Fact-checked by Grok 2 weeks ago

A-sharp

A-sharp (A♯), also known as B-flat (B♭) as its enharmonic equivalent, is a musical note in Western music theory that lies a chromatic semitone above the natural note A and a diatonic semitone below B. It represents one of the twelve distinct pitches in the equal-tempered chromatic scale, typically produced on the black keys of a piano between A and B. In standard tuning, where (the A above middle C) is defined as Hz, the frequency of A♯4 is calculated by multiplying Hz by the twelfth root of 2 (approximately 1.05946), resulting in about 466.16 Hz. This corresponds to note number 70 and is fundamental to constructing scales, chords, and harmonies across various keys. A-sharp plays a key role as an accidental, altering the natural A to fit modal, tonal, or chromatic contexts, such as in the or the scale. However, due to its enharmonic relationship with B-flat, it is more commonly notated as B♭ in practical compositions, particularly in keys with flats like or , to simplify reading and fingering. This notation choice reflects conventions in and , where enharmonic equivalents ensure the same auditory result while optimizing score legibility.

Musical Note

Definition and Notation

A-sharp, denoted as A♯, is the tenth semitone in the ascending from C, located one above A and enharmonically equivalent to B-flat. This positioning places it between A and B in the twelve-tone system, raising the pitch of A by a . In standard staff notation, A-sharp is represented by the note head for A with a sharp symbol (♯) prefixed to it, either as an accidental or within a . The placement of the note A varies by and : in the , for instance, A4 (the A above middle C) occupies the second space from the bottom of the staff, while in the bass clef, it appears on the second line from the top. Ledger lines extend the staff for higher or lower s, such as A♯5 above the treble staff. The sharp symbol alters only the specified or those on the same line/space unless canceled by a natural sign. The sharp symbol's development traces back to medieval music theory in the 11th century, when d'Arezzo introduced in his treatise Micrologus to navigate . It evolved from a square form of the letter "b" (b quadratum), representing the hard hexachord on G with B natural, contrasting the soft "b" (b rotundum) for B flat; over time, a through this "b" led to the modern ♯. By the , as staff notation standardized during the era, the sharp achieved its current vertical, hashtag-like form for precise pitch alteration in printed scores. In systems, pronunciation of A-sharp differs by tradition. Fixed-do, prevalent in Romance-language countries like , assigns syllables to absolute pitches, naming A as "la" and thus A-sharp as "la dièse" (pronounced approximately "lah dee-ehz"). Movable-do, common in English-speaking contexts, ties syllables to degrees relative to the , so A-sharp's name varies—for example, "ri" as the raised second or "ti" as the seventh in keys—emphasizing functional over fixed .

Enharmonic Equivalents

A-sharp (A♯) is primarily enharmonically equivalent to B-flat (B♭), representing the same in but notated differently to suit the musical context, such as or . This equivalence arises because both notations occupy the same position on the , a above A and a below B. In more extended theoretical contexts, such as transpositions or altered scales, A♯ can also equate to rarer spellings like C-double-flat (C𝄫), which lowers C by two semitones to match the same pitch, though this is uncommon outside specific harmonic analyses. The choice between A♯ and B♭ depends on the prevailing key signature: A♯ is favored in sharp-heavy keys, such as F♯ major, to maintain consistency with the scale's accidentals, while B♭ is preferred in flat keys, like E♭ major, for the same reason. In , enharmonic spelling impacts instrumental execution. For example, in the last measure of Debussy's La Mer, A♯ is assigned to the first in the high register for soft playing.

in

In standard tuning, where the note A4 above middle C is defined as 440 Hz, the of A♯4 is 466.16 Hz. This value is derived from the equal-temperament scale using the formula f = 440 \times 2^{1/12}, where $2^{1/12} approximates the interval ratio. A♯4 resides in the octave spanning from middle C (C4) to the B above it, as designated by scientific pitch notation under the ISO 16 standard for musical pitch, which specifies A4 at exactly 440 Hz and was internationally adopted in 1955 following proposals from the Acoustical Society of America in 1939. The corresponding wavelength of A♯4 in dry air at room temperature (20°C), where the speed of sound is approximately 343 m/s, is about 0.74 meters, calculated as \lambda = v / f with v as the speed of sound and f as the frequency. Frequencies double with each ascending octave and halve with each descending octave relative to A♯4, following f_n = 466.16 \times 2^n, where n is the number of octaves (positive above, negative below). For example, A♯3 vibrates at 233.08 Hz, while A♯5 reaches 932.33 Hz. A♯ shares this frequency with its enharmonic equivalent B♭ in .

