1 give an approximate value, in vibration cycles per second (or Hertz: Hz), for the vibration frequency corresponding to each. More exactly they are the frequencies of each C of the so-called ‘philosophical pitch’, built up by octaves from an initial frequency of 1 Hz, which makes middle C correspond to 256 Hz (see Pitch).

No attempt will be made here to catalogue all the systems of pitch nomenclature used by different writers, most of which are for specialist use or variants of established systems. The apparent confusion is clarified by some acquaintance with their history and by their relationship to the nomenclature of the gamut.

The following explanatory comments on the various schemes set out in ex.1 are numbered to correspond with the lines of the table.

(1) The pitch designation on which this is based is often called the Helmholtz system because its use by Hermann von Helmholtz in his Tonempfindungen (1863) made it familiar in Britain. As in three if not four of the systems that follow, the notes are named in octave groups extending from C to the B above. As it is the most widely used pitch nomenclature it is used throughout this dictionary when such a designation is wanted: the usage here prefers C' (etc.) to Helmholtz’s original C'.

(2) This line of ex.1 really groups together, because they are in general consistent, three more or less separate English systems.

The middle portion of the nomenclature in this line was used by Robert Smith (iii) in his Harmonics (1748). By this date a pitch classification using C, c, c', c'' and so on had come into use in England, though its use may not have been at all general. This scheme used C for the note called C fa ut in the gamut, and c for middle C, which was called c sol fa ut in the gamut. Logically there is much to be said for this system. For since very high and very low notes are the natural extremes in music there would be some advantage in taking middle C as a starting point, and using capital letters for all notes below it and lower-case for all above. On the other hand, the Helmholtz system, not used for organs in Britain, would seem to be more logical for organs, for it would be based on C as the bottom note of an 8' stop on the manuals. This indeed was its origin in Germany, as is indicated by Helmholtz. The reason why the Helmholtz designations differ from those of this English system, which had a less technical origin, is to be found in that fact.

The use of repeated letters in the left-hand part of line (2) extending downwards through three octaves from the C in the bass staff, is now commonly employed by English organ builders for specifications. Like the names C and c in the middle of the line, the capital C used here is evidently derived from the names given to C in the gamut. Interesting light is thrown on the development of the nomenclature used by English organ builders by the historical section of Hopkins’s article ‘Organ’ in the first edition of this dictionary. If two things are remembered, there is no difficulty in fixing the pitches intended by Hopkins by the designations he used or quoted. First, the number of notes in each organ stop gives a definite indication of its compass. Thus an interval of two octaves and a 5th, say from ‘fiddle G to D in alt’, the compass Hopkins gave for the Swell in the organ of St Mary Redcliffe, Bristol, 1726, would contain 32 notes (for ‘in alt’, see below). Secondly, an open pipe of 8' nominal length would sound CC, one of 16' nominal length would sound CCC, and one of 12' nominal length would sound FFF a 4th higher.

The earliest English organ specification recorded by Hopkins is that for a ‘payer of organs’ for the parish ‘of Alhalowe, Barking, next ye Tower of London’, 1519. The compass was to be from ‘dowble Ce fa ut’, which shows why CC would be two leger lines below the bass staff. From the specifications as a whole it is clear that, for some three centuries, the sequence in this organ nomenclature was CC, DD, EE, FF, G, A, B, C and so on, and in it the point of change from capital to lower-case letters as shown in Morley’s diagram of the gamut is shifted down by a whole tone. The reason is evident. It was inconvenient to use GG for Gam ut which originally used the Greek capital gamma. So G was used instead. The specification for the Swell in the organ for St James’s, Bermondsey, 1829 (see Grove 1), ran from ‘Gamut G’, which is an octave higher than GG on the Great, as is shown by the number of notes in the two organs, 47 and 59 respectively, both rising to F in alt (f'''). Also GGG on the pedals of this organ used a pipe of nominal length 211/3', a 4th below the 16' CCC. To take the change of lettering between FFF and GG was important in the older organs, in which the manuals usually ran down to GG, a note between CCC and CC, and not, as we might expect, above CC. Today, when the manuals always run down to CC, the old point of change loses its significance. The modern English organ-builder commonly speaks of the succession of C’s in the keyboard of full compass, with 61 notes (five octaves), as Bottom C (CC), Tenor C (C), Middle C, Treble C, High C (C in alt) and Top C (C in altissimo) and the necessity to distinguish in lettering between FFF and GG does not arise. (Another system calls them respectively Great C, Small C, One-line C, Two-line C and so on; an octave below Great C is Contra C.)

