Symmetric scale

For scale symmetry, see Symmetry § Scale symmetry and fractals.

In music, a music scale can have certain symmetries, namely translational symmetry and inversional or mirror symmetry.

The most prominent examples are scales which equally divides the octave.[1] The concept and term appears to have been introduced by Joseph Schillinger[1] and further developed by Nicolas Slonimsky as part of his famous Thesaurus of Scales and Melodic Patterns. In twelve-tone equal temperament, the octave can only be equally divided into two, three, four, six, or twelve parts, which consequently may be filled in by adding the same exact interval or sequence of intervals to each resulting note (called "interpolation of notes").[2]

This leads to scales with translational symmetry which include the octatonic scale (also known as the symmetric diminished scale; its mirror image is known as the inverse symmetric diminished scale[citation needed]) and the two-semitone tritone scale:

Two-semitone tritone scale on C divides the octave into two equal parts (C-F♯ & F# to (octave above) C) and fills in the resulting tritone gaps with two semitones (Db-D, G-Ab).

As explained above, both are composed of repeating sub-units within an octave. This property allows these scales to be transposed to other notes, yet retain exactly the same notes as the original scale (Translational symmetry).

This may be seen quite readily with the whole tone scale on C:

  • {C, D, E, F♯, G♯, A♯, C}
Whole tone scale on C
Synthesized sampleⓘ

If transposed up a whole tone to D, contains exactly the same notes in a different permutation:

  • {D, E, F♯, G♯, A♯, C, D}

In the case of inversionally symmetrical scales, the inversion of the scale is identical.[3] Thus the intervals between scale degrees are symmetrical if read from the "top" (end) or "bottom" (beginning) of the scale (mirror symmetry). Examples include the Neapolitan Major scale (fourth mode of the Major Locrian scale), the Javanese slendro,[4] the chromatic scale, whole-tone scale, Dorian scale, the Aeolian Dominant scale (fifth mode of the melodic minor), and the double harmonic scale.

Pitch constellations of five symmetric scales.

Asymmetric scales are "far more common" than symmetric scales and this may be accounted for by the inability of translational symmetric scales to possess the property of uniqueness (containing each interval class a unique number of times) which assists with determining the location of notes in relation to the first note of the scale.[4]

See also

References

  1. ^ a b Slonimsky, Nicolas (Jul 1946). "Untitled review of". The Musical Quarterly. 32 (3): 465–470 [469]. doi:10.1093/mq/xxxii.3.465.
  2. ^ Slonimsky, Nicolas (1987) [First published 1947]. Thesaurus of Scales and Melodic Patterns. Music Sales Corp. ISBN 0-8256-7240-6. Retrieved Jul 8, 2009.
  3. ^ Clough, John; Douthett, Jack; Ramanathan, N.; Rowell, Lewis (Spring 1993). "Early Indian Heptatonic Scales and Recent Diatonic Theory". Music Theory Spectrum. 15 (1): 48. doi:10.1525/mts.1993.15.1.02a00030. pp. 36-58.
  4. ^ a b Patel, Aniruddh (2007). Music, Language, and the Brain. p. 20. ISBN 978-0-19-512375-3.

Further reading

  • Yamaguchi, Masaya. 2006. The Complete Thesaurus of Musical Scales, revised edition. New York: Masaya Music Services. ISBN 0-9676353-0-6.
  • Yamaguchi, Masaya. 2006. Symmetrical Scales for Jazz Improvisation, revised edition. New York: Masaya Music Services. ISBN 0-9676353-2-2.
  • Yamaguchi, Masaya. 2012. Lexicon of Geometric Patterns for Jazz Improvisation. New York: Masaya Music Services. ISBN 0-9676353-3-0.

Read other articles:

List of FBI forms

The United States Federal Bureau of Investigation has a number of bureaucratic forms that must be filled out in the commission of any activities by its agents. These are typically mandatory, and are often presented at legal hearings as evidence of context. FD-209 An FD-209 form is used by FBI agents to record their contacts with unofficial criminal informants.[1] FD-292 An FD-292 form is used by FBI agents to notify the agency that they are getting married or divorced.[2] FD-...

 

Bastille

Untuk kegunaan lain, lihat Bastille (disambiguasi). Gambar Bastille yang diterbitkan tahun 1896. Bastille ialah sebuah kata bahasa Prancis yang berarti kastel. Bila disebutkan De Bastille, kata itu dimaksudkan untuk merujuk pada bekas penjara Bastille Saint-Antoine di Paris. Kastel ini dibangun sekitar tahun 1370 sebagai bagian dari perlindungan atas Paris. Pada abad ke-17 bangunan baru digunakan sebagai penjara. Banyak tahanan terkemuka yang dipenjara di sini, yang dari sini Lelaki Bertopeng...

