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<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">Neutral interval</span></span>
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<p>In <a href="Music_theory" title="Music theory">music theory</a>, a <b>neutral interval</b>, (also known as a <b>submajor interval</b>, or a <b>superminor interval</b>), is an <a href="Interval_(music)" title="Interval (music)">interval</a> that is neither <a href="Major_and_minor" title="Major and minor">major nor minor</a>, but is, instead, in-between major and minor. In <a href="Quarter_tone" title="Quarter tone">24-Tone Equal Temperament</a>, it is called the <i><b>neutral interval</b></i>. In <a href="Just_Intonation" class="mw-redirect" title="Just Intonation">Just Intonation</a>, it is called the <i><b>submajor interval</b></i> or the <i><b>superminor interval</b></i>. For example, in <a href="Equal_temperament#Twelve-tone_equal_temperament" title="Equal temperament">equal temperament</a>, a <a href="Major_third" title="Major third">major third</a> is 400 <a href="Cent_(music)" title="Cent (music)">cents</a>, a <a href="Minor_third" title="Minor third">minor third</a> is 300 cents, and a neutral third is 350 cents. A neutral interval <a href="Inversion_(interval)" class="mw-redirect" title="Inversion (interval)">inverts</a> to a neutral interval. For example, the inverse of a neutral third is a neutral sixth.
</p><p>Roughly, neutral intervals are a <a href="Quarter_tone" title="Quarter tone">quarter tone</a> sharp from minor intervals and a quarter tone flat from major intervals. In just intonation, as well as in tunings such as <a href="31_equal_temperament" title="31 equal temperament">31-ET</a>, <a href="41_equal_temperament" title="41 equal temperament">41-ET</a>, or <a href="72_equal_temperament" title="72 equal temperament">72-ET</a>, which more closely approximate just intonation, the intervals are closer together.
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<ul><li><a href="#Neutral_second">Neutral second</a></li>
<li><a href="Neutral_third" title="Neutral third">Neutral third</a></li>
<li><a href="Neutral_sixth" title="Neutral sixth">Neutral sixth</a></li>
<li><a href="#Neutral_seventh">Neutral seventh</a></li></ul>
<table class="wikitable">
<tbody><tr>
<td>
</td>
<td>minor
</td>
<th>neutral
</th>
<td>major
</td></tr>
<tr>
<td>seconds
</td>
<td>D<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span>
</td>
<td>≊ D<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="mw-default-size skin-invert" typeof="mw:File"></span></span>
</td>
<td>D<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-natural">♮</span></span>
</td></tr>
<tr>
<td>thirds
</td>
<td>E<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span>
</td>
<td>≊ E<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="mw-default-size skin-invert" typeof="mw:File"></span></span>
</td>
<td>E<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-natural">♮</span></span>
</td></tr>
<tr>
<td>sixths
</td>
<td>A<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span>
</td>
<td>≊ A<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="mw-default-size skin-invert" typeof="mw:File"></span></span>
</td>
<td>A<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-natural">♮</span></span>
</td></tr>
<tr>
<td>sevenths
</td>
<td>B<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span>
</td>
<td>≊ B<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="mw-default-size skin-invert" typeof="mw:File"></span></span>
</td>
<td>B<span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-natural">♮</span></span>
</td></tr></tbody></table>
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<div class="mw-heading mw-heading2"><h2 id="Second">Second </h2></div>
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</style><table class="infobox"><caption class="infobox-title">Neutral second</caption><tbody><tr><th scope="row" class="infobox-label"><a href="Inversion_(interval)" class="mw-redirect" title="Inversion (interval)">Inverse</a></th><td class="infobox-data"><a href="Neutral_seventh" class="mw-redirect" title="Neutral seventh">neutral seventh</a></td></tr><tr><th colspan="2" class="infobox-header" style="background-color:palegoldenrod;">Name</th></tr><tr><th scope="row" class="infobox-label">Abbreviation</th><td class="infobox-data">n2</td></tr><tr><th colspan="2" class="infobox-header" style="background-color:palegoldenrod;">Size</th></tr><tr><th scope="row" class="infobox-label"><a href="Semitone" title="Semitone">Semitones</a></th><td class="infobox-data">~<style data-mw-deduplicate="TemplateStyles:r1154941027">
