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In music, the tonic is the first scale degree of a diatonic scale and the tonal center or final resolution tone.^[4] The triad formed on the tonic note, the tonic chord, is thus the most significant chord. More generally, the tonic is the pitch upon which all other pitches of a piece are hierarchically referenced. Scales are named after their tonics, thus the tonic of the scale of C is the note C.

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The tonic is often confused with the root, which is the reference note of a chord, rather than that of the scale. It is also represented with the Roman numeral I.

Importance and function

In western European tonal music of the 18th and 19th centuries, the tonic center was the most important of all the different tone centers which a composer used in a piece of music, with most pieces beginning and ending on the tonic, usually modulating to the dominant (the fifth above the tonic, or the fourth note down from the tonic) in between.

Two parallel keys have the same tonic. For example, in both C major and C minor, the tonic is C. However, relative keys (two different scales that share a key signature) have different tonics. For example, C major and A minor share a key signature that feature no sharps or flats, despite having different tonic pitches (C and A, respectively).

<Tone center>...</Tone center>Tonic may be reserved exclusively for use in tonal contexts while tonal center and/or pitch center may be used in post- and atonal music: "For purposes of non-tonal centric music, it might be a good idea to have the term 'tone center' refer to the more general class of which 'tonics' (or tone centers in tonal contexts) could be regarded as a subclass."^[5] Thus a pitch center may function referentially or contextually in an atonal context, often acting as axis or line of symmetry in an interval cycle.^[6] Pitch centricity was coined by Arthur Berger in his "Problems of Pitch Organization in Stravinsky".^[7]

The tonic diatonic function includes four separate activities or roles as the principal goal tone, initiating event, generator of other tones, and the stable center neutralizing the tension between dominant and subdominant.

References

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.

In computational complexity theory, the potential method is a method used to analyze the amortized time and space complexity of a data structure, a measure of its performance over sequences of operations that smooths out the cost of infrequent but expensive operations.^[8]^[9]

Definition of amortized time

In the potential method, a function Φ is chosen that maps states of the data structure to non-negative numbers. If S is a state of the data structure, Φ(S) may be thought of intuitively as an amount of potential energy stored in that state;^[8]^[9] alternatively, Φ(S) may be thought of as representing the amount of disorder in state S or its distance from an ideal state. The potential value prior to the operation of initializing a data structure is defined to be zero.

Let o be any individual operation within a sequence of operations on some data structure, with S_before denoting the state of the data structure prior to operation o and S_after denoting its state after operation o has completed. Then, once Φ has been chosen, the amortized time for operation o is defined to be

T_{\mathrm {amortized} }(o)=T_{\mathrm {actual} }(o)+C\cdot (\Phi (S_{\mathrm {after} })-\Phi (S_{\mathrm {before} })),

where C is a non-negative constant of proportionality (in units of time) that must remain fixed throughout the analysis. That is, the amortized time is defined to be the actual time taken by the operation plus C times the difference in potential caused by the operation.^[8]^[9]

Relation between amortized and actual time

Despite its artificial appearance, the total amortized time of a sequence of operations provides a valid upper bound on the actual time for the same sequence of operations. That is, for any sequence of operations $o_{0},o_{1},\dots$ , the total amortized time $\sum _{i}T_{\mathrm {amortized} }(o_{i})$ is always at least as large as the total actual time $\sum _{i}T_{\mathrm {actual} }(o_{i})$ . In more detail,

\sum _{i}T_{\mathrm {amortized} }(o_{i})=\sum _{i}\left(T_{\mathrm {actual} }(o_{i})+C\cdot (\Phi (S_{i+1})-\Phi (S_{i}))\right)=\left(\sum _{i}T_{\mathrm {actual} }(o_{i})\right)+C\cdot (\Phi (S_{\mathrm {final} })-\Phi (S_{\mathrm {initial} }))\geq \sum _{i}T_{\mathrm {actual} }(o_{i}),

where the sequence of potential function values forms a telescoping series in which all terms other than the initial and final potential function values cancel in pairs, and where the final inequality arises from the assumptions that $\Phi (S_{\mathrm {final} })\geq 0$ and $\Phi (S_{\mathrm {initial} })=0$ . Therefore, amortized time can be used to provide accurate predictions about the actual time of sequences of operations, even though the amortized time for an individual operation may vary widely from its actual time.

