en>BG19bot: /* Stability */WP:CHECKWIKI error fix for #64. Do general fixes if a problem exists. - using AWB (9399)

2013-08-10T08:20:36Z

Stability: WP:CHECKWIKI error fix for #64. Do general fixes if a problem exists. - using AWB (9399)

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	~~If an existing Word - Press code~~ is ~~found vulnerable, Word - Press will immediately issue~~ an ~~update for that~~. It ~~is thus~~, ~~on these grounds that compel various web service provider companies to integrate~~ the same in ~~their packages too~~. ~~SEO Ultimate - I think this plugin deserves more recognition than it's gotten up till now~~. ~~They found out all~~ the ~~possible information about bringing up your baby~~ and ~~save money at the same time. Over a million people are using Wordpress~~ to ~~blog~~ and ~~the number of Wordpress users is increasing every day~~. ~~<br><br>~~		In [[music theory]], the '''spiral array model''' is an extended type of [[pitch space]]. It represents human perceptions of [[pitch (music)\|pitch]], [[chord (music)\|chord]] and [[key (music)\|key]] in the same [[space\|geometric space]], as a mathematical model involving concentric [[helix]]es (an "array of [[spiral]]s"). It was proposed in 2000 by Prof. Elaine Chew in her MIT doctoral thesis "Toward a Mathematical Model of [[Tonality]]". Further research by Chew and others have produced modifications of the spiral array model, and, applied it to various problems in music theory and practice, such as key finding and pitch spelling.

	~~Creating a website from scratch~~ can be ~~such~~ a ~~pain~~. ~~When you write a new post~~, ~~you'll see a small bar that goes across~~ the ~~text input area~~. This ~~plugin is a must have for anyone who is serious about using Word - Press. You can up your site's rank with~~ the ~~search engines by simply taking a bit~~ of ~~time with your site~~. For ~~a Wordpress website~~, you ~~don't need~~ a ~~powerful web hosting account~~ to ~~host your site~~. ~~<br><br>If you loved this report~~ and ~~you would like to acquire far more data~~ with ~~regards to~~ [~~http://2am~~.~~eu/wordpressdropboxbackup21027 backup plugin] kindly stop~~ by the ~~webpage~~. ~~Your Word - Press blog~~ or ~~site will also require a domain name which many hosting companies can also provide~~. ~~Now if we talk about them one~~ by ~~one then -wordpress blog customization means customization~~ of ~~your blog such~~ as ~~installation~~ of ~~wordpress on your server~~ by ~~wordpress developer which will help you to acquire~~ the ~~SEO friendly blog application integrated with your site design as well as separate blog administration panel for starting up your own business blog~~,~~which demands~~ a ~~experienced wordpress designer~~. ~~Whether or not it's an viewers on your web page~~, ~~your social media pages~~, ~~or your web page~~, ~~those who have~~ a ~~present~~ and ~~effective viewers~~ of ~~"fans" are best best for provide provides~~, ~~reductions~~, and ~~deals~~ to ~~help re-invigorate their viewers~~ and ~~add to~~ their ~~main point here~~. ~~Our skilled expertise~~, ~~skillfulness~~ and ~~excellence have been well known all across~~ the ~~world~~. ~~Have you heard about niche marketing~~ and ~~advertising~~. <br><br>~~You can add keywords but it~~ is ~~best to leave this alone. I have compiled~~ a ~~few tips on how you can start a food blog~~ and ~~hopefully~~ the ~~following information~~ and ~~tips can help you~~ to ~~get started on your food blogging creative journey~~. ~~Enterprise~~, ~~when they plan~~ to ~~hire Word - Press developer resources still PHP~~, My - ~~SQL~~ and ~~watch with great expertise in codebase~~. It'~~s now become a great place~~ to ~~sell it thanks~~ to ~~Woo - Commerce. Fortunately~~, ~~Word - Press Customization Service is available these days~~, ~~right from custom theme design~~, to ~~plugin customization and modifying your website, you can take any bespoke service for your Word - Press development project~~. <br><br>~~This advice~~ is ~~critical because you don't want to waste too expensive time establishing your Word~~ - ~~Press blog~~ the ~~exact method~~. ~~Here's a list~~ of ~~some exciting Word~~ - ~~Press features that have created waves in the web development industry~~:. ~~Word~~ - ~~Press can also be quickly extended however improvement API is not as potent as Joomla's~~. ~~And~~, ~~it is better that you leave it on for the duration you are writing plugin code~~. ~~Press CTRL and the numbers one to six to choose your option~~.		The spiral array model can be viewed as an extension of the [[tonnetz]], which maps pitches into a two-dimensional lattice structure. Just like the tonnetz, the spiral array models higher order structures such as chords and keys in the same space as the low level structure: pitches. This allows the spiral array model to produce geometric interpretations of relationships between low and high level structures. For example, you can measure the geometric distance between a particular pitch and a particular key (both represented as points). Like the tonnetz, when applied to [[equal temperament]], the spiral array model folds into a torus as octaves overlap.

