Major fourth and minor fifth#Major fourth
{{Infobox Interval
| main_interval_name = Major fourth
| inverse = Minor fifth
| complement = Minor fifth
| other_names = Eleventh harmonic
Paramajor fourth
| abbreviation = M4
| semitones = ~5½
| interval_class = ~5½
| just_interval = 11:8
| cents_equal_temperament =
| cents_24T_equal_temperament = 550
| cents_just_intonation = 551.32
}}
{{Infobox Interval
| main_interval_name = Minor fifth
| inverse = Major fourth
| complement = Major fourth
| other_names = Eleventh subharmonic
Paraminor fifth
| abbreviation = m5
| semitones = ~6½
| interval_class = ~5½
| just_interval = 16:11
| cents_equal_temperament =
| cents_24T_equal_temperament = 650
| cents_just_intonation = 648.68
}}
File:Eleventh harmonic on C.png – can be approximated by the major fourth.]]
{{multiple image
| caption_align=center
| header_align=center
| width=150
| image1=Just augmented fourth on C.png
| alt1=
| image2=Just tritone on C.png
| alt2=
| footer=Just augmented fourth on C {{audio|Just augmented fourth on C.mid|Play}} and its inverse, the just tritone on C {{audio|Just tritone on C.mid|Play}}
}}
In music, the major fourth and minor fifth, also known as the paramajor fourth and paraminor fifth, are intervals from the quarter-tone scale, named by Ivan Wyschnegradsky to describe the tones surrounding the tritone (F{{music|sharp}}/G{{music|b}}) found in the more familiar twelve-tone scale,Skinner, Miles Leigh (2007). Toward a Quarter-tone Syntax: Analyses of Selected Works by Blackwood, Haba, Ives, and Wyschnegradsky, p.25. ProQuest. {{ISBN|9780542998478}}. as shown in the table below:
| class="wikitable" width="60%" style="text-align:center"
! width="5%" | ! width="11%" | perfect fourth ! width="11%" | (para)major fourth ! width="11%" | tritone ! width="11%" | (para)minor fifth ! width="11%" | perfect fifth |
| In C:
| F | ≊ F{{music|t}} | F{{music|sharp}}/G{{music|b}} | ≊ G{{music|d}} | G |
|---|
| In cents:
| 500 | 550 | 600 | 650 | 700 |
Major fourth
A major fourth ({{Audio|Eleven quarter tones on C.mid|Play}}) is the interval that lies midway between the perfect fourth (500 cents) and the augmented fourth (600 cents) and is thus 550 cents (F{{music|t}}). It inverts to a minor fifth. Wyschnegradsky considered it a good approximation of the eleventh harmonic (11:8 or 551.32 cents).{{Cite book|title=Music: A Mathematical Offering|last=Benson|first=Dave|date=2007-01-01|publisher=Cambridge University Press|isbn=9780521853873|page=370|language=en}} A narrower undecimal major fourth is found at 537 cents (the ratio 15:11). 31 equal temperament has an interval of 542 cents, which lies in between the 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 25:18, or 568.72 cents (F{{music|sharp}}).(1832). [https://books.google.com/books?id=ZuNEAQAAMAAJ The Edinburgh Encyclopaedia], Volume 9, p.249. Joseph Parker. {{pre-ISBN}}
Minor fifth
A minor fifth ({{Audio|Thirteen quarter tones on C.mid|Play}}) is the interval midway between the diminished fifth (600 cents) and the perfect fifth (700 cents) and thus 650 cents (G{{music|d}}). It inverts to a major fourth. It approximates the eleventh subharmonic (G{{music|down}}), 16:11 (648.68 cents).
The term may also be applied to the ratio 64:45 (G{{music|b}}-) or 609.77 cents ({{audio|Just tritone on C.mid|Play}}), formed from the perfect fourth (4/3 = 498.04) and the major semitone (16/15 = 111.73),Richard Mackenzie Bacon (1821). "Manuscript Work of Francesco Bianchl", The Quarterly Musical Magazine and Review, Volume 3, p.56. which is sharp of the G{{music|flat}} tritone. The "comma-redundant minor fifth" has the ratio 36:25 (G{{music|b}}), or 631.28 cents, and is formed from two minor thirds. The tridecimal minor fifth (13:9), or tridecimal tritone, is slightly larger at 636.6 cents.
Other
The term major fourth may also be applied to the follow, as minor fifth may be applied to their inversions (in the sense of augmented and diminished):
- The "comma-deficient major fourth" (or "chromatic major fourth") is the ratio 25:18, or 568.72 cents (F{{music|sharp}}).
- 45:32 (F{{music|#}}+) or 590.22 cents ({{Audio|Just augmented fourth on C.mid|Play}}), formed from the major third (5/4 = 386.31) and the major tone (9/8 = 203.91) or two major tones (9:8) and one minor tone (10:9)
- 729:512 (F{{music|#}}++) or 611.73 cents ({{audio|Pythagorean augmented fourth on C.mid|Play}}), formed from the perfect fourth and the apotome.
See also
References
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{{Intervals}}
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