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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
It is well-known that there are infinite possible intervals, even if one confines one's view to a single octave. This includes the rational intervals of [[Just_intonation|Just Intonation]] and the irrational intervals of [[EDO|EDO]]s, [[edonoi|EDONOI]]s, and other systems. However, it is helpful to consider interval categories, which there may be a finite number to consider.
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2016-02-16 16:47:15 UTC</tt>.<br>
: The original revision id was <tt>575000159</tt>.<br>
: The revision comment was: <tt></tt><br>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
<h4>Original Wikitext content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">It is well-known that there are infinite possible intervals, even if one confines one's view to a single octave. This includes the rational intervals of [[Just Intonation]] and the irrational intervals of [[EDO]]s, [[EDONOI]]s, and other systems. However, it is helpful to consider interval categories, which there may be a finite number to consider.


==The Schulter System==  
==The Schulter System==


[[Margo Schulter]] describes her system for categorizing intervals in [[http://www.bestii.com/%7Emschulter/IntervalSpectrumRegions.txt|Regions of the Interval Spectrum]], which begins:
[[Margo_Schulter|Margo Schulter]] describes her system for categorizing intervals in [http://www.bestii.com/%7Emschulter/IntervalSpectrumRegions.txt Regions of the Interval Spectrum], which begins:


//"In naming categories of intervals, or regions of the spectrum in which they are found, there may be many valid and desirable schemes reflecting the diversity of viewpoints and styles to be found in world musics. What I describe here is merely one possible solution, and one influenced by my own musicmaking experience and philosophy which seeks an equitable and inclusive balance between intervals at or near simple integer ratios, and those having a more complex or active nature."//
''"In naming categories of intervals, or regions of the spectrum in which they are found, there may be many valid and desirable schemes reflecting the diversity of viewpoints and styles to be found in world musics. What I describe here is merely one possible solution, and one influenced by my own musicmaking experience and philosophy which seeks an equitable and inclusive balance between intervals at or near simple integer ratios, and those having a more complex or active nature."''


Schulter proposes the following categories and gives a tentative range of cents values for intervals that fall within those categories. In //Regions//, she points out, "A main caution is that the borders are inevitably 'fuzzy,' so that one region shades into another and suggested values in cents are more illustrative than definitive."
Schulter proposes the following categories and gives a tentative range of cents values for intervals that fall within those categories. In ''Regions'', she points out, "A main caution is that the borders are inevitably 'fuzzy,' so that one region shades into another and suggested values in cents are more illustrative than definitive."


