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Flat and sharp are mutually inverse isomorphisms of smooth vector bundles, hence, for each p in M, there are mutually inverse vector space isomorphisms between T p M and T ∗ p M. The flat and sharp maps can be applied to vector fields and covector fields by applying them to each point. Hence, if X is a vector field and ω is a covector field,
G clef (Treble clef) The spiral of a G clef (not a point on the spiral, but the center around which the spiral is drawn) shows where the G above middle C is located on the staff. A G clef with the spiral centered on the second line of the staff is called treble clef. [2] The treble clef is the most commonly encountered clef in modern notation ...
Treble clef C major scale, treble clef. Play ⓘ The only G-clef still in use is the treble clef, with the G-clef placed on the second line. This is the most common clef in use and is generally the first clef learned by music students. [2] For this reason, the terms "G-clef" and "treble clef" are often seen as synonymous.
Even so, Johannes Brahms still felt the need to rewrite his C-sharp minor piano quartet in C minor, which was published as Piano Quartet No. 3 in C minor, Op. 60. [citation needed] The last intermezzo from his Three Intermezzi for piano, Op. 117 is in C-sharp minor. Alkan composed the second movement (Adagio) for Concerto for Solo Piano in C ...
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Baroque music written in minor keys often was written with a key signature with fewer flats than we now associate with their keys; for example, movements in C minor often had only two flats (because the A ♭ would frequently have to be sharpened to A ♮ in the ascending melodic minor scale, as would the B ♭).
Comparison between tunings: Pythagorean, equal-tempered, quarter-comma meantone, and others.For each, the common origin is arbitrarily chosen as C. The degrees are arranged in the order or the cycle of fifths; as in each of these tunings except just intonation all fifths are of the same size, the tunings appear as straight lines, the slope indicating the relative tempering with respect to ...
In Hungarian Rhapsody No. 6, Franz Liszt takes the unusual step of changing the key from D-flat major to C-sharp major near the start of the piece, and then back again to B-flat minor. Maurice Ravel selected C-sharp major as the tonic key of "Ondine" from his piano suite Gaspard de la nuit .