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Interval in classical music
Diesis (128:125) demonstration The octave C-C′, the three justly tuned major thirds C-E-G♯-B♯ and the descending diesis C′-B♯ are played (see example)
Diesis
music, septimal diesis (or slendro diesis) is an interval with the ratio of 49:48 [citation needed] play, which is the difference between the septimal whole
Septimal_diesis
Pythagorean comma. The composition of the septimal comma and the syntonic comma is 36/35, known as the septimal diesis. Its size is 48.8 cents, making it practically
Septimal_comma
twenty-eighth harmonics. It may be considered a diesis. The septimal 1/3-tone, along with the septimal diesis is tempered out by five-tone equal temperament
Septimal_third_tone
Topics referred to by the same term
Septimal diatonic semitone, the interval 15:14, about 119.44 cents Septimal diesis, an interval with the ratio of 49:48, about 38.71 cents Septimal kleisma
Septimal
Musical interval
meantone temperament, however, this is a diesis (128:125) less than an octave: Aug 4 + Aug 4 = Perf 8 − diesis. In just intonation, several different sizes
Tritone
Musical interval encompassing three half steps
horn part three times. Other pitch ratios are given related names, the septimal minor third with ratio 7:6 and the tridecimal minor third with ratio 13:11
Minor_third
Musical interval
to call them greater tone and lesser tone (see also greater and lesser diesis).[citation needed] Two major tones equal a ditone.[citation needed] Epogdoon
Major_second
Musical interval
In music, the septimal minor third, also called the subminor third (e.g., by Ellis) or septimal subminor third, is the musical interval exactly or approximately
Septimal_minor_third
Musical parts sounding at the same pitch
cents) Lesser diesis (41.1 cents) Greater diesis (62.6 cents) Septimal diesis (35.7 cents) Diaschisma (19.5 cents) Semicomma (10.1 cents) Septimal semicomma
Unison
Musical interval
The Mathematical Theory of Tone Systems, p.xxiii. ISBN 0-8247-4714-3. Septimal minor sixth. Jan Haluska (2003). The Mathematical Theory of Tone Systems
Minor_sixth
Musical interval
In music, the septimal whole tone, septimal major second, supermajor second, or septimal supermajor second play is the musical interval exactly or approximately
Septimal_whole_tone
Musical interval of 9 semitones
is the 12:7 septimal major sixth or supermajor sixth, the inversion of the septimal minor third, of approximately 933 cents. The septimal major sixth
Major_sixth
Musical interval
408 cents (play), about 22 cents sharp from the harmonic ratio of 5:4 . The septimal major third is 9:7 (435 cents), the undecimal major third is 14:11 (418 cents)
Major_third
In music, the septimal semicomma, a seven-limit semicomma, is the ratio 126/125 and is equal to approximately 13.79 cents (play).[citation needed] It is
Septimal_semicomma
In music, the ratio 225/224 is called the septimal kleisma or marvel comma (play). It is a minute comma type interval of approximately 7.7 cents. Factoring
Septimal_kleisma
Musical interval
and B (tuned to 15:8). It is very close to the 7:6 septimal minor third, differing by a septimal kleisma. Benward & Saker (2003). Music: In Theory and
Augmented_second
A septimal tritone is a tritone (about one half of an octave) that involves the factor seven. There are two that are inverses. The lesser septimal tritone
Septimal_tritone
Musical interval
(81:80) on C In music theory, the syntonic comma, also known as the chromatic diesis, the Didymean comma, the Ptolemaic comma, or the diatonic comma, is a small
Syntonic_comma
Musical interval
cents) Lesser diesis (41.1 cents) Greater diesis (62.6 cents) Septimal diesis (35.7 cents) Diaschisma (19.5 cents) Semicomma (10.1 cents) Septimal semicomma
Minor_seventh
intonation—a ratio of numbers with prime factors no higher than five. Septimal, undecimal, tridecimal, and septendecimal mean, respectively, 7, 11, 13
List_of_pitch_intervals
Musical interval
between a minor third (6:5) and septimal minor third (7:6). Composer Ben Johnston, to accommodate the just septimal quarter tone, uses a small "7" ()
Quarter_tone
Musical interval
The harmonic seventh interval (also known as the septimal minor seventh, or subminor seventh) is one with an exact 7:4 ratio (about 969 cents). This is
