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Key signature
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For use in cryptography, see Key signature (cryptography).
Key signature A major / F♯ minor with three sharps placed after the clef.
In musical notation, a key signature is a set of sharp (♯), flat (♭), and rarely, natural (♮) symbols placed together on the staff. Key signatures are generally written immediately after the clef at the beginning of a line of musical notation, although they can appear in other parts of a score, notably after a double barline.
A key signature designates notes that are to be played higher or lower than the corresponding natural notes and applies through to the end of the piece or up to the next key signature. A sharp symbol on a line or space in the key signature raises the notes on that line or space one semitone above the natural, and a flat lowers such notes one semitone. Further, a symbol in the key signature affects all the notes of one letter: for instance, a sharp on the top line of the treble staff applies to Fs not only on that line, but also to Fs in the bottom space of the staff, and to any other Fs. This convention was not universal until the late Baroque and early Classical period, however; music published in the 1720s and 1730s, for example, uses key signatures showing sharps or flats on both octaves for notes which fall within the staff.[citation needed]
An accidental is an exception to the key signature, applying only in the measure in which it appears.
Although a key signature may be written using any combination of sharp and flat symbols, a series of thirteen homogeneous key signatures, ranging from between six flats to six sharps and each flat or sharp being on notes separated by a perfect fifth from each other, are by far the most commonly used; their use is assumed in much of this article. A piece scored using a single diatonic key signature and no accidentals contains notes of at most seven of the twelve pitch classes, which seven being determined by the particular key signature.
Each major and minor key has an associated key signature that sharpens or flattens the notes which are used in its scale. However, it is not uncommon for a piece to be written with a key signature that does not match its key, for example, in some Baroque pieces,[1] or in transcriptions of traditional modal folk tunes.[2]
Later on, this use of a key signature that is theoretically incorrect for a piece as a whole or a self-contained section of a piece became less common (in contrast to brief passages within a piece, which, as they modulate from key to key often temporarily disagree with the key signature); but it can be found at least as late as one of Beethoven's very late piano sonatas. For example, in his Sonata No. 31 in A♭ major, Op. 110, the first appearance of the Arioso section in the final movement is notated throughout in six flats; but it both begins and ends in A♭ minor and has a significant modulation to C♭ major, and both these keys theoretically require seven flats in their key signature. (The second appearance later in the movement of this same section, a semitone lower, in G minor, uses the correct key signature of two flats.)
Contents
[hide]
1 Conventions
1.1 Notational conventions
1.2 Variants of standard conventions
2 Major scale structure
2.1 Scales with sharp key signatures
2.2 Scales with flat key signatures
3 Relationship between key signature and key
3.1 Additional terminology
4 Exceptions
4.1 Unusual signatures
5 History
6 Table
7 See also
8 References
Conventions[edit]
1. B major scale: no key signature; accidentals required throughout
2. B major scale: key signature; accidentals not needed
In principle, any piece can be written with any key signature, using accidentals to correct the pattern of whole and half steps. The purpose of the key signature is to minimize the number of such accidentals required to notate the music. The sequence of sharps or flats in key signatures is generally rigid in modern music notation. This allows musicians to identify the key simply by the number of sharps or flats (which is the same in any clef), rather than their position on the staff. For example, if a key signature has only one sharp, it must be an F-sharp,[3] which corresponds to a G major or an E minor key.
However, in 20th-century music, there are occasional exceptions to this, where a piece uses an unorthodox or synthetic scale, where a key signature may be invented to reflect this. This may consist of a number of sharps or flats that are not the normal ones (such as a signature of just C♯ or E♭), or it may consist of one or more sharps combined with one or more flats (such as a signature containing both F♯ and B♭). Key signatures of this kind can be found in the music of Béla Bartók, for example.
The effect of a key signature continues throughout a piece or movement, unless explicitly cancelled by another key signature. For example, if a five-sharp key signature is placed at the beginning of a piece, every A in the piece in any octave will be played as A sharp, unless preceded by an accidental (for instance, the A in scale 2 illustrated – the next-to-last note – is played as an A♯ even though the A♯ in the key signature (the last sharp sign) is written an octave lower).[3]
In a score containing more than one instrument, all the instruments are usually written with the same key signature. Exceptions include:
If an instrument is a transposing instrument.
If an instrument is a percussion instrument with indeterminate pitch.
Composers usually omit the key signature for timpani parts. Besides not using a key signature, timpani parts were early on also treated often as transposing instrument parts, the pitch of the high drum being written as C and, as timpani were almost always tuned a perfect fourth apart (dominant on the low drum and tonic on the high drum), the pitch of the low drum being written as G, with the actual pitches indicated at the beginning of the part, e.g. "timpani in D–A", if they were tuned A (low drum) and D (high drum).
Composers may omit the key signature for horn and occasionally trumpet parts. This is perhaps reminiscent of the early days of brass instruments, when crooks would be added to them, in order to change the length of the tubing and allow playing in different keys.[citation needed]
On occasion, in more modern works, instruments may be notated in different keys even when they are not transposing instruments, because the music is polytonal and the different parts are actually in different keys which sound together.
Circle of fifths showing major and minor keys and their signatures
Notational conventions[edit]
The convention for the notation of key signatures follows the circle of fifths. Starting from C major (or equivalently A minor) which has no sharps or flats, successively raising the key by a fifth adds a sharp, going clockwise round the circle of fifths. The new sharp is placed on the new key's leading note (seventh degree) for major keys or supertonic (second degree) for minor keys. Thus G major (E minor) has one sharp which is on the F; then D major (B minor) has two sharps on F and C and so on.
