# Neutral interval > Mediated Wiki article. Canonical URL: https://mediated.wiki/source/Neutral_interval > Markdown URL: https://mediated.wiki/source/Neutral_interval.md > Source: https://en.wikipedia.org/wiki/Neutral_interval > Source revision: 1321534451 > License: Creative Commons Attribution-ShareAlike 4.0 International (https://creativecommons.org/licenses/by-sa/4.0/) thumb|Neutral third In [music theory](/source/music_theory), a '''neutral interval''' in [24 TET](/source/Quarter_tone) (including extensions), (but also known as a '''submajor interval''', or as a '''superminor interval''', in [Just Intonation](/source/Just_Intonation)), is an [interval](/source/interval_(music)) that is neither [major nor minor](/source/major_and_minor), but is, instead, in-between them. In [12 TET](/source/Equal_temperament), these intervals are a [quarter tone](/source/quarter_tone) sharper than minor intervals and a quarter tone flatter than major intervals. For example, the [minor third](/source/minor_third) is tuned at 300 [¢](/source/cent_(music)), while the [major third](/source/major_third) is a semitone (100 [¢](/source/cent_(music))) sharper (400 [¢](/source/cent_(music))), and so the [neutral third](/source/neutral_third) lies between them at 350 [¢](/source/cent_(music)). A neutral interval [inverts](/source/Inversion_(interval)) to another neutral interval. In just intonation, as well as in tunings such as [31-ET](/source/31_equal_temperament), [41-ET](/source/41_equal_temperament), or [72-ET](/source/72_equal_temperament), which more closely approximate it with more of them, such intervals can be closer together. {|class="wikitable" |intervals |minor !neutral |major |- |seconds |D{{music|b}} |[D](/source/Neutral_interval)alt=half flat|class=mw-file-element|12x12px |D{{music|natural}} |- |thirds |E{{music|b}} |[E](/source/Neutral_third){{music|d}} |E{{music|natural}} |- |sixths |A{{music|b}} |[A](/source/Neutral_sixth){{music|d}} |A{{music|natural}} |- |sevenths |B{{music|b}} |[B](/source/Neutral_interval){{music|d}} |B{{music|natural}} |} ==Second {{anchor|Neutral second}}{{anchor|Lesser undecimal neutral second}}{{anchor|Greater undecimal neutral second}}== {{Infobox Interval| main_interval_name = Neutral second| inverse = [neutral seventh](/source/neutral_seventh)| complement = [neutral seventh](/source/neutral_seventh)| other_names = | abbreviation = n2 | semitones = ~{{frac|1|1|2}} | interval_class = ~{{frac|1|1|2}} | just_interval = 11:10 or 12:11Haluska, Jan (2003). ''The Mathematical Theory of Tone Systems'', p.xxiii. {{ISBN|0-8247-4714-3}}. 3/4-tone, undecimal neutral second and 21/4-tone, undecimal neutral seventh.| cents_equal_temperament = 100 or 200| cents_24T_equal_temperament = 150| cents_just_intonation = 165 or 151 }} thumb|right|Neutral second on C {{audio|Neutral second on C.mid|Play}}. A '''neutral second''' or '''medium second''' is an interval wider than a [minor second](/source/minor_second) and narrower than a [major second](/source/major_second). Three distinct intervals may be termed neutral seconds: * The intermediate neutral second, called the '''lesser undecimal neutral second''' {{Audio|Lesser undecimal neutral second on C.mid|play}}, has a ratio between the higher-[frequency](/source/frequency) tone to the lower-frequency tone of 12:11 and is about 150.64 cents wide, while the larger one, * the '''greater undecimal neutral second''' {{Audio|Greater undecimal neutral second on C.mid|play}}, has a ratio of 11:10 between the two tones and is about 165.00 cents wide. The lesser undecimal neutral second may be derived from the [harmonic series](/source/Harmonic_series_(music)) as the interval between the [eleventh](/source/eleventh_harmonic) and twelfth harmonics. The greater undecimal neutral second may be derived from the [harmonic series](/source/Harmonic_series_(music)) as the interval between the tenth and eleventh harmonics. * An ''[equal-tempered](/source/equal_temperament) neutral second'' {{Audio|Neutral second on C.mid|play}} is characterized by a difference in 150 [cents](/source/Cent_(music)) between the two tones, a hair smaller than a ratio of frequencies between the two tones of 12:11, and exactly half of an equal-tempered minor third. The equal-tempered neutral is found in some traditional [Arabic music](/source/Arabic_music) (see also [Arab tone system](/source/Arab_tone_system)). Because the equal tempered neutral second is essentially a semitone (minor second) plus a quarter-tone, they may be considered [three-quarter tone](/source/three-quarter_tone)s in the [quarter tone scale](/source/quarter_tone_scale). ===In equal temperament=== Approximations to the 12:11 and 11:10 neutral seconds can be found in a number of equally tempered tuning systems. 