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In music, a symmetric scale is a music scale which equally divides the octave. The concept and term appears to have been introduced by Joseph Schillinger 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"). This may be seen quite readily with the whole tone scale on C:

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  • Escala simètrica (ca)
  • Escala simétrica (es)
  • Symmetric scale (en)
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  • En una escala simétrica el esquema de tonos y semitonos es el mismo en dirección ascendente y descendente. Un ejemplo de escala simétrica es la escala dórica (T-S-T-T-T-S-T). * Datos: Q7661315 (es)
  • En música, una escala simètrica és una escala musical que divideix de manera igual les octaves. El concepte i el terme semblen haver estat introduïts per i desenvolupats posteriorment per Nicolas Slonimsky com a part del seu famós "Thesaurus of Scales and Melodic Patterns". En dodecafonia temperament igual, l'octava només pot ser dividida igualment en dos, tres, quatre, sis o dotze parts, que en conseqüència es poden omplir mitjançant l'addició d'aquest interval exacte o seqüència d'intervals per a cada nota resultant (anomenada "interpolació de notes"). * {C, D, E, F♯, G♯, A♯, C} (?·pàg.) (ca)
  • In music, a symmetric scale is a music scale which equally divides the octave. The concept and term appears to have been introduced by Joseph Schillinger 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"). This may be seen quite readily with the whole tone scale on C: (en)
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  • http://commons.wikimedia.org/wiki/Special:FilePath/Whole_tone_scale_on_C.png
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  • En música, una escala simètrica és una escala musical que divideix de manera igual les octaves. El concepte i el terme semblen haver estat introduïts per i desenvolupats posteriorment per Nicolas Slonimsky com a part del seu famós "Thesaurus of Scales and Melodic Patterns". En dodecafonia temperament igual, l'octava només pot ser dividida igualment en dos, tres, quatre, sis o dotze parts, que en conseqüència es poden omplir mitjançant l'addició d'aquest interval exacte o seqüència d'intervals per a cada nota resultant (anomenada "interpolació de notes"). Com a exemples hi ha l'escala octatònica (també coneguda com a escala simètrica disminuïda, i la seva imatge mirall és coneguda com l'escala simètrica inversa disminuïda i la escala tríton de dos semitons: Com s'explica anteriorment, ambdues estan compostes de subunitats repetides dins d'una octava. Aquesta propietat permet que aquestes escales siguin transposades a altres notes, encara que conservin exactament les mateixes notes que l'escala original (simetria de translació). Això es pot veure molt fàcilment amb tota l'escala de tons en C: * {C, D, E, F♯, G♯, A♯, C} (?·pàg.) Si es trasllada fins a un a D, conté exactament les mateixes notes en una permutació diferent: * {D, E, F♯, G♯, A♯, C, D} En el cas d'escales inversament simètriques la inversió de l'escala és idèntica. Així, els intervals entre els graus de l'escala són simètrics si es llegeixen des del "dalt" (fi) o "baix" (inici) de l'escala (simetria de mirall). Els exemples inclouen l'escala Dorian B9 d'Ucraïna (sisè manera de l'escala Major hongaresa), l'escala b5 Menor Jazz (cinquena manera de la involució de l'escala major hongaresa), l'escala napolità major (quart manera de l'escala major locriana), el slendro javanès, l'escala cromàtica, , escala dòrica, escala harmònica menor, escala eòlica dominant (cinquena manera de l'escala menor), la sisena escala frígia dominant major (cinquena manera de la ), i l'escala doble harmònica major. Les escales asimètriques són "molt més comunes" que les escales simètriques i això pot explicar-se per la incapacitat de les escales simètriques de posseeir la propietat d'unicitat (on cada classe interval conté un nombre únic de temps) que ajuda a determinar la ubicació de les notes en relació a la primera nota de l'escala. (ca)
  • En una escala simétrica el esquema de tonos y semitonos es el mismo en dirección ascendente y descendente. Un ejemplo de escala simétrica es la escala dórica (T-S-T-T-T-S-T). * Datos: Q7661315 (es)
  • In music, a symmetric scale is a music scale which equally divides the octave. The concept and term appears to have been introduced by Joseph Schillinger 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"). Examples include the octatonic scale (also known as the symmetric diminished scale; its mirror image is known as the inverse symmetric diminished scale) and the two-semitone tritone scale: 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} 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. 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 Ukrainian Dorian b9 scale (sixth mode of the Hungarian Major scale), the Jazz Minor b5 scale (third mode of the Hungarian Major Inverse), the Neapolitan Major scale (fourth mode of the Major Locrian scale), the Javanese slendro, the chromatic scale, whole-tone scale, Dorian scale, the Aeolian Dominant scale (fifth mode of the melodic minor), the Harmonic Minor scale, the Major Locrian Major 7th/Harmonic Major b5 scale, the Chromatic Lydian scale (fourth mode of Blues Leading-Tone scale), the Phrygian Major Lydian scale (fourth mode of Neapolitan Major b5 scale), and the double harmonic scale. Asymmetric scales are "far more common" than symmetric scales and this may be accounted for by the inability of 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. (en)
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