Scientific pitch notation
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Scientific pitch notation in Western music is a method of naming the notes of the standard Western chromatic scale by combining a letter-name, accidentals, and an Hindu-Arabic numeral identifying the pitch's octave.
As an example, "A4" refers to the A above middle C (that is, A440, the note that has a frequency of 440 Hz). Middle C is set as "C4" (261.6 Hz). In this notation, C is considered to be the beginning of an octave, so "D4" through "B4" all refer to notes above middle C.
Scientific pitch notation is an example of a note-octave notation, see below.
Scientific pitch notation is often used to specify the range of an instrument. It provides an unambiguous means of identifying a note in terms of musical notation rather than frequency, while at the same time avoiding the transposition conventions that are used in writing the music for instruments such as the clarinet and guitar. The conventional octave naming system, where for example C0 is written as ′′C, or CCC, or referred to as subcontra C, and C4 is written as c′ or one-lined C, applies to the written notes that may or may not be transposed. For example, a d′ played on a B♭ trumpet is actually a C4 in scientific pitch notation.
Three cautions should be observed:
- Several variant systems (perhaps originally in error) use the same symbols as scientific pitch notation, but differ from it in the numbering of the octaves. Some MIDI documentation uses C3 to represent middle C; other writers have used C5. Notation that appears to be scientific pitch notation may be one of these variant systems. While they are still note-octave systems, when they are called scientific pitch notation (as does occur) this is certainly in error.
- The notation is sometimes used in the context of meantone temperament, and does not always assume equal temperament nor the standard concert A of 440 Hz; this is particularly the case in connection with earlier music.
- There is some possible confusion as to assigning the correct octave to C♭. The convention is that the letter name is first combined with the Arabic numeral to determine a specific pitch, which is then altered by applying accidentals. For example, the symbol C♭4 means "the pitch one chromatic step below the pitch C4" and not "the pitch-class C♭ in octave 4", so C♭4 is the same pitch as B3, not B4.
The matter is clarified by viewing "♭" and "♯" as denoting a certain fixed amount of cents flat or sharp. In equal temperament, that amount is exactly 100 cents, whereas in 1/4 comma meantone it is precisely 57/4/2048, or 76.049 cents, taking other values for other meantone tunings. Hence "C♭4" is the same as "C4♭", which in equal temperament is 100 cents below middle C, and equal to B3, and in 1/4 comma meantone is 76 cents below C4, and sharper than B3, which is 117 cents below C4.
This is not a great problem in practice, as in most usages of scientific pitch notation one is notating equal temperament, and neither C♭ nor B♯ need be used at all; rather these notes could be, and usually are, simply named B and C respectively.
Scientific pitch notation is a logarithmic frequency scale. Very occasionally, it is used to describe frequencies outside the range of human hearing. For example, when pressure fronts were observed propagating away from a black hole by the Chandra X-ray Observatory, the frequency of the waves was reported in the popular media as the B♭ 57 octaves below middle C, or B♭−53, corresponding to one oscillation every 10 million years. Audible sounds have frequencies of tens to thousands of oscillations per second (Hertz).
| Table of note frequencies Key: Frequency in hertz (semitones above or below middle C) |
||||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Octave → Note ↓ |
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| C | 16.35 (−48) | 32.70 (−36) | 65.41 (−24) | 130.8 (−12) | 261.6 (0) | 523.3 (+12) | 1047 (+24) | 2093 (+36) | 4186 (+48) | 8372 (+60) |
| C♯/D♭ | 17.32 (−47) | 34.65 (−35) | 69.30 (−23) | 138.6 (−11) | 277.2 (+1) | 554.4 (+13) | 1109 (+25) | 2217 (+37) | 4435 (+49) | 8870 (+61) |
| D | 18.35 (−46) | 36.71 (−34) | 73.42 (−22) | 146.8 (−10) | 293.7 (+2) | 587.3 (+14) | 1175 (+26) | 2349 (+38) | 4699 (+50) | 9397 (+62) |
| D♯/E♭ | 19.45 (−45) | 38.89 (−33) | 77.78 (−21) | 155.6 (−9) | 311.1 (+3) | 622.3 (+15) | 1245 (+27) | 2489 (+39) | 4978 (+51) | 9956 (+63) |
| E | 20.60 (−44) | 41.20 (−32) | 82.41 (−20) | 164.8 (−8) | 329.6 (+4) | 659.3 (+16) | 1319 (+28) | 2637 (+40) | 5274 (+52) | 10548 (+64) |
| F | 21.83 (−43) | 43.65 (−31) | 87.31 (−19) | 174.6 (−7) | 349.2 (+5) | 698.5 (+17) | 1397 (+29) | 2794 (+41) | 5588 (+53) | 11175 (+65) |
| F♯/G♭ | 23.12 (−42) | 46.25 (−30) | 92.50 (−18) | 185.0 (−6) | 370.0 (+6) | 740.0 (+18) | 1480 (+30) | 2960 (+42) | 5920 (+54) | 11840 (+66) |
| G | 24.50 (−41) | 49.00 (−29) | 98.00 (−17) | 196.0 (−5) | 392.0 (+7) | 784.0 (+19) | 1568 (+31) | 3136 (+43) | 6272 (+55) | 12544 (+67) |
| G♯/A♭ | 25.96 (−40) | 51.91 (−28) | 103.80 (−16) | 207.7 (−4) | 415.3 (+8) | 830.6 (+20) | 1661 (+32) | 3322 (+44) | 6645 (+56) | 13290 (+68) |
| A | 27.50 (−39) | 55.00 (−27) | 110.00 (−15) | 220.0 (−3) | 440.0 (+9) | 880.0 (+21) | 1760 (+33) | 3520 (+45) | 7040 (+57) | 14080 (+69) |
| A♯/B♭ | 29.14 (−38) | 58.27 (−26) | 116.50 (−14) | 233.1 (−2) | 466.2 (+10) | 932.3 (+22) | 1865 (+34) | 3729 (+46) | 7459 (+58) | 14917 (+70) |
| B | 30.87 (−37) | 61.74 (−25) | 123.50 (−13) | 246.9 (−1) | 493.9 (+11) | 987.8 (+23) | 1976 (+35) | 3951 (+47) | 7902 (+59) | 15804 (+71) |
