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Letter notation
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In music, letter notation is a system of representing a set of pitches, for example, the notes of a scale, by letters. For the complete Western diatonic scale, for example, these would be the letters A-G, possibly with a trailing symbol to indicate a half-step raise (sharp, ♯) or a half-step lowering (flat, ♭). This is the most common way of specifying a note in speech or in written text in English or German. In Germany, Scandinavia, and parts of Central and Eastern Europe, H is used instead of B, and B is used instead of B♭.
If we consider the chromatic scale, new sounds are obtained by lowering or raising the seven diatonic notes by a semitone by means of flats (♭) and sharps (♯). Use of solfege or letter names depends on language. For a more complete table and explanation, see Musical note.
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Western letter pitch notation has the virtue of identifying discrete pitches, but among its disadvantages are its occasional inability to represent pitches or inflections lying outside those theoretically derived, or (leaving aside chordal and tablature notations) representing the relationship between pitches—e.g., it does not indicate the difference between a whole step and a half step, knowledge of which was so critical to Medieval and Renaissance performers and theorists.
History
[edit]The earliest known letter notation in the Western musical tradition appear in the textbook on music De institutione musica by the 6th-century philosopher Boethius. A modified form is next found in the Dialogus de musica (ca. 1000) by Pseudo-Odo, in a discussion of the division of the monochord.[1]
Guitar chords
[edit]Letter notation is the most common way of indicating chords for accompaniment, such as guitar chords, for example B♭7. The bass note may be specified after a /, for example C/G is a C major chord with a G bass.
Where a capo is indicated, there is little standardisation. For example, after capo 3, most music sheets will write A to indicate a C chord, that is, they give the chord shape rather than its pitch, but some specify it as C, others give two lines, either the C on top and the A on the bottom or vice versa. A few even use the /, writing C/A or A/C, but this notation is more commonly used for specifying a bass note and will confuse most guitarists.
Choice of note names
[edit]In the context of a piece of music, notes must be named for their diatonic functionality. For example, in the key of D major, it is not generally correct to specify G♭ as a melodic note, although its pitch may be the same as F♯, as F♯ is diatonic to D major, while G♭ is not.[2] (In many tuning systems other than twelve tone equal temperament, the pitch of G♭ is not the same as that of F♯). This is normally only an issue in describing the notes corresponding to the black keys of the piano; there is little temptation to write C as B♯ although both may be valid names of the same note. Each is correct in its context.
Note names are also used for specifying the natural scale of a transposing instrument such as a clarinet, trumpet, or saxophone. The note names used are conventional, for example a clarinet is said to be in B♭, E♭, or A (the three most common registers), never in A♯, and D♯, and B
(double-flat), while an alto flute is in G.[2]
Octaves
[edit]Note names can also be qualified to indicate the octave in which they are sounded. There are several schemes for this, the most common being scientific pitch notation.
Scientific pitch notation is often used to specify the range of an instrument. Where sharps or flats are necessary for this, these are related to the natural scale of the instrument if it has one, otherwise the choice is arbitrary.
Other note naming schemes
[edit]
Fixed do solfège (Si,La diesis, Si bemolle)
English system (B, A#, Bb)
German system (H, Ais,B)
Dutch system (B, Ais,Bes)
Danish system (H, A#, Bb)
No data
- In many languages (such as those in the Romance and Slavic families), notes are named by solmization syllables (do, re, mi,...) instead of letters.
- Tonic sol-fa is a type of notation using the initial letters of solfege.
- Alpha is a chromatic extension of the letter notation proposed by the French musician Raphaël André.[3]
See also
[edit]- Antiphonary of St. Benigne, letter notation by William of Volpiano
- Abc notation, a letter notation based file format for computer storage of music
- Helmholtz pitch notation
- Keyboard tablature
- Musical notation
- Solfege
- Swara
References
[edit]- ^ See "Medieval letter notations: a survey of the sources" by Alma Colk Browne (Ph. D. thesis. University of Illinois at Urbana-Champaign, 1979) and "Medieval Canonics" by Jan Herlinger, in The Cambridge History of Western Music Theory, Thomas Christensen, ed., 2002. Cambridge University Press, ISBN 0-521-62371-5
- ^ a b Kostka, Stefan M.; Payne, Dorothy (2004). Tonal harmony, with an introduction to twentieth-century music (5th ed.). Boston: McGraw-Hill. ISBN 978-0-07-285260-8.
