49/25: Difference between revisions

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wart notation
 
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{{Infobox Interval
{{Infobox interval
| Name = BP eighth
| Name = jubilismic suboctave, BP eighth
| Color name = zzgg9, bizogu 9th
| Color name = zzgg9, bizogu 9th
| Comma = no
| Comma = no
}} The BP eighth, 49/25, is an interval approximated by many notable tunings, including but not limited to [[Bohlen-Pierce]], [[27edo]], [[34edo]], [[53edo]] and [[72edo]]. As a stack of two diminished fifths [[7/5]], it can be thought of as a diminished 9th.
}}
'''49/25''', the '''jubilismic suboctave''', is a [[jubilisma]] short of the [[2/1|octave]]. As a stack of two [[7/5]] diminished fifths, it can be thought of as a diminished ninth. It is also called the '''BP eighth''' in the [[Bohlen–Pierce]] scale.
 
It is approximated by many notable tunings besides Bohlen–Pierce, including but not limited to [[27edo]], [[34edo]], [[53edo]] and [[72edo]], though for 34edo neither the [[patent val]] nor the 34d val (written with [[wart notation]]) actually maps it to the closest step, but the [[68edo]] mapping must be used instead.
 
== Approximation ==
== Approximation ==
{{Interval_Edo_Approximation | 49/25}}
{{Interval edo approximation|49/25}}
 
== See also ==
* [[50/49]] – its octave complement

Latest revision as of 00:57, 27 April 2026

Interval information
Ratio 49/25
Factorization 5-2 × 72
Monzo [0 0 -2 2
Size in cents 1165.024¢
Names jubilismic suboctave,
BP eighth
Color name zzgg9, bizogu 9th
FJS name [math]\displaystyle{ \text{d9}^{7,7}_{5,5} }[/math]
Special properties reduced
Tenney norm (log2 nd) 10.2586
Weil norm (log2 max(n, d)) 11.2294
Wilson norm (sopfr(nd)) 24
Open this interval in xen-calc

49/25, the jubilismic suboctave, is a jubilisma short of the octave. As a stack of two 7/5 diminished fifths, it can be thought of as a diminished ninth. It is also called the BP eighth in the Bohlen–Pierce scale.

It is approximated by many notable tunings besides Bohlen–Pierce, including but not limited to 27edo, 34edo, 53edo and 72edo, though for 34edo neither the patent val nor the 34d val (written with wart notation) actually maps it to the closest step, but the 68edo mapping must be used instead.

Approximation

Edo approximations for 49/25 (1165.02 ¢)
≤ 80edo, relative error ≤ 10%
Edo Step size Cents (¢) Absolute error (¢) Relative error (%)
2 2\2 1200.00 +34.98 +5.83
3 3\3 1200.00 +34.98 +8.74
31 30\31 1161.29 -3.73 -9.65
32 31\32 1162.50 -2.52 -6.73
33 32\33 1163.64 -1.39 -3.82
34 33\34 1164.71 -0.32 -0.90
35 34\35 1165.71 +0.69 +2.01
36 35\36 1166.67 +1.64 +4.93
37 36\37 1167.57 +2.54 +7.84
66 64\66 1163.64 -1.39 -7.63
67 65\67 1164.18 -0.85 -4.72
68 66\68 1164.71 -0.32 -1.80
69 67\69 1165.22 +0.19 +1.11
70 68\70 1165.71 +0.69 +4.02
71 69\71 1166.20 +1.17 +6.94
72 70\72 1166.67 +1.64 +9.85

See also

  • 50/49 – its octave complement