Harmonic_seventh
Musical interval
In music, the septimal major third play, also called the supermajor third (by Hermann von Helmholtz among others), septimal supermajor third, and sometimes
Septimal_major_third
Interval between one musical pitch and another with double its frequency
cents) Lesser diesis (41.1 cents) Greater diesis (62.6 cents) Septimal diesis (35.7 cents) Diaschisma (19.5 cents) Semicomma (10.1 cents) Septimal semicomma
Octave
Difference in pitch between two notes
cents). A septimal comma is 64:63 (27.3 cents), and is the difference between the Pythagorean or 3-limit "7th" and the "harmonic 7th". A diesis is generally
Interval_(music)
the septimal minor third (7:6) and two Bohlen–Pierce small semitones (27:25 Play one). It is also the difference between minor Bohlen–Pierce diesis (245:243)
Ragisma
Musical interval
seventh play. Four distinct intervals may be termed neutral sevenths: A septimal neutral seventh play has a ratio of 64:35 or about 1045 cents. The just
Neutral_interval
Musical interval
as a just minor seventh. 35:18, or 1151.23 cents, is the ratio of the septimal semi-diminished octave. The 15:8 just major seventh occurs arises in the
Major_seventh
Musical interval
cents) Lesser diesis (41.1 cents) Greater diesis (62.6 cents) Septimal diesis (35.7 cents) Diaschisma (19.5 cents) Semicomma (10.1 cents) Septimal semicomma
Thirteenth_(interval)
2401:2400, which is the difference between the septimal diesis (49:48, also known as Slendro diesis) and the septimal sixth-tone (50:49, also known as jubilisma)
Breedsma
Small interval between musical notes
cents) Lesser diesis (41.1 cents) Greater diesis (62.6 cents) Septimal diesis (35.7 cents) Diaschisma (19.5 cents) Semicomma (10.1 cents) Septimal semicomma
Pythagorean_comma
Septimal quarter tone on C Just minor third on C Problems playing these files? See media help. A septimal quarter tone (in music) is an interval with
Septimal_quarter_tone
In music, ratio of pitch frequencies
cents) Lesser diesis (41.1 cents) Greater diesis (62.6 cents) Septimal diesis (35.7 cents) Diaschisma (19.5 cents) Semicomma (10.1 cents) Septimal semicomma
Interval_ratio
Interval 21:20, about 84.47 cents
In music, a septimal chromatic semitone or minor semitone is the interval 21:20 (Play). It is about 84.47 cents. The septimal chromatic semitone may be
Septimal_chromatic_semitone
Musical interval
cents) Lesser diesis (41.1 cents) Greater diesis (62.6 cents) Septimal diesis (35.7 cents) Diaschisma (19.5 cents) Semicomma (10.1 cents) Septimal semicomma
Major_fourth_and_minor_fifth
Very small interval arising from discrepancies in tuning
the diesis, as well as a variety of other commas. 19 TET tempers out the septimal diesis and syntonic comma, but does not temper out the diesis. 22 TET
Comma_(music)
Musical interval
slightly wider than a major third, and is instead the same width as the septimal major third. The Pythagorean diminished fourth (F♭, 8192:6561 = 384.36
Diminished_fourth
Basic musical interval
6 cents), the outer differ by the greater diesis (648:625 or 62.6 cents). In 7 limit tuning there is the septimal diatonic semitone of 15:14 (play) available
Semitone
Musical tuning system with 19 pitches per octave
the power of four) is 62.565 cents sharper than an octave; this "greater" diesis is almost exactly a nineteenth of an octave. Likewise, five chromatic semitones
19_equal_temperament
example of such an interval is the ratio 7:6 (E♭), or 266.87 cents, the septimal minor third, the inverse of the supermajor sixth. Another example is the
Subminor_and_supermajor
Dissonant musical interval
flatter than an equal tempered 700 cents, (or exactly one twelfth of a diesis) and so the wolf is about 737.637 cents, or 35.682 cents sharper than a
Wolf_interval
Musical interval
cents) Lesser diesis (41.1 cents) Greater diesis (62.6 cents) Septimal diesis (35.7 cents) Diaschisma (19.5 cents) Semicomma (10.1 cents) Septimal semicomma
Perfect_fifth
Musical interval
cents) Lesser diesis (41.1 cents) Greater diesis (62.6 cents) Septimal diesis (35.7 cents) Diaschisma (19.5 cents) Semicomma (10.1 cents) Septimal semicomma
Augmented_fifth
Musical interval
cents) Lesser diesis (41.1 cents) Greater diesis (62.6 cents) Septimal diesis (35.7 cents) Diaschisma (19.5 cents) Semicomma (10.1 cents) Septimal semicomma