Similarly successively lowering the key by a fifth adds a flat, going counterclockwise around the circle of fifths. The new flat is placed on the subdominant (fourth degree) for major keys or submediant (sixth degree) for minor keys. Thus F major (D minor) has one flat which is on the B; then B♭ major (G minor) has two flats (on B and E) and so on.
Put another way: for key signatures with sharps, the first sharp is placed on F with subsequent sharps on C, G, D, A, E and B; for key signatures with flats, the first flat is placed on B with subsequent flats on E, A, D, G, C and F. There are thus 15 conventional key signatures, with up to seven sharps or flats and including the empty signature of C major (A minor).
Corollaries:
Starting from a key with flats in its key signature: raising by fifths successively reduces the flats to zero at C major (A minor). Further such raising adds sharps as described above.
Starting from a key with sharps: lowering by fifths successively reduces those sharps to zero. Further such lowering adds flats as described above.
When the process of raising by a fifth (adding a sharp) produces more than five or six sharps, successive such raising generally involves changing to the enharmonic equivalent key using a flat-based signature. Typically this is at F♯ = G♭, but may also be at C♯ = D♭ or B = C♭. The same principle applies to the process of successive lowering by a fifth.
The relative minor is a minor third down from the major, regardless of whether it is a flat or a sharp key signature.
The key signatures with seven flats (♭) and seven sharps (♯) are rarely used because they have simpler enharmonic equivalents. For example, the key of C♯ major (seven sharps) is more simply represented as D♭ major (five flats). For modern practical purposes these keys are (in twelve tone equal temperament) the same, because C♯ and D♭ are enharmonically the same note. Pieces are written in these extreme sharp or flat keys, however: for example, Bach's Prelude and Fugue No. 3 from Book 1 of The Well-Tempered Clavier BWV 848 is in C♯ major. The modern musical Seussical by Flaherty and Ahrens also has several songs written in these extreme keys.
Key signatures can be further extended through double sharps and double flats (for example, a piece in the key of G♯ major can be expressed with a double sharp on F and six sharps on the other six pitches). As with the seven-sharp and seven-flat examples, it is rarely necessary to express music in such keys when simpler enharmonic examples can instead be used (in the case of G♯, the same passage could be expressed in A♭ with only four flats).
Natural key signature: a key signature with seven naturals (♮) used to cancel the seven sharps (♯) of the previous signature.
The key signature may be changed at any time in a piece, usually at the beginning of a measure, simply by notating the new signature, although if the new signature has no sharps or flats, a signature of naturals, as shown, is needed to cancel the preceding signature. If a change in signature occurs at the start of a new line on the page, where a signature would normally appear anyway, the new signature is customarily repeated at the end of the previous line to make the change more conspicuous.
Variants of standard conventions[edit]
In traditional use, when the key signature change goes from sharps to flats or vice versa, the old key signature is cancelled with the appropriate number of naturals before the new one is inserted; but many more recent publications (whether of newer music or newer editions of older music) dispense with the naturals and simply insert the new signature.
Similarly, when a signature with either flats or sharps in it changes to a smaller signature of the same type, strict application of tradition or convention would require that naturals first be used to cancel just those flats or sharps that are being subtracted in the new signature before the new signature itself is written; but, again, more modern usage often dispenses with these naturals.
When the signature changes from a smaller to a larger signature of the same type, the new signature is simply written in by itself, in both traditional and newer styles.
At one time it was usual to precede the new signature with a double barline (provided the change occurred between bars and not inside a bar), even if it was not required by the structure of the music to mark sections within the movement; but more recently it has increasingly become usual to use just a single barline. The courtesy signature that appears at the end of a line immediately before a change is usually preceded by an additional barline; the line at the very end of the staff is omitted in this case.
If both naturals and a new key signature appear at a key signature change, there are also more recently variations about where a barline will be placed (in the case where the change occurs between bars). For example, in some scores by Debussy, in this situation the barline is placed after the naturals but before the new key signature. Hitherto, it would have been more usual to place all the symbols after the barline.
In key signatures of five or more sharps or of seven flats, one occasionally encounters variant positions of particular symbols in the key signatures, both of them in the bass clef.
The A♯ which is the fifth sharp in the sharp signatures may occasionally be notated on the top line of the bass staff, whereas it is more usually found in the lowest space on that staff. An example of this can be seen in the full score of Ottorino Respighi's Pines of Rome, in the third section, "Pines of the Janiculum" (which is in B major), in the bass-clef instrumental parts.
In the case of seven-flat key signatures, the final F♭ may occasionally be seen on the second-top line of the bass staff, whereas it would more usually appear below the bottom line. An example of this can be seen in Isaac Albéniz's Iberia: first movement, "Evocación", which is in A♭ minor.
Major scale structure[edit]
Except for C major, key signatures appear in two varieties, "sharp key signatures" ("sharp keys") and "flat key signatures" ("flat keys"), so called because they contain only one or other.[4]
Scales with sharp key signatures[edit]
Sharp key signatures consist of a number of sharps between one and seven, applied in this order: F C G D A E B.[5][6] A mnemonic device often used to remember this is "Father Charles Goes Down And Ends Battle."[4][not in citation given]Schonbrun indeed offers this mnemonic, but makes no claim whatever about frequency of use, or indeed whether it had ever been used before Schonbrun concocted it for his book.--> The key note or tonic of a piece in a major key is immediately above the last sharp in the signature.[7] For example, one sharp (F♯) in the key signature of a piece in a major key indicates the key of G major, the next note above F♯. (Six sharps, the last one being E♯ (an enharmonic spelling of F♮) indicate the key of F♯ major, since F has already been sharped in the key signature.)