{| class="wikitable"
|-
! | Interval Category
! | Associated Ranges of Cents Values (borders are "fuzzy")
|-
| | [[Unison|Pure Unison]] (1:1)
| | 0
|-
| | [[Comma|Comma]]s
| | 0-30
|-
| | [[Diesis|Dieses]]
| | 30-60
|-
| | [[Minor_Second|Minor Second]]s
| | 60-125
|-
| | *small
| | 60-80
|-
| | *middle
| | 80-100
|-
| | *large
| | 100-125
|-
| | [[Neutral_Second|Neutral Second]]s
| | 125-170
|-
| | *small
| | 125-135
|-
| | *middle
| | 135-160
|-
| | *large
| | 160-170
|-
| | Equable Heptatonic
| | 160-182
|-
| | [[Major_Second|Major Second]]s
| | 180-240
|-
| | *small
| | 180-200
|-
| | *middle
| | 200-220
|-
| | *large
| | 220-240
|-
| | [[Interseptimal|Interseptimal]] (Maj2-min3)
| | 240-260
|-
| | [[Minor_Third|Minor Third]]s
| | 260-330
|-
| | *small
| | 260-280
|-
| | *middle
| | 280-300
|-
| | *large
| | 300-330
|-
| | [[Neutral_Third|Neutral Third]]s
| | 330-372
|-
| | *small
| | 330-342
|-
| | *middle
| | 342-360
|-
| | *large
| | 360-372
|-
| | [[Major_Third|Major Third]]s
| | 372-440
|-
| | *small
| | 372-400
|-
| | *middle
| | 400-423
|-
| | *large
| | 423-440
|-
| | [[Interseptimal|Interseptimal]] (Maj3-4)
| | 440-468
|-
| | [[Perfect_fourth|Perfect Fourth]]s
| | 468-528
|-
| | *small
| | 468-491
|-
| | *middle
| | 491-505
|-
| | *large
| | 505-528
|-
| | [[Superfourth|Superfourth]]s
| | 528-560
|-
| | [[Tritone|Tritonic Region]]
| | 560-640
|-
| | *small
| | 560-577
|-
| | *middle
| | 577-623
|-
| | *large
| | 623-640
|-
| | [[Subfifth|Subfifth]]s
| | 640-672
|-
| | [[perfect_fifth|Perfect Fifth]]s
| | 672-732
|-
| | *small
| | 672-695
|-
| | *middle
| | 695-709
|-
| | *large
| | 709-732
|-
| | [[Interseptimal|Interseptimal]] (5-min6)
| | 732-760
|-
| | [[Minor_Sixth|Minor Sixth]]s
| | 760-828
|-
| | *small
| | 760-777
|-
| | *middle
| | 777-800
|-
| | *large
| | 800-828
|-
| | [[Neutral_Sixth|Neutral Sixth]]s
| | 828-870
|-
| | *small
| | 828-840
|-
| | *middle
| | 840-858
|-
| | *large
| | 858-870
|-
| | [[Major_Sixth|Major Sixth]]s
| | 870-940
|-
| | *small
| | 870-900
|-
| | *middle
| | 900-920
|-
| | *large
| | 920-940
|-
| | [[Interseptimal|Interseptimal]] (Maj6-min7)
| | 940-960
|-
| | [[Minor_Seventh|Minor Seventh]]s
| | 960-1025
|-
| | *small
| | 960-987
|-
| | *middle
| | 987-1000
|-
| | *large
| | 1000-1025
|-
| | Equable Heptatonic
| | 1018-1040
|-
| | [[Neutral_Seventh|Neutral Seventh]]s
| | 1030-1075
|-
| | *small
| | 1030-1043
|-
| | *middle
| | 1043-1065
|-
| | *large
| | 1065-1075
|-
| | [[Major_Seventh|Major Seventh]]s
| | 1075-1140
|-
| | *small
| | 1075-1100
|-
| | *middle
| | 1100-1120
|-
| | *large
| | 1120-1140
|-
| | Octave less diesis
| | 1140-1170
|-
| | Octave less comma
| | 1170-1200
|-
| | [[Octave|Pure Octave]] (2:1)
| | 1200
|}


||~ Interval Category ||~ Associated Ranges of Cents Values (borders are "fuzzy") ||
See: [[Interval_size_measure|interval size measure]], [[Gallery_of_Just_Intervals|Gallery of Just Intervals]]
|| [[Unison|Pure Unison]] (1:1) || 0 ||
|| [[Comma]]s || 0-30 ||
|| [[Diesis|Dieses]] || 30-60 ||
|| [[Minor Second]]s || 60-125 ||
|| *small || 60-80 ||
|| *middle || 80-100 ||
|| *large || 100-125 ||
|| [[Neutral Second]]s || 125-170 ||
|| *small || 125-135 ||
|| *middle || 135-160 ||
|| *large || 160-170 ||
|| Equable Heptatonic || 160-182 ||
|| [[Major Second]]s || 180-240 ||
|| *small || 180-200 ||
|| *middle || 200-220 ||
|| *large || 220-240 ||
|| [[Interseptimal]] (Maj2-min3) || 240-260 ||
|| [[Minor Third]]s || 260-330 ||
|| *small || 260-280 ||
|| *middle || 280-300 ||
|| *large || 300-330 ||
|| [[Neutral Third]]s || 330-372 ||
|| *small || 330-342 ||
|| *middle || 342-360 ||
|| *large || 360-372 ||
|| [[Major Third]]s || 372-440 ||
|| *small || 372-400 ||
|| *middle || 400-423 ||
|| *large || 423-440 ||
|| [[Interseptimal]] (Maj3-4) || 440-468 ||
|| [[Perfect Fourth]]s || 468-528 ||
|| *small || 468-491 ||
|| *middle || 491-505 ||
|| *large || 505-528 ||
|| [[Superfourth]]s || 528-560 ||
|| [[Tritone|Tritonic Region]] || 560-640 ||
|| *small || 560-577 ||
|| *middle || 577-623 ||
|| *large || 623-640 ||
|| [[Subfifth]]s || 640-672 ||
|| [[Perfect Fifth]]s || 672-732 ||
|| *small || 672-695 ||
|| *middle || 695-709 ||
|| *large || 709-732 ||
|| [[Interseptimal]] (5-min6) || 732-760 ||
|| [[Minor Sixth]]s || 760-828 ||
|| *small || 760-777 ||
|| *middle || 777-800 ||
|| *large || 800-828 ||
|| [[Neutral Sixth]]s || 828-870 ||
|| *small || 828-840 ||
|| *middle || 840-858 ||
|| *large || 858-870 ||
|| [[Major Sixth]]s || 870-940 ||
|| *small || 870-900 ||
|| *middle || 900-920 ||
|| *large || 920-940 ||
|| [[Interseptimal]] (Maj6-min7) || 940-960 ||
|| [[Minor Seventh]]s || 960-1025 ||
|| *small || 960-987 ||
|| *middle || 987-1000 ||
|| *large || 1000-1025 ||
|| Equable Heptatonic || 1018-1040 ||
|| [[Neutral Seventh]]s || 1030-1075 ||
|| *small || 1030-1043 ||
|| *middle || 1043-1065 ||
|| *large || 1065-1075 ||
|| [[Major Seventh]]s || 1075-1140 ||
|| *small || 1075-1100 ||
|| *middle || 1100-1120 ||
|| *large || 1120-1140 ||
|| Octave less diesis || 1140-1170 ||
|| Octave less comma || 1170-1200 ||
|| [[Octave|Pure Octave]] (2:1) || 1200 ||
 
