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Wikipedia:Articles for deletion/C.S. Manning

 This page is an archive of the discussion about the proposed deletion of the article below. This page is no longer live. Further comments should be made on the article's talk page rather than here so that this page is preserved as an historic record. The result of the debate was speedy delete. —Korath (Talk) 01:37, Feb 16, 2005 (UTC)

C.S. Manning
Non-notable. He's 23 years old and "is an aspiring novelist and filmmaker, who is currently completing a B.A. in Modern European History at Columbia University". -- Scott eiπ + 1 = 0  06:31, Feb 12, 2005 (UTC)

 * good call. delete him.
 * Unsigned vote by User:160.39.244.167, who strangely enough, created the article.  -- Scott  eiπ + 1 = 0  07:09, Feb 12, 2005 (UTC)
 * 07:30, Feb 12, 2005 Academic Challenger deleted C.S. Manning ((blanked by only contributor) content was: ' ') —Korath (Talk) 01:37, Feb 16, 2005 (UTC)

This page is now preserved as an archive of the debate and, like some other VfD subpages, is no longer 'live'. Subsequent comments on the issue, the deletion, or the decision-making process should be placed on the relevant 'live' pages. Please do not edit this page.


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Pam Robinson

Pam Robinson is the co-founder, with Hank Glamann, of the American Copy Editors Society. She was born at Walter Reed Army Hospital in Washington, D.C. and grew up in Lorain, Ohio, a blue-collar city on Lake Erie, 27 miles west of Cleveland. The Robinson Prize is named for her.

Career
While a part-time sportswriter and student, she was assigned to cover a Southview High School football game at George Daniel Field in Lorain but barred from using the pressbox because female sportswriters were not permitted. The reason cited was the bad language used by visiting coaches, though female members of the school board were admitted. The bar was lifted a week later after The Journal, her employer, created a fuss.

She served as the first president of ACES, stepping down in 2001, and was succeeded by John Early McIntyre.

She is the owner and publisher of HuntingtonNow.com, covering the town of Huntington, NY.

ACES grew from several streams, from a report of the American Society of Newspaper Editors citing dissatisfaction among copy editors, to gatherings of copy editors led by Dorothy Wilson and Beryl Adcock and such academic leaders as Bill Cloud, and industry executives, such as Bob Mong and Merv Aubespin. The professional journalism organization offers advice, collegiality and training, including an annual national conference that has become well known in the newspaper industry for its focus on its valuable workshops.

Besides The Lorain Journal, now named The Morning Journal, she worked at the Danbury News-Times, Hartford Courant, New London Day, Newsday, The New York Times and the Los Angeles Times. She also spent a year working for a refugee resettlement program at the National Council of Churches.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Pam Robinson


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Wikipedia:Categories for deletion/Playstation games

Category:Playstation games listed for deletion on February 2, 2005. Consensus was to delete due to existing alternate category. RedWolf 06:34, Feb 12, 2005 (UTC)

Redundant because of Category:PlayStation games. This has most likely been deleted in the past. Xezbeth 11:31, Feb 2, 2005 (UTC)
 * Perhaps it should be turned into a redirect, if it's been deleted before ? 132.205.45.148 20:32, 2 Feb 2005 (UTC)
 * Unfortunately, categories can't redirect to categories. --Boco XLVII 21:22, 2 Feb 2005 (UTC)
 * But there's a "soft redirect" that has been used, see Template:Categoryredirect. -- Rick Block 18:13, 3 Feb 2005 (UTC)
 * This was actually deleted in September. I figure we should just keep the redirect to prevent it being recreated again. -Aranel (" Sarah ") 17:56, 4 Feb 2005 (UTC)

If this is a redirect already, and worse, it has already been deleted, then it needs to be a soft redirect and should not be deleted. Really, the soft redirect is a form of deletion, so deleting this would be redundant. --ssd 06:56, 5 Feb 2005 (UTC)


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Salsoloideae

The Salsoloideae are a subfamily of the Amaranthaceae, formerly in family Chenopodiaceae.

Description
These are herbs, subshrubs, shrubs and some trees. Stems and leaves are often succulent. The ovary contains a spiral embryo. In most genera, scarious wings develop at the outside of the fruiting perianth, allowing for dispersal by the wind (anemochory). In tribe Caroxyleae, the stamens have vesiculose anther appendages, discolor with anthers, that probably play a role for insect pollination. In tribe Salsoleae the anther appendages are absent or small and inconspicuous.

Distribution
The area with most species (center of diversity) are the deserts and semideserts of Central-Asia and the Middle East. Distribution of the subfamily extends to the Mediterranean, to Middle-Europe, north and south Africa, and Australia, some species have also been introduced to America. Many species grow in dry habitats (xerophytes) or tolerate salty soils (halophytes), some are ruderals.

Photosynthesis pathway
Salsoloideae are plants (with a few exceptions in tribe Salsoleae). Tribe Caroxyleae is exclusively of the NAD-malic enzyme subtype. Most Salsoleae also use the NADP-malic enzyme.

Taxonomy

The type genus of subfamily Salsoloideae is Salsola L. According to recent research, the former classification did not reflect the phylogenetic relationship, so that the subfamily had to be reclassified; it is now split in two tribes, Caroxyleae and Salsoleae (in the strict sense). The tribe Camphorosmeae is now treated in its own subfamily, Camphorosmoideae.

Caroxyleae
Caroxyleae Akhani & E. H. Roalson (as "Caroxyloneae")
 * Akhania Sukhor., with 5 species
 * Caroxylon Thunb., with 128 species
 * Climacoptera Botsch., with 41 species
 * Halanthium K.Koch, with 5 species
 * Halarchon Bunge, with one species
 * Halarchon vesiculosum (Moq.) Bunge
 * Halimocnemis C. A. Mey., with 27 species (Syn. Gamanthus Bunge , Halotis Bunge )
 * Halocharis Moq., with 7 species
 * Kaviria Akhani & E. H. Roalson, with 10 species
 * Nanophyton Less., with ca. 10 species
 * Ofaiston Raf., with one species
 * Ofaiston monandrum (Pall.) Moq.
 * Petrosimonia Bunge, with 12 species
 * Piptoptera Bunge, with one species
 * Piptoptera turkestana Bunge
 * Physandra Botsch., with one species
 * Physandra halimocnemis ( Botsch.) Botsch.
 * Pyankovia Akhani & E. H. Roalson, with one species
 * Pyankovia brachiata (Pall.) Akhani & E. H. Roalson

Salsoleae

 * Anabasis L. ( incl. Fredolia (Coss. & Durieu ex Bunge) Ulbr. ), with 29 species
 * Arthrophytum Schrenk, with 9 species
 * Cornulaca Delile, with 5 species
 * Cyathobasis Aellen, with one species:
 * Cyathobasis fruticulosa (Bunge) Aellen
 * Girgensohnia Bunge ex Fenzl, with 4 species
 * Halogeton C. A. Mey, with 5 species. (Syn. Agathophora (Fenzl) Bunge , Micropeplis Bunge )
 * Halothamnus Jaub. & Spach, with 21 species
 * Haloxylon Bunge
 * Hammada Iljin, with 12 species
 * Horaninovia Fisch. & C. A. Mey, with 8 species
 * Lagenantha Chiov. (Syn.: Gyroptera Botsch. ) Classification not sure. With 1-3 species.
 * Noaea Moq., with 3 species
 * Nucularia Batt., Classification not sure. With one species:
 * Nucularia perrini Batt.
 * Oreosalsola
 * Rhaphidophyton Iljin, with one species
 * Rhaphidophyton regelii (Bunge) Iljin
 * Salsola L., with 56 species. (Syn. Darneilla Maire & Weiller , Fadenia Aellen & Townsend , Neocaspia Tzvelev , Hypocylix Wol. , Kali Mill. )
 * Soda (synonym Seidlitzia Bunge ex Boiss. )
 * Sympegma Bunge
 * Traganum Del., with 2 species
 * Traganopsis Maire et Wilczek, with one species
 * Traganopsis glomerata Maire & Wilczek
 * Turania Akhani & E. H. Roalson, with 4 species
 * Xylosalsola Tzvelev, with 4 species

Classification in subfamily not sure

 * Iljinia Korovin, with one species:
 * Iljinia regelii

title: Salsoloideae


text: Template:La Crosse–Onalaska

title: Template:La Crosse–Onalaska


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Marion Boyd

Phyllis Marion Boyd ( Watt; March 26, 1946 – October 11, 2022) was a Canadian politician in Ontario. She was a New Democratic member of the Legislative Assembly of Ontario from 1990 to 1999 who represented the riding of London Centre. She served as a member of cabinet in the government of Bob Rae.