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</style><span class="frac">1<span class="sr-only">+</span><span class="num">1</span>⁄<span class="den">2</span></span></td></tr><tr><th scope="row" class="infobox-label"><a href="Interval_class" title="Interval class">Interval class</a></th><td class="infobox-data">~<span class="frac">1<span class="sr-only">+</span><span class="num">1</span>⁄<span class="den">2</span></span></td></tr><tr><th scope="row" class="infobox-label"><a href="Just_intonation" title="Just intonation">Just interval</a></th><td class="infobox-data">11:10 or 12:11<sup id="cite_ref-Haluska_1-0" class="reference"><a href="#cite_note-Haluska-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup></td></tr><tr><th colspan="2" class="infobox-header" style="background-color:palegoldenrod;"><a href="Cent_(music)" title="Cent (music)">Cents</a></th></tr><tr><th scope="row" class="infobox-label"><a href="Equal_temperament#Twelve-tone_equal_temperament" title="Equal temperament">12-Tone equal temperament</a></th><td class="infobox-data">100 or 200</td></tr><tr><th scope="row" class="infobox-label"><a href="Quarter_tone" title="Quarter tone">24-Tone equal temperament</a></th><td class="infobox-data">150</td></tr><tr><th scope="row" class="infobox-label"><a href="Just_intonation" title="Just intonation">Just intonation</a></th><td class="infobox-data">165 or 151</td></tr></tbody></table>
<p>A <b>neutral second</b> or <b>medium second</b> is an interval wider than a <a href="Minor_second" class="mw-redirect" title="Minor second">minor second</a> and narrower than a <a href="Major_second" title="Major second">major second</a>. Three distinct intervals may be termed neutral seconds:
</p>
<ul><li>The intermediate neutral second, called the <b>lesser undecimal neutral second</b> <span class="ext-phonos"><span data-nosnippet="" id="ooui-php-2" class="noexcerpt ext-phonos-PhonosButton oo-ui-widget oo-ui-widget-enabled oo-ui-buttonElement oo-ui-buttonElement-frameless oo-ui-iconElement oo-ui-labelElement oo-ui-buttonWidget" data-ooui="{"_":"mw.Phonos.PhonosButton","href":"\/\/upload.wikimedia.org\/wikipedia\/commons\/transcoded\/3\/30\/Lesser_undecimal_neutral_second_on_C.mid\/Lesser_undecimal_neutral_second_on_C.mid.mp3","rel":["nofollow"],"framed":false,"icon":"volumeUp","label":{"html":"play"},"data":{"ipa":"","text":"","lang":"en","wikibase":"","file":"Lesser undecimal neutral second on C.mid"},"classes":["noexcerpt","ext-phonos-PhonosButton"]}"><a role="button" tabindex="0" href="https://upload.wikimedia.org/wikipedia/commons/transcoded/3/30/Lesser_undecimal_neutral_second_on_C.mid/Lesser_undecimal_neutral_second_on_C.mid.mp3" rel="nofollow" aria-label="Play audio" title="Play audio" class="oo-ui-buttonElement-button"><span class="oo-ui-labelElement-label">play</span></a></span><sup class="ext-phonos-attribution noexcerpt navigation-not-searchable">ⓘ</sup></span>, has a ratio between the higher-<a href="Frequency" title="Frequency">frequency</a> tone to the lower-frequency tone of 12:11 and is about 150.64 cents wide, while the larger one,</li>
<li>the <b>greater undecimal neutral second</b> <span class="ext-phonos"><span data-nosnippet="" id="ooui-php-3" class="noexcerpt ext-phonos-PhonosButton oo-ui-widget oo-ui-widget-enabled oo-ui-buttonElement oo-ui-buttonElement-frameless oo-ui-iconElement oo-ui-labelElement oo-ui-buttonWidget" data-ooui="{"_":"mw.Phonos.PhonosButton","href":"\/\/upload.wikimedia.org\/wikipedia\/commons\/transcoded\/7\/79\/Greater_undecimal_neutral_second_on_C.mid\/Greater_undecimal_neutral_second_on_C.mid.mp3","rel":["nofollow"],"framed":false,"icon":"volumeUp","label":{"html":"play"},"data":{"ipa":"","text":"","lang":"en","wikibase":"","file":"Greater undecimal neutral second on C.mid"},"classes":["noexcerpt","ext-phonos-PhonosButton"]}"><a role="button" tabindex="0" href="https://upload.wikimedia.org/wikipedia/commons/transcoded/7/79/Greater_undecimal_neutral_second_on_C.mid/Greater_undecimal_neutral_second_on_C.mid.mp3" rel="nofollow" aria-label="Play audio" title="Play audio" class="oo-ui-buttonElement-button"><span class="oo-ui-labelElement-label">play</span></a></span><sup class="ext-phonos-attribution noexcerpt navigation-not-searchable">ⓘ</sup></span>, 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 <a href="Harmonic_series_(music)" title="Harmonic series (music)">harmonic series</a> as the interval between the <a href="Eleventh_harmonic" class="mw-redirect" title="Eleventh harmonic">eleventh</a> and twelfth harmonics. The greater undecimal neutral second may be derived from the <a href="Harmonic_series_(music)" title="Harmonic series (music)">harmonic series</a> as the interval between the tenth and eleventh harmonics.</li>