Major key
Number
of sharps
Sharp notes
Minor key
Enharmonic
equivalent
C major 0 A minor None
G major 1 F♯ E minor None
D major 2 F♯, C♯ B minor None
A major 3 F♯, C♯, G♯ F♯ minor None
E major 4 F♯, C♯, G♯, D♯ C♯ minor None
B major 5 F♯, C♯, G♯, D♯, A♯ G♯ minor C♭ major/A♭ minor
F♯ major 6 F♯, C♯, G♯, D♯, A♯, E♯ D♯ minor G♭ major/E♭ minor
C♯ major 7 F♯, C♯, G♯, D♯, A♯, E♯, B♯ A♯ minor D♭ major/B♭ minor
This table shows that each scale starting on the fifth scale degree of the previous scale has one new sharp, added in the order given above.[6]
Scales with flat key signatures[edit]
"Flat key signatures" consist of one to seven flats, applied as: B E A D G C F[5][6] The mnemonic device is then reversed for use in the flat keys: "Battle Ends And Down Goes Charles' Father".[4] The major scale with one flat is F major. In all other "flat major scales", the tonic or key note of a piece in a major key is four notes below the last flat, which is the same as the second-to-last flat in the signature.[7] In the major key with four flats (B♭ E♭ A♭ D♭), for example, the penultimate flat is A♭, indicating a key of A♭ major.
Major key
Number
of flats
Flat notes
Minor key
Enharmonic
equivalent
C major 0 A minor None
F major 1 B♭ D minor None
B♭ major 2 B♭, E♭ G minor None
E♭ major 3 B♭, E♭, A♭ C minor None
A♭ major 4 B♭, E♭, A♭, D♭ F minor None
D♭ major 5 B♭, E♭, A♭, D♭, G♭ B♭ minor C♯ major/A♯ minor
G♭ major 6 B♭, E♭, A♭, D♭, G♭, C♭ E♭ minor F♯ major/D♯ minor
C♭ major 7 B♭, E♭, A♭, D♭, G♭, C♭, F♭ A♭ minor B major/G♯ minor
In this case each new scale starts a fifth below (or a fourth above) the previous one.
Relationship between key signature and key[edit]
A key signature is not the same as a key; key signatures are merely notational devices. They are convenient principally for diatonic or tonal music.
The key signature defines the diatonic scale that a piece of music uses without the need for accidentals. Most scales require that some notes be consistently sharped or flatted. For example, the only sharp in the G major scale is F sharp, so the key signature associated with the G major key is the one-sharp key signature. However, it is only a notational convenience; a piece with a one-sharp key signature is not necessarily in the key of G major, and likewise, a piece in G major may not always be written with a one-sharp key signature; this is particularly true in pre-Baroque music, when the concept of key had not yet evolved to its present state.
In any case, more extensive pieces often change key (modulate) during contrasting sections, and only sometimes is this change indicated with a change of key signature; if not, the passage in the second key will not have a matching key signature.
Bach Cantata 106 is almost entirely in E♭ major, but has only two flats, not three, in the key signature Play (help·info)
The Toccata and Fugue in D minor, BWV 538 by Bach has no key signature, leading it to be called the Dorian, but it is still in D minor; the B♭s that occur in the piece are written with accidentals.
Additional terminology[edit]
Keys which are associated with the same key signature are called relative keys.
When musical modes, such as Lydian or Dorian, are written using key signatures, they are called transposed modes.
Exceptions[edit]
D Freygish scale Play (help·info)
Exceptions to common-practice-period use may be found in Klezmer scales, such as Freygish (Phrygian). In the 20th century, composers such as Bartók and Rzewski (see below) began experimenting with unusual key signatures that departed from the standard order.
Because of the limitations of the traditional highland bagpipe scale, key signatures are often omitted from written pipe music, which otherwise would be written with two sharps, the usual F♯ and C♯.[8] (In this case the pipes are incapable of playing F♮ and C♮ so it is not necessary to specify the sharps.)
Variant key signatures in a Victoria motet. In the superius (soprano) part the E♭ appears first, and in two other parts a flat occurs in two octaves.
Unusual signatures[edit]
Further information: Anhemitonic scale § Modes of the ancohemitonic heptatonic scales and the key signature system
The above 15 key signatures only express diatonic scales and are therefore sometimes called standard key signatures. Other scales are written either with a standard key signature and use accidentals as required, or with a nonstandard key signature. Examples of the latter include the E♭ (right hand), and F♭ and G♭ (left hand) used for the E♭ diminished (E♭ octatonic) scale in Bartók's Crossed Hands (no. 99, vol. 4, Mikrokosmos), or the B♭, E♭ and F♯ used for the D Phrygian dominant scale in Frederic Rzewski's God to a Hungry Child.
The absence of a key signature does not always mean that the music is in the key of C major / A minor as each accidental may be notated explicitly as required, or the piece may be modal or atonal. An example is Bartók's Piano Sonata, which has no fixed key and is highly chromatic.
If not bound by common practice conventions, microtones can also be notated in a key signature; which microtonal symbols are used depends on the system.