Early life
Boyd was born in Toronto on March 26, 1946, to Bill and Dorothy Watt. She studied at Glendon College, graduating with a Bachelor of Arts in English and history in 1968. From 1968 to 1973, she worked as an assistant to the president of York University. In 1975–76, she helped faculty members of York University win their first union contract. She subsequently worked as an executive director of the London Battered Women's Advocacy Clinic, and served two terms as president of the London Status of Women Action Group. She was widely known as a feminist.

Politics
In 1985, Boyd was the NDP candidate in London North in the provincial election of 1985, but finished third against incumbent Liberal Ron Van Horne. She ran in London Centre in the 1987 election, and lost to sitting Premier David Peterson by almost 9,000 votes. She campaigned as a federal New Democrat in the 1988 general election, finished third behind Liberal Joe Fontana and Progressive Conservative Jim Jepson in London East.

Boyd sought a rematch against Peterson in the 1990 provincial election. This time she won, defeating the Premier by more than 8,000 votes. It was almost unheard of for a provincial premier to be defeated in his own riding, and the size of Boyd's victory was all the more surprising. The NDP won the election, and the new Premier, Bob Rae, appointed her as Minister of Education on October 1, 1990.

When fellow cabinet member Anne Swarbrick resigned due to health issues, Boyd took over responsibility for Women's Issues on September 11, 1991. Boyd launched a high-profile campaign against domestic abuse in the same year. She was transferred to the Ministry of Community and Social Services on October 15, 1991, when Zanana Akande resigned due to a conflict of interest.

Boyd was promoted to Attorney General of Ontario on February 3, 1993, the first woman to hold that position as well as the first non-lawyer. In this capacity she was responsible for the Equality Rights Statute Amendment Act (Bill 167), that would have provided same-sex couples with rights and obligations mostly equal to those of opposite-sex common law couples. The bill failed on a free vote when twelve NDP members voted with the opposition parties against the bill. The bill's failure was a personal disappointment for Boyd, who had invested considerable effort in promoting its passage. The Progressive Conservative Party, which voted unanimously against Bill 167, formed government after the next election and ultimately passed similar legislation five years later when required by the Supreme Court of Canada's ruling in M v H.

Boyd also approved a highly controversial plea-bargain deal that allowed serial killer Karla Homolka to receive a 12-year prison sentence in return for testimony which led to the conviction of Homolka's then-husband, Paul Bernardo. The deal was criticized in much of the Canadian media, and many questioned Boyd's judgment in the matter. At the time the extent of Homolka's personal involvement in Bernardo's crimes was not known.

Boyd remained as Attorney General until the Rae government was defeated in the 1995 election. She was one of seventeen NDP MPPs to successfully retain their seats in that election, defeating PC candidate Patrick McGuinness by 1,732 votes. Boyd remained a high-profile MPP, serving as the NDP's Health Critic from 1997 to 1999.

The London Centre riding was eliminated by redistribution in 1996. Boyd ran against fellow incumbent Dianne Cunningham of the Progressive Conservative Party in London North Centre, and lost by just over 1,700 votes.

Cabinet positions
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London East
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London North
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London Centre
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London North Centre
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After politics
Boyd was appointed chair to the Task Force on the Health Effects of Woman Abuse in 2000. It was convened in response to the problem of domestic violence against women. Later that year the task force produced a report with 29 recommendations. The key conclusion was that doctors should begin screening female patients as young as 12 years old for signs of abuse.

In December 2003, it came to light that religious tribunals had some legal basis under the Arbitration Act. Some argued that this interpretation allowed for Muslim Sharia law to be applied in settling family disputes. In the spring of 2004, the issue flared up even more with some claiming that the use of Sharia law tribunals was infringing on the rights of Muslim women. In the summer of 2004, Premier Dalton McGuinty asked Boyd to investigate the issue.

In December 2004, Boyd released a report that found no evidence of complaints with regards to faith-based arbitration. She concluded that no changes to the act were needed with respect to religious tribunals. She made 46 recommendations for changes to the Arbitration Act primarily dealing with arbitrator training and clarifying the roles and responsibilities of tribunals. In 2005, in response to public opinion, McGuinty ignored Boyd's main conclusion and tabled changes to the act under the Family Statute Law Amendment Act.

While incorporating many of Boyd's recommendations, the act specifically removed any legal status for the arbitration of custodial and marital disputes by religious tribunals. The act mandated that all family law arbitrations in Ontario be conducted only in accordance with Canadian law. Some critics argued that this was a missed opportunity to incorporate aspects of Islamic law into the Canadian judicial system.

Boyd died in Inverhuron, Ontario on October 11, 2022, at the age of 76.

title: Marion Boyd


text:
Talk:Hydraulic machinery

Definition
A Hydraulic system is a series of pipes for hydraulics, such as you might find in a city. -Protopro — Preceding unsigned comment added by 81.78.96.45 (talk) 00:00, 22 March 2006 (UTC)

Dead Links
I have removed several links to non-existent articles with (hydraulic) in the title which may have been deleted? I have taken several small bites, in case these are in prep somewhere, so they can be undone piecemeal Timpo (talk) 13:40, 12 July 2010 (UTC)

Image
Maybe usefull image? --Snek01 23:30, 4 July 2006 (UTC) There is also a page Hydraulics in Wikipedia. Maybe somebody can bring hydraulic, hydraulics and hydraulic machinery together. Jeff
 * "Hydraulics" is often refered to as water hydraulics. It might be useful to separate this and the water-hydraulics used long time ago from oil-hydraulics that is used in hydraulic machinery. Perhaps there is a special name for hydraulics involving water. I have an old book called 'Handbook of Applied Hydraulics' by MacGrawhill, Inc. 1969, nothing is mensioned about oil.