<li>An <i><a href="Equal_temperament" title="Equal temperament">equal-tempered</a> neutral second</i> <span class="ext-phonos"><span data-nosnippet="" id="ooui-php-4" class="noexcerpt ext-phonos-PhonosButton oo-ui-widget oo-ui-widget-enabled oo-ui-buttonElement oo-ui-buttonElement-frameless oo-ui-iconElement oo-ui-labelElement oo-ui-buttonWidget" data-ooui="{"_":"mw.Phonos.PhonosButton","href":"\/\/upload.wikimedia.org\/wikipedia\/commons\/transcoded\/2\/2d\/Neutral_second_on_C.mid\/Neutral_second_on_C.mid.mp3","rel":["nofollow"],"framed":false,"icon":"volumeUp","label":{"html":"play"},"data":{"ipa":"","text":"","lang":"en","wikibase":"","file":"Neutral second on C.mid"},"classes":["noexcerpt","ext-phonos-PhonosButton"]}"><a role="button" tabindex="0" href="https://upload.wikimedia.org/wikipedia/commons/transcoded/2/2d/Neutral_second_on_C.mid/Neutral_second_on_C.mid.mp3" rel="nofollow" aria-label="Play audio" title="Play audio" class="oo-ui-buttonElement-button"><span class="oo-ui-labelElement-label">play</span></a></span><sup class="ext-phonos-attribution noexcerpt navigation-not-searchable">ⓘ</sup></span> is characterized by a difference in 150 <a href="Cent_(music)" title="Cent (music)">cents</a> 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.</li></ul>
<p>The equal-tempered neutral is found in some traditional <a href="Arabic_music" title="Arabic music">Arabic music</a> (see also <a href="Arab_tone_system" title="Arab tone system">Arab tone system</a>). Because the equal tempered neutral second is essentially a semitone (minor second) plus a quarter-tone, they may be considered <a href="Three-quarter_tone" class="mw-redirect" title="Three-quarter tone">three-quarter tones</a> in the <a href="Quarter_tone_scale" class="mw-redirect" title="Quarter tone scale">quarter tone scale</a>.
</p>
<div class="mw-heading mw-heading3"><h3 id="In_equal_temperament">In equal temperament</h3></div>
<p>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 <a href="22_equal_temperament" title="22 equal temperament">22-ET</a>, whereas 12:11 is matched by <a href="Quarter_tone" title="Quarter tone">24-ET</a>, <a href="31_equal_temperament" title="31 equal temperament">31-ET</a> and <a href="41_equal_temperament" title="41 equal temperament">41-ET</a>. <a href="72_equal_temperament" title="72 equal temperament">72-ET</a> matches both intervals closely and is also the smallest widely used equal temperament that uniquely matches both intervals. Tuning systems that temper out the <a href="Comma_(music)" title="Comma (music)">comma</a> of 121:120 do not distinguish between the two intervals. <a href="17_equal_temperament" title="17 equal temperament">17-ET</a> has a neutral second between 12:11 and 13:12, and a neutral third between 16:13 and 11:9.
</p>
<div class="mw-heading mw-heading2"><h2 id="Seventh">Seventh</h2></div>
<p>
</p>
<table class="infobox"><caption class="infobox-title">Neutral seventh</caption><tbody><tr><th scope="row" class="infobox-label"><a href="Inversion_(interval)" class="mw-redirect" title="Inversion (interval)">Inverse</a></th><td class="infobox-data"><a href="Neutral_second" class="mw-redirect" title="Neutral second">neutral second</a></td></tr><tr><th colspan="2" class="infobox-header" style="background-color:palegoldenrod;">Name</th></tr><tr><th scope="row" class="infobox-label">Other names</th><td class="infobox-data">-</td></tr><tr><th scope="row" class="infobox-label">Abbreviation</th><td class="infobox-data">n7</td></tr><tr><th colspan="2" class="infobox-header" style="background-color:palegoldenrod;">Size</th></tr><tr><th scope="row" class="infobox-label"><a href="Semitone" title="Semitone">Semitones</a></th><td class="infobox-data">~<span class="frac">10<span class="sr-only">+</span><span class="num">1</span>⁄<span class="den">2</span></span></td></tr><tr><th scope="row" class="infobox-label"><a href="Interval_class" title="Interval class">Interval class</a></th><td class="infobox-data">~<span class="frac">1<span class="sr-only">+</span><span class="num">1</span>⁄<span class="den">2</span></span></td></tr><tr><th scope="row" class="infobox-label"><a href="Just_intonation" title="Just intonation">Just interval</a></th><td class="infobox-data">11:6,<sup id="cite_ref-Haluska_1-1" class="reference"><a href="#cite_note-Haluska-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> 64:35,<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> or 24:13</td></tr><tr><th colspan="2" class="infobox-header" style="background-color:palegoldenrod;"><a href="Cent_(music)" title="Cent (music)">Cents</a></th></tr><tr><th scope="row" class="infobox-label"><a href="Equal_temperament#Twelve-tone_equal_temperament" title="Equal temperament">12-Tone equal temperament</a></th><td class="infobox-data">1000 or 1100</td></tr><tr><th scope="row" class="infobox-label"><a href="Quarter_tone" title="Quarter tone">24-Tone equal temperament</a></th><td class="infobox-data">1050</td></tr><tr><th scope="row" class="infobox-label"><a href="Just_intonation" title="Just intonation">Just intonation</a></th><td class="infobox-data">1049, 1045, or 1061</td></tr></tbody></table>
