 Diesis

This article is about music. For other uses, see Diesis (disambiguation).
In classical music from Western culture, a diesis (difference, Greek: "leak or "escape"^{[1]}) is either an accidental (see sharp), or a comma type of musical interval, usually defined as the difference between an octave (in the ratio 2:1) and three justly tuned major thirds (tuned in the ratio 5:4), equal to 128:125 or about 41.06 cents. In 12tone equal temperament (on a piano for example) three major thirds in a row equal an octave, but three justlytuned major thirds fall quite a bit narrow of an octave, and the diesis describes the amount by which they are short. For instance, an octave (2:1) spans from C to C', and three justly tuned major thirds (5:4) span from C to B♯ (namely, from C, to E, to G♯, to B♯). The difference between CC' (2:1) and CB♯ (125:64) is the diesis (128:125). Notice that this coincides with the interval between B♯ and C', also called a diminished second.
The 128:125 interval is also known as a lesser diesis, as opposed to a wider comma (648:625) known as greater diesis. As shown in the picture, in the quartercomma meantone tuning system (a tuning system in which, by definition, major thirds are justly tuned), the diminished second coincides with the diesis.
Contents
Alternative definitions
In any tuning system, the deviation of an octave from three major thirds, however large that is, is typically referred to as a diminished second. The diminished second is an interval between pairs of enharmonically equivalent notes; for instance the interval between E and F♭. As mentioned above, the term diesis most commonly refers to the diminished second in quartercomma meantone temperament. Less frequently and less strictly, the same term is also used to refer to a diminished second of any size. In thirdcomma meantone, the diminished second is typically denoted as a greater diesis (see below).
In quartercomma meantone, since major thirds are justly tuned, the width of the diminished second coincides with the above mentioned value of 128:125. Notice that 128:125 is larger than a unison (1:1). This means that, for instance, C' is sharper than B♯. In other tuning systems, the diminished second has different widths, and may be smaller than a unison (e.g. C' may be flatter than B♯):
 a greater diesis above unison (648:625) for thirdcomma meantone temperament (see below),
 a diaschisma above unison (2048:2025) for sixthcomma,
 a schisma below unison (32768:32805) for twelfthcomma, and
 a Pythagorean comma below unison (524288:531441) for Pythagorean tuning.
In eleventhcomma meantone, the diminished second is within 1/716 (0.0014) of a cent above unison, so it closely resembles the 1:1 unison ratio of twelvetone equal temperament.
The word diesis has also been used to describe a large number of intervals, of varying sizes, but typically around 50 cents. Philolaus used it to describe the interval now usually called a limma, that of a justly tuned perfect fourth (4:3) minus two whole tones (9:8), equal to 256:243 or about 90.22 cents. Other theorists have used it for various other intervals.
Greater and lesser diesis
Some acoustics texts use the term greater diesis^{[1]} for the difference between an octave and four justly tuned minor thirds (tuned in the ratio 6:5), which is equal to three syntonic commas minus a schisma, equal to 648:625 or about 62.57 cents (almost one 63.16cent division in 19 equal temperament). Being larger, this diesis was termed "greater" while the 128:125 diesis was termed "lesser".^{[2]}
The small diesis Play (help·info) is 3125:3072 or approximately 28 cents.^{[3]}
Septimal and undecimal diesis
The septimal diesis (or slendro diesis) is an interval with the ratio of 49:48 play (help·info), which is the difference between the septimal whole tone and the septimal minor third. It is about 35.70 cents wide
The undecimal diesis is equal to 45:44 or about 38.91 cents, closely approximated by 31 equal temperament's 38.71 cent interval.
See also
References
 ^ ^{a} ^{b} Benson, Dave (2006). Music: A Mathematical Offering, p.171. ISBN 0521853877. Based on the technique of playing the aulos, where pitch is raised a small amount by slightly raising the finger on the lowest closed hole, letting a small amount of air "escape".
 ^ Don Michael Randel, The Harvard Dictionary of Music, Fourth Edition. Cambridge, MA: Belknap Press, 2003, p. 241.
 ^ John Fonville. "Ben Johnston's Extended Just Intonation A Guide for Interpreters", p.111, Perspectives of New Music, Vol. 29, No. 2 (Summer, 1991), pp. 106137.
Intervals (list) Numbers in brackets are the number of semitones in the interval.
Fractional semitones are approximate.Twelvesemitone
(Western)PerfectMajorMinorAugmentedDiminishedCompoundOther systems SupermajorNeutralSubminor7limitchromatic semitone (⅔) · diatonic semitone (1⅙) · whole tone (2⅓) · subminor third (2⅔) · supermajor third (4⅓) · harmonic (subminor) seventh (9⅔)Other intervals GroupsPythagorean comma · Pythagorean apotome · Pythagorean limma · Diesis · Septimal diesis · Septimal comma · Syntonic comma · Schisma · Diaschisma · Major limma · Ragisma · Breedsma · Kleisma · Septimal kleisma · Septimal semicomma · Orwell comma · Semicomma · Septimal sixthtone · Septimal quarter tone · Septimal thirdtone
MeasurementOthersCategories: Commas
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Diesis — Saltar a navegación, búsqueda La diesis (o diesis menor) es una coma o pequeño intervalo musical que aparece en el sistema de afinación justo jugando el mismo papel que la coma pitagórica juega en el sistema de Pitágoras. Así como el círculo de… … Wikipedia Español
Diësis — (griech.), in der griech. Musik nach Pythagoras der Überschuß der Quarte über zwei Ganztöne, d. h. der nachmals Limma genannte Pythagoreische Halbton 256: 243; später erhielten die Pykna (kleinen Intervalle, Vierteltöne) des enharmonischen… … Meyers Großes KonversationsLexikon
diesis — /di ɛzis/ s.m. [dal lat. diĕsis, gr. díesis passaggio, intervallo ]. (mus.) [segno musicale che, anteposto a una nota, prescrive l alterazione della stessa di un semitono ascendente] ▶◀ ⇑ accidente, alterazione. ◀▶ bemolle. ‖ bequadro. ⋰ doppio d … Enciclopedia Italiana
Diĕsis — (gr.), Tonerhöhung; daher das Kreuz … Pierer's UniversalLexikon
diesis — dȉesis m DEFINICIJA kršć. lik. u crkvenoj ikonografiji prikaz Krista na prijestolju, uzdignutih ruku, upućuju mu molitvu Majka Božja i Sv. Ivan Krstitelj; motiv se prvo javlja u Bizantu ETIMOLOGIJA grč. díēsis: molitva … Hrvatski jezični portal
Diesis — Di e*sis, n.; pl. {Dieses}. [NL., fr. Gr. ?, fr. ? to let go through, dissolve; dia through + ? to let go, send.] 1. (Mus.) A small interval, less than any in actual practice, but used in the mathematical calculation of intervals. [1913 Webster]… … The Collaborative International Dictionary of English
Diesis — Diesis, griech., Tonerhöhung, das die Noten um einen halben Ton erhöhende Kreuz (♯) … Herders ConversationsLexikon
diesis — ou Diese. Terme de Musique. Sorte de marque qui estant mise auprés d une note la fait hausser d un demi ton … Dictionnaire de l'Académie française
diesis — f. diesi … Diccionario de la lengua española
diesis — [dī′ə sis] n. pl. dieses [dī′əsēz΄] [L < Gr < diienai, to send through < dia , through + hienai, to send: see JET1] DOUBLE DAGGER … English World dictionary