The image you show is too far away. A closer photo might be useful. Caterpillar have an Image gallery for the press but they don´t approve to use it if it's not used in an article about CAT. Cat must put it into Wikipedia themselves. Lidingo SWE (talk) 14:59, 21 October 2008 (UTC)

Present layout
There is more to come on the hydraulic system/machinery article. Maybe this article should be divided into 3 parts; (1) Basic hydraulics, (2) System layout and (3) Basic calculations. Hydraulic systems have become more and more important in the mobile machinery as well as the importance to reduce power losses by using new system design features. The problem is to cover this in a dictionary such as Wikipedia, but never the less, hydraulics is an important technical area and should be covered somehow. /Lidingo SWE, 15th jan. 2007
 * sounds good, I like the idea of a Basic calculations section in particular. Also, Lidingo, you can automatically add your signature to talk page posts with four tildas ( ~ ). --Duk 17:15, 15 January 2007 (UTC)

// "Rating" refers to max. technical data as I know ?? See changes in the article Lidingo SWE 18:18, 15 January 2007 (UTC)

There should be a complete new set of contributions starting under the general title "drive systems": Mechanical drive systems, electrical drive systems, hydraulic drive systems and pneumatic drive systems. But this is a lot of work. Hydraulic machinery is not a good title for hydraulics. This however costs a lot of time and effort. A great dusadvantage is the fact that images are very rare at Wikipedia and it is very difficult to get pictures accepted by "the board" here. Maybe somebody can easily get some pictures of components etc? Jeff 17:28, 10 February 2007 (UTC)

Open center circuits and closed center circuits
I worked 35 years in hydraulics, but I never heard these words. I know open and closed loop systems, but I think open center and close center come from a schoolbook. I never heard them. Can anybody explain to me where it comes from, before I edit the main page? Jamclaassen 14:55, 27 January 2007 (UTC)
 * It might differ between US and Europe. Anyway, Open center/Closed center refer to the valves connected to the pump. Today most of the high power hydraulics have closed center valve type, where the pumpflow is blocked when valve spool is in neutral. When LS-valves are used combined with fixed displacement pumps, a special valve is incorporated in the inlet section of the the valveblock to unload the pump, making the system work as an "open center" but the valves are still closed centers in neutral. Lidingo SWE (talk) 14:24, 21 October 2008 (UTC)

Sorry
I donot know how its waste work came in the article, it was not written on purpose Jeff 17:28, 10 February 2007 (UTC)

New article "Hydraulic drive system"
Under the article hydraulics I made a new chapter "Hydraulic drive system". If we make a new article with this name we can describe hydraulics in this new article better than in hydraulic machinery. Write it step by step and delete nonsens as issometimes written here. Who is able and willing to do this or want to assist me?Jeff 12:42, 28 February 2007 (UTC)

 * Looks like that was eventually done (Hydraulic drive system) but nobody bothered to note it here. --Treekids (talk) 17:08, 22 April 2008 (UTC)

Efficiency & subjectivity
"Gear pump: cheap, durable, simple. Less efficient," ... than what? Let's get an objective factual table in here, people! --Treekids (talk) 17:06, 22 April 2008 (UTC)
 * Compared to axial piston units with fixed displacement. Axial units have much higher efficiency, is much more expensive to produce but lasts much longer. However, a table showing efficiencies depending on type of unit is a good idea. Most manufacturers have these datas in their general information materials about hydraulics. I have some datas but I don't think it is up to date. Lidingo SWE (talk) 14:14, 21 October 2008 (UTC)

Fun Fact
This isn't really a constructive comment, but I found this mildly hilarious. This article is cited as a reference in my fluid mechanics textbook (p. 62, Engineering Fluid Mechanics, Crowe et. al., Ninth Edition) for which I paid about 180 bucks. Bendhoward (talk) 04:47, 21 October 2008 (UTC)
 * The best education material about hydraulics you can get without charge from Bosch-Rexroth or from Eaton Hydraulics/Vickers. Sauer-Sundstrand also have good documentation, i particular about hydrostatic closed loop transmissions. Hydrostatics today for mobile machinery however is very much related to the electronic control programs involved. No really good official documentation exists about how to design the programs as this information is a vital part of the companies topsecret know-how and it differs for each type of machine. Lidingo SWE (talk) 14:37, 21 October 2008 (UTC)

Merge of hydraulic manifold

 * Oppose The only reason I can see for a merge is the poor current quality of hydraulic manifold. That's not a good reason for a merge. If the quality is a problem, it's not improved by merging. If the topic isn't notable, it's a deletion not a merge. I don't see that the (very broad scoped) hydraulic machinery article would be improved by any such merge. Nor is this article in a much better state. Andy Dingley (talk) 17:41, 28 September 2019 (UTC)
 * Comment We seem to have a lot of articles that begin with the word "hydraulic". Surely some of these can be merged into others.  I myself looked at this article and thought, "Couldn't this be merged into something else?" before I even knew there was a merge discussion on the table!  So while I might not support a merge of "hydraulic manifold" into this article, I would almost certainly support an analogous move of other hydraulic-related articles into other, broader hydraulic articles.  It is important that we keep information centralized, and a hundred articles on hydraulics does not do anyone any good!  A loose necktie (talk) 04:54, 18 December 2019 (UTC)
 * Merge anything and everything, just because the names overlap? What we really need here is better article content being written, and merging away articles is a great discouragement to anyone bothering to do that. Andy Dingley (talk) 10:46, 18 December 2019 (UTC)

title: Talk:Hydraulic machinery


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Il me reste un pays

"Il me reste un pays" ("There is still a country for me") is a song written by Gilles Vigneault, a Quebec francophone, and Gaston Rochon.

title: Il me reste un pays


text: User talk:81.156.177.48

title: User talk:81.156.177.48


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Altacast

Altacast (formerly known as Edcast and Oddcast) is a free and open-source audio encoder that can be used to create Internet streams of varying types. Many independent and commercial broadcasters use Altacast to create Internet radio stations, such as those listed on the Icecast, Loudcaster and Shoutcast station directories.

Development
The original streaming software, Oddcast, was developed from 2000 to 2010. The official site at Oddsock.org hosted streaming media tools, which included Oddcast, Stream Transcoder, Icecast Station Browser plugin, Song Requester plugin and Do Something plugin. In late November 2010, Oddsock.org was shut down.

Edcast, a fork of Oddcast, is being updated and hosted at Club RIO. In early 2012, development of Edcast was moved to Google Code and SourceForge. As of October 30, 2011, the latest stable version is 3.33.2011.1026 and the latest beta version is 3.37.2011.1214.

In September 2012, a second fork, Altacast was released. The Standalone & DSP edition are derived from GPL software and is available on GitHub, while the RadioDJ edition is written in .NET Framework and developed separately. A version 2.0 for the Standalone & DSP edition that will be SHOUTcast v2 compatible is planned for the future.

Altacast plugin for RadioDJ will no longer function with new versions of RadioDJv2 - Altacast is not supported by the developer of RadioDJ due to legal issues.

Features
Altacast is supported on Windows. It will run in conjunction with various media players compatible with Winamp plugins, such as AIMP, JetAudio, KMPlayer, MediaMonkey, MusicBee and foobar2000, as well as a standalone encoder.

Altacast Standalone & DSP can stream to Icecast and SHOUTcast servers in Ogg Vorbis and Ogg FLAC out-of-the-box. MP3, AAC and AAC+ support can be added via the LAME encoder (lame_enc.dll), FAAC encoder (libFAAC.dll), and CT-aacPlus encoder (enc_aacplus.dll obtainable from Winamp 5.61) respectively. Adjustable settings for each encoder include bitrate (for MP3, AAC+, Ogg Vorbis), quality (for AAC, Ogg Vorbis), sample rate (22050 Hz or 44100 Hz) and channels (Parametric Stereo is available for AAC+ up till 56 kbit/s).

SHOUTcast v2 is currently not officially supported in Altacast Standalone & DSP. However, it is possible to connect to stream ID no. 1 of a SHOUTcast v2 server in legacy (v1) mode. As a temporary workaround, the SHOUTcast DSP 1.9.2 plugin for Winamp-compatible media players may be used to broadcast to alternate mount points (e.g. stream ID no. 2).

SHOUTcast v2 and Opus support is available in v1.4 onwards in the plugin.