Amortized analysis of worst-case inputs

Typically, amortized analysis is used in combination with a worst case assumption about the input sequence. With this assumption, if X is a type of operation that may be performed by the data structure, and n is an integer defining the size of the given data structure (for instance, the number of items that it contains), then the amortized time for operations of type X is defined to be the maximum, among all possible sequences of operations on data structures of size n and all operations o_i of type X within the sequence, of the amortized time for operation o_i.

With this definition, the time to perform a sequence of operations may be estimated by multiplying the amortized time for each type of operation in the sequence by the number of operations of that type.

Example

A dynamic array is a data structure for maintaining an array of items, allowing both random access to positions within the array and the ability to increase the array size by one. It is available in Java as the "ArrayList" type and in Python as the "list" type. A dynamic array may be implemented by a data structure consisting of an array A of items, of some length N, together with a number n ≤ N representing the positions within the array that have been used so far. With this structure, random accesses to the dynamic array may be implemented by accessing the same cell of the internal array A, and when n < N an operation that increases the dynamic array size may be implemented simply by incrementing n. However, when n = N, it is necessary to resize A, and a common strategy for doing so is to double its size, replacing A by a new array of length 2n.^[10]

This structure may be analyzed using a potential function Φ = 2n − N. Since the resizing strategy always causes A to be at least half-full, this potential function is always non-negative, as desired. When an increase-size operation does not lead to a resize operation, Φ increases by 2, a constant. Therefore, the constant actual time of the operation and the constant increase in potential combine to give a constant amortized time for an operation of this type.

However, when an increase-size operation causes a resize, the potential value of n prior to the resize decreases to zero after the resize. Allocating a new internal array A and copying all of the values from the old internal array to the new one takes O(n) actual time, but (with an appropriate choice of the constant of proportionality C) this is entirely cancelled by the decrease of n in the potential function, leaving again a constant total amortized time for the operation.

The other operations of the data structure (reading and writing array cells without changing the array size) do not cause the potential function to change and have the same constant amortized time as their actual time.^[9]

Therefore, with this choice of resizing strategy and potential function, the potential method shows that all dynamic array operations take constant amortized time. Combining this with the inequality relating amortized time and actual time over sequences of operations, this shows that any sequence of n dynamic array operations takes O(n) actual time in the worst case, despite the fact that some of the individual operations may themselves take a linear amount of time.^[9]

Applications

The potential function method is commonly used to analyze Fibonacci heaps, a form of priority queue in which removing an item takes logarithmic amortized time, and all other operations take constant amortized time.^[11] It may also be used to analyze splay trees, a self-adjusting form of binary search tree with logarithmic amortized time per operation.^[12]

References

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro. Template:Chords

Warning: Default sort key "Tonic (Music)" overrides earlier default sort key "Potential Method".

↑ Benward & Saker (2003). Music: In Theory and Practice, Vol. I, p.229. Seventh Edition. ISBN 978-0-07-294262-0.
↑ ^2.0 ^2.1 Benward & Saker (2003), p.230.
↑ Berg, Shelly (2005). Alfred's Essentials of Jazz Theory, Book 3, p.90. ISBN 978-0-7390-3089-9.
↑ Benward & Saker (2003), p.33.
↑ Berger (1963), p. 12. cited in Swift, Richard. "A Tonal Analog: The Tone-Centered Music of George Perle", p.258. Perspectives of New Music, Vol. 21, No. 1/2, (Autumn, 1982 - Summer, 1983), pp. 257-284.
↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 Template:Page needed
↑ One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
↑ ^8.0 ^8.1 ^8.2 Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010.
↑ ^9.0 ^9.1 ^9.2 ^9.3 ^9.4 Template:Introduction to Algorithms
↑ Goodrich and Tamassia, 1.5.2 Analyzing an Extendable Array Implementation, pp. 139–141; Cormen et al., 17.4 Dynamic tables, pp. 416–424.
↑ Cormen et al., Chapter 20, "Fibonacci Heaps", pp. 476–497.
↑ Goodrich and Tamassia, Section 3.4, "Splay Trees", pp. 185–194.