The common practice period conventions are so firmly established that some musical notation programs have been unable to show nonstandard key signatures until recently.[9]
History[edit]
The use of a one-flat signature developed in the Medieval period, but signatures with more than one flat did not appear until the 16th century, and signatures with sharps not until the mid-17th century.[10]
When signatures with multiple flats first came in, the order of the flats was not standardized, and often a flat appeared in two different octaves, as shown at right. In the late 15th and early 16th centuries, it was common for different voice parts in the same composition to have different signatures, a situation called a partial signature or conflicting signature. This was actually more common than complete signatures in the 15th century.[11] The 16th-century motet Absolon fili mi attributed to Josquin des Prez features two voice parts with two flats, one part with three flats, and one part with four flats.
Baroque music written in minor keys often was written with a key signature with fewer flats than we now associate with their keys; for example, movements in C minor often had only two flats (because the A♭ would frequently have to be sharpened to A♮ in the ascending melodic minor scale, as would the B♭).
Table[edit]
Key signature
Major key
Minor key

no sharps or flats C major A minor
Key signature
Added ♯
Major key
Minor key
Key signature
Added ♭
Major key
Minor key

1 sharp F♯ G major E minor
1 flat B♭ F major D minor

2 sharps C♯ D major B minor
2 flats E♭ B♭ major G minor

3 sharps G♯ A major F♯ minor
3 flats A♭ E♭ major C minor

4 sharps D♯ E major C♯ minor
4 flats D♭ A♭ major F minor

5 sharps A♯ B major G♯ minor
5 flats G♭ D♭ major B♭ minor

6 sharps E♯ F♯ major D♯ minor
6 flats C♭ G♭ major E♭ minor

7 sharps B♯ C♯ major A♯ minor
7 flats F♭ C♭ major A♭ minor
See also[edit]
Key signature names and translations
Major and minor
Parallel key
Relative key
Theoretical key
Universal key
References[edit]
Jump up ^ Schulenberg, David. Music of the Baroque. New York: Oxford University Press, 2001. p. 72.. "(…) to determine the key of a Baroque work one must always analyze its tonal structure rather than rely on the key signature."
Jump up ^ Cooper, David. The Petrie Collection of the Ancient Music of Ireland. Cork: Cork University Press, 2005. p. 22. "In a few cases Petrie has given what is clearly a modal melody a key signature which suggests that it is actually in a minor key. For example, Banish Misfortune is presented in D minor, although it is clearly in the Dorian mode."
^ Jump up to: a b |url=http://www.dummies.com/how-to/content/how-to-read-key-signatures.html |title=How to Read Key Signatures|accessdate=29 January 2014
^ Jump up to: a b c Schonbrun, Marc (2005). The Everything Music Theory Book, p.68. ISBN 1-59337-652-9.
^ Jump up to: a b Bower, Michael. 2007. "All about Key Signatures". Modesto, CA: Capistrano School (K–12) website. (Accessed 17 March 2010).
^ Jump up to: a b c Jones, George Thaddeus. 1974. Music Theory: The Fundamental Concepts of Tonal Music Including Notation, Terminology, and Harmony, p.35. Barnes & Noble Outline Series 137. New York, Hagerstown, San Francisco, London: Barnes & Noble. ISBN 9780064601375.
^ Jump up to: a b Kennedy, Michael. 1994. "Key-Signature". Oxford Dictionary of Music, second edition, associate editor, Joyce Bourne. Oxford and New York: Oxford University Press. ISBN 0-19-869162-9.
Jump up ^ Nienhuys, Han-Wen; Nieuwenhuizen, Jan (2009). "GNU LilyPond — Notation Reference". 2.6.2 Bagpipes. Retrieved 2010-03-28. Bagpipe music nominally uses the key of D Major (even though that isn’t really true). However, since that is the only key that can be used, the key signature is normally not written out.
Jump up ^ One of the most popular musical notation programs, Finale, has only included the option to create a nonstandard key signature since their 2009 version: Finale 2009 User Manual for Windows. "Non-Standard Key Signature." http://www.finalemusic.com/UserManuals/Finale2009Win/Finale.htm (accessed February 17, 2011).
Jump up ^ "Key Signature", Harvard Dictionary of Music, 2nd ed.
Jump up ^ "Partial Signature", Harvard Dictionary of Music, 2nd ed.
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Arkwright (Open All Hours)
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Arkwright
Open All Hours character
Portrayed by
Ronnie Barker
Duration
1973–85
First appearance
Pilot: Open All Hours
Last appearance
"The Mystical Boudoir of Nurse Gladys Emmanuel"
Profile
Occupation
Shopkeeper
Home
Yorkshire
[show]Family
Father
Mr Arkwright
Mother
Mrs Arkwright
Stepmother
Unnamed
Half-sisters
Unnamed (deceased)
Lily
Wife
Gladys Emmanuel (fiancée)
Uncles
Dudley
Nephews
Granville
Leroy Arkwright (great)
Albert E. Arkwright, usually referred to simply as Arkwright, is a fictional character and the main protagonist of the British sitcom, Open All Hours, played by Ronnie Barker. Arkwright is the uncle of Granville and the proprietor of an old fashioned Yorkshire corner shop, which in the era of the programme (1970s and 1980s) was a product of a bygone age. Arkwright's signature characteristic is his stutter, which Granville never misses an opportunity to mock.