- ^ "AlphabetChromatique". souslepont.org (in French). 2022-05-18. Retrieved 2023-01-03.
Letter notation
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Fundamentals
Definition and Purpose
Letter notation is a fundamental system in Western music theory for naming musical pitches using the alphabetic letters A through G, which correspond to the seven natural notes of the diatonic scale and repeat cyclically across octaves. This approach provides a straightforward method for identifying and referencing specific pitches without relying on graphical staff positions alone.[6] The primary purpose of letter notation is to enable rapid recognition and communication of pitches in various musical contexts, such as scores, chord diagrams, and analytical discussions. By assigning fixed letter names to pitch classes, it allows musicians to identify specific notes regardless of key or transposition, with additional octave designations enabling notation of absolute pitches, contrasting with relative systems like solfège (do-re-mi) that emphasize intervallic relationships rather than specific frequencies.[7][8] A key advantage lies in its accessibility, especially for English speakers, due to the intuitive alphabetical sequence that mirrors the layout of white keys on keyboard instruments, progressing from A to G in ascending order. This direct mapping simplifies learning and visualization for beginners and supports practical applications in performance and composition.[9][10] Emerging prominently within English-speaking musical traditions yet drawing from the historical development of Western notation systems, letter notation remains widely used today in popular music education, jazz theory for chord construction and improvisation, and digital tools like Guitar Pro for tablature and score editing.[8][11]Basic Note Names
Letter notation assigns the seven letters A through G to the natural pitches of the diatonic scale, corresponding to fixed-do solfège syllables as follows: A to la, B to ti (or si), C to do, D to re, E to mi, F to fa, and G to sol.[12] These assignments represent specific pitches with approximate acoustic frequencies determined relative to a standard reference, such as A above middle C (A4) at 440 Hz, as defined by the International Organization for Standardization.[13] The diatonic scale in letter notation follows a repeating pattern of whole steps (W) and half steps (H): W-W-H-W-W-W-H, which outlines the major scale when starting on C as C-D-E-F-G-A-B.[14] This interval structure ensures each consecutive letter name advances through the scale without repetition until the octave returns to the starting pitch. In letter notation, each letter denotes a distinct pitch within the chromatic spectrum, allowing for enharmonic equivalents such as B♯ for C or F♭ for E, which sound identical but serve different contextual roles in harmony and key signatures.[7] This absolute designation contrasts with the relational nature of movable-do solfège, where syllables indicate scale degrees relative to a tonic rather than fixed pitches. While predominant in English-speaking contexts, letter notation varies culturally; for instance, German practice uses H for B natural and B for B♭, though the A-G sequence is standardized internationally in scientific and acoustic measurements.[15]Historical Development
Origins in Medieval Music
The roots of letter notation in Western music trace back to ancient Greek practices, where an alphabetical system was used to represent pitches within scales and modes such as the Dorian and Phrygian. This non-graphical notation employed letters from the Greek alphabet to symbolize individual notes, facilitating the documentation of melodic structures in theoretical treatises. The transmission of this system to medieval Europe occurred primarily through the Roman philosopher Boethius in the early 6th century; in his seminal work De institutione musica, Boethius adapted the Greek method by assigning Roman letters A through O to the 15 tones of the greater perfect system, thereby preserving and disseminating knowledge of modal pitches like those in the Dorian (from D to D) and Phrygian (from E to E) modes.[16][17] In the 9th and 10th centuries, Byzantine musical traditions further shaped early Western notation through cultural exchanges and Arabic translations of Greek and Byzantine texts, introducing elements of neumatic systems that emphasized melodic contour and pitch relationships. These influences, mediated via Islamic scholars who translated Byzantine works on music theory, contributed to the evolution of diastematic notations in Europe, where symbols began to indicate relative pitch heights more precisely than earlier cheironomic signs. By the 12th century, this groundwork enabled the transition from non-diastematic neumes—simple mnemonic aids for plainchant melody—to staff-based systems, with letters serving as supplementary guides for pitch identification in liturgical manuscripts, enhancing the accuracy of monophonic chant performance.