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A septimal comma is a small musical interval in just intonation that contains the number seven in its prime factorization. There is more than one such
Septimal_comma
Very small interval arising from discrepancies in tuning
are a septimal kleisma apart. Translated in this context, "comma" means "a hair" as in "off by just a hair"[citation needed]. The word "comma" came via
Comma_(music)
Musical interval
Syntonic comma (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
Syntonic_comma
cents (play).[citation needed] It is also called the small septimal comma and the starling comma after its use in starling temperament. Factored into primes
Septimal_semicomma
tone and the septimal minor third. It is about 35.7 cents wide, which is narrower than a quarter-tone but wider than the septimal comma. It may also be
Septimal_diesis
Small interval between musical notes
Pythagorean comma (531441:524288) on C In musical tuning, the Pythagorean comma (or ditonic comma), named after the ancient mathematician and philosopher
Pythagorean_comma
Musical interval
augmented sixth of 225 / 128 by a septimal kleisma ( 225 / 224 , 7.71 cents), or about 1 / 3 Pythagorean comma. The harmonic seventh note is about
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
Basic musical interval
harmonic seventh (7:4). There is also a smaller septimal chromatic semitone of 21:20 (play) between a septimal minor seventh and a fifth (21:8) and an octave
Semitone
Interval in classical music
61 cents. The septimal diesis (or slendro diesis) is an interval with the ratio of 49:48 play, which is the difference between the septimal whole tone and
Diesis
Dissonant musical interval
example is the abnormally small fifth that results from the Pythagorean comma. Particularly out of tune intervals produce an unpleasant effect that remind
Wolf_interval
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
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
Difference in pitch between two notes
plus a major third. It is expressed by the ratio 81:80 (21.5 cents). A septimal comma is 64:63 (27.3 cents), and is the difference between the Pythagorean
Interval_(music)
Musical tuning system with 15 pitches equally-spaced on a logarithmic scale
meantone system, rather being a superpyth system (tempering out 64:63, the septimal comma). Guitars have been constructed for 15-ET tuning. The American musician
15_equal_temperament
Topics referred to by the same term
septimal in Wiktionary, the free dictionary. Septimal may refer to: Septimal chromatic semitone, the interval 21:20, about 84.47 cents Septimal comma
Septimal
approximation of a quarter tone. The septimal quarter tone can be viewed either as a musical interval in its own right, or as a comma; if it is tempered out in a
Septimal_quarter_tone
Division of an octave
temper out the syntonic comma of 81/80, but instead exaggerates its size by mapping it to one step. In the 7-limit, the septimal minor seventh (7/4) can
22_equal_temperament
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 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
distinguished in other tunings. In tunings near quarter-comma meantone it approximates the septimal minor third of ratio 7:6 (Play). In pythagorean tuning
Augmented_second
Musical interval
performance techniques. p. 147. ISBN 0-520-22409-4. ... septimal tritone, 10:7; smaller septimal tritone, 7:5; ... This list is not exhaustive, even when
Tritone
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
about 62.96 cents wide. The septimal 1/3-tone can be viewed either as a musical interval in its own right, or as a comma; if it is tempered out in a given
Septimal_third_tone
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 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
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 parts sounding at the same pitch
Septimal quarter tone Undecimal quarter tone Commas Pythagorean comma (23.5 cents) Syntonic comma (21.5 cents) Holdrian comma (22.6 cents) Septimal comma
Unison
Musical interval
Septimal quarter tone Undecimal quarter tone Commas Pythagorean comma (23.5 cents) Syntonic comma (21.5 cents) Holdrian comma (22.6 cents) Septimal comma
Perfect_fifth
ratio of 21/41, or 29.27 cents (Play), an interval close in size to the septimal comma. 41-ET can be seen as a tuning of the schismatic, magic and miracle
41_equal_temperament
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
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
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
Musical interval
Septimal quarter tone Undecimal quarter tone Commas Pythagorean comma (23.5 cents) Syntonic comma (21.5 cents) Holdrian comma (22.6 cents) Septimal comma
Minor_seventh
Musical interval
81/64. The ditone differs from the just major third (5/4) by the syntonic comma (81/80). Likewise, the difference between the tone and the perfect fourth
Pythagorean_interval
Microtonal tuning system in music
quarter-comma meantone. Huygens not only realized this, he went farther and noted that 31 EDO provides an excellent approximation of septimal, or 7 limit