Pythagorean_interval
Musical interval
cents) Lesser diesis (41.1 cents) Greater diesis (62.6 cents) Septimal diesis (35.7 cents) Diaschisma (19.5 cents) Semicomma (10.1 cents) Septimal semicomma
Ninth_(interval)
Interval in music
cents) Lesser diesis (41.1 cents) Greater diesis (62.6 cents) Septimal diesis (35.7 cents) Diaschisma (19.5 cents) Semicomma (10.1 cents) Septimal semicomma
Ditone
Musical interval
music utilizes the 13th harmonic. It is the mediant of the septimal major third 9/7 and septimal minor third 7/6, and as such, enjoys an analogous property
Neutral_third
Musical interval
In music, a septimal diatonic semitone (or major diatonic semitone) is the interval 15:14 Play. It is about 119.44 cents. The septimal diatonic semitone
Septimal_diatonic_semitone
Musical interval unit
cents) Lesser diesis (41.1 cents) Greater diesis (62.6 cents) Septimal diesis (35.7 cents) Diaschisma (19.5 cents) Semicomma (10.1 cents) Septimal semicomma
Cent_(music)
Musical interval
Mathematical Theory of Tone Systems, p. xxvi. ISBN 0-8247-4714-3. Minor diesis, diminished second. Rushton, Julian. "Unison (prime)]". Grove Music Online
Diminished_second
Musical interval which is not a perfect harmonic
cents) Lesser diesis (41.1 cents) Greater diesis (62.6 cents) Septimal diesis (35.7 cents) Diaschisma (19.5 cents) Semicomma (10.1 cents) Septimal semicomma
Pseudo-octave
Musical interval
producing 36 pitches per octave. Septimal sixth tone Varieties of equal temperament 72 equal temperament Septimal diesis Gann, Kyle (September 16, 2019)
Sixth_tone
cents) Lesser diesis (41.1 cents) Greater diesis (62.6 cents) Septimal diesis (35.7 cents) Diaschisma (19.5 cents) Semicomma (10.1 cents) Septimal semicomma
Major_limma
Musical compound interval
cents) Lesser diesis (41.1 cents) Greater diesis (62.6 cents) Septimal diesis (35.7 cents) Diaschisma (19.5 cents) Semicomma (10.1 cents) Septimal semicomma
Tenth_(interval)
Musical interval
semitone is ~ 55 cents. In septimal meantone temperament the diminished third is considered to approximate the interval of a septimal major second (play), with
Diminished_third
Musical tuning system of 53 pitches
= 7 / 4 in 53 TET, and using it for 7-limit harmony means that the septimal kleisma, the interval 225 / 224 , is also tempered out. Theoretical
53_equal_temperament
Unit of measurement for musical intervals
cents) Lesser diesis (41.1 cents) Greater diesis (62.6 cents) Septimal diesis (35.7 cents) Diaschisma (19.5 cents) Semicomma (10.1 cents) Septimal semicomma
Millioctave
Musical interval
Substance. p. 523. ISBN 0-918728-60-6. Monzo, Joe; Rousseau, Kami (2005). "Septimal-comma". TonalSoft.com. Encyclopedia of Microtonal Music Theory. Retrieved
Schisma
Musical interval
cents) Lesser diesis (41.1 cents) Greater diesis (62.6 cents) Septimal diesis (35.7 cents) Diaschisma (19.5 cents) Semicomma (10.1 cents) Septimal semicomma
Diaschisma
Musical interval
cents) Lesser diesis (41.1 cents) Greater diesis (62.6 cents) Septimal diesis (35.7 cents) Diaschisma (19.5 cents) Semicomma (10.1 cents) Septimal semicomma
Perfect_fourth
Microtonal tuning system in music
into 31 steps arose naturally out of Renaissance music theory; the lesser diesis – the ratio of an octave to three major thirds, 128:125 or 41.06 cents
31_equal_temperament
Musical interval
renders a perceptibly consonant harmonic seventh in some tuning systems: In septimal meantone temperament, an augmented sixth is specifically assigned to the
Augmented_sixth
American composer (1943–2020)
third plus a septimal whole tone is also equated with the 11th harmonic. This means that the gap between a minor third plus a septimal whole tone ( 8
George_Secor
Musical interval
cents) Lesser diesis (41.1 cents) Greater diesis (62.6 cents) Septimal diesis (35.7 cents) Diaschisma (19.5 cents) Semicomma (10.1 cents) Septimal semicomma
Fifteenth_(interval)
Musical interval
cents) Lesser diesis (41.1 cents) Greater diesis (62.6 cents) Septimal diesis (35.7 cents) Diaschisma (19.5 cents) Semicomma (10.1 cents) Septimal semicomma
Diminished_seventh
Musical tuning system
cents), and for 1/6 down and up (2 steps = 33+1/3 cents), and and for septimal quarter up and down (3 steps = 50 cents = half a 12-EDO sharp). They may
72_equal_temperament