[18][19][20] The adoption of letter notation gained momentum in the 11th century through the innovations of Guido d'Arezzo, whose hexachord system—dividing the octave into overlapping six-note segments—indirectly bolstered letter-based pitch labeling by systematizing solmization syllables alongside staff lines, aiding singers in navigating modal scales. This development culminated in practical application during the 13th century, particularly in English polyphonic compositions, marking one of the earliest documented instances of such labeling in insular music sources. Regional variations highlighted the divergence between Anglo-Saxon preferences for alphabetic notation, rooted in practical manuscript aids for chant and organum, and the continental European reliance on solmization derived from the Ut queant laxis hymn, which emphasized syllable-based naming (ut, re, mi, fa, sol, la) for pedagogical purposes in monastic schools.[21][22][23]Evolution in Modern Notation
During the Renaissance, the printing of music played a pivotal role in standardizing letter notation. Ottaviano Petrucci's pioneering use of movable type in Venice, beginning with his 1501 publication Harmonice Musices Odhecaton, enabled the widespread dissemination of polyphonic scores and promoted consistent application of the A-G pitch letters within staff notation across Europe.[24] This innovation shifted music from manuscript copying to printed editions, fostering uniformity in how pitches were labeled and notated.[25] In England, 16th-century theorists like Thomas Morley further codified the A-G system in contexts such as lute tablature and instructional texts; Morley's A Plaine and Easie Introduction to Practical Musicke (1597) exemplified this by integrating letter names into examples of counterpoint and accompaniment for lute and voice.[26] By the 18th and 19th centuries, letter notation had become embedded in keyboard pedagogy, particularly through piano method books that reinforced A-G as the foundational pitch identifiers. Carl Czerny's influential works, such as his Letters to a Young Lady on the Art of Playing the Pianoforte (1837), assumed readers' familiarity with these letters for teaching scales, chords, and fingerings, reflecting their adoption in European conservatory training.[27] Concurrently, regional variations emerged, including the German convention of denoting B natural as H and B flat as B, a practice rooted in earlier hexachord traditions but persisting in German-speaking areas; however, the A-G sequence dominated international printed scores and orchestral parts.[28] The 20th century brought refinements that entrenched letter notation in global and technical standards. The International Organization for Standardization's ISO/R 16 (1955) established A4 at precisely 440 Hz, formalizing scientific pitch notation where letters A-G combined with octave numbers (e.g., A4) provided unambiguous frequency references for tuning and recording.[29] In popular genres, letter notation adapted via chord symbols; conventions like Cmaj7 for a C major triad with major seventh arose in early 20th-century lead sheets for jazz and Tin Pan Alley songs, later extending to rock for quick harmonic communication among performers.[30] The MIDI (Musical Instrument Digital Interface) protocol, released in 1983, incorporated this system by mapping note numbers (0-127) to letter-octave names, with middle C as note 60 (C4 in scientific notation), enabling seamless digital interchange in synthesizers and software.[31] Colonialism and missionary education exported letter notation beyond Europe, integrating it into non-Western traditions. In India, following the 1857 uprising and the establishment of British Raj institutions, Western music curricula in schools and colleges introduced A-G notation as part of colonial reforms, blending it with indigenous systems like sargam to teach hymns and band music.[32] This spread, evident in 19th-century treatises and early 20th-century conservatories, facilitated hybrid practices while prioritizing Western standardization in formal education.[33]Notation Conventions
Octave Designation
In letter notation, the sequence of pitch names A through G cycles repeatedly across octaves, with no inherent letter designating the octave itself; instead, pitches are distinguished by their register using numerical or symbolic modifiers appended to the letter name. This system allows for efficient representation of the full pitch range in music, from subsonic lows to ultrasonic highs, without altering the core letter cycle. For example, the note immediately below middle C is notated as B3, while the one above is C5, emphasizing the continuity of the A-G pattern while clarifying vertical position in the frequency spectrum. The most widely adopted modern system for octave designation is scientific pitch notation, proposed by the Acoustical Society of America in 1939, where middle C (approximately 261.63 Hz) is denoted as C4.