Major fourth and minor fifth

{{Infobox Interval | main_interval_name = Major fourth | inverse = Minor fifth | complement = Minor fifth | other_names = Eleventh harmonic<br />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<br />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|thumb|The eleventh harmonic {{audio|Eleventh harmonic on C.mid|Play}} – shown using the Ben Johnston notation – 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,<ref name="Skinner">Skinner, Miles Leigh (2007). ''Toward a Quarter-tone Syntax: Analyses of Selected Works by Blackwood, Haba, Ives, and Wyschnegradsky'', p.25. ProQuest. {{ISBN|9780542998478}}.</ref> 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<ref name="Skinner"/> (11:8 or 551.32 cents).<ref>{{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}}</ref> 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"<ref name="Bacon"/>), which is the ratio 25:18, or 568.72 cents (F{{music|sharp}}).<ref name="Edinburgh">(1832). ''[https://books.google.com/books?id=ZuNEAQAAMAAJ The Edinburgh Encyclopaedia]'', Volume 9, p.249. Joseph Parker. {{pre-ISBN}}</ref>

==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),<ref name="Bacon">Richard Mackenzie Bacon (1821). "Manuscript Work of Francesco Bianchl", ''The Quarterly Musical Magazine and Review'', Volume 3, p.56.</ref> 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.<ref name="Edinburgh"/> 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"<ref name="Bacon"/>) is the ratio 25:18, or 568.72 cents (F{{music|sharp}}).<ref name="Edinburgh"/> *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)<ref name="Bacon"/> *729:512 (F{{music|#}}++) or 611.73 cents ({{audio|Pythagorean augmented fourth on C.mid|Play}}), formed from the perfect fourth and the apotome.<ref name="Bacon"/>

==References== {{reflist}}

Category:Fifths (music) Category:Fourths (music) Category:Major intervals Category:Minor intervals Category:Quarter tones