<p>A <b>neutral seventh</b> is a musical interval wider than a <a href="Minor_seventh" title="Minor seventh">minor seventh</a> <span class="ext-phonos"><span data-nosnippet="" id="ooui-php-6" class="noexcerpt ext-phonos-PhonosButton oo-ui-widget oo-ui-widget-enabled oo-ui-buttonElement oo-ui-buttonElement-frameless oo-ui-iconElement oo-ui-labelElement oo-ui-buttonWidget" data-ooui="{"_":"mw.Phonos.PhonosButton","href":"\/\/upload.wikimedia.org\/wikipedia\/commons\/transcoded\/a\/a5\/Minor_seventh_on_C.mid\/Minor_seventh_on_C.mid.mp3","rel":["nofollow"],"framed":false,"icon":"volumeUp","label":{"html":"play"},"data":{"ipa":"","text":"","lang":"en","wikibase":"","file":"Minor seventh on C.mid"},"classes":["noexcerpt","ext-phonos-PhonosButton"]}"><a role="button" tabindex="0" href="https://upload.wikimedia.org/wikipedia/commons/transcoded/a/a5/Minor_seventh_on_C.mid/Minor_seventh_on_C.mid.mp3" rel="nofollow" aria-label="Play audio" title="Play audio" class="oo-ui-buttonElement-button"><span class="oo-ui-labelElement-label">play</span></a></span><sup class="ext-phonos-attribution noexcerpt navigation-not-searchable">ⓘ</sup></span> but narrower than a <a href="Major_seventh" title="Major seventh">major seventh</a> <span class="ext-phonos"><span data-nosnippet="" id="ooui-php-7" class="noexcerpt ext-phonos-PhonosButton oo-ui-widget oo-ui-widget-enabled oo-ui-buttonElement oo-ui-buttonElement-frameless oo-ui-iconElement oo-ui-labelElement oo-ui-buttonWidget" data-ooui="{"_":"mw.Phonos.PhonosButton","href":"\/\/upload.wikimedia.org\/wikipedia\/commons\/transcoded\/c\/cb\/Major_seventh_on_C.mid\/Major_seventh_on_C.mid.mp3","rel":["nofollow"],"framed":false,"icon":"volumeUp","label":{"html":"play"},"data":{"ipa":"","text":"","lang":"en","wikibase":"","file":"Major seventh on C.mid"},"classes":["noexcerpt","ext-phonos-PhonosButton"]}"><a role="button" tabindex="0" href="https://upload.wikimedia.org/wikipedia/commons/transcoded/c/cb/Major_seventh_on_C.mid/Major_seventh_on_C.mid.mp3" rel="nofollow" aria-label="Play audio" title="Play audio" class="oo-ui-buttonElement-button"><span class="oo-ui-labelElement-label">play</span></a></span><sup class="ext-phonos-attribution noexcerpt navigation-not-searchable">ⓘ</sup></span>. Four distinct intervals may be termed neutral sevenths:
</p>
<ul><li>A <i>septimal neutral seventh</i> <span class="ext-phonos"><span data-nosnippet="" id="ooui-php-8" class="noexcerpt ext-phonos-PhonosButton oo-ui-widget oo-ui-widget-enabled oo-ui-buttonElement oo-ui-buttonElement-frameless oo-ui-iconElement oo-ui-labelElement oo-ui-buttonWidget" data-ooui="{"_":"mw.Phonos.PhonosButton","href":"\/\/upload.wikimedia.org\/wikipedia\/commons\/transcoded\/7\/76\/Septimal_neutral_seventh_on_C.mid\/Septimal_neutral_seventh_on_C.mid.mp3","rel":["nofollow"],"framed":false,"icon":"volumeUp","label":{"html":"play"},"data":{"ipa":"","text":"","lang":"en","wikibase":"","file":"Septimal neutral seventh on C.mid"},"classes":["noexcerpt","ext-phonos-PhonosButton"]}"><a role="button" tabindex="0" href="https://upload.wikimedia.org/wikipedia/commons/transcoded/7/76/Septimal_neutral_seventh_on_C.mid/Septimal_neutral_seventh_on_C.mid.mp3" rel="nofollow" aria-label="Play audio" title="Play audio" class="oo-ui-buttonElement-button"><span class="oo-ui-labelElement-label">play</span></a></span><sup class="ext-phonos-attribution noexcerpt navigation-not-searchable">ⓘ</sup></span> has a ratio of 64:35 or about 1045 cents.</li>
<li>The just <i>undecimal neutral seventh</i> has a ratio of 11:6 between the <a href="Frequencies" class="mw-redirect" title="Frequencies">frequencies</a> of the two tones,<sup id="cite_ref-Cooking_3-0" class="reference"><a href="#cite_note-Cooking-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> or about 1049 cents <span class="ext-phonos"><span data-nosnippet="" id="ooui-php-9" class="noexcerpt ext-phonos-PhonosButton oo-ui-widget oo-ui-widget-enabled oo-ui-buttonElement oo-ui-buttonElement-frameless oo-ui-iconElement oo-ui-labelElement