Contents
[hide]
1 Character
2 Relationships
2.1 Granville
2.2 Nurse Gladys Emmanuel
3 External links
Character[edit]
Arkwright is a pragmatic, miserly man with old-fashioned values, whose world seems to stop at his shop door, except for his uncontrollable lust for Nurse Gladys Emmanuel (Lynda Baron), which may prompt him on occasion to wander across the road, usually with a ladder, to gain access to her bedroom window. Arkwright is a devious, and mildly dishonest character, who has many crafty tricks to try to persuade a customer to leave his store having bought at least one thing, and will avoid spending his own money at all cost. He is also very conservative about his savings, keeping some in his pocket wrapped in a fine gold chain, and some in an old, battered Oxo tin that he hides under the kitchen sink. This includes, or so he claims, coins from before 1922, when they were "solid silver". He loves money so much that the last time he spent a whole night away from the shop was in 1957, when he went to have his appendix out. The till itself is old fashioned, and possesses a tight spring-clip that regularly puts Granville and his fingers in danger. Arkwright refuses to replace it because of the price of a replacement, and because it prevents people from taking his precious money. Although an avid political commentator, he has few political convictions and never sides with either the left or right wing, instead implying they are all useless. Arkwright does however seem fervently opposed to nationalisation, once commenting "My top lip went all stiff and dead, as if it had been nationalised." His political comments usually show no allegiances, instead making remarks like When Wales get home rule, do you think they'll nationalise Clive Jenkins?
Arkwright maintains an openly polite demeanour around customers, but will often insult those who offend him in a veiled or open manner.
Arkwright appears to believe in God, although he is certainly not portrayed as a religious man. Most episodes end with him on the pavement outside the shop during closing time, contemplating on the days' events. His thoughts often start with an expression like "Soon they'll only be me and thee that aren't either nationalised or a limited company."
Arkwright, like most characters in the series, is a rational, practical man, who shows no signs of any sentimentality, unlike Granville, who seems to dream away most of his days, and longs for a life away from the shop.
Arkwright speaks with a stammer, which he acknowledges sometimes makes it difficult to express himself. He often makes his impediment into a joke, for example asking: Granville, how do you spell P-p-p-pepper? Is it 6 Ps or 7?, Granville occasionally mocks his uncle's speech pattern (such as calling the "weather fore-fore-forecast" the "weather twelvecast", and referring to the "B-B-B-B-B-B-B-B-B-B-BC" as morse code), although never in a malicious or hurtful manner. Arkwright was shocked on one occasion to find that he also appears to stutter even when thinking to himself.
By the time of the 2013 episode Still Open All Hours and the sequel series of the same name, Arkwright has long since died (Barker died in 2005), but almost all of his personality traits have passed onto Granville. Granville keeps a framed photograph of Arkwright in the shop's kitchen which he occasionally talks to. Several people in the town, including Granville, believe that Arkwright's ghost still haunts the shop, particularly the cash register, attributing events such as the lights switching on and off or the register randomly opening and closing to him.
Relationships[edit]
Granville[edit]
Arkwright's sister, whose name is never known, died shortly after giving birth to Granville. Less as an act of love and more as a source of free labour, Arkwright brought up the child. Arkwright paints a picture of his sister being a floozy and possibly a part-time prostitute. He sees no harm in this, seeing this as an enterprising choice of career. This is often implied by phrases such as "Just take the man's money and smile Granville, that's what your mother would have done", "You're j-just like your mother, happiness is h-horizontal", or, "Now, d-don't misunderstand me, s-some people loved dearly! Others used to get it on discount". Granville once takes a call from someone he addresses as "Auntie Lily"; seeing as his father is unknown, this would have to be another sister of Arkwright's.
Granville is often made to pay for anything he takes from the shop's shelves, even if Arkwright was the one who gave it to him. In later life, Granville demonstrates a great deal of affection and respect for his uncle after his death, taking comfort in his apparent poltergeist activities around the shop, saying: "I like having him still around... So long as he pays his own electric,"
Nurse Gladys Emmanuel[edit]
Gladys is the district nurse, who Arkwright is informally engaged to. Their engagement doesn't seem to be serious, however they do seem to be fond of each other. Most of the characters who use the shop are old-fashioned, domesticated characters, and while Gladys is very straight forward and Arkwright is somewhat eccentric, she does seem to find company in him, as he is probably more enlightened than most in the area. Gladys always says she won't marry Arkwright until her mother (who is in her eighties) dies, a day that Arkwright seems to look forward to. However, Gladys has also claimed on several occasions that she refrains from marrying him because of his excessively tight-fisted ways or his overworking of Granville. Nurse Gladys Emmanuel is Arkwright's sexual conquest, although he never manages it in the series, he does come close, with the two of them attempting to make love in the back of a Mini van, but with the van being too small for them, they give up. Arkwright and Nurse Gladys apparently never got around to marriage before Arkwright's death, which Nurse Gladys describes as dying to save the cost of the church.
External links[edit]
[show]
v
t
e
Open All Hours
Open All Hours
episodes
Still Open All Hours (episodes)
Characters
Arkwright
Granville
Related
Seven of One
The Funny Side of Christmas
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Receptive field
From Wikipedia, the free encyclopedia
Jump to navigation Jump to search
Not to be confused with Reflexogenous zone.
The receptive field of an individual sensory neuron is the particular region of the sensory space (e.g., the body surface, or the visual field) in which a stimulus will modify the firing of that neuron. This region can be a hair in the cochlea or a piece of skin, retina, tongue or other part of an animal's body. Additionally, it can be the space surrounding an animal, such as an area of auditory space that is fixed in a reference system based on the ears but that moves with the animal as it moves (the space inside the ears), or in a fixed location in space that is largely independent of the animal's location (place cells). Receptive fields have been identified for neurons of the auditory system, the somatosensory system, and the visual system.
