SCIENTIFIC PITCH NOTATION

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 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. Audible sounds have frequencies in the range of about 20 to 20,000 oscillations per second (Hertz) but very occasionally, it is used to describe frequencies 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 popular media 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).

Contents

Example

Usage

Variant systems

Meantone temperament

C flat problems

Table of note frequencies

References

See also

External links

Example

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.

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.

Variant systems

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 due to the fact that 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.

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 America² 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.

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.
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.

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)''

References

1. Harvard Dictionary of Music
2. The Journal of the Acoustical Society of America -- July 1939 -- Volume 11, Issue 1, pp. 134-139

See also

★ Helmholtz pitch notation

★ MIDI

★ MIDI Tuning Standard

★ Piano key frequencies

★ Keyboard tablature

External links

★ http://www.dolmetsch.com/musictheory1.htm#uspitch