			==Structure of the spiral array==
			The model covering basic pitch, major chords, minor chords, major keys and minor keys comprises five concentric helixes. Starting with a formulation of the pitch spiral, inner spirals are generated by a [[convex combination]] of points on outer spirals. For example, the pitches C, E, and G are represented as points by the cartesian coordinates C(x,y,z), E(x,y,z) and G(x,y,z). The convex combination formed by the points CEG is a triangle, and represents the "center of effect" of the three pitches. This convex combination represents the triad, or chord, CEG (the C major chord) in the spiral array model. The geometric center (or other point chosen by a weighting of the constituent points, as seen in the equations below) of the C major chord (formed by CEG) can be called the "center" of the C major chord, and assigned a point CM(x,y,z). Similarly, keys may be constructed by the centers of effect of their I, IV, and V chords.

			# The outer helix represents pitches classes. Neighboring pitch classes are a music interval of a perfect fifth, and spatially a quarter rotation, apart. The order of the pitch classes can be determined by the [[circle of fifths]]. For example, C would be followed by G, which would be followed D, etc. As a result of this structure, and one of the important properties leading to its selection, vertical neighbors are a music interval of a major third apart. Thus, a pitch class's nearest neighbors and itself form perfect fifth and major third intervals.
			# By taking every consecutive triad along the helix, and projecting their centers of effect, a second helix is formed inside the pitch helix, representing the major chords.
			# Similarly, by taking the proper minor triads and projecting their centers of effect, a third helix is formed, representing the minor chords.
			# The major key helix is formed by projections of the I, IV, and V chords from points on the major chord
			# The minor key helix is formed by similar projects of minor chords.

			==Equations==

			The '''pitch spiral P''', is represented in parametric form by:

			<math>P(k) = \begin{bmatrix}

			x_{k} \\
			y_{k} \\
			z_{k} \\
			\end{bmatrix} = \begin{bmatrix}

			r sin (k \cdot \pi / 2)\\
			r cos (k \cdot \pi / 2) \\
			kh
			\end{bmatrix}</math>

			Where k is an integer representing a semitone, r is the radius of the spiral, and h is the "rise" of the spiral

			The '''major chord C<sub>M</sub>''' is represented by:

			<math>C_M(k) = w_1 \cdot P(k) + w_2 \cdot P(k + 1) + w_3 \cdot P(k+4)</math>

			where <math>w_{1} \ge w_{2} \ge w_{3} > 0</math> and <math>\sum_{i=1}^3 w_{i} = 1</math>

			The weights "w" effect how close the center of effect are to the fundamental, major third, and perfect fifth of the chord. By changing the relative values of these weights, the spiral array model effects how "close" the resulting chord is to the three constituent pitches. Generally in western music, the fundamental is given the greatest weight in identifying the chord (w1), followed by the fifth (w2), followed by the third (w3).

			The '''minor chord C<sub>m</sub>''' is represented by:

			<math>C_m(k) = u_1 \cdot P(k) + u_2 \cdot P(k + 1) + u_3 \cdot P(k-3)</math>

			where <math>u_1 \ge u_2 \ge u_3 > 0</math> and <math>\sum_{i=1}^3 u_i = 1</math>

			The weights "u" function similarly to the major chord.