The term receptive field was first used by Sherrington (1906)[1] to describe the area of skin from which a scratch reflex could be elicited in a dog. According to Alonso and Chen (2008)[2] it was Hartline (1938) who applied the term to single neurons, in this case from the retina of a frog.
The concept of receptive fields can be extended further up the nervous system; if many sensory receptors all form synapses with a single cell further up, they collectively form the receptive field of that cell. For example, the receptive field of a ganglion cell in the retina of the eye is composed of input from all of the photoreceptors which synapse with it, and a group of ganglion cells in turn forms the receptive field for a cell in the brain. This process is called convergence.
Contents
1 Auditory system
2 Somatosensory system
3 Visual system
3.1 Retinal ganglion cells
3.2 Lateral geniculate nucleus
3.3 Visual cortex
3.4 Extrastriate visual areas
4 Computational theories of visual and auditory receptive fields
5 In the context of neural networks
6 See also
7 References
8 External links
Auditory system[edit]
The auditory system processes the temporal and spectral (i.e. frequency) characteristics of sound waves, so the receptive fields of neurons in the auditory system are modeled as spectro-temporal patterns that cause the firing rate of the neuron to modulate with the auditory stimulus. Auditory receptive fields are often modeled as spectro-temporal receptive fields (STRFs), which are the specific pattern in the auditory domain that causes modulation of the firing rate of a neuron. Linear STRFs are created by first calculating a spectrogram of the acoustic stimulus, which determines the how the spectral density of the acoustic stimulus changes over time, often using the Short-time Fourier transform (STFT). Firing rate is modeled over time for the neuron, possibly using a peristimulus time histogram if combining over multiple repetitions of the acoustic stimulus. Then, linear regression is used to predict the firing rate of that neuron as a weighted sum of the spectrogram. The weights learned by the linear model are the STRF, and represent the specific acoustic pattern that causes modulation in the firing rate of the neuron. STRFs can also be understood as the transfer function that maps an acoustic stimulus input to a firing rate response output.[3]
Somatosensory system[edit]
In the somatosensory system, receptive fields are regions of the skin or of internal organs. Some types of mechanoreceptors have large receptive fields, while others have smaller ones.
Large receptive fields allow the cell to detect changes over a wider area, but lead to a less precise perception. Thus, the fingers, which require the ability to detect fine detail, have many, densely packed (up to 500 per cubic cm) mechanoreceptors with small receptive fields (around 10 square mm), while the back and legs, for example, have fewer receptors with large receptive fields. Receptors with large receptive fields usually have a "hot spot", an area within the receptive field (usually in the center, directly over the receptor) where stimulation produces the most intense response.[citation needed]
Tactile-sense-related cortical neurons have receptive fields on the skin that can be modified by experience or by injury to sensory nerves resulting in changes in the field's size and position. In general these neurons have relatively large receptive fields (much larger than those of dorsal root ganglion cells). However, the neurons are able to discriminate fine detail due to patterns of excitation and inhibition relative to the field which leads to spatial resolution.
Visual system[edit]
See also: Visual system
r e c e p t i v e f i e l d = c e n t e r + s u r r o u n d {\displaystyle receptive\ field=center+surround}
In the visual system, receptive fields are volumes in visual space. They are smallest in the fovea where they can be a few minutes of arc like a dot on this page, to the whole page. For example, the receptive field of a single photoreceptor is a cone-shaped volume comprising all the visual directions in which light will alter the firing of that cell. Its apex is located in the center of the lens and its base essentially at infinity in visual space. Traditionally, visual receptive fields were portrayed in two dimensions (e.g., as circles, squares, or rectangles), but these are simply slices, cut along the screen on which the researcher presented the stimulus, of the volume of space to which a particular cell will respond. In the case of binocular neurons in the visual cortex, receptive fields do not extend to optical infinity. Instead, they are restricted to a certain interval of distance from the animal, or from where the eyes are fixating (see Panum's area).
The receptive field is often identified as the region of the retina where the action of light alters the firing of the neuron. In retinal ganglion cells (see below), this area of the retina would encompass all the photoreceptors, all the rods and cones from one eye that are connected to this particular ganglion cell via bipolar cells, horizontal cells, and amacrine cells. In binocular neurons in the visual cortex, it is necessary to specify the corresponding area in both retinas (one in each eye). Although these can be mapped separately in each retina by shutting one or the other eye, the full influence on the neuron's firing is revealed only when both eyes are open.
Hubel and Wiesel [4] advanced the theory that receptive fields of cells at one level of the visual system are formed from input by cells at a lower level of the visual system. In this way, small, simple receptive fields could be combined to form large, complex receptive fields. Later theorists elaborated this simple, hierarchical arrangement by allowing cells at one level of the visual system to be influenced by feedback from higher levels.
Receptive fields have been mapped for all levels of the visual system from photoreceptors, to retinal ganglion cells, to lateral geniculate nucleus cells, to visual cortex cells, to extrastriate cortical cells. Studies based on perception do not give the full picture of the understanding of visual phenomena, so the electrophysiological tools must be used, as the retina, after all, is an outgrowth of the brain.
Retinal ganglion cells[edit]
On center and off center retinal ganglion cells respond oppositely to light in the center and surround of their receptive fields. A strong response means high frequency firing, a weak response is firing at a low frequency, and no response means no action potential is fired.
A computer emulation of "edge detection" using retinal receptive fields. On-centre and off-centre stimulation is shown in red and green respectively.
Each ganglion cell or optic nerve fiber bears a receptive field, increasing with intensifying light. In the largest field, the light has to be more intense at the periphery of the field than at the center, showing that some synaptic pathways are more preferred than others.