[34] In this convention, the octave number increases by 1 for each doubling of frequency starting from the reference point, with notes from C to B sharing the same numeral; thus, the great octave spans C0 (16.35 Hz) to B0, the first octave C1 to B1, and so on up to higher registers like C8 (4186.01 Hz). This numerical approach provides a precise, octave-independent way to specify pitches, facilitating communication in composition, performance, and acoustics. Older methods, such as those from 19th-century German notation, used superscripts or primes to indicate octaves above a central register (e.g., C′ for one octave above middle C) and subscripts for those below (e.g., C,, for two octaves down), though these have largely been supplanted by numerical systems for their clarity in printed scores and digital tools. This octave numbering aligns closely with the visual and tactile layout of keyboard instruments like the piano, where each octave block begins on C and ends on B, reinforcing the A-G sequence through the instrument's repeating white-key pattern. The lowest octave on a standard 88-key piano is A0 (27.50 Hz) to B0, followed by C1 through the highest C8, allowing performers to intuitively map letter names to physical positions without needing to recount octaves manually. Conceptually, each successive octave represents a frequency multiplication by 2, so a note's pitch in higher registers doubles (or halves in lower ones) relative to its counterpart in the adjacent octave, preserving harmonic relationships while spanning the audible range from about 20 Hz to 20,000 Hz. This exponential scaling underscores why letter notation pairs seamlessly with octave modifiers, as the perceptual interval of an octave feels equivalent regardless of register. In electronic music production, octave designation extends to synthesizer programming and MIDI protocols, where pitches are often labeled from A-1 (low bass, around 13.75 Hz) to G9 (extreme highs beyond typical human hearing), enabling precise patch selection and tuning in digital audio workstations. This range accommodates the extended capabilities of virtual instruments and modular synths, where scientific notation ensures interoperability across software like Ableton Live or hardware like the Moog synthesizer lineage.Sharps, Flats, and Accidentals
In letter notation, pitches are altered chromatically using accidentals, which are symbols placed before a note to raise or lower its pitch relative to the natural note name. The sharp symbol (#) raises a pitch by one semitone, as in changing A to A♯.[35] The flat symbol (♭) lowers a pitch by one semitone, such as altering B to B♭.[35] The natural symbol (♮) cancels any previous sharp or flat, restoring the pitch to its unaltered state.[35] For larger alterations, double sharps (𝄪 or x) raise a pitch by two semitones, while double flats (𝄫 or bb) lower it by two semitones.[35] Enharmonic equivalents refer to pitches that sound identical but are notated differently, allowing flexibility in spelling based on the musical context or key.[36] For example, C♯ and D♭ produce the same pitch, as do F♯ and G♭, with the choice often determined by the prevailing key signature to simplify reading.[36] This equivalence arises because the twelve semitones of the chromatic scale can be approached from adjacent natural notes, such as sharpening the note below or flattening the one above.[7] Key signatures employ multiple sharps or flats at the beginning of a staff to indicate the scale of a piece, systematically altering the natural pitches throughout.[37] Sharps are added in the order F♯, C♯, G♯, D♯, A♯, E♯, B♯, while flats follow B♭, E♭, A♭, D♭, G♭, C♭, F♭.[37] For instance, the key of F♯ major uses six sharps—F♯, C♯, G♯, D♯, A♯, E♯—affecting all corresponding notes in the piece unless overridden.[37] In standard notation, an accidental applies to the note it precedes and to all subsequent notes of the same pitch class within the same measure (bar), unless canceled by another accidental or a natural sign.[7] This rule ensures continuity within the measure but resets at the barline, promoting clarity in reading; if a note is tied across measures, the accidental carries over to the tied portion.[7] Contemporary extensions of letter notation incorporate microtonal accidentals to notate intervals smaller than a semitone, such as quarter tones, which are relevant in modern composition exploring non-tempered scales.[38] These often use additional symbols like up or down arrows (e.g., A with an up arrow for A+1/4 tone) or specialized signs such as a quarter-sharp to raise a pitch by half a semitone, building on traditional accidentals for 24-tone equal temperament systems.[38]Applications in Music
Guitar and Chord Notation