See: [[interval size measure]], [[Gallery of Just Intervals]]
 
[[code]]
Pure unison (1:1)          0 cents


<pre>Pure unison (1:1)          0 cents
 
Commas                  0-30 cents        (Section 11)
Commas                  0-30 cents        (Section 11)
 
 
Dieses                  30-60 cents        (Section 11)
Dieses                  30-60 cents        (Section 11)
 
 
Minor seconds          60-125 cents        (Section 5)
Minor seconds          60-125 cents        (Section 5)
         small              60-80 cents
         small              60-80 cents
         middle            80-100 cents
         middle            80-100 cents
         large            100-125 cents
         large            100-125 cents
 
 
Neutral seconds      125-170 cents        (Section 6)
Neutral seconds      125-170 cents        (Section 6)
         small              125-135 cents
         small              125-135 cents
         middle            135-160 cents
         middle            135-160 cents
         large              160-170 cents
         large              160-170 cents
 
 
Equable heptatonic
Equable heptatonic
(heartland range)    160-182 cents        (Section 12)
(heartland range)    160-182 cents        (Section 12)
 
 
Major seconds
Major seconds
(or tones)            180-240 cents        (Section 4)
(or tones)            180-240 cents        (Section 4)
Line 120: Line 263:
         middle            200-220 cents
         middle            200-220 cents
         large              220-240 cents
         large              220-240 cents
 
 
Interseptimal
Interseptimal
(Maj2-min3)          240-260 cents        (Section 9)
(Maj2-min3)          240-260 cents        (Section 9)
 
 
Minor thirds          260-330 cents        (Section 2)
Minor thirds          260-330 cents        (Section 2)
         small              260-280 cents
         small              260-280 cents
         middle            280-300 cents
         middle            280-300 cents
         large              300-330 cents
         large              300-330 cents
 
 
Neutral thirds        330-372 cents        (Section 3)
Neutral thirds        330-372 cents        (Section 3)
         small              330-342 cents
         small              330-342 cents
         middle            342-360 cents
         middle            342-360 cents
         large              360-372 cents
         large              360-372 cents
 
 
Major thirds          372-440 cents        (Section 2)
Major thirds          372-440 cents        (Section 2)
         small              372-400 cents
         small              372-400 cents
         middle            400-423 cents
         middle            400-423 cents
         large              423-440 cents
         large              423-440 cents
 
 
Interseptimal        440-468 cents        (Section 9)
Interseptimal        440-468 cents        (Section 9)
(Maj3-4)
(Maj3-4)
 
 
Perfect fourths      468-528 cents        (Section 7)
Perfect fourths      468-528 cents        (Section 7)
         small              468-491 cents
         small              468-491 cents
         middle            491-505 cents
         middle            491-505 cents
         large              505-523 cents
         large              505-523 cents
 
 
Superfourths          528-560 cents        (Section 10)
Superfourths          528-560 cents        (Section 10)
 
 
Tritonic region      560-640 cents        (Section 8)
Tritonic region      560-640 cents        (Section 8)
         small              560-577 cents
         small              560-577 cents
         middle            577-623 cents
         middle            577-623 cents
         large              623-640 cents
         large              623-640 cents
 
 
Subfifths            640-672 cents        (Section 10)
Subfifths            640-672 cents        (Section 10)
 
 
Perfect fifths        672-732 cents        (Section 7)
Perfect fifths        672-732 cents        (Section 7)
         small              672-695 cents
         small              672-695 cents
         middle            695-709 cents
         middle            695-709 cents
         large              709-732 cents
         large              709-732 cents
 