oo-ui-buttonWidget" data-ooui="{"_":"mw.Phonos.PhonosButton","href":"\/\/upload.wikimedia.org\/wikipedia\/commons\/transcoded\/4\/4e\/Undecimal_neutral_seventh_on_C.mid\/Undecimal_neutral_seventh_on_C.mid.mp3","rel":["nofollow"],"framed":false,"icon":"volumeUp","label":{"html":"play"},"data":{"ipa":"","text":"","lang":"en","wikibase":"","file":"Undecimal neutral seventh on C.mid"},"classes":["noexcerpt","ext-phonos-PhonosButton"]}"><a role="button" tabindex="0" href="https://upload.wikimedia.org/wikipedia/commons/transcoded/4/4e/Undecimal_neutral_seventh_on_C.mid/Undecimal_neutral_seventh_on_C.mid.mp3" rel="nofollow" aria-label="Play audio" title="Play audio" class="oo-ui-buttonElement-button"><span class="oo-ui-labelElement-label">play</span></a></span><sup class="ext-phonos-attribution noexcerpt navigation-not-searchable">ⓘ</sup></span>. Alternately, 13:7<sup id="cite_ref-Cooking_3-1" class="reference"><a href="#cite_note-Cooking-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> or about 1071.7 cents <span class="ext-phonos"><span data-nosnippet="" id="ooui-php-10" class="noexcerpt ext-phonos-PhonosButton oo-ui-widget oo-ui-widget-enabled oo-ui-buttonElement oo-ui-buttonElement-frameless oo-ui-iconElement oo-ui-labelElement oo-ui-buttonWidget" data-ooui="{"_":"mw.Phonos.PhonosButton","href":"\/\/upload.wikimedia.org\/wikipedia\/commons\/transcoded\/4\/44\/Tridecimal_neutral_seventh_on_C.mid\/Tridecimal_neutral_seventh_on_C.mid.mp3","rel":["nofollow"],"framed":false,"icon":"volumeUp","label":{"html":"play"},"data":{"ipa":"","text":"","lang":"en","wikibase":"","file":"Tridecimal neutral seventh on C.mid"},"classes":["noexcerpt","ext-phonos-PhonosButton"]}"><a role="button" tabindex="0" href="https://upload.wikimedia.org/wikipedia/commons/transcoded/4/44/Tridecimal_neutral_seventh_on_C.mid/Tridecimal_neutral_seventh_on_C.mid.mp3" rel="nofollow" aria-label="Play audio" title="Play audio" class="oo-ui-buttonElement-button"><span class="oo-ui-labelElement-label">play</span></a></span><sup class="ext-phonos-attribution noexcerpt navigation-not-searchable">ⓘ</sup></span>.</li>
<li>A <i>tridecimal neutral seventh</i> <span class="ext-phonos"><span data-nosnippet="" id="ooui-php-11" class="noexcerpt ext-phonos-PhonosButton oo-ui-widget oo-ui-widget-enabled oo-ui-buttonElement oo-ui-buttonElement-frameless oo-ui-iconElement oo-ui-labelElement oo-ui-buttonWidget" data-ooui="{"_":"mw.Phonos.PhonosButton","href":"\/\/upload.wikimedia.org\/wikipedia\/commons\/transcoded\/4\/44\/Tridecimal_neutral_seventh_on_C.mid\/Tridecimal_neutral_seventh_on_C.mid.mp3","rel":["nofollow"],"framed":false,"icon":"volumeUp","label":{"html":"play"},"data":{"ipa":"","text":"","lang":"en","wikibase":"","file":"Tridecimal neutral seventh on C.mid"},"classes":["noexcerpt","ext-phonos-PhonosButton"]}"><a role="button" tabindex="0" href="https://upload.wikimedia.org/wikipedia/commons/transcoded/4/44/Tridecimal_neutral_seventh_on_C.mid/Tridecimal_neutral_seventh_on_C.mid.mp3" rel="nofollow" aria-label="Play audio" title="Play audio" class="oo-ui-buttonElement-button"><span class="oo-ui-labelElement-label">play</span></a></span><sup class="ext-phonos-attribution noexcerpt navigation-not-searchable">ⓘ</sup></span> has a ratio of 24:13 between the <a href="Frequencies" class="mw-redirect" title="Frequencies">frequencies</a> 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 <a href="Harmonic" title="Harmonic">harmonic</a>.</li>
<li>An <i><a href="Equal_temperament" title="Equal temperament">equal-tempered</a> neutral seventh</i> <span class="ext-phonos"><span data-nosnippet="" id="ooui-php-12" class="noexcerpt ext-phonos-PhonosButton oo-ui-widget oo-ui-widget-enabled oo-ui-buttonElement oo-ui-buttonElement-frameless oo-ui-iconElement oo-ui-labelElement oo-ui-buttonWidget" data-ooui="{"_":"mw.Phonos.PhonosButton","href":"\/\/upload.wikimedia.org\/wikipedia\/commons\/transcoded\/6\/60\/Neutral_seventh_on_C.mid\/Neutral_seventh_on_C.mid.mp3","rel":["nofollow"],"framed":false,"icon":"volumeUp","label":{"html":"play"},"data":{"ipa":"","text":"","lang":"en","wikibase":"","file":"Neutral seventh on C.mid"},"classes":["noexcerpt","ext-phonos-PhonosButton"]}"><a role="button" tabindex="0" href="https://upload.wikimedia.org/wikipedia/commons/transcoded/6/60/Neutral_seventh_on_C.mid/Neutral_seventh_on_C.mid.mp3" rel="nofollow" aria-label="Play audio" title="Play audio" class="oo-ui-buttonElement-button"><span class="oo-ui-labelElement-label">play</span></a></span><sup class="ext-phonos-attribution noexcerpt navigation-not-searchable">ⓘ</sup></span> is characterized by a difference in 1050 <a href="Cent_(music)" title="Cent (music)">cents</a> 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).</li></ul>
<p>These intervals are all within about 12 cents of each other and are difficult for most people to distinguish.