Reception
In 2007 Oddcast was used in a document from the Department of Audio Communication of the Technical University of Berlin as part of description to set up an internet radio broadcast system. Use of edcast for a similar purpose was described in a 2010 article in the PCWorld magazine. A 2016 thesis for Oulu University of Applied Sciences has described the used of Altacast in the implementation of an internet radio station while the for a 2018 article in the Linux Journal recommended it as a compatible source client for Microsoft Windows in setting up a freeware internet radio station using Liquidsoap, icecast and open standards. Académie d'Orléans-Tours has used web radio (internet radio) for broadcasts for students and the use of edcast subsequently altacast in the system has been described.

title: Altacast


text:
User talk:Blondiepunkgrrl

Hey im blondie i don't really understand wiki but im just getting to figure out the basic activities i can do on the website.

title: User talk:Blondiepunkgrrl


text:
Maximal compact subgroup

In mathematics, a maximal compact subgroup K of a topological group G is a subgroup K that is a compact space, in the subspace topology, and maximal amongst such subgroups.

Maximal compact subgroups play an important role in the classification of Lie groups and especially semi-simple Lie groups. Maximal compact subgroups of Lie groups are not in general unique, but are unique up to conjugation – they are essentially unique.

Example
An example would be the subgroup O(2), the orthogonal group, inside the general linear group GL(2, R). A related example is the circle group SO(2) inside SL(2, R). Evidently SO(2) inside GL(2, R) is compact and not maximal. The non-uniqueness of these examples can be seen as any inner product has an associated orthogonal group, and the essential uniqueness corresponds to the essential uniqueness of the inner product.

Definition
A maximal compact subgroup is a maximal subgroup amongst compact subgroups – a maximal (compact subgroup) – rather than being (alternate possible reading) a maximal subgroup that happens to be compact; which would probably be called a compact (maximal subgroup), but in any case is not the intended meaning (and in fact maximal proper subgroups are not in general compact).

Existence and uniqueness
The Cartan-Iwasawa-Malcev theorem asserts that every connected Lie group (and indeed every connected locally compact group) admits maximal compact subgroups and that they are all conjugate to one another. For a semisimple Lie group uniqueness is a consequence of the Cartan fixed point theorem, which asserts that if a compact group acts by isometries on a complete simply connected negatively curved Riemannian manifold then it has a fixed point.

Maximal compact subgroups of connected Lie groups are usually not unique, but they are unique up to conjugation, meaning that given two maximal compact subgroups K and L, there is an element g ∈ G such that gKg−1 = L. Hence a maximal compact subgroup is essentially unique, and people often speak of "the" maximal compact subgroup.

For the example of the general linear group GL(n, R), this corresponds to the fact that any inner product on Rn defines a (compact) orthogonal group (its isometry group) – and that it admits an orthonormal basis: the change of basis defines the conjugating element conjugating the isometry group to the classical orthogonal group O(n, R).

Proofs
For a real semisimple Lie group, Cartan's proof of the existence and uniqueness of a maximal compact subgroup can be found in and. and discuss the extension to connected Lie groups and connected locally compact groups.

For semisimple groups, existence is a consequence of the existence of a compact real form of the noncompact semisimple Lie group and the corresponding Cartan decomposition. The proof of uniqueness relies on the fact that the corresponding Riemannian symmetric space G/K has negative curvature and Cartan's fixed point theorem. showed that the derivative of the exponential map at any point of G/K satisfies |d exp X| ≥ |X|. This implies that G/K is a Hadamard space, i.e. a complete metric space satisfying a weakened form of the parallelogram rule in a Euclidean space. Uniqueness can then be deduced from the Bruhat-Tits fixed point theorem. Indeed, any bounded closed set in a Hadamard space is contained in a unique smallest closed ball, the center of which is called its circumcenter. In particular a compact group acting by isometries must fix the circumcenter of each of its orbits.

Proof of uniqueness for semisimple groups
also related the general problem for semisimple groups to the case of GL(n, R). The corresponding symmetric space is the space of positive symmetric matrices. A direct proof of uniqueness relying on elementary properties of this space is given in.

Let $$\mathfrak{g}$$ be a real semisimple Lie algebra with Cartan involution σ. Thus the fixed point subgroup of σ is the maximal compact subgroup K and there is an eigenspace decomposition

 * $$\displaystyle{\mathfrak{g}=\mathfrak{k}\oplus \mathfrak{p},}$$

where $$\mathfrak{k}$$, the Lie algebra of K, is the +1 eigenspace. The Cartan decomposition gives

 * $$\displaystyle{G=K\cdot \exp \mathfrak{p} = K\cdot P = P\cdot K.}$$

If B is the Killing form on $$\mathfrak{g}$$ given by B(X,Y) = Tr (ad X)(ad Y), then

 * $$\displaystyle{(X,Y)_\sigma=-B(X,\sigma(Y))}$$

is a real inner product on $$\mathfrak{g}$$. Under the adjoint representation, K is the subgroup of G that preserves this inner product.

If H is another compact subgroup of G, then averaging the inner product over H with respect to the Haar measure gives an inner product invariant under H. The operators Ad p with p in P are positive symmetric operators. This new inner produst can be written as

 * $$(S\cdot X,Y)_\sigma,$$

where S is a positive symmetric operator on $$\mathfrak{g}$$ such that Ad(h)tS Ad h = S for h in H (with the transposes computed with respect to the inner product). Moreover, for x in G,

 * $$\displaystyle{\mathrm{Ad}\, \sigma(x)=(\mathrm{Ad}\,(x)^{-1})^t.}$$

So for h in H,

 * $$\displaystyle{S\circ \mathrm{Ad}(\sigma(h))= \mathrm{Ad}(h)\circ S.}$$

For X in $$\mathfrak{p}$$ define

 * $$\displaystyle{f(e^X)=\mathrm{Tr}\, \mathrm{Ad}(e^X) S.}$$

If ei is an orthonormal basis of eigenvectors for S with Sei = λi ei, then

 * $$\displaystyle{f(e^X)=\sum \lambda_i (\mathrm{Ad}(e^X)e_i,e_i)_\sigma \ge (\min \lambda_i)\cdot \mathrm{Tr}\,e^{\mathrm{ad}\,X},}$$

so that f is strictly positive and tends to ∞ as |X| tends to ∞. In fact this norm is equivalent to the operator norm on the symmetric operators ad X and each non-zero eigenvalue occurs with its negative, since i ad X is a skew-adjoint operator on the compact real form $$\mathfrak{k}\oplus i\mathfrak{p}$$.

So f has a global minimum at Y say. This minimum is unique, because if Z were another then

 * $$\displaystyle{e^Z=e^{Y/2} e^X e^{Y/2},}$$

where X in $$\mathfrak{p}$$ is defined by the Cartan decomposition

 * $$\displaystyle{e^{Z/2}e^{-Y/2}=k\cdot e^{X/2}.}$$

If fi is an orthonormal basis of eigenvectors of ad X with corresponding real eigenvalues μi, then

 * $$\displaystyle{g(t)= f(e^{Y/2} e^{tX} e^{Y/2})= \sum e^{\mu_i t} \|Ad(e^{Y/2})f_i\|^2_\sigma.}$$

Since the right hand side is a positive combination of exponentials, the real-valued function g is strictly convex if X ≠ 0, so has a unique minimum. On the other hand, it has local minima at t = 0 and t = 1, hence X = 0 and p = exp Y is the unique global minimum. By construction f(x) = f(σ(h)xh−1) for h in H, so that p = σ(h)ph−1 for h in H. Hence σ(h)= php−1. Consequently, if g = exp Y/2, gHg−1 is fixed by σ and therefore lies in K.

Representation theory
Maximal compact subgroups play a basic role in the representation theory when G is not compact. In that case a maximal compact subgroup K is a compact Lie group (since a closed subgroup of a Lie group is a Lie group), for which the theory is easier.

