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| [[File:pitch constellation chromatic.svg|thumb|400px|Pitch constellations showing all twelve chromatic pitches]]
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| A '''pitch constellation''' is a graphical representation of [[Pitch (music)|pitches]] used to describe [[musical scale]]s, [[Musical mode|modes]], [[Chord (music)|chords]] or other groupings of [[Pitch (music)|pitches]] within an octave range.<ref name="Slonimsky">Slonimsky 1947, {{page needed|date=September 2012}}.</ref><ref name="Burns">Burns 1999, {{page needed|date=September 2012}}.</ref><ref>Lerdahl 2001, {{page needed|date=September 2012}}.</ref> It consists of a circle with markings along the circumference or lines from the center which indicate pitches. Most pitch constellations use of a subset of pitches chosen from the twelve pitch [[chromatic scale]]. In this case the points on the circle are spaced like the twelve hour markings on an analog clock where each tick mark represents a semitone.
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| ==Scales and modes==
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| The pitch constellation provides an easy way to identify certain patterns and similarities between [[Harmony|harmonic]] structures.
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| For example.
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| * A [[major scale]] consists of a circle with markings at 0 (or 12), 2, 4, 5, 7, 9 and 11 o'clock.
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| * A [[minor scale]] consists of a circle with markings at 0 (or 12), 2, 3, 5, 7, 8 and 10 o'clock.
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| [[File:Pitch constellation degrees.svg|400px|Pitch constellations showing major and minor scales in degrees]]
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| The diagrams above show the two scales marked with [[Degree (music)|"scale degrees"]]. It can be observed that the [[Tonic (music)|tonic]], second, fourth and fifth are shared, while the minor scale [[Flat (music)|flattens]] the third, sixth and seventh notes relative to the major scale.<ref name="Glaser">Glaser 1999, {{page needed|date=September 2012}}.</ref> Another observation is that the minor scale's constellation is the same as the major scale, but rotated +90 degrees.
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| In the following drawing all of the major/minor scales are drawn. Note that the constellation for all the major scales or all the minor scales are identical. The different scales are generated by rotating the note overlay. The notes that need to be [[Sharp (music)|sharpened]]/flattened can be easily identified.
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| {| class="wikitable" width=400px
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| {{show
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| |Major and minor scales
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| |[[File:Pitch constellation major scales.svg|400px|Major scales in all keys]]
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| [[File:Pitch constellation minor scales.svg|400px|Minor scales in all keys]]}}
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| |}
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| Moreover, if we draw all seven [[Diatonic and chromatic|diatonic]] [[Musical mode|modes]] we can see them all as rotations of the [[Ionian mode]].<ref name="Slonimsky"/><ref>Yamaguchi 2006, {{page needed|date=September 2012}}.</ref> Note also the significance of the 6 o'clock point. This corresponds to a [[tritone]]. The modes including pitches a tritone from the tonic ([[Locrian mode|Locrian]] and [[Lydian mode|Lydian]]) are least used. The 5 o'clock and 7 o'clock pitches are also important points corresponding to a [[perfect fourth]] and [[perfect fifth]] respectively. The most used scales/modes - major ([[Ionian mode]]), minor ([[Aeolian mode]]) and [[Mixolydian mode|Mixolydian]] - include these pitches.
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| <!--this image is displayed wider than 400px for detail-->
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| [[File:Modes.svg|500px|Modern musical modes]]
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| [[Symmetric scale]]s have simple representations in this scheme.
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| <!--this image is displayed wider than 400px for detail-->
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| [[File:Symmetric.svg|500px|Symmetric scales (as defined by Slonimsky)]]
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| More exotic scales - such as the [[Pentatonic scale|pentatonic]], [[Blues scale|blues]] and [[Octatonic scale|octatonic]] - can also be drawn and related to the common scales.
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| [[File:Exotic.svg|400px|Less common scales]]
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| A more complete [[list of musical scales and modes]]
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| <!--this image is displayed wider than 400px for detail-->
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| [[File:pitch-constellations-44-modes.png|600px]]
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| ==Other overlays==
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| In previous sections we saw how various overlays (scale degrees, semi-tone numbering, notes) can be used to notate the circumference of the constellation. Various other overlays can be laid around the constellation. For example:
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| * [[Interval (music)|Intervals]].