Scales and Keys

Role in Diatonic Scales

In the key of , which consists of the diatonic notes C, D, E, F, G, A, and B with no sharps or flats in its , A♯ functions as an accidental when introduced to alter the pitch temporarily. This raises the sixth scale degree () from A to A♯, often appearing in chromatic passages or to heighten tension, such as in the augmented chord F–A♯–C, which expands the harmony beyond the pure diatonic framework. Within scales, A♯ serves as the (scale degree 7) in , where the scale ascends as B, C♯, D♯, E, F♯, G♯, A♯, returning to B; this half-step below the creates a strong pull toward resolution, characteristic of the mode's seventh degree. In scales, A♯ acts as the raised seventh degree, providing a similar function; for instance, in B (B, C♯, D, E, F♯, G, A♯), it replaces the natural seventh A, forming an augmented second interval with the sixth degree G and enhancing the dominant-to-tonic progression. A♯ participates in key diatonic intervals relative to other notes in these scales. From G natural, it forms an augmented second (three semitones), a non-diatonic interval that arises particularly in harmonic minor contexts due to the raised seventh. From F♯, A♯ creates a (four semitones), common in major scales like where both notes are diatonic. From E, it spans an augmented fourth (six semitones), often appearing as a in dominant harmonies but altered by the sharp notation. In various diatonic modes and keys, A♯ holds specific functional roles. As the (scale degree 2) in (G♯, A♯, B, C♯, D♯, E, F♯), it supports modal mixture and secondary dominants, lying a whole step above the . Similarly, in (F♯, G♯, A♯, B, C♯, D♯, E♯), A♯ is the (scale degree 3), forming the of the and contributing to the bright, stable quality of the major mode.

A-sharp Major Key

The A-sharp major scale is constructed by applying the standard major scale interval pattern—whole step, whole step, half step, whole step, whole step, whole step, half step—starting from the note A♯. The resulting pitches are A♯ (), B♯ (), C♯♯ (), D♯ (), E♯ (), F♯♯ (), G♯♯ (), and A♯ (). This configuration requires multiple double sharps to maintain the structure, contributing to its complexity. The key signature for A-sharp major theoretically comprises ten sharps: F♯, C♯, G♯, D♯, A♯, E♯, B♯, along with double sharps on C, F, and G. However, due to the impracticality of notating so many , A-sharp is almost always respelled enharmonically as , which uses a simpler key signature of two flats (B♭ and E♭). The pitches in B-flat major are enharmonically identical: B♭, C, D, E♭, F, G, A, B♭. The relative minor of A-sharp major is F-double-sharp minor, beginning on the sixth scale degree (F♯♯, enharmonic to G) and sharing the same key signature. On the circle of fifths, A-sharp major follows D-sharp major (nine sharps) and precedes E-sharp major (eleven sharps), positioning it among the more remote sharp keys. This placement underscores its theoretical nature, as keys beyond seven sharps are seldom employed in practice. A-sharp major exhibits a bright yet tense tonal character arising from its abundance of raised pitches and , which create heightened dissonance and resolution demands. Consequently, it is rarely utilized in complete compositions, typically appearing only in brief modulatory passages or as an enharmonic substitute for to suit notational convenience.

A-sharp Minor Key

The A-sharp minor scale is a minor scale with A♯ as its tonic. Its natural minor form consists of the pitches A♯, B♯, C♯, D♯, E♯, F♯, G♯, returning to A♯. The key signature for A-sharp minor includes seven sharps: F♯, C♯, G♯, D♯, A♯, E♯, and B♯. In the harmonic minor variant, the seventh scale degree is raised by a semitone to provide a stronger leading tone, altering G♯ to G♯♯ (enharmonically equivalent to A natural), resulting in the scale A♯, B♯, C♯, D♯, E♯, F♯, G♯♯, A♯. A-sharp minor's relative major is , sharing the identical of seven sharps. Its parallel , A-sharp , is enharmonically equivalent to . Although A-sharp minor remains uncommon in practice due to its position at the extreme of of fifths, it is generally more practical to notate than A-sharp , which requires three double sharps (C𝄪, F𝄪, G𝄪) in its degrees, rendering the major form highly awkward and rarely used outside theoretical contexts.