The operations relating the representation theories of G and K are restricting representations from G to K, and inducing representations from K to G, and these are quite well understood; their theory includes that of spherical functions.

Topology
The algebraic topology of the Lie groups is also largely carried by a maximal compact subgroup K. To be precise, a connected Lie group is a topological product (though not a group theoretic product) of a maximal compact K and a Euclidean space – G = K × Rd – thus in particular K is a deformation retract of G, and is homotopy equivalent, and thus they have the same homotopy groups. Indeed, the inclusion $$K \hookrightarrow G$$ and the deformation retraction $$G \twoheadrightarrow K$$ are homotopy equivalences.

For the general linear group, this decomposition is the QR decomposition, and the deformation retraction is the Gram-Schmidt process. For a general semisimple Lie group, the decomposition is the Iwasawa decomposition of G as G = KAN in which K occurs in a product with a contractible subgroup AN.

title: Maximal compact subgroup


text:
No. 213 Squadron RAF

No. 213 Squadron was a squadron of the Royal Air Force. The squadron was formed on 1 April 1918 from No. 13 (Naval) Squadron of the Royal Naval Air Service. This RNAS squadron was itself formed on 15 January 1918 from the Seaplane Defence Flight which, since its creation in June 1917, had had the task of defending the seaplanes which flew out of Dunkirk.

World War I
Formed originally from the Seaplane Defence Flight, which was itself founded in June 1917 at Dunkirk, it was reorganized as No. 13 Squadron RNAS on 15 January 1918. As the SDF, it operated Sopwith Pups. When the Royal Naval Air Service merged with the Royal Flying Corps to form the Royal Air Force, it was renumbered as 213 Squadron. In this incarnation, it flew Sopwith Baby floatplanes and transitioned to Sopwith Camels. It was during this time that the squadron derived its Hornet insignia and motto for the squadron badge, after overhearing a Belgian General refer to the squadron's defence of his trenches, "Like angry hornets attacking the enemy aircraft". The Hornet became affectionately known as "Crabro," Latin for hornet. The squadron's official motto became, "Irritatus Lacessit Crabro" (The Hornet Attacks When Roused). In March 1919 the squadron went back to the UK where it disbanded on 31 December 1919.

During its wartime existence, the squadron had 14 flying aces serve with it, including such notables as; John Edmund Greene, Colin Brown, George Chisholm MacKay, Leonard Slatter, Maurice Cooper, Miles Day, Ronald Graham, John Paynter, John Pinder, and George Stacey Hodson.

Second World War
The squadron was reformed on 8 March 1937 flying Gloster Gauntlet IIs, converting to Hawker Hurricanes in January 1939 and flew throughout the war. It participated as part of the British Expeditionary Force; then at Dunkirk; the Battle of Britain and finally in the Middle East as part of the Desert Air Force. It also flew Supermarine Spitfires and North American Mustangs.

Post-Second World War
After the war, the squadron remained in the Middle East, first flying Hawker Tempests and then de Havilland Vampires. It was stationed at Deversoir in the Suez Canal Zone from October 1948 till its disbandment there on 30 September 1954.

With Bomber Command to RAF Germany
The squadron reformed once again on 1 September 1955 as an English Electric Canberra squadron, specialising in low level interdiction missions. It was the only squadron to fly the Canberra B(I).6 variant, still with the "Crabro" insignia adorning the tail fin, first from RAF Ahlhorn and later from RAF Bruggen, while a detachment was for a short time in 1956 stationed at Valkenburg Naval Air Base in the Netherlands. The squadron finally disbanded on 31 December 1969.

title: No. 213 Squadron RAF


text:
Wikipedia:Categories for deletion/Ashlee Simpson

Category:Ashlee Simpson listed for deletion on January 28, 2005. Consensus was to delete it and all subcategories.

I know fans do anything for their favorite stars, but I don't think Wikipedia needs a category for Ashlee Simpson. The category has five articles and three subcategories including "Ashlee Simpson albums" (to date she has only one album), "Ashlee Simpson images" (most of them aren't used in articles at all) and "Ashlee Simpson songs" (will there be an article about each?) The only other artist having a category is Elvis Presley and I'm not meaning to hurt Ashlee fans but I don't think the two can be mentioned in one sentence. Alensha 00:44, 28 Jan 2005 (UTC)
 * Keep. Everyking 00:51, 28 Jan 2005 (UTC)
 * Keep. Articles should be categorized as well as possible. Kappa 01:31, 28 Jan 2005 (UTC)
 * Keep since we've got enough articles to (barely) justify this. humblefool 02:07, 28 Jan 2005 (UTC)
 * Delete, despite her obvious fan club here on Wikipedia (and I know judging by the previous VfD votes), looking at the broader picture, I still maintain Ashlee Simpson just isn't that notable enough, compared with other music artists, to justify the creation of such articles. Only thing notable (or perhaps main claim to fame) was her Milli Vanilli like performance on SNL (and even then her fans had to sanitise that article). Megan1967 03:09, 28 Jan 2005 (UTC)
 * Delete, very few people have their own categories, let alone having one for a one album singer. There are far more artists who have made much more significant contributions to music than I project Ashlee could ever even think of doing. RedWolf 03:27, Jan 28, 2005 (UTC)
 * It does not matter whether someone else has done more than her. What absurd logic does it take to reject information on one topic because there's another topic that's more significant? Many of these articles have survived VfD, some with significant majorities. So why should we not have them properly categorized? Everyking 03:30, 28 Jan 2005 (UTC)
 * Keep As much as I hate to agree with Everyking on this, if 4 Non Blondes can have an album category when they were a minor 1 hit wonder, I see no reason Ashlee cant have an album category. As there are so many articles on Ashlee they need an all encompasing category (an Albums category is just not enough).  ALKIVAR ™[[Image:Radioactive.svg|18px|]] 04:02, 28 Jan 2005 (UTC)
 * Delete subcategories, keep main category, since we have so many Ashlee Simpson articles. silsor 03:53, Jan 28, 2005 (UTC)
 * Agree entirely with Silsor. Mind you, it's likely Everyking will soon have written 10,000 articles on Ashlee Simpson for Wikipedia, so we may yet need all these categories (It would be wonderful if he wrote about something worth writing that much about!). Grutness|hello? [[Image:Grutness.jpg|25px|]] 04:26, 28 Jan 2005 (UTC)
 * Delete. There are other good categories for these things -- song categories, artist categories, album categories -- that make more sense. Madame Sosostris 06:09, 28 Jan 2005 (UTC)
 * If this category is kept, this will set a precedent and the floodgates will open. One album wonders don't deserve a category either. RedWolf 06:53, Jan 28, 2005 (UTC)
 * Delete this and other categories for artists with only one or two albums. Gamaliel 07:04, 28 Jan 2005 (UTC)
 * Delete. Evil Monkey → Talk 07:47, Jan 28, 2005 (UTC)
 * Delete BlankVerse 08:23, 28 Jan 2005 (UTC)
 * Delete agree with the reverse of Alkivar's logic, and think 4 Non Blondes should not have their own category either. Worldtraveller 13:23, 28 Jan 2005 (UTC)
 * Delete - kaal 02:56, 30 Jan 2005 (UTC)
 * Keep This is just another example of the category system becoming more detailed over time. Philip 13:08, 31 Jan 2005 (UTC)
 * Delete. Merge all of the fancruft back into one manageable article.  RickK 07:12, Feb 1, 2005 (UTC)
 * Delete subcategories or just delete, 1 album, 15 images, 3 songs, and 5 articles. 1 album does not justify a category.  3 songs does not justify a category.  For 5 articles & 15 images (most are wallpaper-ish), one category for her should suffice. 07:39, 1 Feb 2005 (UTC)
 * Keep I would support deleting the subcats, though.  Tuf-Kat 22:30, Feb 1, 2005 (UTC)
 * Delete. Gamaliel 22:46, 1 Feb 2005 (UTC)
 * I think it would create a dangerous precedent if every band and artist had their own category, which would then be a subcategory of every applicable subcategorization of the Music category. For instance, the Ashlee Simpson category is a subcategory of Category:1984 births, Category:American actors, Category:American singers, Category:Female singers, Category:Pop singers, and Category:Rock singers.  It's absurd.  Now imagine that multiplied for every somewhat popular music group or singer with all of the categories they'd be listed under.  It's a mess to look at the Category page for Category:American actors to use just one example.  Listed in it are 100s of articles across several pages.  On the first page alone is the sole subcategory African-American actors, which makes sense in the category hierarchy.  But to scroll several pages and see Ashlee Simpson as a subcategory, as well as an article in the category, is a bit of a surprise, and it doesn't make much sense.  Ultimately, every article (or every popular article) would be both a subcategory and an article, and it tends to get messy.  We need to set an example of how we want Wikipedia to work.  I don't think it should work this way.  A simpler scheme would be to have the main article Ashlee Simpson placed in the appropriate categories (as it is now) and have all Ashlee Simpson-related articles appear as links from the main article instead of as members of a separate Ashlee Simpson category.  An alternative would be to have the Ashlee Simpson-related articles members of an Ashlee Simpson category, but this category would be a part of a different supercategory (i.e. "Bands/Singers with their own categories") instead of being part of so many different categories as the Ashlee Simpson category is now.  Any ideas? —Brim 23:09, Feb 1, 2005 (UTC)
 * I vote Delete for Category:Ashlee Simpson, Category:Ashlee Simpson albums, and Category:Ashlee Simpson images, but I vote keep for Category:Ashlee Simpson songs. WJ 02:17, 7 Feb 2005 (UTC)

