page_title: 53 equal temperament
section_title: Notation
hierarchical_section_title: 53 equal temperament / Notation
caption_attribution_description: English: The basic notes named according to the solfege system and thus, for example, "Do" is C and "Re" is D. English: Commas horizontally: DO sharps, RE flats Türkçe: DO diyezler, RE Bemoller
context_page_description: In music, 53 equal temperament, called 53 TET, 53 EDO, or 53 ET, is the tempered scale derived by dividing the octave into 53 equal steps. Each step represents a frequency ratio of 2​¹⁄⁵³, or 22.6415 cents, an interval sometimes called the Holdrian comma.
  53-EDO is a tuning of equal temperament in which the tempered perfect fifth is 701.89 cents wide, as shown in Figure 1.
  The 53-EDO tuning equates to the unison, or tempers out, the intervals ​³²⁸⁰⁵⁄₃₂₇₆₈, known as the schisma, and ​¹⁵⁶²⁵⁄₁₅₅₅₂, known as the kleisma. These are both 5 limit intervals, involving only the primes 2, 3 and 5 in their factorization, and the fact that 53 ET tempers out both characterizes it completely as a 5 limit temperament: it is the only regular temperament tempering out both of these intervals, or commas, a fact which seems to have first been recognized by Japanese music theorist Shohé Tanaka. Because it tempers these out, 53-EDO can be used for both schismatic temperament, tempering out the schisma, and Hanson temperament, tempering out the kleisma.
context_section_description: Attempting to use standard notation, seven letter notes plus sharps or flats, can quickly become confusing. This is unlike the case with 19-EDO and 31-EDO where there is little ambiguity. By not being meantone, it adds some problems that require more attention. Specifically, the major third is different from a ditone, two tones, each of which is two fifths minus an octave. Likewise, the minor third is different from a semiditone. The fact that the syntonic comma is not tempered out means that notes and intervals need to be defined more precisely. Ottoman classical music uses a notation of flats and sharps for the 9-comma tone.
  In this article, diatonic notation will be used creating the following chromatic scale, where sharps and flats aren't enharmonic, only E and B are enharmonic with F and C. For the other notes, triple and quadruple sharps and flats aren't enharmonic.
  C, C♯, C, C♯, C, D, D, D, D♭,
  D, D♯, D, D♯, D, E, E, E, E♭,
  E, E♯, E/F, F♭,
  F, F♯, F, F♯, F, G, G, G, G♭,
  G, G♯, G, G♯, G, A, A, A, A♭,
  A, A♯, A, A♯, A, B, B, B, B♭,
  B, B♯, B/C, C♭, C
caption: Notation used in Ottoman classical music, where the tone is divided into 9 commas