Theoretical and Practical Usage

In Equal Temperament

In twelve-tone equal temperament, the standard tuning system in Western music, the octave is divided into twelve equal semitones, each separated by an interval of exactly 100 cents, where one cent equals 1/100th of a semitone. This logarithmic division ensures that A-sharp (A♯) is precisely one semitone above A, corresponding to an interval of 100 cents from A4 at the standard concert pitch of 440 Hz. The frequency ratio for each semitone in this system is given by the twelfth root of 2, mathematically expressed as $2^{1/12} \approx 1.05946, which is applied multiplicatively to the base frequency. For A♯4, this yields a frequency of approximately 466.16 Hz when starting from A4 = 440 Hz, creating a tempered approximation that deviates slightly from acoustically pure intervals but maintains uniformity across the scale. A key advantage of equal temperament for notes like A♯ is its facilitation of seamless modulation between sharp and flat keys without requiring instrument retuning, as all semitones are identically spaced; this is particularly evident in keyboard instruments such as the piano, where enharmonic equivalents like A♯ and B♭ occupy the same key. The concept of well-tempered tuning, which laid groundwork for , was popularized through Johann Sebastian Bach's (1722), demonstrating playable music in all keys on a single tuning, though Bach likely employed an unequal variant; full adoption of became widespread in the with advancements in instrument manufacturing. On fixed-pitch instruments like the guitar, where determine note positions, A♯ and its enharmonic B♭ are produced at the identical location, treating them as the same tempered pitch regardless of .

In Just Intonation

In just intonation, A-sharp is tuned according to simple frequency ratios that prioritize harmonic consonance, often derived from the natural series rather than equal division of the . A common placement positions A-sharp as the minor second above A, with a ratio of \frac{16}{15} (approximately 111.8 cents), or as an augmented unison equivalent to B-flat at a ratio of \frac{1}{1}. In some scalings, it serves as the above G-sharp, employing the whole-tone of \frac{9}{8} (203.9 cents) for that . These ratios ensure intervals like thirds and sixths align closely with low s, producing beats-free consonance when performed in compatible keys. Relative to a reference pitch of at approximately 432 Hz, the frequency of A-sharp4 in via the \frac{16}{15} above A is about 460.8 Hz; this tuning emphasizes purity but varies by context, such as key or scale construction. For comparison, in standard with A4 = 440 Hz, A-sharp4 yields roughly 469.3 Hz under the same ratio, notably higher than equal temperament's 466.16 Hz, highlighting just intonation's deviation for harmonic accuracy over uniformity. The Pythagorean variant, a subset of just intonation limited to powers of the primes 2 and 3 (ratios like \frac{3}{2} for perfect fifths and \frac{9}{8} for whole tones), tunes the interval from A to A-sharp as the diatonic semitone of \frac{256}{243} (about 90.2 cents). Constructing a full chromatic scale this way accumulates the Pythagorean comma (\frac{531441}{524288} \approx 23.46 cents), resulting in "wolf" intervals—such as a narrowed fifth—that disrupt consonance in remote keys. Just intonation finds application in genres seeking maximal consonance, including vocal ensembles where singers instinctively approximate ratios like \frac{5}{4} for major thirds, and like string quartets, as in Ben Johnston's quartets (e.g., Nos. 1–10, recorded by the Kepler Quartet), which exploit pure intervals for timbral depth unavailable in tempered systems. This approach yields "sweeter" harmonies by aligning with the harmonic series, eschewing equal temperament's tempered compromises that introduce subtle beating. A key limitation is its key-dependence: pure ratios shift with the tonic (e.g., a \frac{3}{2} fifth in C becomes \frac{40}{27} in D), necessitating retuning for each on non-flexible instruments like keyboards, thereby constraining compositional freedom in modulating works.

Notable Musical Examples

bands like Metallica frequently center riffs on A-sharp power chords, as heard in tracks such as "" (1991), contributing to the genre's aggressive, low-end drive. In , A-sharp serves as a or altered tone in improvisations, adding bluesy tension. Full works in A-sharp major are rare owing to the impracticality of its eight-sharp , with composers typically respelling it enharmonically as to simplify notation, as seen in parts of Giuseppe Verdi's opera (1871), such as "Celeste Aida" in , where such key choices prioritize performability.

