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Diatonic Transposition
In music, transposition refers to the process or operation of moving a collection of notes ( pitches or pitch classes) up or down in pitch by a constant interval. For example, a music transposer might transpose an entire piece of music into another key. Similarly, one might transpose a tone row or an unordered collection of pitches such as a chord so that it begins on another pitch. The transposition of a set ''A'' by ''n'' semitones is designated by ''T''''n''(''A''), representing the addition ( mod 12) of an integer ''n'' to each of the pitch class integers of the set ''A''. Thus the set (''A'') consisting of 0–1–2 transposed by 5 semitones is 5–6–7 (''T''5(''A'')) since , , and . Scalar transpositions In scalar transposition, every pitch in a collection is shifted up or down a fixed number of scale steps within some scale. The pitches remain in the same scale before and after the shift. This term covers both chromatic and diatonic transpositions as follows. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transposition Example From Koch
Transposition may refer to: Logic and mathematics * Transposition (mathematics), a permutation which exchanges two elements and keeps all others fixed * Transposition, producing the transpose of a matrix ''A''T, which is computed by swapping columns for rows in the matrix ''A'' * Transpose of a linear map * Transposition (logic), a rule of replacement in philosophical logic * Transpose relation, another name for converse relation Games * Transposition (chess), different moves or a different move order leading to the same position, especially during the openings * Transposition table, used in computer games to speed up the search of the game tree Biology * Transposition (birth defect), a group of congenital defects involving an abnormal spatial arrangement of Tissue (biology), tissue or Organ (anatomy), organ ** Transposition of the great vessels, cardiac transposition, a congenital heart defect with malformation of any of the major vessels ** Transposition of teeth ** Pe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Modular Math
In mathematics, modular arithmetic is a system of arithmetic operations for integers, other than the usual ones from elementary arithmetic, where numbers "wrap around" when reaching a certain value, called the modulus. The modern approach to modular arithmetic was developed by Carl Friedrich Gauss in his book ''Disquisitiones Arithmeticae'', published in 1801. A familiar example of modular arithmetic is the hour hand on a 12-hour clock. If the hour hand points to 7 now, then 8 hours later it will point to 3. Ordinary addition would result in , but 15 reads as 3 on the clock face. This is because the hour hand makes one rotation every 12 hours and the hour number starts over when the hour hand passes 12. We say that 15 is ''congruent'' to 3 modulo 12, written 15 ≡ 3 (mod 12), so that 7 + 8 ≡ 3 (mod 12). Similarly, if one starts at 12 and waits 8 hours, the hour hand will be at 8. If one instead waited twice as long, 16 hours, the hour hand would be on 4. This can be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Enharmonic Equivalence
In music, two written notes have enharmonic equivalence if they produce the same pitch (music), pitch but are musical notation, notated differently. Similarly, written Interval (music), intervals, Chord (music), chords, or key signatures are considered enharmonic if they represent identical pitches that are notated differently. The term derives from Latin , in turn from Late Latin , from Ancient Greek (), from ('in') and ('harmony'). Definition The predominant musical tuning, tuning system in Western music is 12 tone equal temperament, twelve-tone equal temperament (12 ), where each octave is divided into twelve equivalent half steps or semitones. The notes F and G are a whole step apart, so the note one semitone above F (F) and the note one semitone below G (G) indicate the same pitch. These written notes are ''enharmonic'', or ''enharmonically equivalent''. The choice of notation for a pitch can depend on its diatonic function, role in harmony; this notation keeps modern ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transpositionally Equivalent
In music, transposition refers to the process or operation of moving a collection of notes ( pitches or pitch classes) up or down in pitch by a constant interval. For example, a music transposer might transpose an entire piece of music into another key. Similarly, one might transpose a tone row or an unordered collection of pitches such as a chord so that it begins on another pitch. The transposition of a set ''A'' by ''n'' semitones is designated by ''T''''n''(''A''), representing the addition ( mod 12) of an integer ''n'' to each of the pitch class integers of the set ''A''. Thus the set (''A'') consisting of 0–1–2 transposed by 5 semitones is 5–6–7 (''T''5(''A'')) since , , and . Scalar transpositions In scalar transposition, every pitch in a collection is shifted up or down a fixed number of scale steps within some scale. The pitches remain in the same scale before and after the shift. This term covers both chromatic and diatonic transpositions as follows. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Degree (music)
