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Scientific pitch notation
From Wikipedia, the free encyclopedia
Almost all authorities[1] agree that there is no universal system for indicating a pitch's octave; the name scientific pitch notation is given to one of several methods that name the notes of the standard Western chromatic scale by combining a letter-name, accidentals, and a number identifying the pitch's octave. The definition of scientific pitch notation in this article is identical to one proposed to the Acoustical Society Of America in 1939[2], which is based on C0 being in the region of the lowest possible audible frequency.
Scientific pitch notation is a logarithmic frequency scale. Although pitch notation is intended to describe audible sounds, it is occasionally used to specify the frequency of non-audible phenomona. 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 press as the B♭ 57 octaves below middle C, or B♭−53, corresponding to one oscillation every 10 million years.
Scientific pitch notation is an example of a note-octave notation (see below).
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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 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.
Several other systems 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. This is because the MIDI standard only defined pitches in terms of numbers (e.g. middle C is note 60), so any MIDI editing software must make its own decision about octave numbering.
Notation that appears to be scientific pitch notation may be based on one of these alternative 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.
The standard proposed to the Acoustical Society Of America[2] explicitly states a logarithmic scale for frequency, which excludes meantone temperament, and the base frequency it uses does gives A4 a frequency of almost exactly 440Hz (it comes out as approximately 439.96Hz, which is a difference of 0.01 cents). However, when dealing with earlier music that did not use equal temperament, it is understandably easier to simply refer to notes by their closest modern equivalent, as opposed to specifying the error using cents every time.
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.
| Frequency in hertz (semitones above or below middle C) | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Octave → Note ↓ |
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| C | 16.352 (−48) | 32.703 (−36) | 65.406 (−24) | 130.81 (−12) | 261.63 (0) | 523.25 (+12) | 1046.5 (+24) | 2093.0 (+36) | 4186.0 (+48) | 8372.0 (+60) |
| C♯/D♭ | 17.324 (−47) | 34.648 (−35) | 69.296 (−23) | 138.59 (−11) | 277.18 (+1) | 554.37 (+13) | 1108.7 (+25) | 2217.5 (+37) | 4434.9 (+49) | 8869.8 (+61) |
| D | 18.354 (−46) | 36.708 (−34) | 73.416 (−22) | 146.83 (−10) | 293.66 (+2) | 587.33 (+14) | 1174.7 (+26) | 2349.3 (+38) | 4698.6 (+50) | 9397.3 (+62) |
| D♯/E♭ | 19.445 (−45) | 38.891 (−33) | 77.782 (−21) | 155.56 (−9) | 311.13 (+3) | 622.25 (+15) | 1244.5 (+27) | 2489.0 (+39) | 4978.0 (+51) | 9956.1 (+63) |
| E | 20.602 (−44) | 41.203 (−32) | 82.407 (−20) | 164.81 (−8) | 329.63 (+4) | 659.26 (+16) | 1318.5 (+28) | 2637.0 (+40) | 5274.0 (+52) | 10548 (+64) |
| F | 21.827 (−43) | 43.654 (−31) | 87.307 (−19) | 174.61 (−7) | 349.23 (+5) | 698.46 (+17) | 1396.9 (+29) | 2793.8 (+41) | 5587.7 (+53) | 11175 (+65) |
| F♯/G♭ | 23.125 (−42) | 46.249 (−30) | 92.499 (−18) | 185.00 (−6) | 369.99 (+6) | 739.99 (+18) | 1480.0 (+30) | 2960.0 (+42) | 5919.9 (+54) | 11840 (+66) |
| G | 24.500 (−41) | 48.999 (−29) | 97.999 (−17) | 196.00 (−5) | 392.00 (+7) | 783.99 (+19) | 1568.0 (+31) | 3136.0 (+43) | 6271.9 (+55) | 12544 (+67) |
| G♯/A♭ | 25.957 (−40) | 51.913 (−28) | 103.83 (−16) | 207.65 (−4) | 415.30 (+8) | 830.61 (+20) | 1661.2 (+32) | 3322.4 (+44) | 6644.9 (+56) | 13290 (+68) |
| A | 27.500 (−39) | 55.000 (−27) | 110.00 (−15) | 220.00 (−3) | 440.00 (+9) | 880.00 (+21) | 1760.0 (+33) | 3520.0 (+45) | 7040.0 (+57) | 14080 (+69) |
| A♯/B♭ | 29.135 (−38) | 58.270 (−26) | 116.54 (−14) | 233.08 (−2) | 466.16 (+10) | 932.33 (+22) | 1864.7 (+34) | 3729.3 (+46) | 7458.6 (+58) | 14917 (+70) |
| B | 30.868 (−37) | 61.735 (−25) | 123.47 (−13) | 246.94 (−1) | 493.88 (+11) | 987.77 (+23) | 1975.5 (+35) | 3951.1 (+47) | 7902.1 (+59) | 15804 (+71) |