 

Pyotr Nesterov

Pyotr Nikolayevich NesterovПётр Николаевич НестеровLahir(1887-02-15)15 Februari 1887Nizhny NovgorodMeninggal8 September 1914(1914-09-08) (umur 27)Żółkiew, Kerajaan Galisia dan Lodomeria, Austria-Hungaria(sekarang Zhovkva, Ukraina)Pengabdian Kekaisaran RusiaDinas/cabang Angkatan Darat Kekaisaran Rusia Penugasan Udara Kekaisaran RusiaLama dinas1906—1914PangkatStabskapitänPerang/pertempuranPerang Dunia Pertama Pyotr Nikolayevich Nesterov (bahasa Rusia&#...

Vigna mungo

Vigna mungo Dry urad beansTaksonomiDivisiTracheophytaSubdivisiSpermatophytesKladAngiospermaeKladmesangiospermsKladeudicotsKladcore eudicotsKladSuperrosidaeKladrosidsKladfabidsOrdoFabalesFamiliFabaceaeSubfamiliFaboideaeTribusPhaseoleaeGenusVignaSpesiesVigna mungo Hepper Tata namaBasionimPhaseolus mungo (en) Sinonim takson Azukia mungo (L.) Masam. Phaseolus hernandezii Savi Phaseolus mungo L. Phaseolus roxburghii Wight & Arn. [1]lbs Vigna mungo adalah kacang yang ditanam di anak ben...

 

Bishop of Limerick and Killaloe

The Bishop of Limerick, Killaloe and Ardfert or the Bishop of Limerick and Killaloe (/ˌkɪləˈluː/ kil-ə-LOO; Full title: Bishop of Limerick, Ardfert, Aghadoe, Killaloe, Kilfenora, Clonfert, Kilmacduagh and Emly) is the Church of Ireland Ordinary of the united Diocese of Limerick and Killaloe in the Province of Dublin.[1] Since 2022, the bishop has been Michael Burrows.[2][3] Cathedrals The united bishopric has three cathedrals: St Mary's Cathedral, Limerick[4...

 

1977 NCAA Division I basketball tournament

Edition of USA college basketball tournament See also: 1977 NCAA Division I Basketball Championship Game 1977 NCAA Division Ibasketball tournamentSeason1976–77Teams32Finals siteThe OmniAtlantaChampionsMarquette Warriors (1st title, 2nd title game,2nd Final Four)Runner-upNorth Carolina Tar Heels (4th title game,7th Final Four)SemifinalistsUNLV Runnin' Rebels (1st Final Four)UNC Charlotte 49ers (1st Final Four)Winning coachAl McGuire (1st title)MOPButch Lee (Marquette)Attendance241,610Top...

Mont-de-Marsan

This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed.Find sources: Mont-de-Marsan – news · newspapers · books · scholar · JSTOR (December 2015) (Learn how and when to remove this template message) Prefecture and commune in Nouvelle-Aquitaine, FranceMont-de-MarsanPrefecture and communeConfluence of the Douze and Midou rivers C...

 

XXII Copa de España (football americano)

XXII Copa de EspañaCopa de España Competizione Copa de España Sport Football americano Edizione 22ª Organizzatore FEFA Date dal 12 novembre 2017al 25 novembre 2017 Luogo  Spagna Partecipanti 3 Formula Semifinale e finale Sede finale Polideportivo Batiste Subies, La Pobla de Farnals Risultati Vincitore  Badalona Dracs(3º titolo) Secondo  Las Rozas Black Demons Semi-finalisti  Camioneros de Coslada Statistiche Incontri disputati 2 Punti segnati 46 (23 per ...

 

История христианства в Центральной Азии

ХристианствоБиблия Ветхий Завет Новый Завет Евангелие Десять заповедей Нагорная проповедь Апокрифы Бог, Троица Бог Отец Иисус Христос Святой Дух История христианства Апостолы Хронология христианства Раннее христианство Гностическое христианство Вселенские соборы Н...

Bahra

BahraLingkunganNegaraArab SaudiProvinsiProvinsi MakkahPemerintahan • Wali kotaHani Abu Ras[1] • Gubernur kotaMish'al Al-SaudKetinggian12 m (39 ft)Zona waktuUTC+3 (AST) • Musim panas (DST)ASTKode pos(5 kode digit dimulai dari 23; e.g. 23434)Kode area telepon+966-12Situs webwww.jeddah.gov.sa/english/index.php Bahra adalah sebuah permukiman padat penduduk di kota Jeddah di Provinsi Makkah, tepatnya di sebelah barat Arab Saudi.[3] Liha...

 

羅德島州

本條目存在以下問題，請協助改善本條目或在討論頁針對議題發表看法。 此條目需要擴充。 (2013年1月1日)请協助改善这篇條目，更進一步的信息可能會在討論頁或扩充请求中找到。请在擴充條目後將此模板移除。 此條目需要补充更多来源。 (2013年1月1日)请协助補充多方面可靠来源以改善这篇条目，无法查证的内容可能會因為异议提出而被移除。致使用者：请搜索一下条目的...