11:10 is very closely matched by [22-ET](/source/22_equal_temperament), whereas 12:11 is matched by [24-ET](/source/quarter_tone), [31-ET](/source/31_equal_temperament) and [41-ET](/source/41_equal_temperament). [72-ET](/source/72_equal_temperament) matches both intervals closely and is also the smallest widely used equal temperament that uniquely matches both intervals. Tuning systems that temper out the [comma](/source/comma_(music)) of 121:120 do not distinguish between the two intervals. [17-ET](/source/17_equal_temperament) has a neutral second between 12:11 and 13:12, and a neutral third between 16:13 and 11:9. ==Seventh== {{anchor|Neutral seventh}} {{Infobox Interval| main_interval_name = Neutral seventh| inverse = [neutral second](/source/neutral_second)| complement = [neutral second](/source/neutral_second)| other_names = - | abbreviation = n7 | semitones = ~{{frac|10|1|2}} | interval_class = ~{{frac|1|1|2}} | just_interval = 11:6, 64:35,Haluska (2003), p.?. Septimal neutral seventh. or 24:13| cents_equal_temperament = 1000 or 1100| cents_24T_equal_temperament = 1050| cents_just_intonation = 1049, 1045, or 1061 }} thumb|right|Neutral seventh on C {{audio|Neutral seventh on C.mid|Play}}. A '''neutral seventh''' is a musical interval wider than a [minor seventh](/source/minor_seventh) {{Audio|Minor seventh on C.mid|play}} but narrower than a [major seventh](/source/major_seventh) {{Audio|Major seventh on C.mid|play}}. Four distinct intervals may be termed neutral sevenths: * A ''septimal neutral seventh'' {{Audio|Septimal neutral seventh on C.mid|play}} has a ratio of 64:35 or about 1045 cents. * The just ''undecimal neutral seventh'' has a ratio of 11:6 between the [frequencies](/source/frequencies) of the two tones,Andrew Horner, Lydia Ayres (2002). ''Cooking with Csound: Woodwind and Brass Recipes'', p.131. {{ISBN|0-89579-507-8}}. or about 1049 cents {{Audio|Undecimal neutral seventh on C.mid|play}}. Alternately, 13:7 or about 1071.7 cents {{Audio|Tridecimal neutral seventh on C.mid|play}}. * A ''tridecimal neutral seventh'' {{Audio|Tridecimal neutral seventh on C.mid|play}} has a ratio of 24:13 between the [frequencies](/source/frequencies) of the two tones, or about 1061 cents. This is the largest neutral seventh, and occurs infrequently in music, as little music utilizes the 13th [harmonic](/source/harmonic). * An ''[equal-tempered](/source/equal_temperament) neutral seventh'' {{Audio|Neutral seventh on C.mid|play}} is characterized by a difference in 1050 [cents](/source/Cent_(music)) between the two tones, a hair larger than the 11:6 ratio, and exactly half of an equal-tempered major thirteenth (octave plus major sixth). These intervals are all within about 12 cents of each other and are difficult for most people to distinguish. A neutral seventh can be formed by stacking a [neutral third](/source/neutral_third) together with a [perfect fifth](/source/perfect_fifth). Based on its positioning in the harmonic series, the undecimal neutral seventh implies a [root](/source/root_(chord)) one perfect fifth below the lower of the two notes. ==See also== *[Major fourth and minor fifth](/source/Major_fourth_and_minor_fifth) *[Subminor and supermajor](/source/Subminor_and_supermajor) * [List of pitch intervals](/source/List_of_pitch_intervals) * [Microtonal music](/source/Microtonal_music) ==References== {{reflist}} {{Intervals}} Category:Neutral intervals Category:Quarter tones --- Adapted from the Wikipedia article [Neutral interval](https://en.wikipedia.org/wiki/Neutral_interval) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Neutral_interval?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.