Scientific pitch notation
Scientific pitch notation (SPN), also known as American standard pitch notation (ASPN) and international pitch notation (IPN),
Although scientific pitch notation was originally designed as a companion to
Nomenclature
The notation makes use of the traditional tone names (A to G) which are followed by numbers showing which octave they are part of.
For standard A440 pitch equal temperament, the system begins at a frequency of 16.35160 Hz, which is assigned the value C0.
The octave 0 of the scientific pitch notation is traditionally called the
The octave number increases by 1 upon an ascension from B to C. Thus, A0 refers to the first A above C0 and
The octave number is tied to the alphabetic character used to describe the pitch, with the division between note letters ‘B’ and ‘C’, thus:
Use
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 textual notation rather than frequency, while at the same time avoiding the
4 is a lower frequency than B3; but such paradoxes usually do not arise in a scientific context.
Scientific pitch notation avoids possible confusion between various derivatives of Helmholtz notation which use similar symbols to refer to different notes. For example, "C" in Helmholtz's original notation
Although pitch notation is intended to describe sounds audibly perceptible as pitches, it can also be used to specify the frequency of non-pitch phenomena. Notes below E0 or higher than E♭
10 are outside most humans'
Similar systems
There are pitch-octave notation conventions that appear similar to scientific pitch notation but are based on an alternative octave convention that differs from scientific pitch notation, usually by one octave. For example, middle C ("C4" in ISPN) appears in some
Using scientific pitch notation consistently, the MIDI NoteOn message assigns MIDI note 0 to C−1 (five octaves below C4 or Middle C; lowest note on the two largest organs of the world; about one octave below the human hearing threshold: its overtones, however, are audible), MIDI note 21 to A0 (the bottom key of an 88-key piano), MIDI note 60 to C4 (Middle C), MIDI note 69 to A4 (A440), MIDI note 108 to C8 (the top key of an 88-key piano), and MIDI note 127 to G9 (beyond the piano; one octave above the highest note on some keyboard glockenspiels; some notes above the highest-pitched organ pipes).
This creates a linear pitch space in which an octave spans 12
French–Belgian notation system
The French–Belgian system defines the note C placed two ledger lines below the bass staff as Do1 and middle C as Do3. As in the scientific pitch notation, the index of a Do is shared with all notes above it until the next Do. However, no octave receives the index zero, the octave right below 1 receiving the index -1. Therefore while C4 in SPN equates to Do3 in the French–Belgian system, C1 in SPN equates to Do-1.[5]
Meantone temperament
The notation is sometimes used in the context of meantone temperament, and does not always assume equal temperament nor the standard concert A4 of 440 Hz; this is particularly the case in connection with earlier music.
The standard proposed to the Acoustical Society of America[6] explicitly states a logarithmic scale for frequency, which excludes meantone temperament, and the base frequency it uses gives A4 a frequency of exactly 440 Hz. 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 difference using cents every time.[a]
Table of note frequencies
The table below gives notation for pitches based on standard
Octave Note |
−1 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
---|---|---|---|---|---|---|---|---|---|---|---|---|
C | 8.175799 (0) | 16.35160 (12) | 32.70320 (24) | 65.40639 (36) | 130.8128 (48) | 261.6256 (60) | 523.2511 (72) | 1046.502 (84) | 2093.005 (96) | 4186.009 (108) | 8372.018 (120) | 16744.04 |
C♯/D♭ | 8.661957 (1) | 17.32391 (13) | 34.64783 (25) | 69.29566 (37) | 138.5913 (49) | 277.1826 (61) | 554.3653 (73) | 1108.731 (85) | 2217.461 (97) | 4434.922 (109) | 8869.844 (121) | 17739.69 |