Other Contexts

In Computing

A# is a programming language that serves as a port of the Ada programming language to the Microsoft .NET framework, originally developed at the Department of Computer Science of the United States Air Force Academy around 2003. It supports Ada's strong typing, modularity, and real-time features while enabling interoperability with .NET libraries and components. Key syntax elements of A# retain Ada's tasking and protected types for concurrency, alongside .NET-specific mappings such as structs to tagged null records and properties to Ada functions, facilitating multilanguage programming in embedded systems and educational contexts. It integrates with tools like GNAT for compilation and Visual Studio for development, allowing Ada code to leverage .NET's common language runtime. As of November 2025, A# remains available as open-source software under the GNU General Public License, with the last major release (version 2.01) in 2004 and no activity since 2006 on SourceForge; it is compatible with older .NET frameworks up to approximately .NET 2.0 but has seen limited updates and adoption primarily within academic and Ada enthusiast communities. In music software and APIs, the A♯ symbol is used to denote the musical note in code representations, such as in MIDI protocols where A♯4 corresponds to note number 70. This notation appears in libraries for digital audio workstations and sequencing tools to specify pitches programmatically.

In Popular Culture

The British sitcom A Sharp Intake of Breath (1977–1981), created by Ronnie Taylor and starring as the beleaguered Barnes, derives its title from the idiomatic expression for a sudden gasp of shock or surprise, with no connection to . The series, which aired on and ran for four seasons, humorously depicted Barnes's battles against bureaucracy and everyday absurdities, earning praise for Jason's comedic timing. Indie game developer A Sharp, LLC, founded by David Dunham, has produced narrative-driven titles such as King of Dragon Pass (1999), a involving clan management in a mythological world, and Six Ages: Ride Like the Wind (2018), a sequel blending and decision-making elements. The studio's name, while evoking the musical note A-sharp, stems from unrelated origins and focuses on storytelling in fantasy settings rather than music-themed content. In literature, "sharp" often serves as a metaphor for acuity or tension, occasionally intersecting with musical references in ; for instance, Gillian Flynn's Sharp Objects (2006) employs the term in its title to convey cutting emotional precision, though it does not directly invoke the note A♯. Similarly, Christine Carbo's mystery A Sharp Solitude (2018) uses "sharp" to describe isolated, piercing atmospheres in its crime narrative set in Montana's National Park. A♯ appears in music production apps like , where users can select keys including those enharmonic to A-sharp major for smart instruments and loops, facilitating composition in that scale without manual retuning. Online music forums feature memes highlighting enharmonic between A♯ and B♭, such as jokes comparing note naming to grammatical errors like "there/their," underscoring the arbitrary conventions of .

