25/21: Difference between revisions

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{{Infobox Interval
{{Infobox Interval
| Icon =
| Ratio = 25/21
| Monzo = 0 -1 2 -1
| Cents = 301.84652
| Name = quasi-tempered minor third
| Name = quasi-tempered minor third
| Color name = ryy2, ruyoyo 2nd
| Color name = ryy2, ruyoyo 2nd
| FJS name = A2<sup>25</sup><sub>7</sub>
| Sound = jid_25_21_pluck_adu_dr220.mp3
| Sound = jid_25_21_pluck_adu_dr220.mp3
}}
}}
'''25/21''', the '''quasi-tempered minor third''', is the interval between [[6/5]] and [[10/7]], and also [[7/5]] and [[5/3]]. It is [[225/224]] sharp of [[32/27]], [[126/125]] flat of [[6/5]], and [[tempering out]] 126/125 makes the 1–6/5–10/7 triad into a [[diminished triad]] where two minor thirds make up a [[tritone]]. It is extremely close to 3 steps of [[12edo]] (300 cents).


'''25/21''', the '''quasi-tempered minor third''', is the interval between [[6/5]] and [[10/7]], and also [[7/5]] and [[5/3]]. It is [[126/125]] flat of [[6/5]], and tempering 126/125 out makes the 1-6/5-10/7 triad into a diminished triad where two minor thirds make up a [[tritone]]. It is extremely close to 3 steps of [[12edo]] (300 cents).
25/21 is also an important interval in the [[Bohlen–Pierce scale]], where it represents a "BP whole tone", i.e. the large step in the [[4L 5s (3/1-equivalent)|Lambda scale]].
 
== Approximation ==
{{Interval edo approximation|25/21}}


== See also ==
== See also ==
 
* [[42/25]] its [[octave complement]]
* [[42/25]] - its [[octave complement]]
* [[63/50]] its [[fifth complement]]
* [[63/50]] - its [[fifth complement]]
* [[28/25]] – its [[fourth complement]]
* [[Gallery of just intervals]]
* [[Gallery of just intervals]]
* [[File:Ji-25-21-csound-foscil-220hz.mp3]] [[:File:Ji-25-21-csound-foscil-220hz.mp3|(info)]]
* [[:File:Ji-25-21-csound-foscil-220hz.mp3]] - another sound example


[[Category:7-limit]]
[[Category:Third]]
[[Category:Interval]]
[[Category:Minor third]]
[[Category:Ratio]]
[[Category:Marvel]]
[[Category:Starling]]

Latest revision as of 13:11, 12 December 2025

Interval information
Ratio 25/21
Factorization 3-1 × 52 × 7-1
Monzo [0 -1 2 -1
Size in cents 301.8465¢
Name quasi-tempered minor third
Color name ryy2, ruyoyo 2nd
FJS name [math]\displaystyle{ \text{A2}^{5,5}_{7} }[/math]
Special properties reduced
Tenney norm (log2 nd) 9.03617
Weil norm (log2 max(n, d)) 9.28771
Wilson norm (sopfr(nd)) 20

[sound info]
Open this interval in xen-calc

25/21, the quasi-tempered minor third, is the interval between 6/5 and 10/7, and also 7/5 and 5/3. It is 225/224 sharp of 32/27, 126/125 flat of 6/5, and tempering out 126/125 makes the 1–6/5–10/7 triad into a diminished triad where two minor thirds make up a tritone. It is extremely close to 3 steps of 12edo (300 cents).

25/21 is also an important interval in the Bohlen–Pierce scale, where it represents a "BP whole tone", i.e. the large step in the Lambda scale.

Approximation

Edo approximations for 25/21 (301.85 ¢)
≤ 80edo, relative error ≤ 10%
Edo Step size Cents (¢) Absolute error (¢) Relative error (%)
4 1\4 300.00 -1.85 -0.62
8 2\8 300.00 -1.85 -1.23
12 3\12 300.00 -1.85 -1.85
16 4\16 300.00 -1.85 -2.46
20 5\20 300.00 -1.85 -3.08
24 6\24 300.00 -1.85 -3.69
28 7\28 300.00 -1.85 -4.31
32 8\32 300.00 -1.85 -4.92
36 9\36 300.00 -1.85 -5.54
40 10\40 300.00 -1.85 -6.16
44 11\44 300.00 -1.85 -6.77
48 12\48 300.00 -1.85 -7.39
52 13\52 300.00 -1.85 -8.00
56 14\56 300.00 -1.85 -8.62
60 15\60 300.00 -1.85 -9.23
64 16\64 300.00 -1.85 -9.85

See also