31_equal_temperament
Musical interval
ratio and is 18 cents smaller. Their size differs by exactly one syntonic comma (81:80, or about 21.5 cents). Some equal temperaments, such as 15-ET and
Major_second
7:4 interval in septimal meantone. There are several slightly adjusted meantone tunings very nearly equivalent to exact quarter comma meantone, which
Septimal_meantone_temperament
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 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
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 unit
Iring noticed that the Grad/Werckmeister (1.96 cents, 12 per Pythagorean comma) and the schisma (1.95 cents) are nearly the same (≈ 614 steps per octave)
Cent_(music)
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
Musical interval
that interval a "diminished comma" or comma minor. A diaschisma is the difference between a schisma and a syntonic comma, as well as the difference between
Diaschisma
Musical interval
Septimal quarter tone Undecimal quarter tone Commas Pythagorean comma (23.5 cents) Syntonic comma (21.5 cents) Holdrian comma (22.6 cents) Septimal comma
Perfect_fourth
Ratio of two consecutive integers
septimal sixth-tone B♯- 64:63 27.26 septimal comma, 63rd subharmonic C- 81:80 21.51 syntonic comma C+ 126:125 13.79 septimal semicomma D 128:127 13.58 127th
Superparticular_ratio
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
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, the septimal whole tone, septimal major second, supermajor second, or septimal supermajor second play is the musical interval exactly or approximately
Septimal_whole_tone
(music) Septet Septimal chromatic semitone Septimal comma Septimal diatonic semitone Septimal diesis Septimal kleisma Septimal major third Septimal meantone
Index_of_music_articles
Interval between one musical pitch and another with double its frequency
Septimal quarter tone Undecimal quarter tone Commas Pythagorean comma (23.5 cents) Syntonic comma (21.5 cents) Holdrian comma (22.6 cents) Septimal comma
Octave
In music, ratio of pitch frequencies
Septimal quarter tone Undecimal quarter tone Commas Pythagorean comma (23.5 cents) Syntonic comma (21.5 cents) Holdrian comma (22.6 cents) Septimal comma
Interval_ratio
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
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 interval
Septimal quarter tone Undecimal quarter tone Commas Pythagorean comma (23.5 cents) Syntonic comma (21.5 cents) Holdrian comma (22.6 cents) Septimal comma
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
Musical interval
two types of undecimal major fourth. The term may also be applied to the "comma-deficient major fourth" (or "chromatic major fourth"), which is the ratio
Major_fourth_and_minor_fifth
a "♯" to indicate a note is raised 92 cents, the value of the syntonic comma and the just chromatic semitone. Fonville, John (Summer 1991). "Ben Johnston's
Major_limma
Musical interval
Septimal quarter tone Undecimal quarter tone Commas Pythagorean comma (23.5 cents) Syntonic comma (21.5 cents) Holdrian comma (22.6 cents) Septimal comma
Neutral_sixth
Interval in music
cents) by a syntonic comma (81/80, 21.51 cents). Because it is a comma wider than a "perfect" major third of 5:4, it is called a "comma-redundant" interval
Ditone
Musical compound interval
Septimal quarter tone Undecimal quarter tone Commas Pythagorean comma (23.5 cents) Syntonic comma (21.5 cents) Holdrian comma (22.6 cents) Septimal comma
Tenth_(interval)
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
extended-quarter-comma meantone ... the 5:4 ratio [whose] extended-sixth-comma meantone corresponds to the 55 division ... extended-fifth-comma meantone [corresponds
List_of_meantone_intervals
Musical interval
Septimal quarter tone Undecimal quarter tone Commas Pythagorean comma (23.5 cents) Syntonic comma (21.5 cents) Holdrian comma (22.6 cents) Septimal comma
Diminished_seventh
Musical scale with a 96-step octave
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 126:125 0013.79 play
96_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
Tuning system for musical instruments
justest possible ratios, namely 7/5 (about 582.512 cents, also known as septimal tritone) and 10/7 (about 617.488 cents). These ratios are more consonant
Five-limit_tuning
Musical interval
Septimal quarter tone Undecimal quarter tone Commas Pythagorean comma (23.5 cents) Syntonic comma (21.5 cents) Holdrian comma (22.6 cents) Septimal comma
Diminished_octave
Musical interval
Septimal quarter tone Undecimal quarter tone Commas Pythagorean comma (23.5 cents) Syntonic comma (21.5 cents) Holdrian comma (22.6 cents) Septimal comma
Ninth_(interval)
Musical interval of ten diatonic steps
Septimal quarter tone Undecimal quarter tone Commas Pythagorean comma (23.5 cents) Syntonic comma (21.5 cents) Holdrian comma (22.6 cents) Septimal comma
Eleventh_(interval)
Musical interval
multiples, the diminished second is a distinct interval. It can be viewed as a comma, the minute interval between two enharmonically equivalent notes tuned in
Diminished_second