In guitar music, letter notation forms the basis of chord symbols, where a capital letter indicates the root note of the chord, such as C for a C major triad or G7 for a G dominant seventh chord, with suffixes like "maj" or "Δ" for major seventh, "m" or "min" for minor, and "sus" for suspended chords to specify quality and extensions. These symbols are placed above the staff in lead sheets, allowing guitarists to interpret and voice chords flexibly while accompanying melodies. For instance, in popular genres, a progression like C - Am - F - G uses these letter-based symbols to denote triads built from the major scale. Letter notation integrates with guitar tablature (tab), where numerical fret positions outline fingerings on the six strings, but chord roots and names are labeled using letters above the tab lines for quick reference, such as an "A" chord shown as a barred E-shape at the second fret. This combination facilitates visual learning, with software like MuseScore rendering interactive chord grids and tabs based on letter symbols, enabling transposition across the fretboard.[39] In chord diagrams, dots represent fretted notes, open circles indicate open strings, and the letter name confirms the root, as seen in standard representations of E, A, and D major open chords. Common guitar voicings rely on letter notation to name shapes that align with the instrument's standard EADGBE tuning. Open chords like E major (root on the open low E string), A major (root on the second fret of the low E), and D major (root on the open D string) follow the alphabetical sequence of note names, providing foundational triads accessible to beginners. Barre chords extend this by transposing open shapes up the neck using the index finger as a bar; for example, the E major shape barred at the third fret produces a G major chord, with the root letter shifting according to the fret's pitch (each fret raises the letter by a half step). This movable system allows guitarists to play any root letter without learning unique shapes for each chord. In popular music contexts like folk and rock, letter-based chord notation is standard for lead sheets and charts, as evidenced in Beatles arrangements where songs like "Let It Be" use simple progressions such as C - G - Am - F, rendered with guitar diagrams for strumming accompaniment. This format promotes improvisation and ensemble play, with software tools generating letter-labeled grids for these genres.[40] For alternate tunings, letter notation adapts by retaining root names while adjusting relative voicings; in DADGAD (D-A-D-G-A-D), the open strings form a Dsus4 chord, shifting traditional shapes so that a G major voicing might use open strings and minimal fretting, emphasizing modal drones over standard triads.Keyboard and Other Instruments
In keyboard instruments such as the piano and organ, letter notation corresponds directly to the physical layout of the keys, with the white keys arranged from left to right in the sequence A, B, C, D, E, F, and G, repeating across octaves that are stacked vertically from low to high pitch.[7][41] The black keys, positioned in groups of two and three between the white keys, represent the sharps and flats of these letter names—for instance, the black key between C and D is both C♯ and D♭—allowing performers to visualize and navigate the chromatic scale intuitively on the fixed keyboard grid.[42] Letter notation facilitates transposition on keyboards by enabling musicians to shift entire pieces based on the root letter of the key, such as moving from C major (rooted on C) to G major (rooted on G) by raising all note letters by a perfect fifth while preserving intervals.[43] This method simplifies key changes without altering finger positions relative to the keyboard's layout, a technique commonly taught in music education to build harmonic awareness.[44] Beyond keyboards, letter notation maps to fingerings on string instruments like the violin, where each string's open note (G, D, A, E from lowest to highest) serves as a reference, and finger positions produce the corresponding letters in sequence—for example, first finger on the A string yields B.[45] In vocal pedagogy, particularly for choral sight-singing, letters A–G are used to name pitches on the staff, helping singers in ensembles quickly identify and intonate notes relative to a given key without relying solely on solfège syllables. In orchestral scores, letter notation accommodates transposing instruments, where the written pitch differs from the sounded pitch; for instance, a B♭ clarinet player reads a written C but produces a concert B♭, requiring conductors and composers to notate parts in the instrument's transposed key to align with the ensemble's concert pitch.[46][47] Digital keyboards and MIDI controllers extend letter notation through on-screen displays that show the letter name of the pressed key, as seen in Yamaha models where note indicators light up or appear in the interface during playback or practice, aiding beginners in associating MIDI note numbers (e.g., 60 for middle C) with their letter equivalents.[48][49]Alternative Naming Systems