This was deleted once on February 4. Why has it been recreated and is still subject to voting? The voting period has ended. RickK 07:50, Feb 9, 2005 (UTC)
 * I believe that is User:RedWolf's fault. Apparently, RedWolf might have been tired or distracted.  After RedWolf began the initial deletions, RedWolf only managed to delete one of the subcategories, but forgot about the other subcategories and the main category.  Also, after beginning the process of the deletions RedWolf forgot to move this in the resolved section and let this continue to accumulate votes past the voting period.
 * If you are going to make a personal attack (which is bad form in the first place), you should at least have the integrity of signing your post. Yes, I had begun with deleting the albums category but it was immediately re-created less than a day later by a new user (perhaps a sock puppet). I re-tagged everything with cfd as the subcats were not tagged. So, technically speaking, 7 more days were required for the subcats although the discussion on the albums talk page has prior discussion of it surviving a previous deletion vote. One album does not a category make. A minimum of three existing commercially released albums should be required before a category is granted, but I digress. RedWolf 03:41, Feb 12, 2005 (UTC)
 * First, it was the songs subcategory you deleted not the albums. Second, why didn't you answer User:RickK's THREE inquiries about the subcategory, one of them can be found here: Administrators' noticeboard/Incidents  Third, if the subcats needed 7 more days why didn't you undelete the songs subcategory or at least helped User:RickK delete the other subcats?  It made it look like Everyking influenced the vote somehow and let only the songs subcat get deleted, while everything else survived.  Fourth, why didn't you answer RickK's above question earlier or did you just see it and pretend to ignore it?
 * That's real sad. You shouldn't resort to a personal attack to get an answer, especially when you don't even sign your posts.  Next time, you should just ask on their talk page instead.  tsk, tsk, tsk. GrazingCow 04:27, 12 Feb 2005 (UTC)

Also, why was only one of the subcategories deleted? All the subcategories including the main category were all suppose to be deleted.


text: Template:Racine County, Wisconsin

title: Template:Racine County, Wisconsin


text:
User:Kaeng~enwiki

Left blank on purpose.

title: User:Kaeng~enwiki


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Alejandro Salazar

Alejandro Salazar (born February 18, 1984) is an American former professional soccer player. He played during the 2000s in the United States and Australia.

Biography
Born in Eugene, Oregon, Salazar's father is marathon runner Alberto Salazar.

Playing career
Salazar played college soccer at the University of Portland from 2002 to 2004, where he was named WCC Freshman of the Year as a freshman, and was the Conference Player of the Year as a sophomore. He left Portland after his junior year to join the newly formed Australian A-league, having registered 64 goals and 42 assists as a Pilot. Salazar didn't have much gaming time for Sydney FC and was released after the 10th round of the season.

Salazar is still remembered in Sydney as a player who was hyped up by the media but did not make an impact at club. His only pre-season appearance in a Sydney FC shirt in Australia being in the second half of a friendly game in 2005. Salazar made his debut coming on as a substitute replacing Steve Corica on the 66th minute in the Semi Final against Adelaide United assisting Mark Rudan's winning goal. Salazar featured in Sydney's campaign to qualify for the Oceania Club Championship, scoring 2 goals in 4 matches. He did get into a small rift with then coach Pierre Littbarski, which soured their relationship. In 2007 Lokomotiv Cove, the unofficial football team of Sydney FC supporters, named their lowest grade team "Team Salazar" in his honour.

title: Alejandro Salazar


text:
Heptatonic scale

A heptatonic scale is a musical scale that has seven pitches, or tones, per octave. Examples include:
 * the diatonic scale; e.g., in C major: C D E F G A B C—and in the relative minor, A minor, natural minor: A B C D E F G A
 * the melodic minor scale, A B C D E F♯G♯A ascending, A G F E D C B A descending
 * the harmonic minor scale, A B C D E F G♯A
 * the harmonic major scale, C D E F G A♭B C.

Indian classical theory postulates seventy-two seven-tone scale types, collectively called melakarta or thaat, whereas others postulate twelve or ten (depending on the theorist) seven-tone scale types.

Several heptatonic scales in Western, Roman, Spanish, Hungarian, and Greek music can be analyzed as juxtapositions of tetrachords. All heptatonic scales have all intervals present in their interval vector analysis, and thus all heptatonic scales are both hemitonic and tritonic. There is a special affinity for heptatonic scales in the Western key signature system.

Diatonic scale
A diatonic scale is any seven-note scale constructed sequentially using only whole tones and half tones, repeating at the octave, having a tonal center, and comprising only one tritone interval between any two scale members, which ensures that the half tone intervals are as far apart as possible. In Western music, there are seven such scales, and they are commonly known as the modes of the major scale (Ionian, Dorian, Phrygian, Lydian, Mixolydian, Aeolian, and Locrian).

Melodic minor scale

In traditional classical theory, the melodic minor scale has two forms, as noted above, an ascending form and a descending form. Although each of these forms of itself comprises seven pitches, together they comprise nine, which might seem to call into question the scale's status as a heptatonic scale. In certain twentieth-century music, however, it became common systematically to use the ascending form for both ascending and descending passages. Such a use has been notably ascribed to the works of Béla Bartók and to bop and post-bop jazz practice. The traditional descending form of the melodic minor scale is equivalent to the natural minor scale in both pitch collection (which is diatonic) and tonal center.

Harmonic minor scale
The harmonic minor scale is so called because in tonal music of the common practice period (from approximately 1600 to approximately 1900) chords or harmonies are derived from it more than from the natural minor scale or the melodic minor scale. The augmented second between its sixth degree and its raised seventh degree (the "leading tone"), traditionally considered undesirable in melodic progression, is avoided by placing these pitches in different voices in adjacent chords, as in this progression: F A♭ D, F G B, F A♭ C (ii°b–V7d–iv in C minor). The A♭ in the middle voice does not ascend to B, and the B in the upper voice does not descend to A♭.