</p><p>A neutral seventh can be formed by stacking a <a href="Neutral_third" title="Neutral third">neutral third</a> together with a <a href="Perfect_fifth" title="Perfect fifth">perfect fifth</a>. Based on its positioning in the harmonic series, the undecimal neutral seventh implies a <a href="Root_(chord)" title="Root (chord)">root</a> one perfect fifth below the lower of the two notes.
</p>
<div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2></div>
<ul><li><a href="Major_fourth_and_minor_fifth" title="Major fourth and minor fifth">Major fourth and minor fifth</a></li>
<li><a href="Subminor_and_supermajor" title="Subminor and supermajor">Subminor and supermajor</a></li>
<li><a href="List_of_pitch_intervals" title="List of pitch intervals">List of pitch intervals</a></li>
<li><a href="Microtonal_music" class="mw-redirect" title="Microtonal music">Microtonal music</a></li></ul>
<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>
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</style><div class="reflist">
<div class="mw-references-wrap"><ol class="references">
<li id="cite_note-Haluska-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-Haluska_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Haluska_1-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text">Haluska, Jan (2003). <i>The Mathematical Theory of Tone Systems</i>, p.xxiii. <style data-mw-deduplicate="TemplateStyles:r1238218222">
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</style><a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0-8247-4714-3</bdi>. 3/4-tone, undecimal neutral second and 21/4-tone, undecimal neutral seventh.</span>
</li>
<li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text">Haluska (2003), p.?. Septimal neutral seventh.</span>
</li>
<li id="cite_note-Cooking-3"><span class="mw-cite-backlink">^ <a href="#cite_ref-Cooking_3-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Cooking_3-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text">Andrew Horner, Lydia Ayres (2002). <i>Cooking with Csound: Woodwind and Brass Recipes</i>, p.131. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0-89579-507-8</bdi>.</span>
</li>
</ol></div></div>
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</style><div id="Intervals258" style="font-size:114%;margin:0 4em"><a href="Interval_(music)" title="Interval (music)">Intervals</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Equal_temperament" title="Equal temperament">Twelve-<br>semitone</a><br>(post-Bach<br>Western)</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th id="(Numbers_in_bracketsare_the_number_ofsemitones_in_theinterval.)86" scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><i>(Numbers in brackets<br>are the number of<br><a href="Semitone" title="Semitone">semitones</a> in the<br>interval.)</i></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:6em;font-weight:normal;">Perfect</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em">
<ul><li><a href="Unison" title="Unison">unison</a> (0)</li>
<li><a href="Perfect_fourth" title="Perfect fourth">fourth</a> (5)</li>
<li><a href="Perfect_fifth" title="Perfect fifth">fifth</a> (7)</li>
<li><a href="Octave" title="Octave">octave</a> (12)</li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em;font-weight:normal;"><a href="Major_and_minor#Intervals_and_chords" title="Major and minor">Major</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em">
<ul><li><a href="Major_second" title="Major second">second</a> (2)</li>
<li><a href="Major_third" title="Major third">third</a> (4)</li>
<li><a href="Major_sixth" title="Major sixth">sixth</a> (9)</li>
<li><a href="Major_seventh" title="Major seventh">seventh</a> (11)</li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em;font-weight:normal;"><a href="Major_and_minor#Intervals_and_chords" title="Major and minor">Minor</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em">
<ul><li><a href="Minor_second" class="mw-redirect" title="Minor second">second</a> (1)</li>
<li><a href="Minor_third" title="Minor third">third</a> (3)</li>
<li><a href="Minor_sixth" title="Minor sixth">sixth</a> (8)</li>
<li><a href="Minor_seventh" title="Minor seventh">seventh</a> (10)</li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em;font-weight:normal;"><a href="Augmentation_(music)#Augmentation_of_intervals" title="Augmentation (music)">Augmented</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em">
<ul><li><a href="Augmented_unison" title="Augmented unison">unison</a> (1)</li>
<li><a href="Augmented_second" title="Augmented second">second</a> (3)</li>
<li><a href="Augmented_third" title="Augmented third">third</a> (5)</li>
<li><a href="Tritone" title="Tritone">fourth</a> (6)</li>
<li><a href="Augmented_fifth" title="Augmented fifth">fifth</a> (8)</li>
<li><a href="Augmented_sixth" title="Augmented sixth">sixth</a> (10)</li>