			The '''major key T<sub>M</sub>''' is represented by:

			<math>T_M(k) = W_1 \cdot P(k) + W_2 \cdot P(k + 1) + W_3 \cdot P(k-1)</math>

			where <math>W_1 \ge W_2 \ge W_3 > 0</math> and <math>\sum_{i=1}^3 W_i = 1</math>

			Similar to the weights controlling how close constituent pitches are to the center of effect of the chord they produce, the weights "W" control the relative effect of the I, IV, and V chord in determining how close they are to the resultant key.

			The '''minor key T<sub>m</sub>''' is represented by:

			<math>T_m(k) = V_1 \cdot C_M(k) + V_2 \cdot (\alpha \cdot C_M(k+1) + (1-\alpha) \cdot C_m(k+1)) + V_3 \cdot (\beta * C_m(k-1) + (1 - \beta) \cdot C_M(k - 1))</math>

			where <math>V_1 \ge V_2 \ge V_3 > 0</math> and <math>V_1 + V_2 + V_3 = 1</math> and <math>0 \ge \alpha \ge 1</math> and <math>\beta \ge 1</math>.

			==References==
			* Chuan, C.-H., Chew, E. (2005). Applying the Spiral Array Key-finding Algorithm to Polyphonic Audio. In Proceedings of the 9th INFORMS Computing Society Conference (invited sessions on Music, Computation and AI), Annapolis, MD, Jan 5-7, 2005.
			* Chew, Elaine (2002). [http://www-rcf.usc.edu/~echew/papers/ICMAI2/ec-icmai.pdf The Spiral Array: An Algorithm for Determining Key Boundaries]
			* Chew, Elaine (2000). Towards a Mathematical Model of Tonality. Ph.D. dissertation. Operations Research Center, MIT. Cambridge, MA.

			{{Pitch space}}

			[[Category:Pitch space]]

en>Peter James at 17:13, 28 May 2012

2012-05-28T17:13:10Z

New page

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Creating a website from scratch can be such a pain. When you write a new post, you'll see a small bar that goes across the text input area. This plugin is a must have for anyone who is serious about using Word - Press. You can up your site's rank with the search engines by simply taking a bit of time with your site. For a Wordpress website, you don't need a powerful web hosting account to host your site. If you loved this report and you would like to acquire far more data with regards to [http://2am.eu/wordpressdropboxbackup21027 backup plugin] kindly stop by the webpage. Your Word - Press blog or site will also require a domain name which many hosting companies can also provide. Now if we talk about them one by one then -wordpress blog customization means customization of your blog such as installation of wordpress on your server by wordpress developer which will help you to acquire the SEO friendly blog application integrated with your site design as well as separate blog administration panel for starting up your own business blog,which demands a experienced wordpress designer. Whether or not it's an viewers on your web page, your social media pages, or your web page, those who have a present and effective viewers of "fans" are best best for provide provides, reductions, and deals to help re-invigorate their viewers and add to their main point here. Our skilled expertise, skillfulness and excellence have been well known all across the world. Have you heard about niche marketing and advertising. You can add keywords but it is best to leave this alone. I have compiled a few tips on how you can start a food blog and hopefully the following information and tips can help you to get started on your food blogging creative journey. Enterprise, when they plan to hire Word - Press developer resources still PHP, My - SQL and watch with great expertise in codebase. It's now become a great place to sell it thanks to Woo - Commerce. Fortunately, Word - Press Customization Service is available these days, right from custom theme design, to plugin customization and modifying your website, you can take any bespoke service for your Word - Press development project. This advice is critical because you don't want to waste too expensive time establishing your Word - Press blog the exact method. Here's a list of some exciting Word - Press features that have created waves in the web development industry:. Word - Press can also be quickly extended however improvement API is not as potent as Joomla's. And, it is better that you leave it on for the duration you are writing plugin code. Press CTRL and the numbers one to six to choose your option.

FTCS scheme - Revision history

en>BG19bot: /* Stability */WP:CHECKWIKI error fix for #64. Do general fixes if a problem exists. - using AWB (9399)

en>Peter James at 17:13, 28 May 2012