D | 9.177024 (2) | 18.35405 (14) | 36.70810 (26) | 73.41619 (38) | 146.8324 (50) | 293.6648 (62) | 587.3295 (74) | 1174.659 (86) | 2349.318 (98) | 4698.636 (110) | 9397.273 (122) | 18794.55 |
E♭/D♯ | 9.722718 (3) | 19.44544 (15) | 38.89087 (27) | 77.78175 (39) | 155.5635 (51) | 311.1270 (63) | 622.2540 (75) | 1244.508 (87) | 2489.016 (99) | 4978.032 (111) | 9956.063 (123) | 19912.13 |
E | 10.30086 (4) | 20.60172 (16) | 41.20344 (28) | 82.40689 (40) | 164.8138 (52) | 329.6276 (64) | 659.2551 (76) | 1318.510 (88) | 2637.020 (100) | 5274.041 (112) | 10548.08 (124) | 21096.16 |
F | 10.91338 (5) | 21.82676 (17) | 43.65353 (29) | 87.30706 (41) | 174.6141 (53) | 349.2282 (65) | 698.4565 (77) | 1396.913 (89) | 2793.826 (101) | 5587.652 (113) | 11175.30 (125) | 22350.61 |
F♯/G♭ | 11.56233 (6) | 23.12465 (18) | 46.24930 (30) | 92.49861 (42) | 184.9972 (54) | 369.9944 (66) | 739.9888 (78) | 1479.978 (90) | 2959.955 (102) | 5919.911 (114) | 11839.82 (126) | 23679.64 |
G | 12.24986 (7) | 24.49971 (19) | 48.99943 (31) | 97.99886 (43) | 195.9977 (55) | 391.9954 (67) | 783.9909 (79) | 1567.982 (91) | 3135.963 (103) | 6271.927 (115) | 12543.85 (127) | 25087.71 |
A♭/G♯ | 12.97827 (8) | 25.95654 (20) | 51.91309 (32) | 103.8262 (44) | 207.6523 (56) | 415.3047 (68) | 830.6094 (80) | 1661.219 (92) | 3322.438 (104) | 6644.875 (116) | 13289.75 | 26579.50 |
A | 13.75000 (9) | 27.50000 (21) | 55.00000 (33) | 110.0000 (45) | 220.0000 (57) | 440.0000 (69) | 880.0000 (81) | 1760.000 (93) | 3520.000 (105) | 7040.000 (117) | 14080.00 | 28160.00 |
B♭/A♯ | 14.56762 (10) | 29.13524 (22) | 58.27047 (34) | 116.5409 (46) | 233.0819 (58) | 466.1638 (70) | 932.3275 (82) | 1864.655 (94) | 3729.310 (106) | 7458.620 (118) | 14917.24 | 29834.48 |
B | 15.43385 (11) | 30.86771 (23) | 61.73541 (35) | 123.4708 (47) | 246.9417 (59) | 493.8833 (71) | 987.7666 (83) | 1975.533 (95) | 3951.066 (107) | 7902.133 (119) | 15804.27 | 31608.53 |
Mathematically, given the number n of semitones above middle C, the fundamental frequency in hertz is given by (see twelfth root of two). Given the MIDI NoteOn number m, the frequency of the note is normally Hz, using standard tuning.
Scientific pitch versus scientific pitch notation
The current international pitch standard, using A4 as exactly 440 Hz, had been informally adopted by the music industry as far back as 1926, and A440 became the official international pitch standard in 1955. SPN is routinely used to designate pitch in this system. A4 may be tuned to other frequencies under different tuning standards, and SPN octave designations still apply (ISO 16).[7]
With changes in concert pitch and the widespread adoption of A440 as a musical standard, new scientific frequency tables were published by the Acoustical Society of America in 1939, and adopted by the International Organization for Standardization in 1955. C0, which was exactly 16 Hz under the scientific pitch standard, is now 16.352 Hz under the current international standard system.[6]
See also
- Music and mathematics
- Helmholtz pitch notation
- MIDI
- MIDI tuning standard
- Piano key frequencies
- Keyboard tablature
- Letter notation
Footnotes
- enharmonic notes, such as A♯ and B♭, are a different pitch, with A♯ at a lower frequency than the enharmonic B♭. With the single exception of equal temperament(which fits in among meantone systems as a special case) enharmonic notes always have slightly different frequencies.
References
- ^ International Pitch Notation
- ISBN 978-1-4191-7893-1 – via Internet Archive.
- ^ "Black hole sound waves" (Press release). NASA.
Sound waves 57 octaves lower than middle-C are rumbling away from a supermassive black hole in the Perseus cluster.
- ISBN 1-929685-66-1.
- ISBN 978-8482362533.
- ^ .
- ^ ISO 16:1975 Acoustics – Standard tuning frequency (Standard musical pitch). International Organization for Standardization. 1975.
External links
- English Octave-Naming Convention – Dolmetsch Music Theory Online
- Notefreqs – A complete table of note frequencies and ratios for midi, piano, guitar, bass, and violin. Includes fret measurements (in cm and inches) for building instruments.