References

  1. [1]
    https://human.libretexts.org/Bookshelves/Music/Music_Theory/Music_Fundamentals_(Ewell_and_Schmidt-Jones)/01:_Pitch_and_Major_Scales_and_Keys/1.04:_Pitch-_Sharp_Flat_and_Natural_Notes
  2. [2]
    [PDF] Piano key frequencies
    For example, to get the frequency a semitone up from A4 (A♯4), multiply 440 by the twelfth root of two. To go from A4 to B4 (up a whole tone, or two semitones), ...
  3. [3]
    Making Tones and Making Music | Sound Examples - GitHub Pages
    So the next note up from middle A, A-sharp 4, is 1.05946 * 440, or 466.16 Hz. The next note after that, B4, is 1.05946 * 466.16, or 493.88 Hz. The step ...
  4. [4]
    Enharmonic Notes - Music Theory for the 21st-Century Classroom
    When two notes sound the same but are written as two different notes on the staff, the written notes are said to be enharmonic.
  5. [5]
    A-sharp (note) on Piano, Guitar, and Ukulele | Musicca
    A-sharp is the note a half step above A. In music notation, A-sharp is written by adding a sharp sign (♯) to the note A.
  6. [6]
    1.4: Pitch- Sharp, Flat, and Natural Notes - Humanities LibreTexts
    Jul 15, 2023 · A sharp sign means "the note that is one half step higher than the natural note". A flat sign means "the note that is one half step lower than the natural note ...
  7. [7]
    Music 101: What Is a Sharp Note? Learn About Sharp ... - MasterClass
    Sep 2, 2022 · Sharp notes are notes that sound a semitone higher than notes that appear on the lines and spaces of a musical staff. As an example, the note G ...
  8. [8]
    Sharps and Flats - Music Theory Academy
    Sharps (#) raise a note by a semitone, flats (b) lower it. The symbol goes before the note, and double sharps/flats raise/lower by two semitones.
  9. [9]
    How to Identify and Use the Sharp Symbol (♯) in Music
    The sharp symbol (♯) raises a note by one semitone, either in a key signature or as an accidental, and is spoken after the note's letter name.<|separator|>
  10. [10]
    Where did the symbols ♭ and ♯ originate from, and why those?
    Jul 23, 2016 · The natural sign ♮ and the sharp sign ♯ derive from variations of a square b that signified the hard hexachord, hexachordum durum, where the ...The definition, and the origin of this sign notation "x" - MusicWhat does this sharp sign with an arrow mean? - MusicMore results from music.stackexchange.com
  11. [11]
    Where did the symbols ♭ and ♯ originate from, and why those?
    Apr 20, 2019 · The earliest usage of accidentals dates back to the 11th century, when the Italian-born Guido of Arezzo published Micrologus, a book for singing instruction.
  12. [12]
    What are the Solfège names of the semitones between the basic do ...
    Mar 6, 2013 · For example, a sharp do becomes di, flat sol becomes se, and flat re becomes ra. There are chromatic variants of fixed-do solfège similar to the ...Fixed-Do Solfege in A Major scale with accidentals - MusicDo accidental notes have their own name? - Music Stack ExchangeMore results from music.stackexchange.com
  13. [13]
    Movable do and fixed do solfège syllables - MyEarTraining
    Solfège. There are two types of solfège (or solfeggio) used in music. fixed do - syllables represent fixed tones (Do = C); movable do - syllables represent ...
  14. [14]
    Half Steps, Whole Steps, and Accidentals – Open Music Theory
    Notes have enharmonic equivalence when they are spelled differently but sound the same.
  15. [15]
    Double Sharps/Flats and Enharmonics - My Music Theory
    An enharmonic equivalent is simply another way to “spell” the same note. F sharp and G flat are “enharmonic equivalents” because they sound the same, but have ...
  16. [16]
    Enharmonic Equivalents - Music Theory Academy
    A sharp minor/B flat minor. In each of these enharmonic pairs the number of sharps and flats always adds up to 12 – (for example, C sharp major has 7 sharps ...
  17. [17]
    [PDF] The Study of - Orchestration
    ... enharmonic spelling may be necessitated by a passage or a chord which calls for both F and F# for instance, in which case the F would have to be spelled E# ...
  18. [18]
    Accidentals - Music Theory for the 21st-Century Classroom
    The sharp symbol—♯—raises a pitch a half step. The flat symbol—♭—lowers a pitch a half step. The double sharp symbol—𝄪—raises a pitch two half steps, or a ...
  19. [19]
    Intervals – Open Music Theory - VIVA's Pressbooks
    Augmented intervals are one half step larger than a perfect or major interval. Diminished intervals are one half step smaller than a perfect or minor interval.<|separator|>
  20. [20]
    Major Key Signatures - Music Theory for the 21st-Century Classroom
    The key signature reminds the performer which sharps or flats are in the scale (or key) of the piece and prevents the composer or arranger from writing every ...
  21. [21]