 

List of hotels in Ireland

According to the Irish Hotels Federation (IHF), it represents nearly 1,000 hotels and guesthouses in Ireland.[1] This is a list of notable hotels in Ireland, mostly historic hotels, or four or five-star modern hotels. It is intended they are covered in multiple secondary sources. They are arranged by the Counties of Ireland. Hotels and guesthouses with a Michelin Star includes: K Club and Wild Honey Inn. This is a dynamic list and may never be able to satisfy particular standards for...

一中同表

一中同表，是台灣处理海峡两岸关系问题的一种主張，認為中华人民共和国與中華民國皆是“整個中國”的一部份，二者因為兩岸現狀，在各自领域有完整的管辖权，互不隶属，同时主張，二者合作便可以搁置对“整个中國”的主权的争议，共同承認雙方皆是中國的一部份，在此基礎上走向終極統一。最早是在2004年由台灣大學政治学教授張亞中所提出，希望兩岸由一中各表�...

 

Thiaridae

Family of gastropods ThiaridaeTemporal range: Lower Cretaceous[1] or Eocene-Recent[2] PreꞒ Ꞓ O S D C P T J K Pg N A live individual of Red-rimmed melania, Melanoides tuberculata, crawling on the glass of an aquarium Scientific classification Domain: Eukaryota Kingdom: Animalia Phylum: Mollusca Class: Gastropoda Subclass: Caenogastropoda Superfamily: Cerithioidea Family: ThiaridaeGill, 1871 (1823) Synonyms Melaniidae Children, 1823[5] Melanoididae Ihering, 1909[...

 

Critics' Choice Television Award for Best Supporting Actress in a Movie/Miniseries

Critics' Choice Television Award for Best Supporting Actress in a Limited Series or Movie Made for TelevisionThe 2024 recipient: Maria BelloCountryUnited StatesPresented byCritics Choice AssociationFirst awarded2013Currently held byMaria Bello – Beef (2024)Websitecriticschoice.com The Critics' Choice Television Award for Best Supporting Actress in a Movie/Miniseries is one of the award categories presented annually by the Critics' Choice Television Awards (BTJA) to recognize the work done b...

Sir David Mathew

Welsh knight (1400–1484) Alabaster effigy of Sir David Mathew, north aisle, Llandaff Cathedral. He wears the Lancastrian livery collar of Esses Effigy of Sir David Mathew, side-view from north, north aisle, Llandaff Cathedral Full-length view of effigy of Sir David Mathew, Llandaff Cathedral Arms of Mathew[1]left: Mathew of Llandaff: Or, a lion rampant sable.;right: Mathew of Radyr: Sable, a lion rampant argent. Heraldic achievement at top of mural memorial tablet erected 1987 in Ll...

 

Arrondissement de Thionville-Ouest

Ne doit pas être confondu avec Canton de Thionville-Ouest. Arrondissement de Thionville-Ouest Situation de l'arrondissement de Thionville-Ouest dans le département Moselle. Administration Pays France Région Lorraine Département et collectivité territoriale Moselle Chef-lieu Thionville Code arrondissement 57 8 Démographie Population 121 156 hab. (2011) Densité 475 hab./km2 Géographie Coordonnées 49° nord, 6° est Superficie 255 km2 Subdivisions Cantons ...

 

Westbrook station (Connecticut)

Railway station in Westbrook, CT WestbrookA westbound Shore Line East train at Westbrook station in 2017General informationLocationNorris Avenue and Essex RoadWestbrook, ConnecticutCoordinates41°17′20″N 72°26′52″W / 41.2888°N 72.4479°W / 41.2888; -72.4479Owned byConnDOTLine(s)Amtrak Northeast CorridorPlatforms2 side platformsTracks2Connections Estuary Transit DistrictConstructionParking210 spacesAccessibleYesHistoryOpened1852 (NH&NL)May 29, 1990 (SLE)&#...

Televisión de alta definición

Este artículo o sección se encuentra desactualizado.La información suministrada ha quedado obsoleta o es insuficiente, pero puede consultarse actualizada en tema del artículo.Este aviso fue puesto el 31 de agosto de 2020. Etiqueta oficial europea (EICTA) La televisión de alta definición (HDTV) es un sistema de televisión digital que proporciona una resolución de imagen mucho más alta que la de la televisión de definición estándar. HDTV es el formato de vídeo estándar actual uti...

 

Chorges

ChorgesChòrjas (oc) La place du Fort. Blason Administration Pays France Région Provence-Alpes-Côte d’Azur Département Hautes-Alpes Arrondissement Gap Intercommunalité Communauté de communes Serre-Ponçon Maire Mandat Christian Durand 2020-2026 Code postal 05230 Code commune 05040 Démographie Gentilé Caturiges[1] Populationmunicipale 3 065 hab. (2021 ) Densité 57 hab./km2 Géographie Coordonnées 44° 32′ 47″ nord, 6° 16′ 38″ es...