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| * [[Solfège]].
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| * [[Interval ratio|Pitch ratios]] (ratios of pitch frequencies).
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| <!--this image is displayed wider than 400px for detail-->
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| [[File:Overlays.svg|500px|Pitch constellation overlays (i.e. - the hour markings)]]
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| Note that once a pitch constellation has been determined, any number of overlays (notes, solfège, intervals, etc.) may be placed on top for analysis/comparison. Often generating one harmonic relationship from another is simply a matter of rotating the overlay or constellation or shifting one or two pitch locations.
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| ==Chords==
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| Similarities between [[Chord (music)|chords]] can also be observed as well as the significance of [[Augmentation (music)|augmented/diminished]] notes.<ref name="Burns"/><ref name="Glaser"/>
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| For [[Triad (music)|triads]] we have the following:
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| [[File:Pitch constellation triads.svg|400px|Triadic chords (key of C)]]
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| And for [[seventh chord]]s:
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| [[File:Sev chord.svg|400px|Seventh chords (key of C)]]
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| ==Circle of fifths==
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| Beginning with a pitch constellation of a chromatic scale, the notes of a [[circle of fifths]] can be easily generated. Starting at C and moving across the circle and then one tick clockwise a line is draw with an arrow indicating the direction moved. Continuing from that point (across the circle and one tick clockwise) all points are connected. Moving through this pattern the notes of the circle of fifths
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| can be determined (C, G, D, A ...).
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| [[File:Pitch constellation fifths.svg|400px|Generating notes for a circle of fifths from a pitch constellation of a chromatic scale]]
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| ==Technical note==
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| The ratio of the frequencies between two pitches in the constellation can be determined as follows.<ref>Josephs 1967, {{page needed|date=September 2012}}.</ref> Take the length of the arc (measured clockwise) between the two points and divide by the circumference of the circle. The frequency ratio is two raised to this power. For example, for a fifth ('''P5''', which is located at 7 o'clock relative to the tonic '''T''') the frequency ratio is:
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| <math>{\text{f}_\text{P5} \over \text{f}_\text{T}} = 2 ^ {( 7 / 12 )} \approx 1.49821 \approx {3 \over 2}</math>
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| ==Notes==
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| <references/>
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| == References ==
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| * {{Citation
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| | last = Burns
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| | first = Edward M.
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| | year = 1999
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| | title = Intervals, Scales, and Tuning. The Psychology of Music.
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| | publisher = Academic Press
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| | isbn = 0-12-213564-4
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| }}
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| * {{Citation
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| | last = Glaser
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| | first = Matt
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| | year = 1999
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| | title = Ear Training for Instrumentalists (Audio CD)
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| | publisher = Homespun
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| | isbn = 0-634-00385-2
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| }}
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| * {{Citation
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| | last = Josephs
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| | first = Jess L.
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| | year = 1967
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| | title = The Physics of Musical Sound
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| | publisher = Van Nostrand Company
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| | isbn =
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| }}
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| * {{Citation
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| | last = Lerdahl
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| | first = Fred
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| | year = 2001
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| | title = Tonal Pitch Space
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| | publisher = Oxford University Press
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| | isbn = 0-19-505834-8
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| }}
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| * {{Citation
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| | last = Olson
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| | first = Harry F.
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| | year = 1967
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| | title = Music, Physics and Engineering
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| | publisher = Dover Publications
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| | isbn = 0-486-21769-8
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| }}
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| * {{Citation
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| | last = Slonimsky
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| | first = Nicolas
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| | year = 1947
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| | title = Thesaurus of Scales and Melodic Patterns
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| | publisher = Music Sales America
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| | isbn = 0-8256-1449-X
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| }}
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| * {{Citation
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| | last = Yamaguchi
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| | first = Masaya
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| | year = 2006
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| | title = Symmetrical Scales for Jazz Improvisation
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| | publisher = Masaya Music
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| | isbn = 0-9676353-2-2
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| }}
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| == External links ==
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| * [http://tcolgan.freeshell.org/pub/mandolinnotes.pdf PDF of musical scales]
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| {{Pitch space}}
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| [[Category:Pitch space]]
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Hi!
My name is Arnette and I'm a 30 years old boy from Australia.
Visit my web site: buy essay now