    B harmonic minor scale - Musicca
    The B harmonic minor scale is a seven-note scale consisting of the notes B, C♯, D, E, F♯, G, and A♯. The scale corresponds to the B natural minor scale.
  22. [22]
    Specific Intervals - musictheory.net
    Specific intervals are measured both on the staff and in half steps on the keyboard. As you learned in the previous lesson, C to D and C to Db are both generic ...<|separator|>
  23. [23]
    G sharp minor scale - Music theory games
    The key signature of G sharp minor scale has five sharps (5♯) because its relative major key is B Major scale.
  24. [24]
    F Sharp Major Scale Explained: The Complete Guide - Jade Bultitude
    Apr 14, 2023 · The F Sharp Major scale contains 7 notes: F#, G#, A#, B, C#, D and E#. Learn more about this diatonic scale and how to play it!
  25. [25]
    Major Scales, Scale Degrees, and Key Signatures - VIVA's Pressbooks
    In sharp key signatures, the last sharp is a half step below the tonic (the first note of a scale). In flat key signatures, the second-to-last flat is the ...
  26. [26]
    A Sharp (A#) Major Scale on Guitar - Chords and Theory
    Relative scales are major and natural minor scales that share the same notes and chords. That means they are in the same key signature but start on a different ...A# Major Scale on One String · Sharp Major Scale Degrees · A# Major Triads
  27. [27]
    1.12: Major Scales, Scale Degrees, and Key Signatures
    Aug 29, 2025 · The order of sharps in key signatures is F, C, G, D, A, E, B, while the order of flats is the opposite: B, E, A, D, G, C, F. In sharp key ...
  28. [28]
    Key of A sharp minor, chords - Piano-Keyboard-Guide.com
    The notes of the A# minor natural scale are: A# B# C# D# E# F# G#. To learn more about chords by key (what chords are in what key and why), check out my book, ...
  29. [29]
    A# Minor Scale | Circle of Fifths
    This is the Key Signature for A Sharp Minor as shown on the circle of fifths worksheet. There are seven Sharps. ... The order of Sharps is always F, C, G, D, A, E ...
  30. [30]
    How to Build an A Sharp Minor Scale on the Piano - Julie Swihart
    To build an A sharp harmonic minor scale, we'll start with an A natural minor scale. Then we'll raise the seventh note G♯, by 1/2 step, to G♯♯ (“G double-sharp”) ...<|control11|><|separator|>
  31. [31]
    A Sharp Minor Scale - Applied Guitar Theory
    Relative and Parallel Scales. Relative Major of A# Minor: C# Major | C# – D#m – E#m – F# – G# -A#m – B ...
  32. [32]
    A -Mol key | A sharp minor scale - Chordour
    ... A sharp minor key is available. ... Its relative major is C♯ major and its parallel major is B♭ major. The A ...
  33. [33]
    The Impractical Mode - Modes that Don't Work - Online Guitar Books
    Take A sharp major scale, for example. The notes in A# major are A# – B# – Cx – D# – E# – Fx – Gx. The A# major scale contains 3 double sharps (x). This by ...
  34. [34]
    Minor Scales with 7 Sharps/Flats - My Music Theory
    A# minor and Ab minor are minor scales with 7 sharps/flats. A# minor is relative to C# major, and Ab minor to Cb major. Both are rarely used.<|control11|><|separator|>
  35. [35]
    Equal Temperament
    In 1939, an International Conference met in London and unanimously adopted 440 Hz as the standard frequency for the pitch A4, and that is the almost universal ...
  36. [36]
    What are the advantages of the equal temperament? | Hans Rudolf ...
    Mar 17, 2022 · 1. One single tuning serves all keys: the fundamental tone is freely selectable. · 2. Free modulation · 3. “Bonus keys” · 4. Polytonality.
  37. [37]
    Happy Birthday, Well-Tempered Clavier - JSTOR Daily
    Nov 2, 2022 · For years, many scholars argued that by writing The Well-Tempered Clavier Bach was advocating the use of equal temperament over mean ...
  38. [38]
    What is the difference between equivalent Flat and Sharp keys as far ...
    Feb 10, 2014 · For fixed pitch instruments there is no difference, but for other pitched instruments (including vocals) it should make a difference. That ...
  39. [39]
    Just Intonation Explained - Kyle Gann
    In the notation of just-intonation (pure) tuning, pitches are given as fractions, which are actually ratios between the named pitch and a constant fundamental.
  40. [40]
    Intervals
    Using the just intonation based on harmonic partials, we have seen that certain intervals can be described by ratios of small integers such as 1:1 1 : 1 (unison) ...
  41. [41]
    The Psychology of Music and the 'tuneR' Package - John Myles White
    Oct 25, 2011 · Tuning Systems: Pythagorean, Just and 12-Tet ; A#, 469.3333, 16/15 ; B · 495, 9/8 ; C · 528, 6/5 ; C#, 550, 5/4.<|control11|><|separator|>
  42. [42]
    Pythagorean Intervals - UConn Physics