The organization of ganglion cells' receptive fields, composed of inputs from many rods and cones, provides a way of detecting contrast, and is used for detecting objects' edges.[citation needed] Each receptive field is arranged into a central disk, the "center", and a concentric ring, the "surround", each region responding oppositely to light. For example, light in the centre might increase the firing of a particular ganglion cell, whereas light in the surround would decrease the firing of that cell.
There are two types of retinal ganglion cells: "on-center" and "off-center". An on-center cell is stimulated when the center of its receptive field is exposed to light, and is inhibited when the surround is exposed to light. Off-center cells have just the opposite reaction. On the edge between the two, in mammals, an on-off effect (i.e., discharging at switching on or off but not at a duration of either state) is present.[5] Stimulation of the center of an on-center cell's receptive field produces depolarization and an increase in the firing of the ganglion cell, stimulation of the surround produces a hyperpolarization and a decrease in the firing of the cell, and stimulation of both the center and surround produces only a mild response (due to mutual inhibition of center and surround). An off-center cell is stimulated by activation of the surround and inhibited by stimulation of the center (see figure).
Photoreceptors that are part of the receptive fields of more than one ganglion cell are able to excite or inhibit postsynaptic neurons because they release the neurotransmitter glutamate at their synapses, which can act to depolarize or to hyperpolarize a cell, depending on whether there is a metabotropic or ionotropic receptor on that cell.
The center-surround receptive field organization allows ganglion cells to transmit information not merely about whether photoreceptor cells are exposed to light, but also about the differences in firing rates of cells in the center and surround. This allows them to transmit information about contrast. The size of the receptive field governs the spatial frequency of the information: small receptive fields are stimulated by high spatial frequencies, fine detail; large receptive fields are stimulated by low spatial frequencies, coarse detail. Retinal ganglion cell receptive fields convey information about discontinuities in the distribution of light falling on the retina; these often specify the edges of objects. In dark adaptation, the peripheral opposite activity zone becomes inactive, but, since it is a diminishing of inhibition between center and periphery, the active field can actually increase, allowing more area for summation.[5]
The receptive field tends to favor movement (such as a light or dark spot moving over the field, as in center-to-periphery (or vice versa)), as well as contours (due to their nonuniformity in the receptive fields). The center of the visual field has as much diameter as its dendrite spread, so the periphery is founded by amacrine cells connecting a wide area of bipolars to the ganglion. These amacrine cells can also inhibit signals of the periphery from being transmitted to the ganglion, thus rendering it on-center, off-periphery. In the rabbit, one direction, the "preferred," of a moving patch of light will excite a ganglion cell, whereas the opposite ("null") direction will not, also inhibiting spontaneous activity. Thus, there may be a linear nature of photoreceptors, one inhibiting its following neighbor when moving in the null direction, but arriving too late at the adjacent cell when traveling in the preferred direction.[5]
Lateral geniculate nucleus[edit]
Main article: lateral geniculate nucleus
Further along in the visual system, groups of ganglion cells form the receptive fields of cells in the lateral geniculate nucleus. Receptive fields are similar to those of ganglion cells, with an antagonistic center-surround system and cells that are either on- or off center.
Visual cortex[edit]
Main article: visual cortex
Receptive fields of cells in the visual cortex are larger and have more-complex stimulus requirements than retinal ganglion cells or lateral geniculate nucleus cells. Hubel and Wiesel (e.g., Hubel, 1963; Hubel-Wiesel 1959) classified receptive fields of cells in the visual cortex into simple cells, complex cells, and hypercomplex cells. Simple cell receptive fields are elongated, for example with an excitatory central oval, and an inhibitory surrounding region, or approximately rectangular, with one long side being excitatory and the other being inhibitory. Images for these receptive fields need to have a particular orientation in order to excite the cell. For complex-cell receptive fields, a correctly oriented bar of light might need to move in a particular direction in order to excite the cell. For hypercomplex receptive fields, the bar might also need to be of a particular length.
Original Organization of Visual Processing Cells by Hubel and Wiesel
Cell Type
Selectivity
Location
Simple orientation, position Brodmann area 17
Complex orientation, motion, direction Brodmann area 17 and 18
Hypercomplex orientation, motion, direction, length Brodmann areas 18 and 19
Extrastriate visual areas[edit]
In extrastriate visual areas, cells can have very large receptive fields requiring very complex images to excite the cell. For example, in the inferotemporal cortex, receptive fields cross the midline of visual space and require images such as radial gratings or hands. It is also believed that in the fusiform face area, images of faces excite the cortex more than other images. This property was one of the earliest major results obtained through fMRI (Kanwisher, McDermott and Chun, 1997); the finding was confirmed later at the neuronal level (Tsao, Freiwald, Tootell and Livingstone, 2006). In a similar vein, people have looked for other category-specific areas and found evidence for regions representing views of places (parahippocampal place area) and the body (Extrastriate body area). However, more recent research has suggested that the fusiform face area is specialised not just for faces, but also for any discrete, within-category discrimination.[6]
Computational theories of visual and auditory receptive fields[edit]
Idealized models of visual receptive fields similar to those found in the retina, lateral geniculate nucleus (LGN) and the primary visual cortex of higher mammals can be derived in an axiomatic way from structural requirements on the first stages of visual processing that reflect symmetry properties of the surrounding world.[7][8] Specifically, functional models for linear receptive fields can be derived in a principled manner to constitute a combination of Gaussian derivatives over the spatial domain and either non-causal Gaussian derivatives or truly time-causal temporal scale-space kernels over the temporal domain. Such receptive fields can be shown to enable computation of invariant visual representations under natural image transformations.[9] By these results, the different shapes of receptive field profiles found in biological vision, which are tuned to different sizes and orientations in the image domain as well as to different image velocities in space-time, can be seen as well adapted to structure of the physical world and be explained from the requirement that the visual system should be invariant to the natural types of image transformations that occur in its environment.[7][8][9]
A computational theory for auditory receptive fields can be expressed in a structurally similar way, permitting the derivation of auditory receptive fields in two stages:[10]
a first stage of temporal receptive fields corresponding to an idealized cochlea model modeled as window Fourier transform with either Gabor functions in the case of non-causal time or gammatone functions alternatively generalized gammatone functions for a truly time-causal model in which the future cannot be accessed,
a second layer of spectra-temporal receptive fields modeled as Gaussian functions over the log-spectral domain and either Gaussian kernels over time in the case of non-causal time or first-order integrators (truncated exponential kernels) coupled in cascade in the case of truly time-causal operations.