[B&S-1] Benward & Saker (2003). Music: In Theory and Practice, Vol. I, p.229. Seventh Edition. ISBN 978-0-07-294262-0.

[B&S_230-2] 2.0 ^2.1 Benward & Saker (2003), p.230.

[3] Berg, Shelly (2005). Alfred's Essentials of Jazz Theory, Book 3, p.90. ISBN 978-0-7390-3089-9.

[4] Benward & Saker (2003), p.33.

[5] Berger (1963), p. 12. cited in Swift, Richard. "A Tonal Analog: The Tone-Centered Music of George Perle", p.258. Perspectives of New Music, Vol. 21, No. 1/2, (Autumn, 1982 - Summer, 1983), pp. 257-284.

[6] 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 Template:Page needed

[7] One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang

[gt-ad-8] 8.0 ^8.1 ^8.2 Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010.

[clrs-9] 9.0 ^9.1 ^9.2 ^9.3 ^9.4 Template:Introduction to Algorithms

[10] Goodrich and Tamassia, 1.5.2 Analyzing an Extendable Array Implementation, pp. 139–141; Cormen et al., 17.4 Dynamic tables, pp. 416–424.

[11] Cormen et al., Chapter 20, "Fibonacci Heaps", pp. 476–497.

[12] Goodrich and Tamassia, Section 3.4, "Splay Trees", pp. 185–194.