<li><a href="Augmented_seventh" title="Augmented seventh">seventh</a> (12)</li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em;font-weight:normal;"><a href="Diminution#Diminution_of_intervals" title="Diminution">Diminished</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em">
<ul><li><a href="Diminished_second" title="Diminished second">second</a> (0)</li>
<li><a href="Diminished_third" title="Diminished third">third</a> (2)</li>
<li><a href="Diminished_fourth" title="Diminished fourth">fourth</a> (4)</li>
<li><a href="Tritone" title="Tritone">fifth</a> (6)</li>
<li><a href="Diminished_sixth" title="Diminished sixth">sixth</a> (7)</li>
<li><a href="Diminished_seventh" title="Diminished seventh">seventh</a> (9)</li>
<li><a href="Diminished_octave" title="Diminished octave">octave</a> (11)</li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em;font-weight:normal;"><a href="Interval_(music)#Simple_and_compound" title="Interval (music)">Compound</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em">
<ul><li><a href="Ninth" title="Ninth">ninth</a> (13 or 14)</li>
<li><a href="Third_(chord)" title="Third (chord)">tenth</a> (15 or 16)</li>
<li><a href="Eleventh" title="Eleventh">eleventh</a> (17 or 18)</li>
<li><a href="Fifth_(chord)" title="Fifth (chord)">twelfth</a> (18 or 19)</li>
<li><a href="Thirteenth" title="Thirteenth">thirteenth</a> (20 or 21)</li>
<li><a href="Seventh_(chord)" title="Seventh (chord)">fourteenth</a> (22 or 23)</li>
<li><a href="Fifteenth" title="Fifteenth">fifteenth</a> (24)</li></ul>
</div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other<br>tuning<br>systems</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><b><a href="24-tone_equal_temperament" class="mw-redirect" title="24-tone equal temperament">24-tone equal temperament</a></b><br><i>(Numbers in brackets refer<br>to fractional semitones.)</i></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th id="Neutral57" scope="row" class="navbox-group" style="width:5em;font-weight:normal;"><div><br><br><br></div></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em">
<ul><li><a href="Quarter_tone" title="Quarter tone">quarter tone</a> (<span class="frac"><span class="num">1</span>⁄<span class="den">2</span></span>)</li>
<li> (<span class="frac">1<span class="sr-only">+</span><span class="num">1</span>⁄<span class="den">2</span></span>)</li>
<li><a href="Neutral_third" title="Neutral third">third</a> (<span class="frac">3<span class="sr-only">+</span><span class="num">1</span>⁄<span class="den">2</span></span>)</li>
<li><a href="Major_fourth_and_minor_fifth" title="Major fourth and minor fifth">major fourth</a> (<span class="frac">5<span class="sr-only">+</span><span class="num">1</span>⁄<span class="den">2</span></span>)</li>
<li><a href="Major_fourth_and_minor_fifth" title="Major fourth and minor fifth">minor fifth</a> (<span class="frac">6<span class="sr-only">+</span><span class="num">1</span>⁄<span class="den">2</span></span>)</li>
<li><a href="Neutral_sixth" title="Neutral sixth">sixth</a> (<span class="frac">8<span class="sr-only">+</span><span class="num">1</span>⁄<span class="den">2</span></span>)</li>
<li> (<span class="frac">10<span class="sr-only">+</span><span class="num">1</span>⁄<span class="den">2</span></span>)</li></ul>
</div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><b><a href="Just_intonation" title="Just intonation">Just intonations</a></b><br><i>(Numbers in brackets<br>refer to pitch ratios.)</i></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="7-limit_tuning" title="7-limit tuning">7-limit</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="Septimal_quarter_tone" title="Septimal quarter tone">septimal quarter tone</a> (36:35)</li>
<li><a href="Septimal_third_tone" title="Septimal third tone">septimal third tone</a> (28:27)</li>
<li><a href="Septimal_chromatic_semitone" title="Septimal chromatic semitone">septimal chromatic semitone</a> (21:20)</li>
<li><a href="Septimal_diatonic_semitone" title="Septimal diatonic semitone">septimal diatonic semitone</a> (15:14)</li>
<li><a href="Septimal_whole_tone" title="Septimal whole tone">supermajor second</a> (8:7)</li>
<li><a href="Septimal_minor_third" title="Septimal minor third">subminor third</a> (7:6)</li>
<li><a href="Septimal_major_third" title="Septimal major third">supermajor third</a> (9:7)</li>
<li><a href="Septimal_tritone" title="Septimal tritone">subminor fifth</a> (7:5)</li>
<li><a href="Septimal_tritone" title="Septimal tritone">supermajor fourth</a> (10:7)</li>
<li><a href="Harmonic_seventh" title="Harmonic seventh">subminor seventh</a> (7:4)</li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="Limit_(music)" title="Limit (music)">Higher-limit</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="Minor_diatonic_semitone" title="Minor diatonic semitone">minor diatonic semitone</a> (17-limit)</li></ul>