In music theory, the scale degree is the position of a particular note on a scale relative to the tonic—the first and main note of the scale from which each octave is assumed to begin. Degrees are useful for indicating the size of intervals and chords and whether an interval is major or minor. In the most general sense, the scale degree is the number given to each step of the scale, usually starting with 1 for tonic. Defining it like this implies that a tonic is specified. For instance, the 7-tone diatonic scale may become the major scale once the proper degree has been chosen as tonic (e.g. the C-major scale C–D–E–F–G–A–B, in which C is the tonic). If the scale has no tonic, the starting degree must be chosen arbitrarily. In set theory, for instance, the 12 degrees of the chromatic scale are usually numbered starting from C=0, the twelve pitch classes being numbered from 0 to 11. In a more specific sense, scale degrees are given names that indicate their p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Staff Position
In Western musical notation, the staff"staff" in the Collins English Dictionary "in British English: also called: stave; plural: staffs or staves""staff" in the Merriam-Webster Dictionary /ref> ( UK also stave; : ''staffs'' or ''staves''), also occasionally referred to as a pentagram, is a set of five horizontal lines and four spaces that each represent a different musical pitch ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Clef
A clef (from French: 'key') is a musical symbol used to indicate which notes are represented by the lines and spaces on a musical staff. Placing a clef on a staff assigns a particular pitch to one of the five lines or four spaces, which defines the pitches on the remaining lines and spaces. The three clef symbols used in modern music notation are the G-clef, F-clef, and C-clef. Placing these clefs on a line fixes a reference note to that line—an F-clef fixes the F below middle C, a C-clef fixes middle C, and a G-clef fixes the G above middle C. In modern music notation, the G-clef is most frequently seen as treble clef (placing G4 on the second line of the staff), and the F-clef as bass clef (placing F3 on the fourth line). The C-clef is mostly encountered as alto clef (placing middle C on the third line) or tenor clef (middle C on the fourth line). A clef may be placed on a space instead of a line, but this is rare. The use of different clefs makes it possible t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transposing Instrument
A transposing instrument is a musical instrument for which music notation is not written at concert pitch (concert pitch is the pitch on a non-transposing instrument such as the piano). For example, playing a written middle C on a transposing instrument produces a pitch other than middle C; that sounding pitch identifies the interval of transposition when describing the instrument. Playing a written C on clarinet or soprano saxophone produces a concert B (i.e. B at concert pitch), so these are referred to as B instruments. Providing transposed music for these instruments is a convention of musical notation. The instruments do not transpose the music; rather, their music is written at a transposed pitch. Where chords are indicated for improvisation they are also written in the appropriate transposed form. For some instruments, a written C sounds as a C but is in a different octave; these instruments are said to transpose "at the octave". Pitches on the double bass sound an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Key Signature
In Western musical notation, a key signature is a set of sharp (), flat (), or rarely, natural () symbols placed on the staff at the beginning of a section of music. The initial key signature in a piece is placed immediately after the clef at the beginning of the first line. If the piece contains a section in a different key, the new key signature is placed at the beginning of that section. In a key signature, a sharp or flat symbol on a line or space of the staff indicates that the note represented by that line or space is to be played a semitone higher (sharp) or lower (flat) than it would otherwise be played. This applies through the rest of the piece or until another key signature appears. Each symbol applies to comparable notes in all octaves—for example, a flat on the fourth space of the treble staff (as in the diagram) indicates that all notes notated as Es are played as E-flats, including those on the bottom line of the staff. Most of this article addres ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
