Scientific pitch notation
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Scientific pitch notation is 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 that proposed to the Acoustical Society Of America in 1939[1], where C0 is 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 can also be used to specify the frequency of non-audible phenomena. 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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[edit] Example
"A4" refers to the A above middle C (that is, A440, the note that has a frequency of 440 Hz).
[edit] Usage
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.
[edit] Similar systems
Notation that appears to be scientific pitch notation may actually be based on an alternative octave numbering. While they are still note-octave systems, if they are called "scientific pitch notation", this is certainly an error. For example, MIDI software and hardware often uses C5 or C3 to represent middle C (note 60).[2] This is because the MIDI standard does not specify a particular octave numbering.
[edit] Meantone temperament
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[1] 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 440 Hz (it comes out as approximately 439.96 Hz, 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.
[edit] C flat problems
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.
[edit] Table of note frequencies
| 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) |
[edit] References
- ^ a b The Journal of the Acoustical Society of America -- July 1939 -- Volume 11, Issue 1, pp. 134-139
- ^ Robert Guérin, MIDI Power!, ISBN 1929685661
[edit] See also
[edit] External links
- English Octave-Naming Convention - Music Theory Online