</div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other<br>intervals</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:6em;font-weight:normal;"><b>Groups</b></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em">
<ul><li><a href="Microtonal_music" class="mw-redirect" title="Microtonal music">Microtone</a></li>
<li><a href="List_of_intervals_in_5-limit_just_intonation" title="List of intervals in 5-limit just intonation">5-limit</a></li>
<li><a href="Comma_(music)" title="Comma (music)">Comma</a></li>
<li><a href="Pseudo-octave" title="Pseudo-octave">Pseudo-octave</a></li>
<li><a href="Pythagorean_interval" title="Pythagorean interval">Pythagorean interval</a></li>
<li><a href="Subminor_and_supermajor" title="Subminor and supermajor">Subminor and supermajor</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em;font-weight:normal;"><i><b>Semitones</b></i></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em">
<ul><li><a href="Pythagorean_limma" class="mw-redirect" title="Pythagorean limma">Pythagorean limma</a></li>
<li><a href="Pythagorean_apotome" class="mw-redirect" title="Pythagorean apotome">Pythagorean apotome</a></li>
<li><a href="Major_limma" title="Major limma">Major limma</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em;font-weight:normal;"><i><b>Quarter tones</b></i></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em">
<ul><li><a href="Quarter_tone" title="Quarter tone">Quarter tone</a></li>
<li><a href="Septimal_quarter_tone" title="Septimal quarter tone">Septimal quarter tone</a></li>
<li><a href="Undecimal_quarter_tone" class="mw-redirect" title="Undecimal quarter tone">Undecimal quarter tone</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em;font-weight:normal;"><b><a href="Comma_(music)" title="Comma (music)">Commas</a></b></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em">
<ul><li><a href="Pythagorean_comma" title="Pythagorean comma">Pythagorean comma</a> (23.5 cents)</li>
<li><a href="Syntonic_comma" title="Syntonic comma">Syntonic comma</a> (21.5 cents)</li>
<li><a href="Holdrian_comma" class="mw-redirect" title="Holdrian comma">Holdrian comma</a> (22.6 cents)</li>
<li><a href="Septimal_comma" title="Septimal comma">Septimal comma</a> (27.3 cents)</li></ul>
<ul><li><a href="Diesis" title="Diesis">Lesser diesis</a> (41.1 cents)</li>
<li><a href="Diesis" title="Diesis">Greater diesis</a> (62.6 cents)</li>
<li><a href="Septimal_diesis" title="Septimal diesis">Septimal diesis</a> (35.7 cents)</li></ul>
<ul><li><a href="Diaschisma" title="Diaschisma">Diaschisma</a> (19.5 cents)</li>
<li><a href="Semicomma" title="Semicomma">Semicomma</a> (10.1 cents)</li>
<li><a href="Septimal_semicomma" title="Septimal semicomma">Septimal semicomma</a> (13.8 cents)</li>
<li><a href="Kleisma" title="Kleisma">Kleisma</a> (8.1 cents)</li>
<li><a href="Septimal_kleisma" title="Septimal kleisma">Septimal kleisma</a> (7.7 cents)</li></ul>
<ul><li><a href="Schisma" title="Schisma">Schisma</a> (1.95 cents)</li>
<li><a href="Breedsma" title="Breedsma">Breedsma</a> (0.72 cents)</li>
<li><a href="Ragisma" title="Ragisma">Ragisma</a> (0.4 cents)</li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em;font-weight:normal;"><b>Measurement</b></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em">
<ul><li><a href="Cent_(music)" title="Cent (music)">Cent</a></li>
<li><a href="Cent_(music)#Centitones" title="Cent (music)">Centitone</a></li>
<li><a href="Millioctave" title="Millioctave">Millioctave</a></li>
<li><a href="Savart" title="Savart">Savart</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em;font-weight:normal;"><b>Others</b></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em">
<ul><li><a href="Wolf_interval" title="Wolf interval">Wolf</a></li>
<li><a href="Ditone" title="Ditone">Ditone</a></li>
<li><a href="Semiditone" class="mw-redirect" title="Semiditone">Semiditone</a></li>
<li><a href="George_Secor#Secor" title="George Secor">Secor</a></li>
<li><a href="Incomposite_interval" title="Incomposite interval">Incomposite interval</a></li></ul>
</div></td></tr></tbody></table><div></div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div><span class="noviewer" typeof="mw:File"><span title="List-Class article"></span></span> <a href="List_of_pitch_intervals" title="List of pitch intervals">List of pitch intervals</a></div></td></tr></tbody></table></div></div><!--htdig_noindex--><div><div class="zim-footer">
This article is issued from <a class="external text" title="Last edited on 2025-08-07" href="https://en.wikipedia.org/wiki/?title=Neutral_interval&oldid=1304658045">Wikipedia</a>. The text is available under <a class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.en">Creative Commons Attribution-Share Alike 4.0</a> unless otherwise noted. Additional terms may apply for the media files.
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