Heptatonia prima and secunda
The names heptatonia prima and heptatonia secunda apply to seven-note scales that can be formed using five tones (t) and two semi-tones (s), (also called whole-steps and half-steps), but without two semi-tones in succession. Throughout history and to the present day, some have occurred much more commonly than others, namely Ionian (also called the major scale), Aeolian (also called the natural minor scale), melodic ascending minor, Dorian, Mixolydian, Lydian, Lydian dominant, Aeolian dominant, and altered scales.

Heptatonia prima
In these scales the semi-tones are maximally separated. They are known most commonly as the diatonic modes. Beginning on keynote C and working up the notes of the 'natural minor' scale (A, B, C, D, E, F, G, A), the seven modes are:
 * Aeolian mode (natural minor) t-s-t-t-s-t-t
 * Locrian mode s-t-t-s-t-t-t
 * Ionian mode (major) t-t-s-t-t-t-s
 * Dorian mode t-s-t-t-t-s-t
 * Phrygian mode s-t-t-t-s-t-t
 * Lydian mode t-t-t-s-t-t-s
 * Mixolydian mode t-t-s-t-t-s-t

Heptatonia secunda
While the diatonic modes have two and three tones on either side of each semitone, the heptatonia secunda modes have one and four. These are sometimes called modes of the melodic ascending minor since that is the most commonly used scale of this type, but other modes can be produced by starting on the different scale notes in turn. Thus starting on keynote A as above and following the notes of the ascending melodic minor (A, B, C, D, E, F♯, G♯) yields these seven modes:

 * Ascending melodic minor scale t-s-t-t-t-t-s
 * Dorian %E2%99%AD2 scale or Phrygian ♯6 scale s-t-t-t-t-s-t combines the Phrygian flat second and Dorian raised sixth
 * Lydian augmented scale t-t-t-t-s-t-s combines the Lydian fourth with a raised fifth
 * Acoustic scale or Lydian dominant scale t-t-t-s-t-s-t So-called because it is close to the scale built on natural overtones and combines Lydian raised fourth with Mixolydian (Dominant) flat seventh
 * Aeolian dominant scale or Mixolydian ♭6 scale t-t-s-t-s-t-t Like natural minor (aeolian) but with a major third
 * Half diminished scale t-s-t-s-t-t-t This is like the Locrian with a raised second
 * Altered scale s-t-s-t-t-t-t Like Locrian with diminished fourth

These modes are more awkward to use than those of the diatonic scales due to the four tones in a row yielding augmented intervals on one hand while the one tone between two semitones gives rise to diminished intervals on the other. For example, the last two modes listed above both have 'Locrian' diminished triads built on their tonics, giving them unstable tonality, while the third mode not only has an augmented fourth a la the Lydian mode but also an augmented fifth making the dominant and subdominant essentially unusable.

Heptatonia tertia
The last group of seven-note tone/semitone scales is heptatonia tertia, and consists of scales with two adjacent semitones—which amounts to a whole-tone scale, but with an additional note somewhere in its sequence, e.g., B C D E F♯ G♯ A♯. One such example is the Neapolitan major scale.

Other heptatonic scales
If the interval of the augmented second is used, many other scales become possible. These include Gypsy I-♭II-III-IV-V-♭VI-VII Hungarian I-II-♭III-♯IV-V-♭VI-VII The scales are symmetrical about the tonic and dominant respectively and the names are sometimes used interchangeably.

The double harmonic scale, also known as the Byzantine or Hungarian, scale, contains the notes C D E♭ F♯ G A♭ B C.

Phrygian dominant or dominant harmonic minor I-♭II-III-IV-V-♭VI-♭VII This differs from the Phrygian in having a major third. It may also be considered built on the dominant of the harmonic minor scale.

Neapolitan minor differs from the Phrygian in having a major seventh.

Verdi's Scala Enigmatica I-♭II-III-♯IV-♯V-♯VI-VII i.e. G A♭ B C♯ D♯ E♯ F♯, which is similar to the heptatonia tertia mentioned above, differing only in that the second degree here is flattened.

Melakarta
Melakarta is a South Indian classical method of organizing Raagas based on their unique heptatonic scales. The postulated number of melakarta derives from arithmetical calculation and not from Carnatic practice, which uses far fewer scale forms. Seven-pitch melakarta are considered subsets of a twelve-pitch scale roughly analogous to the Western chromatic scale. The first and fifth melakarta tones, corresponding to the first and eighth chromatic tones, are invariable in inflection, and the fourth melakarta tone, corresponding to the sixth or seventh chromatic tone, is allowed one of two inflections only, a natural (shuddah) position and a raised (tivra) position. The second and third melakarta tones can be picked from the 4 chromatic tones (second through fifth), and similarly for the sixth and seventh. Thus the number of possible forms is equal to twice the square of the number of ways a two-membered subset can be extracted from a four-membered set:

 * $$2\cdot\left(\frac{4!}{2!\cdot2!}\right)^2 = 2\cdot6^2 =72$$

Thaat
Hindustani heptatonic theory additionally stipulates that the second, third, sixth and seventh degrees of heptatonic scale forms (saptak) are also allowed only two inflections each, in this case, one natural position, and one lowered (komal) position. Arithmetically this produces 25, or thirty-two, possibilities, but Hindustani theory, in contradistinction to Carnatic theory, excludes scale forms not commonly used.

Chinese Gongche notation
Gongche notation heptatonic scale gives a do, re, mi, (between fa and fa♯), sol, la, (between ti♭ and ti) heptatonic scale.

title: Heptatonic scale


text:
Hexatonic scale

In music and music theory, a hexatonic scale is a scale with six pitches or notes per octave. Famous examples include the whole-tone scale, C D E F♯ G♯ A♯ C; the augmented scale, C D♯ E G A♭ B C; the Prometheus scale, C D E F♯ A B♭ C; and the blues scale, C E♭ F G♭ G B♭ C. A hexatonic scale can also be formed by stacking perfect fifths. This results in a diatonic scale with one note removed (for example, A C D E F G).

Whole-tone scale
The whole-tone scale is a series of whole tones. It has two non-enharmonically equivalent positions: C D E F♯ G♯ A♯ C and D♭ E♭ F G A B D♭. It is primarily associated with the French impressionist composer Claude Debussy, who used it in such pieces of his as Voiles and Le vent dans la plaine, both from his first book of piano Préludes.

This whole-tone scale has appeared occasionally and sporadically in jazz at least since Bix Beiderbecke's impressionistic piano piece In a Mist. Bop pianist Thelonious Monk often interpolated whole-tone scale flourishes into his improvisations and compositions.

Mode-based hexatonic scale
The major hexatonic scale is made from a major scale and removing the seventh note, e.g., C D E F G A C. It can also be made from superimposing mutually exclusive triads, e.g., C E G and D F A.

Similarly, the minor hexatonic scale is made from a minor scale by removing the sixth note, e.g., C D E♭ F G B♭ C.

Irish and Scottish and many other folk traditions use six-note scales. They can be easily described by the addition of two triads a tone apart, e.g., Am and G in "Shady Grove", or omitting the fourth or sixth from the seven-note diatonic scale.

Augmented scale
The augmented scale, also known in jazz theory as the symmetrical augmented scale, is so called because it can be thought of as an interlocking combination of two augmented triads an augmented second or minor third apart: C E G♯ and E♭ G B. It may also be called the "minor-third half-step scale", owing to the series of intervals produced.