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+[[Image:Ii-V-I turnaround in C.png|thumb|300px|Tonic (I) in [[ii-V-I turnaround]] on C, found at the end of the [[circle progression]] {{audio|Ii-V-I turnaround in C.mid|Play}}]]
+[[Image:Major seventh chord on C.png|thumb|right|Major seventh chord on C {{audio|Major seventh chord on C.mid|Play}}. I<sup>7</sup> or '''tonic seventh chord''' in C major.<ref name="B&S">Benward & Saker (2003). ''Music: In Theory and Practice, Vol. I'', p.229. Seventh Edition. ISBN 978-0-07-294262-0.</ref>]]
+[[Image:Minor seventh chord on C.png|thumb|right|Minor-minor (i<sup>7</sup>) seventh chord on C in natural minor.<ref name="B&S 230">Benward & Saker (2003), p.230.</ref> {{audio|Minor seventh chord on C.mid|Play}}]]
+[[Image:Minor major seventh chord on C.png|thumb|right|Minor major seventh chord on C.<br/> i<math>_M^7</math> in C [[Minor scale#Harmonic and melodic minor|harmonic]] or [[minor scale|ascending melodic minor]].<ref name="B&S 230"/> {{audio|Minor major seventh chord on C.mid|Play}}]]
+[[Image:Minor 6-9 chord on C.png|thumb|right|Tonic minor [[6/9 chord]] on C, featuring the raised sixth degree of the [[jazz minor scale|ascending melodic minor]].<ref>Berg, Shelly (2005). ''Alfred's Essentials of Jazz Theory'', Book 3, p.90. ISBN 978-0-7390-3089-9.</ref> {{audio|Minor 6-9 chord on C.mid|Play}}]]
+In [[music]], the '''tonic''' is the first [[degree (music)|scale degree]] of a [[diatonic scale]] and the [[tonality|tonal]] center or final [[resolution (music)|resolution]] tone.<ref>Benward & Saker (2003), p.33.</ref> The [[triad (music)|triad]] formed on the tonic note, the '''tonic chord''', is thus the most significant [[chord (music)|chord]]. More generally, the '''tonic''' is the [[pitch (music)|pitch]] upon which all other pitches of a piece are [[hierarchy|hierarchically]] referenced. Scales are named after their tonics, thus the tonic of the scale of C is the note C.
+{{quote|In very much conventionally tonal music, harmonic [[musical analysis|analysis]] will reveal a broad prevalence of the [[primary triad|primary]] (often triadic) [[harmony|harmonies]]: tonic, dominant, and [[subdominant]] (i.e., I and its chief auxiliaries a 5th removed), and especially the first two of these.|Berry (1976)<ref name="Berry">Berry, Wallace (1976/1987). ''Structural Functions in Music'', p.62. ISBN 0-486-25384-8.</ref>}}
+The '''tonic''' is often confused with the [[root (chord)|root]], which is the reference note of a chord, rather than that of the scale. It is also represented with the [[Roman numeral analysis|Roman numeral]] I.
+==Importance and function==
+In western European tonal [[music]] of the 18th and 19th centuries, the tonic center was the most important of all the different tone centers which a [[composer]] used in a piece of music, with most pieces beginning and ending on the tonic, usually modulating to the [[dominant (music)|dominant]] (the fifth above the tonic, or the fourth note down from the tonic) in between.
+Two [[parallel key]]s have the same tonic.  For example, in both C major and C minor, the tonic is C.  However, [[relative key]]s  (two different scales that share a [[key signature]]) have different tonics. For example, C major and A minor share a key signature that feature no sharps or flats, despite having different tonic pitches (C and A, respectively).
+{{anchor|Tone center}}''Tonic'' may be reserved exclusively for use in tonal contexts while '''''tonal center''''' and/or '''''pitch center''''' may be used in post- and atonal music: "For purposes of non-tonal centric music, it might be a good idea to have the term 'tone center' refer to the more general class of which 'tonics' (or tone centers in tonal contexts) could be regarded as a subclass."<ref>Berger (1963), p. 12. cited in Swift, Richard. "[http://www.jstor.org/stable/832876 A Tonal Analog: The Tone-Centered Music of George Perle]", p.258. ''Perspectives of New Music'', Vol. 21, No. 1/2, (Autumn, 1982 - Summer, 1983), pp. 257-284.</ref> Thus a pitch center may function referentially or contextually in an [[atonal]] context, often acting as axis or line of symmetry in an [[interval cycle]].<ref>{{Cite book|last=Samson |first=Jim |title=Music in transition: a study of tonal expansion and atonality, 1900-1920 |publisher=[[W. W. Norton & Company]] |location=[[New York City]] |year=1977 |pages= |isbn=0-393-02193-9 |oclc=3240273}}{{Page needed|date=September 2010}}</ref> '''''Pitch centricity''''' was coined by [[Arthur Berger]] in his "Problems of Pitch Organization in Stravinsky".<ref>{{Cite journal|doi=10.2307/832252 |last=Berger |first=Arthur |authorlink=Arthur Berger |date=Fall–Winter 1963 |title=Problems of Pitch Organization in Stravinsky |journal=[[Perspectives of New Music]] |volume=2 |issue=1 |pages=11–42|jstor=832252}}</ref>
+The '''tonic''' [[diatonic function]] includes four separate activities or roles as the principal goal tone, initiating event, generator of other tones, and the stable center neutralizing the tension between dominant and subdominant.
+==See also==
+* [[Final (music)]]
+==References==
+{{Reflist}}
+{{degrees|state=uncollapsed}}
+{{chords}}
+{{DEFAULTSORT:Tonic (Music)}}
+[[Category:Scale degrees|1]]
+[[Category:Diatonic functions]]

Callisto (moon): Difference between revisions

Revision as of 14:51, 3 February 2014

Contents

Importance and function

See also

References

Definition of amortized time

Relation between amortized and actual time

Amortized analysis of worst-case inputs

Example

Applications

References

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Callisto (moon): Difference between revisions

Revision as of 14:51, 3 February 2014

Importance and function

See also

References

Definition of amortized time

Relation between amortized and actual time

Amortized analysis of worst-case inputs

Example

Applications

References

Navigation menu

Search