28/15: Difference between revisions

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{{Infobox Interval
{{Infobox Interval
| Ratio = 28/15
| Monzo = 2 -1 -1 1
| Cents = 1080.55719
| Name = septimal grave major seventh
| Name = septimal grave major seventh
| Color name = zg8, zogu octave
| Color name = zg8, zogu octave
| FJS name = d8<sup>7</sup><sub>5</sub>
| Sound = jid_28_15_pluck_adu_dr220.mp3
| Sound = jid_28_15_pluck_adu_dr220.mp3
}}
}}
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== Terminology ==
== Terminology ==
Despite being approximated by the major seventh in systems like [[septimal meantone]], and even being called the '''septimal grave major seventh''' by some musicians, 28/15 is a diminished octave in just intonation notation systems such as [[Sagittal notation]], [[Helmholtz-Ellis notation]] and the [[Functional Just System]], viewed as the Pythagorean diminished octave ([[4096/2187]]) altered by [[5120/5103]].  
Despite being approximated by the major seventh in systems like [[septimal meantone]], and even being called the '''septimal grave major seventh''' by some musicians, 28/15 is a diminished octave in just intonation notation systems such as [[Sagittal notation]], [[Helmholtz-Ellis notation]] and the [[Functional Just System]], viewed as the Pythagorean diminished octave ([[4096/2187]]) altered by [[5120/5103]].  
== Approximation ==
{{Interval edo approximation|28/15}}


== See also ==
== See also ==
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* [[Gallery of just intervals]]
* [[Gallery of just intervals]]


[[Category:7-limit]]
[[Category:Seventh]]
[[Category:Seventh]]
[[Category:Major seventh]]
[[Category:Major seventh]]
[[Category:Octave]]
[[Category:Octave]]
[[Category:Diminished octave]]
[[Category:Diminished octave]]
[[Category:Pages with internal sound examples]]
{{todo|improve synopsis}}
 
{{todo| expand | improve synopsis | add color name }}

Latest revision as of 13:03, 3 November 2025

Interval information
Ratio 28/15
Factorization 22 × 3-1 × 5-1 × 7
Monzo [2 -1 -1 1
Size in cents 1080.557¢
Name septimal grave major seventh
Color name zg8, zogu octave
FJS name [math]\displaystyle{ \text{d8}^{7}_{5} }[/math]
Special properties reduced
Tenney norm (log2 nd) 8.71425
Weil norm (log2 max(n, d)) 9.61471
Wilson norm (sopfr(nd)) 19

[sound info]
Open this interval in xen-calc

28/15 is a 7-limit just intonation interval of about 1080.6 cents. It is well approximated by 10edo (9\10).

Terminology

Despite being approximated by the major seventh in systems like septimal meantone, and even being called the septimal grave major seventh by some musicians, 28/15 is a diminished octave in just intonation notation systems such as Sagittal notation, Helmholtz-Ellis notation and the Functional Just System, viewed as the Pythagorean diminished octave (4096/2187) altered by 5120/5103.

Approximation

Edo approximations for 28/15 (1080.56 ¢)
≤ 80edo, relative error ≤ 10%
Edo Step size Cents (¢) Absolute error (¢) Relative error (%)
10 9\10 1080.00 -0.56 -0.46
11 10\11 1090.91 +10.35 +9.49
20 18\20 1080.00 -0.56 -0.93
21 19\21 1085.71 +5.16 +9.02
30 27\30 1080.00 -0.56 -1.39
31 28\31 1083.87 +3.31 +8.56
40 36\40 1080.00 -0.56 -1.86
41 37\41 1082.93 +2.37 +8.10
50 45\50 1080.00 -0.56 -2.32
51 46\51 1082.35 +1.80 +7.63
60 54\60 1080.00 -0.56 -2.79
61 55\61 1081.97 +1.41 +7.17
70 63\70 1080.00 -0.56 -3.25
71 64\71 1081.69 +1.13 +6.70
80 72\80 1080.00 -0.56 -3.71

See also