It made one of its most celebrated early appearances in Franz Liszt's Faust Symphony (Eine Faust Symphonie). Another famous use of the augmented scale (in jazz) is in Oliver Nelson's solo on "Stolen Moments". It is also prevalent in 20th century compositions by Alberto Ginastera, Almeida Prado, Béla Bartók, Milton Babbitt, and Arnold Schoenberg, by saxophonists John Coltrane and Oliver Nelson in the late 1950s and early 1960s, and bandleader Michael Brecker. Alternating E major and C minor triads form the augmented scale in the opening bars of the Finale in Shostakovich's Second Piano Trio.

Prometheus scale
The Prometheus scale is so called because of its prominent use in Alexander Scriabin's symphonic poem Prometheus: The Poem of Fire. Scriabin himself called this set of pitches, voiced as the simultaneity (in ascending order) C F♯ B♭ E A D the "mystic chord". Others have referred to it as the "Promethean chord". It may be thought of as C Lydian dominant without the 5th degree.

Blues scale
The blues scale is so named for its use of blue notes. Since blue notes are alternate inflections, strictly speaking there can be no one blues scale, but the scale most commonly called "the blues scale" comprises the minor pentatonic scale and an additional flat 5th scale degree: C E♭ F G♭ G B♭ C.

Tritone scale
The tritone scale, C D♭ E G♭ G(♮) B♭, is enharmonically equivalent to the Petrushka chord; it means a C major chord ( C E G(♮) ) + G♭ major chord's 2nd inversion ( D♭ G♭ B♭ ).

The two-semitone tritone scale, C D♭ D F♯ G A♭, is a symmetric scale consisting of a repeated pattern of two semitones followed by a major third now used for improvisation and may substitute for any mode of the jazz minor scale. The scale originated in Nicolas Slonimsky's book Thesaurus of Scales and Melodic Patterns through the "equal division of one octave into two parts," creating a tritone, and the "interpolation of two notes," adding two consequent semitones after the two resulting notes. The scale is the fifth mode of Messiaen's list.

title: Hexatonic scale


text:
Un Canadien errant

"Un Canadien errant" ("A Wandering Canadian") is a song written in 1842 by Antoine Gérin-Lajoie after the Lower Canada Rebellion of 1837–38. Some of the rebels were condemned to death, others forced into exile to the United States and as far as Australia. Gérin-Lajoie wrote the song, about the pain of exile, while taking his classical exams at the Séminaire de Nicolet. The song has become a patriotic anthem for certain groups of Canadians who have at a point in their history experienced the pain of exile. In addition to those exiled following the Lower Canada Rebellion, it has come to hold particular importance for the rebels of the Upper Canada Rebellion, and for the Acadians, who suffered mass deportation from their homeland in the Great Upheaval between 1755 and 1763. The Acadian version is known as "Un Acadien errant."

Origins
Accounts of the origins of this song vary. In Souvenirs de collège, Antoine Gérin-Lajoie writes that he based his verse on an existing folk tune: "I wrote it in 1842 when I was taking my classical exams at Nicolet. I did it one night in bed at the request of my friend Cyprien Pinard, who wanted a song to the tune of 'Par derrière chez ma tante'... It was published in 1844 in the Charivari canadien with my initials (A.G.L.)."

In that publication the song was titled "Le Proscrit" and the tune said to be "Au bord d'un clair ruisseau."

The melody is from the French Canadian folk tune "J'ai fait une maîtresse" (of which "Si tu te mets anguille" is also a variation). The musical form is "AABB" or double-binary, with the A phrase repeated before moving to the B phrase, which is also repeated. The musical form is reflected in the lyrics as follows:

'A' phrase, with repeat: "Un Canadien errant, Banni de ses foyers, Un Canadien errant, Banni de ses foyers,"

'B' phrase, with repeat: "Parcourait en pleurant Des pays étrangers. Parcourait en pleurant Des pays étrangers."

The rise in the tune on the first line of the B phrase is inverted on the repeat (at the point of "en pleurant"), to make the phrase period, and thus provide closure to the AABB form.

Paul Robeson performed a bilingual version under the title "Le Canadien Errant" and recorded it in the 1950s. This version was included in his 1969 East German compilation album Amerikanische Ballade; the album was released posthumously in the United States in 1977 as American Balladeer.

American audiences were introduced to the song in 1963 with French-language performances by Ian & Sylvia. They included "Un Canadien errant" on their debut 1962 album Ian & Sylvia. They gave it further prominence at the Newport Folk Festival as recorded on the 1996 album Ian & Sylvia Live at Newport.

In the 1969 film, My Side of the Mountain, the folk singer and musicologist Theodore Bikel sang the first part of "Un Canadien Errant" and then played a bit of it on a "homemade" reed flute. The melody refrained throughout the film.

Leonard Cohen recorded "Un Canadien errant" as "The Lost Canadian" on his 1979 Recent Songs album. His own song "The Faith", on his 2004 album Dear Heather, is based on the same melody.

American folk duo John & Mary included an arrangement by Mary Ramsey on their 1991 album Victory Gardens.

Canadian folk rock duo Whitehorse recorded "Un Canadien errant" and included it on their 2013 covers album The Road to Massey Hall. A version performed by the duo is featured on the soundtrack to One Week, a 2008 film starring Joshua Jackson.

The song also made an appearance as the location music for Canada in the Where in the World Is Carmen Sandiego video game (1996), performed by Terry Gadsden & Frederik Kinck-Petersen.

History
Ernest Gagnon in Chansons populaires du Canada (Quebec City 1865) says "the original tune was "J'ai fait une maîtresse," of which the words of the variant "Si tu te mets anguille" are (somewhat altered) fragments.' Gagnon's analysis is considered definitive.

An Acadian variation appeared in 1844 as "Un Acadien Errant", sung to the Gregorian tune "Ave Maris Stella". Otherwise, to a few (and especially to expatriate Canadians), the original song remains a patriotic song; to all, it is a poignant recollection of French Canadian history.

Original lyrics
Original French lyrics: "Un Canadien errant, Banni de ses foyers, Parcourait en pleurant Des pays étrangers.

Un jour, triste et pensif, Assis au bord des flots, Au courant fugitif Il adressa ces mots:

"Si tu vois mon pays, Mon pays malheureux, Va, dis à mes amis Que je me souviens d'eux.

"Ô jours si pleins d'appas Vous êtes disparus, Et ma patrie, hélas! Je ne la verrai plus!

"Non, mais en expirant, Ô mon cher Canada! Mon regard languissant Vers toi se portera...""

English translation "A wandering 'Canadien' Banished from his homeland Travelled, weeping, through foreign lands.

One day, sad and thoughtful, Seated on the river's bank To the fleeing current He spoke these words:

"If you should see my home My sad unhappy land Go, say to all my friends That I remember them

"O days once so full of charm You are all gone away And my homeland, alas! I'll not see her again

"No, but with my last breath O my dear Canada! My sad gaze Will go to you.""

English version
This is the 1927 English version by John Murray Gibbon. Only the first verse preserves the ABAB rhyme pattern of the original French; thereafter it varies. Note that the use of the word 'lad' here means a young adult man, as was common in the time period.

"Once a Canadian lad, Exiled from hearth and home, Wandered, alone and sad, Through alien lands unknown.

Down by a rushing stream, Thoughtful and sad one day, He watched the water pass And to it he did say:

"If you should reach my land, My most unhappy land, Please speak to all my friends So they will understand.

"Tell them how much I wish That I could be once more In my beloved land That I will see no more.

"My own beloved land I'll not forget till death, And I will speak of her With my last dying breath.

"My own beloved land I'll not forget till death, And I will speak of her With my last dying breath.""

title: Un Canadien errant