The shapes of the receptive field functions in these models can be determined by necessity from structural properties of the environment combined with requirements about the internal structure of the auditory system to enable theoretically well-founded processing of sound signals at different temporal and log-spectral scales.[10]
In the context of neural networks[edit]
Neurons of a convolutional layer (blue), connected to their receptive field (red)
CNN layers arranged in three dimensions
The term receptive field is also used in the context of artificial neural networks, most often in relation to convolutional neural networks (CNNs). When used in this sense, the term adopts a meaning reminiscent of receptive fields in actual biological nervous systems. CNNs have a distinct architecture, designed to mimic the way in which real animal brains are understood to function; instead of having every neuron in each layer connect to all neurons in the next layer (Multilayer perceptron), the neurons are arranged in a 3-dimensional structure in such a way as to take into account the spatial relationships between different neurons with respect to the original data. Since CNNs are used primarily in the field of computer vision, the data that the neurons represent is typically an image; each input neuron represents one pixel from the original image. The first layer of neurons is composed of all the input neurons; neurons in the next layer will receive connections from some of the input neurons (pixels), but not all, as would be the case in a MLP and in other traditional neural networks. Hence, instead of having each neuron receive connections from all neurons in the previous layer, CNNs use a receptive field-like layout in which each neuron receives connections only from a subset of neurons in the previous (lower) layer. The receptive field of a neuron in one of the lower layers encompasses only a small area of the image, while the receptive field of a neuron in subsequent (higher) layers involves a combination of receptive fields from several (but not all) neurons in the layer before (i. e. a neuron in a higher layer "looks" at a larger portion of the image than does a neuron in a lower layer). In this way, each successive layer is capable of learning increasingly abstract features of the original image. The use of receptive fields in this fashion is thought to give CNNs an advantage in recognizing visual patterns when compared to other types of neural networks.
See also[edit]
Visual system
Reflexogenic zone
Spatiotemporal receptive field
Spectro-temporal receptive field
Axiomatic theory of receptive fields
Computer vision
Edge detection
Convolutional neural network
References[edit]
Jump up ^ Sherrington, C. S. (1906). "Observations on the scratch-reflex in the spinal dog". Journal of Physiology. 34: 1–50. doi:10.1113/jphysiol.1906.sp001139. PMC 1465804  .
Jump up ^ Alonso, J.-M.; Chen, Y. (2008). "Receptive field". Scholarpedia. 4 (1): 5393. doi:10.4249/scholarpedia.5393.
Jump up ^ "Estimating spatio-temporal receptive fields of auditory and visual neurons from their responses to natural stimuli". Network: Computation in Neural Systems. 12: 289–316. doi:10.1080/net.12.3.289.316.
Jump up ^ e.g., Hubel, 1963; Hubel-Wiesel, 1962
^ Jump up to: a b c "eye, human." Encyclopædia Britannica. Encyclopædia Britannica Ultimate Reference Suite. Chicago: Encyclopædia Britannica, 2010.
Jump up ^ McGugin, RW; Gatenby, JC; Gore, JC; Gauthier, I. "High-resolution imaging of expertise reveals reliable object selectivity in the fusiform face area related to perceptual performance". Proc Natl Acad Sci U S A. 109: 17063–8. doi:10.1073/pnas.1116333109. PMC 3479484  . PMID 23027970.
^ Jump up to: a b T. Lindeberg "A computational theory of visual receptive fields", Biological Cybernetics, 107(6):589-635, 2013
^ Jump up to: a b T. Lindeberg "Time-causal and time-recursive spatio-temporal receptive fields", Journal of Mathematical Imaging and Vision, 55(1):50-88, 2016.
^ Jump up to: a b T. Lindeberg "Invariance of visual operations at the level of receptive fields", PLOS ONE 8(7):e66990, pages 1-33, 2013
^ Jump up to: a b T. Lindeberg and A. Friberg "Idealized computational models of auditory receptive fields", PLOS ONE, 10(3): e0119032, pages 1-58, 2015
Hubel, D. H. (1963). "The visual cortex of the brain". Scientific American. 209 (5): 54–62. doi:10.1038/scientificamerican1163-54.
Kandel E.R., Schwartz, J.H., Jessell, T.M. (2000). Principles of Neural Science, 4th ed., pp. 515–520. McGraw-Hill, New York.
External links[edit]
An open-access, refereed article on receptive fields: Alonso, J.-M., & Chen, Y. (2008). Receptive field. Scholarpedia, 4(1), 5393. doi: 10.4249/scholarpedia.5393
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