    Pythagoras called the relationship between two notes an interval. For example, as mentioned above, when two strings have the same length, they have the same ...
  43. [43]
    Pythagorean Tuning | Azimuth - WordPress.com
    Oct 7, 2023 · An important early tuning system is Pythagorean tuning, where we force all frequency ratios to involve only powers of 2 and 3.
  44. [44]
    Pythagorean Tuning - More details - Medieval Music & Arts Foundation
    ... Pythagorean semitone has a ratio of 256:243. As a vertical interval, it is a strong discord which plays a striking role in various two-voice and multi-voice ...
  45. [45]
    The Just Intonation Issue - | Sound American
    Just intonation is, many believe, a more “pure” way of tuning and offers greater timbral and sonic possibilities than equal-temperament.
  46. [46]
    Why Is Just Intonation Impractical? - Music Stack Exchange
    Dec 10, 2012 · Just intonation scales are based on rational ratios, but not on the harmonic series. They are much more complex than that to achieve more equidistant pitch ...What are the ratios of Just Intonation? - Music Stack ExchangeIn Pythagorean tuning, what's the frequency of the tonic of each key?More results from music.stackexchange.comMissing: A# | Show results with:A#
  47. [47]
    Symphony No. 9 in D minor, Op. 125 “Choral” (1824) – Beethoven ...
    Clear homophonic texture relieves the intense counterpoint of the battle fugue, and D major gains its final victory over B-flat. The Janissary instruments have ...
  48. [48]
    Piano Sonata No.1, Op.6 (Scriabin, Aleksandr) - IMSLP
    General Information ; Scriabin, Aleksandr · Op.6 · IAS 29 · 4 movements: Allegro con fuoco; = 40; Presto; Funebre · 1893.
  49. [49]
    https://soundamerican.org/issues/just-intonation
  50. [50]
    https://music.stackexchange.com/questions/7986/why-is-just-intonation-impractical
  51. [51]
    [PDF] A#: Multilanguage Programming with Ada in .NET - SIGAda
    Dec 8, 2003 · ▫See mgnat\include for the Ada specs for the standard .NET libraries (lots of them). ▫Find help by using SDK Documentation. Page 9 ...Missing: University Pisa
  52. [52]
    Ada for .NET
    A# is a port of Ada to the Microsoft .NET Platform. A# was originally developed at the Department of Computer Science at the United States Air Force Academy.Missing: Pisa | Show results with:Pisa
  53. [53]
    A# (asharp)
    - **Latest Release Date**: Not specified in content.
  54. [54]
    MIDI Octave and Note Numbering Standard
    Jul 30, 2017 · For MIDI, middle C is always note number 60 even though it may be another pitch or described by a different octave designation - C3, C4 or C5.The Midi Tuning Standard – Developers & MIDI 2.0 SpecificationsOfficial Note Name to Midi Number specificationMore results from midi.org
  55. [55]
    MIDI note numbers and center frequencies - Inspired Acoustics
    The following table summarizes the MIDI note numbers as defined in the MIDI standard and matched to the Middle C (note number 60) as C4.
  56. [56]
    A Sharp Intake of Breath (TV Series 1977–1981) - IMDb
    Rating 6.8/10 (131) A Sharp Intake of Breath: Created by Ronnie Taylor. With David Jason, Jacqueline Clarke, Richard Wilson, Alun Armstrong. British sitcom in which ...
  57. [57]
    A Sharp Intake Of Breath - ITV1 Sitcom - British Comedy Guide
    A guide to A Sharp Intake Of Breath, the 1977 - 1981 ITV1 TV sitcom. David Jason stars as Peter Barnes, an average man forever struggling against red tape ...
  58. [58]
    A Sharp
    A Sharp, LLC is the creator of the games King of Dragon Pass, the saga of colonizing a magical land (for iOS, Windows, and Mac), and Jigami, the jigsaw ...
  59. [59]
    David Dunham - Owner - A Sharp, LLC | LinkedIn
    Experience: A Sharp, LLC · Location: Seattle · 500+ connections on LinkedIn. View David Dunham's profile on LinkedIn, a professional community of 1 billion ...
  60. [60]
    Excerpt from Sharp Objects - Penguin Random House Canada
    The next strong literary thriller for TRP's growing list of successful commercial fiction, by Entertainment Weekly's chief TV critic.
  61. [61]
    Q & A #65 – Christine Carbo, “A Sharp Solitude”
    May 30, 2018 · It's quite the plotting feat and gives A Sharp Solitude a feeling of looming dread. The whole book takes place in a week. Like the others ...
  62. [62]
    Download additional sounds and loops for GarageBand on iPhone
    After you install GarageBand, three types of additional content (collectively called content packs) are available to download in the Sound Library.
  63. [63]
    Is this a joke I am too unmusical to get? : r/ExplainTheJoke - Reddit
    Jan 1, 2025 · Just to be pedantic, the correct term for this is to say those two notes are "enharmonic.".ELI5: Why do musical semitones mess around with a ...nobody understands this meme : r/lingling40hrsMore results from www.reddit.comMissing: forums | Show results with:forums