Musical note

${\displaystyle h}$

${\displaystyle v}$

${\displaystyle {\begin{aligned}\log _{2}(f)&={\tfrac {h}{12}}+\log _{2}({\text{440 Hz}})\\&=v+\log _{2}({\text{440 Hz}})\end{aligned}}}$

When dealing specifically with intervals (rather than absolute frequency), the constant ${\displaystyle \log _{2}({\text{440 Hz}})}$ can be conveniently ignored, because the difference between any two frequencies ${\displaystyle f_{1}}$ and ${\displaystyle f_{2}}$ in this logarithmic scale simplifies to:

${\displaystyle {\begin{aligned}\log _{2}(f_{1})-\log _{2}(f_{2})&={\tfrac {h_{1}}{12}}-{\tfrac {h_{2}}{12}}\\&=v_{1}-v_{2}\,.\end{aligned}}}$

Cents are a convenient unit for humans to express finer divisions of this logarithmic scale that are 1⁄100^th of an equally-tempered semitone. Since one semitone equals 100 cents, one octave equals 12 ⋅ 100 cents = 1200 cents. Cents correspond to a difference in this logarithmic scale, however in the regular linear scale of frequency, adding 1 cent corresponds to multiplying a frequency by ¹²⁰⁰√2 (≅ 1.000578).

MIDI

For use with the MIDI (Musical Instrument Digital Interface) standard, a frequency mapping is defined by:

${\displaystyle p=69+12\times \log _{2}{\frac {f}{440{\text{ Hz}}}}\,,}$

where ${\displaystyle p}$ is the MIDI note number. 69 is the number of semitones between C₋₁ (MIDI note 0) and A₄.

Conversely, the formula to determine frequency from a MIDI note ${\displaystyle p}$ is:

${\displaystyle f=2^{\frac {p-69}{12}}\times 440{\text{ Hz}}\,.}$

Pitch names and their history

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Music notation systems have used letters of the

A   B   C   D   E   F   G   H   I   K   L   M   N   O

to signify the notes of the two-octave range that was in use at the time^[10] and in modern scientific pitch notation are represented as

A₂   B₂   C₃   D₃   E₃   F₃   G₃   A₃   B₃   C₄   D₄   E₄   F₄   G₄

Though it is not known whether this was his devising or common usage at the time, this is nonetheless called Boethian notation. Although Boethius is the first author known to use this nomenclature in the literature, Ptolemy wrote of the two-octave range five centuries before, calling it the perfect system or complete system – as opposed to other, smaller-range note systems that did not contain all possible species of octave (i.e., the seven octaves starting from A, B, C, D, E, F, and G). A modified form of Boethius' notation later appeared in the Dialogus de musica (ca. 1000) by Pseudo-Odo, in a discussion of the division of the monochord.^[11]

Following this, the range (or compass) of used notes was extended to three octaves, and the system of repeating letters A–G in each octave was introduced, these being written as

The remaining five notes of the chromatic scale (the black keys on a piano keyboard) were added gradually; the first being B♭, since B was flattened in certain modes to avoid the dissonant tritone interval. This change was not always shown in notation, but when written, B♭ (B flat) was written as a Latin, cursive "𝑏 ", and B♮ (B natural) a Gothic script (known as Blackletter) or "hard-edged" 𝕭. These evolved into the modern flat (♭) and natural (♮) symbols respectively. The sharp symbol arose from a ƀ (barred b), called the "cancelled b".^{[citation needed]}

In parts of Europe, including Germany, the Czech Republic, Slovakia, Poland, Hungary, Norway, Denmark, Serbia, Croatia, Slovenia, Finland, and Iceland (and Sweden before the 1990s), the Gothic 𝕭 transformed into the letter H (possibly for hart, German for "harsh", as opposed to blatt, German for "planar", or just because the Gothic 𝕭 resembles an H). Therefore, in current German music notation, H is used instead of B♮ (B natural), and B instead of B♭ (B flat). Occasionally, music written in German for international use will use H for B natural and B^b for B flat (with a modern-script lower-case b, instead of a flat sign, ♭).^{[citation needed]} Since a Bes or B♭ in Northern Europe (notated B in modern convention) is both rare and unorthodox (more likely to be expressed as Heses), it is generally clear what this notation means.

In Italian, Portuguese, Spanish, French, Romanian, Greek, Albanian, Russian, Mongolian, Flemish, Persian, Arabic, Hebrew, Ukrainian, Bulgarian, Turkish and Vietnamese the note names are do–re–mi–fa–sol–la–si rather than C–D–E–F–G–A–B. These names follow the original names reputedly given by

• Ghost note
• Grace note
• Letter notation
• Musical tone
• Pensato
• Shape note
• Universal key

Notes

References

1. ^ Nattiez 1990, p. 81, note 9.
2. ^ Savas I. Savas (1965). Byzantine Music in Theory and in Practice. Translated by Nicholas Dufault. Hercules Press.
3. ^ ^{a b} -is = sharp; -es (after consonant) and -s (after vowel) = flat
4. ^ -iss = sharp; -ess (after consonant) and -ss (after vowel) = flat
5. ^ diesis = sharp; bemolle = flat
6. ^ diesis (or diez) = sharp; hyphesis = flat
7. ^ 嬰 (ei) = ♯ (sharp); 変 (hen) = ♭ (flat)
8. ^ According to Bhatkhande Notation. Tivra = ♯ (sharp); Komal = ♭ (flat)
9. ^ According to Akarmatrik Notation (আকারমাত্রিক স্বরলিপি). Kôṛi = ♯ (sharp); Komôl = ♭ (flat)
10. ^ Boethius, A.M.S. [[scores:De institutione musica (Boëthius, Anicius Manlius Severinus)  |De institutione musica]]: text at the International Music Score Library Project. Gottfried Friedlein [de] Boethius. Book IV, chapter 14, page 341.
11. ^ Browne, Alma Colk (1979). Medieval letter notations: A survey of the sources (Ph.D. thesis). Urbana-Champaign, IL: University of Illinois.
    Herlinger, Jan (2002). "Medieval canonics". In Christensen, Thomas (ed.). The Cambridge History of Western Music Theory. Cambridge, UK: Cambridge University Press.
    ISBN 0-521-62371-5
    .

Bibliography

• ISBN 0-691-02714-5
  .

External links

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