Ratio of two consecutive integers
28:27 62.96 septimal third-tone D♭- 32:31 54.96 31st subharmonic, inferior quarter tone D♭- 49:48 35.70 septimal diesis D♭ 50:49 34.98 septimal sixth-tone
Superparticular_ratio
Musical interval
cents. Adding a diesis to this makes up an octave. Hence, this interval's complement, the diminished second, is often referred to as a diesis. List of meantone
Augmented_seventh
Musical interval
cents) Lesser diesis (41.1 cents) Greater diesis (62.6 cents) Septimal diesis (35.7 cents) Diaschisma (19.5 cents) Semicomma (10.1 cents) Septimal semicomma
Diminished_octave
cents) Lesser diesis (41.1 cents) Greater diesis (62.6 cents) Septimal diesis (35.7 cents) Diaschisma (19.5 cents) Semicomma (10.1 cents) Septimal semicomma
Third_(chord)
Musical interval
cents) Lesser diesis (41.1 cents) Greater diesis (62.6 cents) Septimal diesis (35.7 cents) Diaschisma (19.5 cents) Semicomma (10.1 cents) Septimal semicomma
Augmented_octave
Small musical interval
the amount by which three tritaves exceed seven minor sixths. Septimal kleisma Septimal semicomma Haluska, Jan (2003). The Mathematical Theory of Tone
Semicomma
tempered out by 41-ET include the lesser diesis (128:125), septimal diesis (49:48), septimal sixth-tone (50:49), septimal comma (64:63), and the syntonic comma
41_equal_temperament
Musical interval
or as the difference between a chromatic semitone (25/24) and a greater diesis (648/625). The interval was named by Shohé Tanaka after the Greek for "closure"
Kleisma
Musical interval
cents) Lesser diesis (41.1 cents) Greater diesis (62.6 cents) Septimal diesis (35.7 cents) Diaschisma (19.5 cents) Semicomma (10.1 cents) Septimal semicomma
Neutral_sixth
Musical interval of ten diatonic steps
cents) Lesser diesis (41.1 cents) Greater diesis (62.6 cents) Septimal diesis (35.7 cents) Diaschisma (19.5 cents) Semicomma (10.1 cents) Septimal semicomma
Eleventh_(interval)
Tuning system for musical instruments
four different sizes: the diaschisma, the lesser diesis, the syntonic comma, and the greater diesis. Since S1 (the just A1) and S3 (the just m2) are the
Five-limit_tuning
is concerned, is the enharmonic diesis, followed—to speak rather roughly—by the semitone, which is twice the diesis, the tone, which is twice the semitone
Incomposite_interval
considered as being derived from ancient Greek intervals (the greater and lesser diesis and the syntonic comma), division into 34 steps did not arise 'naturally'
34_equal_temperament
Division of an octave
reasonably approximate this scale "consistency / consistent". "Marchettus, the cadential diesis, and neo-Gothic tunings". Xenharmonic Wiki article on 58edo
58_equal_temperament
(music) Septet Septimal chromatic semitone Septimal comma Septimal diatonic semitone Septimal diesis Septimal kleisma Septimal major third Septimal meantone
Index_of_music_articles
Concept in musical tuning theory
the syntonic comma, the septimal kleisma (225/224, about 8 cents) and the ratio 1029/1024 (the difference between three septimal whole tones and a perfect
Fokker_periodicity_block
Musical scale with a 96-step octave
play −03.27 undecimal diesis 03 0037.5 45:44 0038.91 play −01.41 septimal comma 02 0025 play 64:63 0027.26 play −02.26 septimal semicomma 01 0012.5 play
96_equal_temperament
/ 3072. In seven-limit tuning, they can be more simply defined as the septimal comma, with a ratio of 64/63. In everyday language, these notes are located
Semantic_system
Classification in ancient Greek music theory
Archytas's diatonic, or Ptolemy's "tonic diatonic", which has an 8:7 tone (see septimal whole tone) and the superparticular 28:27 instead of the complex 256:243
Genus_(music)
Prefix used in music theory
semi-augmented (fourth), semi-diminished (fifth) Tri- 3 Tritone, tritonic Sept- 7 Septimal Undec- 11 Undecimal Tridec- 13 Tridecimal Septen- 17 Septendecimal Novendec-
Musical_prefix
Musical scale
called the minor Bohlen–Pierce diesis) and 3125:3087 (about 21 cents, sometimes called the major Bohlen–Pierce diesis) in the same way that dividing the
Bohlen–Pierce_scale
went farther and noted that 31-ET provides an excellent approximation of septimal, or 7-limit harmony. In the twentieth century, physicist, music theorist
List_of_Dutch_discoveries
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