54/49: Difference between revisions
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{{Infobox Interval | |||
| Name = Zalzal's mujannab, superpythagorean chroma | |||
| Color name = rr1, ruru unison | |||
| Sound = jid_54_49_pluck_adu_dr220.mp3 | |||
}} | |||
'''54/49''', '''Zalzal's mujannab''', is an interval introduced by {{w|Mansour Zalzal}}. It is between [[11/10]] and [[10/9]] in size, being [[540/539]] sharp of 11/10 and [[245/243]] flat of 10/9. It is the interval between [[7/6]] and [[9/7]]. | |||
== Approximation == | |||
{{Interval edo approximation|54/49}} | |||
== Temperaments == | |||
[[Tempering out]] [[540/539]] equates 54/49 with 11/10 and leads to [[swetismic chords]]. Occurring often in JI scales, it is one of the ways 11-limit harmony gets introduced into [[7-limit]] scales. | |||
It is also called the '''superpythagorean chromatic semitone''' or '''superpythagorean chroma'''{{idio}} since, in [[superpyth]] temperament, the minor third is 7/6, the major third is 9/7, and the difference between the two is 54/49. | |||
Moving to [[exotemperament|exotempering]], the interval can be tempered out, leading to the [[2.3.7 subgroup|2.3.7-subgroup]] version of the [[mujannabic]] temperament equating 7/6 and 9/7. However, it is usually better to temper out [[25/24]] instead for a similar structural effect. | |||
== See also == | |||
* [[49/27]] – its [[octave complement]] | |||
* [[Gallery of just intervals]] | |||
[[Category:Second]] | |||
[[Category:Neutral second]] | |||
[[Category:Equable heptatonic]] | |||
Latest revision as of 09:14, 30 May 2026
| Interval information |
superpythagorean chroma
[sound info]
54/49, Zalzal's mujannab, is an interval introduced by Mansour Zalzal. It is between 11/10 and 10/9 in size, being 540/539 sharp of 11/10 and 245/243 flat of 10/9. It is the interval between 7/6 and 9/7.
Approximation
| Edo | Step size | Cents (¢) | Absolute error (¢) | Relative error (%) |
|---|---|---|---|---|
| 7 | 1\7 | 171.43 | +3.22 | +1.88 |
| 14 | 2\14 | 171.43 | +3.22 | +3.75 |
| 21 | 3\21 | 171.43 | +3.22 | +5.63 |
| 22 | 3\22 | 163.64 | -4.58 | -8.39 |
| 28 | 4\28 | 171.43 | +3.22 | +7.50 |
| 29 | 4\29 | 165.52 | -2.70 | -6.52 |
| 35 | 5\35 | 171.43 | +3.22 | +9.38 |
| 36 | 5\36 | 166.67 | -1.55 | -4.64 |
| 43 | 6\43 | 167.44 | -0.77 | -2.76 |
| 50 | 7\50 | 168.00 | -0.21 | -0.89 |
| 57 | 8\57 | 168.42 | +0.21 | +0.99 |
| 64 | 9\64 | 168.75 | +0.54 | +2.86 |
| 71 | 10\71 | 169.01 | +0.80 | +4.74 |
| 72 | 10\72 | 166.67 | -1.55 | -9.28 |
| 78 | 11\78 | 169.23 | +1.02 | +6.61 |
| 79 | 11\79 | 167.09 | -1.12 | -7.40 |
Temperaments
Tempering out 540/539 equates 54/49 with 11/10 and leads to swetismic chords. Occurring often in JI scales, it is one of the ways 11-limit harmony gets introduced into 7-limit scales.
It is also called the superpythagorean chromatic semitone or superpythagorean chroma[idiosyncratic term] since, in superpyth temperament, the minor third is 7/6, the major third is 9/7, and the difference between the two is 54/49.
Moving to exotempering, the interval can be tempered out, leading to the 2.3.7-subgroup version of the mujannabic temperament equating 7/6 and 9/7. However, it is usually better to temper out 25/24 instead for a similar structural effect.