Were a writer on organs today to use the upper part of the nomenclature in line (2), they would (or should) denote the pitches shown. This upper portion of the system was used in the 20th century by some carillon makers and bell-founders. Its immediate source is probably a modern authority, but its ultimate source may be the older English pitch designations used by Robert Smith. It is consistent with the English organ builders’ method of naming pitches, though the scale of a carillon seldom goes below G of the organ builder’s system (G sol re ut, Fiddle G, or g). This appears to be an isolated example of the use of Robert Smith’s nomenclature today. There is no system of pitch definition in use among English makers of wind instruments; no need for one arises in practice.

(3) This line is the pitch nomenclature in use in France. Its origin lies in the gamut, and the names for notes between ut and si will be clear from the octave shown in ex.2. With the development of the leading-note in European music a name was needed for it, and si was adapted from the initials of Sancte Ioannes in the Latin hymn from which Guido took his names for the notes of the hexachord. As in the corresponding German system, shown in line (1) of ex.1, this scheme begins with the bottom C of the organ manual – as ut. The rather clumsy ut-₁ and ut-₂ are therefore used for the notes one and two octaves lower respectively. Some academic musicians and physicists have tended to replace ut -₁ by ut ₀, and ut -₂ by ut ₀₁.

 (4) This line of ex.1 gives the pitch nomenclature in use in Italy. It differs from the French system only in substituting for ut the more singable name do, which appears to have replaced ut in countries other than France.

(5) This is a pitch nomenclature that has been adopted in the USA for scientific work. It starts with C₀ as the lowest C that the human ear can perceive as a musical tone. The deepest audible tone normally has a frequency of about 20 Hz. An instrument tuned in equal temperament with a' at 440 Hz would theoretically produce for the deepest sound of a 32' stop a frequency of 16·352 Hz. This is less than a major 3rd below the sound produced by 20 Hz; no human ear will ever hear a deeper C. Many people cannot hear a pure tone corresponding to 16 Hz; what they hear in the deepest note of the 32' stop in the organ is the effect of its upper partials. This system reckons frequencies in octaves and uses 16·352 Hz as a reference frequency.

(6) and (7). These are American technical methods of defining the notes of keyboard instruments tuned in equal temperament. They are pitch designations only in a narrow sense. In (6) the black and white keys of the piano are numbered consecutively, upwards, the bottom note A being numbered 1. (7) also numbers by the semitones of equal temperament, beginning with the C of the extreme left of the table in ex.1 as 0. In this system, the pitch class C is consequently numbered in multiples of 12, and so c' becomes 48. Other notes which are known by the same letter add constant numbers to these multiples of 12, for example, G always adding 7 and A always adding 9. Thus a' is 48 + 9 = 57. This system of numbering is called ‘semitone count’ (SC). These nomenclatures, like so many others, are confusing in their similarity.

‘In alt’ is a term used to describe notes in the octave immediately above the top line of the treble staff – those running from g'' to f'''. Notes in the next octave (g''' to f'''') are called ‘in altissimo’. The term is derived from the Italian in alto, ‘high’. It was used by Thomas Morley in his Plaine and Easie Introduction, but not in its precise modern sense: he used ‘in alt’ to mean ‘an octave higher’ (and ‘in base’ to mean an octave lower).

Later the term was limited to notes which lay above the gamut. Morley had explained that when Guido enlarged the scale from 15 to 20 notes the result was to ‘fill up … the reach of most voices’. And while he taught Philomathes that ‘there can be no note given so high, but you may give a higher, and none so lowe, but that you may give a lower’, he added that his scale consisted of but 20 notes ‘because that compasse was the reach of most voyces, so that under Gam ut the voice seemed as a kind of humming, and above E la a kinde of constrained skricking’.

It is therefore a reasonable inference that when notes were required to describe the high pitches reached by good sopranos the term ‘in alt’ was employed to describe notes an octave higher than the top seven notes of the gamut, f fa ut to ee la. The note on the top line of the treble staff which had no name in Guido’s hexachords would thus become ‘f fa ut in alt’. That very note was called ‘F in alt’ in the specification for the organ in St James’s, Bermondsey, 1829, already quoted. This doubtless explains an ambiguity that writers have noted in the use of ‘in alt’. In the usage just indicated it would refer to an octave of notes beginning with F on the top line of the treble staff, f'', and running up to E on the third leger line, e'''. But in the 19th century, as musicians forgot the old nomenclature of the gamut, there would be an increasing tendency to use ‘in alt’ with the meaning we began with, for the octave above the treble staff.

BIBLIOGRAPHY

E. Regener: Pitch Notation and Equal Temperament: a Formal Study (Berkeley and Los Angeles, 1973)

LLEWELYN S. LLOYD/RICHARD RASTALL