 
Interseptimal        732-760 cents        (Section 9)
Interseptimal        732-760 cents        (Section 9)
(5-min6)
(5-min6)
 
 
Minor sixths          760-828 cents        (Section 2)
Minor sixths          760-828 cents        (Section 2)
         small              760-777 cents
         small              760-777 cents
         middle            777-800 cents
         middle            777-800 cents
         large              800-828 cents
         large              800-828 cents
 
 
Neutral sixths        828-870 cents        (Section 3)
Neutral sixths        828-870 cents        (Section 3)
         small              828-840 cents
         small              828-840 cents
         middle            840-858 cents
         middle            840-858 cents
         large              858-870 cents
         large              858-870 cents
 
 
Major sixths          870-940 cents        (Section 2)
Major sixths          870-940 cents        (Section 2)
         small              870-900 cents
         small              870-900 cents
         middle            900-920 cents
         middle            900-920 cents
         large              920-940 cents
         large              920-940 cents
 
 
Interseptimal        940-960 cents        (Section 9)
Interseptimal        940-960 cents        (Section 9)
(Maj6-min7)
(Maj6-min7)
 
 
Minor sevenths      960-1025 cents        (Section 4)
Minor sevenths      960-1025 cents        (Section 4)
         small              960-987 cents
         small              960-987 cents
         middle            987-1000 cents
         middle            987-1000 cents
         large            1000-1025 cents
         large            1000-1025 cents
 
 
Equable heptatonic  1018-1040 cents        (Section 12)
Equable heptatonic  1018-1040 cents        (Section 12)
(heartland range)
(heartland range)
 
 
Neutral sevenths    1030-1075 cents        (Section 6)
Neutral sevenths    1030-1075 cents        (Section 6)
         small            1030-1043 cents
         small            1030-1043 cents
         middle          1043-1065 cents
         middle          1043-1065 cents
         large            1065-1075 cents
         large            1065-1075 cents
 
 
Major sevenths      1075-1140 cents        (Section 5)
Major sevenths      1075-1140 cents        (Section 5)
         small            1075-1100 cents
         small            1075-1100 cents
         middle          1100-1120 cents
         middle          1100-1120 cents
         large            1120-1140 cents
         large            1120-1140 cents
 
 
Octave less diesis  1140-1170 cents        (Section 11)
Octave less diesis  1140-1170 cents        (Section 11)
 
 
Octave less comma  1170-1200 cents        (Section 11)
Octave less comma  1170-1200 cents        (Section 11)
 
 
Pure octave (2:1)        1200 cents
Pure octave (2:1)        1200 cents</pre>
[[code]]</pre></div>
[[Category:classification]]
<h4>Original HTML content:</h4>
[[Category:distance_measure]]
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;interval category&lt;/title&gt;&lt;/head&gt;&lt;body&gt;It is well-known that there are infinite possible intervals, even if one confines one's view to a single octave. This includes the rational intervals of &lt;a class="wiki_link" href="/Just%20Intonation"&gt;Just Intonation&lt;/a&gt; and the irrational intervals of &lt;a class="wiki_link" href="/EDO"&gt;EDO&lt;/a&gt;s, &lt;a class="wiki_link" href="/EDONOI"&gt;EDONOI&lt;/a&gt;s, and other systems. However, it is helpful to consider interval categories, which there may be a finite number to consider.&lt;br /&gt;
[[Category:interval]]
&lt;br /&gt;
[[Category:interval_size]]
&lt;!-- ws:start:WikiTextHeadingRule:1:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-The Schulter System"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:1 --&gt;The Schulter System&lt;/h2&gt;
[[Category:measure]]
&lt;br /&gt;
&lt;a class="wiki_link" href="/Margo%20Schulter"&gt;Margo Schulter&lt;/a&gt; describes her system for categorizing intervals in &lt;a class="wiki_link_ext" href="http://www.bestii.com/%7Emschulter/IntervalSpectrumRegions.txt" rel="nofollow"&gt;Regions of the Interval Spectrum&lt;/a&gt;, which begins:&lt;br /&gt;
&lt;br /&gt;
&lt;em&gt;&amp;quot;In naming categories of intervals, or regions of the spectrum in which they are found, there may be many valid and desirable schemes reflecting the diversity of viewpoints and styles to be found in world musics. What I describe here is merely one possible solution, and one influenced by my own musicmaking experience and philosophy which seeks an equitable and inclusive balance between intervals at or near simple integer ratios, and those having a more complex or active nature.&amp;quot;&lt;/em&gt;&lt;br /&gt;
&lt;br /&gt;
Schulter proposes the following categories and gives a tentative range of cents values for intervals that fall within those categories. In &lt;em&gt;Regions&lt;/em&gt;, she points out, &amp;quot;A main caution is that the borders are inevitably 'fuzzy,' so that one region shades into another and suggested values in cents are more illustrative than definitive.&amp;quot;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
 