Solfège and Fixed-Do
Solfège represents a syllable-based system for naming musical pitches, serving as a relational alternative to the absolute pitch designations of letter notation. In the movable-do variant, the syllables do, re, mi, fa, sol, la, and ti correspond to the degrees of the major scale relative to the tonic note, facilitating the recognition of intervals and key relationships.[50] For instance, in C major, do is C, but in G major, do becomes G, allowing musicians to transpose melodies across keys by maintaining the same syllable pattern.[51] This approach underscores the half-step between mi and fa, as well as ti and do, which highlights the structural tensions within diatonic scales.[52] Fixed-do solfège, in contrast, assigns syllables to absolute pitches regardless of key, with do always equating to C, re to D, mi to E, and so forth, thereby functioning as a syllabic mimicry of letter names.[53] This system is prevalent in conservatories of French and Italian traditions, where it supports precise pitch identification in sight-singing and dictation exercises.[54] For example, the pitch C is consistently sung as do, even when serving as the third degree in A minor, blending relational mnemonic benefits with fixed pitch reference.[55] Compared to letter notation, which prioritizes absolute pitches (A through G) for unambiguous identification across all contexts, solfège systems emphasize intervallic relationships and scale degrees, aiding in the internalization of melodic contours.[51] Movable-do particularly excels in relative pitch training by abstracting away from specific keys, whereas fixed-do aligns more closely with letter notation's absolute framework while retaining syllable-based articulation for vocal practice.[52] This distinction makes solfège invaluable for developing aural skills, as the syllables encode both the sound of intervals and their functional roles within harmony. Solfège finds extensive application in music education for ear training, where movable-do is central to the Kodály method, promoting sight-singing, dictation, and relative pitch recognition through sequential exercises.[50] In vocal pedagogy, including opera training, solfège syllables are employed to refine intonation and phrase melodies, with some scores incorporating them as cues to assist singers in internalizing lines.[56]Helmholtz and Scientific Pitch Notation
The Helmholtz pitch notation system was developed by the German physicist and physiologist Hermann von Helmholtz in his 1863 treatise Die Lehre von den Tonempfindungen als physiologische Grundlage für die Theorie der Musik, later translated as On the Sensations of Tone. This system uses uppercase letters for lower registers, lowercase for higher ones, apostrophes (') for ascending octaves, and commas (,) for descending ones, enabling precise identification of pitches across the Western chromatic scale. For instance, middle C is notated as c', the C one octave below as c, and the C two octaves below as C,,. Influenced by German organ and choral traditions, it distinguishes seven primary octaves—from the sub-contra (C,, to B,,) to the contra (C' to b'), great (C to b), small (c to b), one-line (c' to b'), two-line (c'' to b''), and three-line (c''' to b''')—and is widely employed in music theory texts for its clarity in describing intervallic relationships.[57] Building on such letter-based foundations, scientific pitch notation (SPN) provides a numerical extension for even greater specificity, combining note letters (A–G, with accidentals) and subscript integers to denote octaves. Proposed by the Acoustical Society of America (ASA) in 1939 as part of standardized frequency tables and formally adopted by the International Organization for Standardization (ISO) in 1955, SPN designates middle C as C₄, the reference A above it as A₄ at 440 Hz, and the lowest note on a standard 88-key piano as A₀ (27.5 Hz). Unlike basic letter notation, SPN ties pitches to absolute frequencies under equal temperament, where each octave spans 12 semitones; for example, the sub-contra octave begins at C₀ (16.35 Hz), marking the approximate lower limit of human hearing. In the 21st century, SPN has been revised for extended ranges in digital contexts, incorporating negative octaves (e.g., C₋₂) for sub-contra pitches in synthesizers and software, aligning with MIDI standards where note 0 corresponds to C₋₁.[58][29] These systems enhance precision beyond simple letter designations by linking notation to measurable acoustics: in equal temperament, the frequency f of any note n (MIDI number, with A₄ as 69) is calculated as
Hz, assuming A₄ = 440 Hz as the reference. Helmholtz notation, rooted in physiological acoustics, remains prevalent in research analyzing tone sensations and resonator designs, while SPN dominates tuning software for instrument calibration and digital audio production, ensuring consistent pitch across global standards.[59][57][60]