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
Septimal quarter tone Undecimal quarter tone Commas Pythagorean comma (23.5 cents) Syntonic comma (21.5 cents) Holdrian comma (22.6 cents) Septimal comma
Thirteenth_(interval)
Musical interval
Septimal quarter tone Undecimal quarter tone Commas Pythagorean comma (23.5 cents) Syntonic comma (21.5 cents) Holdrian comma (22.6 cents) Septimal comma
Augmented_seventh
Musical interval
Septimal quarter tone Undecimal quarter tone Commas Pythagorean comma (23.5 cents) Syntonic comma (21.5 cents) Holdrian comma (22.6 cents) Septimal comma
Fifteenth_(interval)
Musical interval which is not a perfect harmonic
Septimal quarter tone Undecimal quarter tone Commas Pythagorean comma (23.5 cents) Syntonic comma (21.5 cents) Holdrian comma (22.6 cents) Septimal comma
Pseudo-octave
Septimal quarter tone Undecimal quarter tone Commas Pythagorean comma (23.5 cents) Syntonic comma (21.5 cents) Holdrian comma (22.6 cents) Septimal comma
Third_(chord)
Musical interval
Septimal quarter tone Undecimal quarter tone Commas Pythagorean comma (23.5 cents) Syntonic comma (21.5 cents) Holdrian comma (22.6 cents) Septimal comma
Augmented_fifth
Septimal quarter tone Undecimal quarter tone Commas Pythagorean comma (23.5 cents) Syntonic comma (21.5 cents) Holdrian comma (22.6 cents) Septimal comma
Incomposite_interval
Unit of measurement for musical intervals
58-tone 72-tone 96-tone Linear Meantone (half-comma, third-comma, quarter-comma, fifth-comma, sixth-comma, septimal) Schismatic Miracle Magic Regular diatonic
Millioctave
Division of an octave
58-EDO than in 72-EDO. The two systems temper out different commas; 72-EDO tempers out the comma 169:168, thus equating the 14:13 and 13:12 intervals. On
58_equal_temperament
Musical interval
(Greek: κλείσμα), or semicomma majeur, is a minute and barely perceptible comma type interval important to musical temperaments. It is the difference between
Kleisma
third of a comma, that prove more appropriate for dividing the syntonic comma 81/80 into three harmonic intervals: for example the septimal kleisma 225/224
Semantic_system
Musical tuning based on pure intervals
seven octaves higher than the initial note. This gap is the Pythagorean comma. It is impossible to return to the unison. Another major flaw of the Pythagorean
Just_intonation
Major triad plus the harmonic seventh interval
cents). This interval is somewhat narrower (about 48.77 cents flatter, a septimal quarter tone) and is "sweeter in quality" than an "ordinary" minor seventh
Harmonic_seventh_chord
Musical interval
thus producing 36 pitches per octave. Septimal sixth tone 36 equal temperament 72 equal temperament Septimal diesis Gann, Kyle (September 16, 2019).
Sixth_tone
Musical tuning system with 19 pitches per octave
needed] In 1577, music theorist Francisco de Salinas discussed 1 / 3 comma meantone, in which the tempered perfect fifth is 694.786 cents. Salinas
19_equal_temperament
superparticular ratio). It is usually defined as the difference between the septimal minor third (7:6) and two Bohlen–Pierce small semitones (27:25 Play one)
Ragisma
prime factors 2-3-7, such as the 9 / 7 or septimal major third (435.084 cents) and 7 / 6 or septimal minor third (266.871 cents). At the same time
Regular_diatonic_tuning
Wave with frequency an integer multiple of the fundamental frequency
perfect fifth 2 · P 8 + P 5 3600Hz 702.0 ¢ Play 7th harmonic seventh, septimal minor seventh (‘the lost chord’) 2 · P 8 + m 7↓ 4200Hz 968.8 ¢ Play 8th
Harmonic
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
Concept in musical tuning theory
of 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
Fokker_periodicity_block
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)
Set of notes used in Chinese music
58-tone 72-tone 96-tone Linear Meantone (half-comma, third-comma, quarter-comma, fifth-comma, sixth-comma, septimal) Schismatic Miracle Magic Regular diatonic
Shi'er_lü
Musical tuning system
1/10-schisma temperament. The last named, 171, produces very accurate septimal intervals, but they are hard to reach, as to get to a 7/4 requires 39 fifths
Schismatic_temperament
58-tone 72-tone 96-tone Linear Meantone (half-comma, third-comma, quarter-comma, fifth-comma, sixth-comma, septimal) Schismatic Miracle Magic Regular diatonic
A12_scale
ancient Greek intervals (the greater and lesser diesis and the syntonic comma), division into 34 steps did not arise 'naturally' out of older music theory
34_equal_temperament
Type of musical chord
talking of the augmented second in quarter-comma meantone, a tuning he favored, which is close to the just septimal minor third of 7:6. The most common form
Diminished_seventh_chord
American composer (1926–2019)
scale) above F C G respectively. Johnston introduces new symbols for the septimal ( & ), undecimal (↑ & ↓), tridecimal ( & ), and further prime extensions
Ben_Johnston_(composer)
Musical scale
that dividing the octave into 12 equal steps reduces both 81:80 (syntonic comma) and 128:125 (5-limit limma) to a unison. A 7-limit linear temperament tempers
Bohlen–Pierce_scale
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