 
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;th&gt;Interval Category&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Associated Ranges of Cents Values (borders are &amp;quot;fuzzy&amp;quot;)&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/Unison"&gt;Pure Unison&lt;/a&gt; (1:1)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-30&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/Diesis"&gt;Dieses&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;30-60&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/Minor%20Second"&gt;Minor Second&lt;/a&gt;s&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;60-125&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;*small&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;60-80&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;*middle&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;80-100&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;*large&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;100-125&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/Neutral%20Second"&gt;Neutral Second&lt;/a&gt;s&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;125-170&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;*small&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;125-135&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;*middle&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;135-160&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;*large&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;160-170&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Equable Heptatonic&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;160-182&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/Major%20Second"&gt;Major Second&lt;/a&gt;s&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;180-240&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;*small&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;180-200&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;*middle&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;200-220&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;*large&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;220-240&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/Interseptimal"&gt;Interseptimal&lt;/a&gt; (Maj2-min3)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;240-260&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/Minor%20Third"&gt;Minor Third&lt;/a&gt;s&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;260-330&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;*small&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;260-280&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;*middle&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;280-300&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;*large&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;300-330&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/Neutral%20Third"&gt;Neutral Third&lt;/a&gt;s&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;330-372&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;*small&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;330-342&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;*middle&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;342-360&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;*large&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;360-372&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/Major%20Third"&gt;Major Third&lt;/a&gt;s&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;372-440&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;*small&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;372-400&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;*middle&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;400-423&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;*large&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;423-440&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/Interseptimal"&gt;Interseptimal&lt;/a&gt; (Maj3-4)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;440-468&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/Perfect%20Fourth"&gt;Perfect Fourth&lt;/a&gt;s&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;468-528&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;*small&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;468-491&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;*middle&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;491-505&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;*large&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;505-528&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/Superfourth"&gt;Superfourth&lt;/a&gt;s&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;528-560&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/Tritone"&gt;Tritonic Region&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;560-640&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;*small&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;560-577&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;*middle&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;577-623&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;*large&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;623-640&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/Subfifth"&gt;Subfifth&lt;/a&gt;s&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;640-672&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/Perfect%20Fifth"&gt;Perfect Fifth&lt;/a&gt;s&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;672-732&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;*small&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;672-695&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;*middle&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;695-709&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;*large&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;709-732&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/Interseptimal"&gt;Interseptimal&lt;/a&gt; (5-min6)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;732-760&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/Minor%20Sixth"&gt;Minor Sixth&lt;/a&gt;s&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;760-828&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;*small&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;760-777&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;*middle&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;777-800&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;*large&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;800-828&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/Neutral%20Sixth"&gt;Neutral Sixth&lt;/a&gt;s&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;828-870&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;*small&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;828-840&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;*middle&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;840-858&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;*large&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;858-870&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/Major%20Sixth"&gt;Major Sixth&lt;/a&gt;s&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;870-940&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;*small&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;870-900&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;*middle&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;900-920&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;*large&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;920-940&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/Interseptimal"&gt;Interseptimal&lt;/a&gt; (Maj6-min7)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;940-960&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/Minor%20Seventh"&gt;Minor Seventh&lt;/a&gt;s&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;960-1025&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;*small&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;960-987&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;*middle&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;987-1000&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;*large&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1000-1025&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Equable Heptatonic&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1018-1040&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/Neutral%20Seventh"&gt;Neutral Seventh&lt;/a&gt;s&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1030-1075&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;*small&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1030-1043&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;*middle&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1043-1065&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;*large&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1065-1075&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/Major%20Seventh"&gt;Major Seventh&lt;/a&gt;s&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1075-1140&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;*small&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1075-1100&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;*middle&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1100-1120&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;*large&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1120-1140&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Octave less diesis&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1140-1170&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Octave less comma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1170-1200&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/Octave"&gt;Pure Octave&lt;/a&gt; (2:1)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1200&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;br /&gt;
See: &lt;a class="wiki_link" href="/interval%20size%20measure"&gt;interval size measure&lt;/a&gt;, &lt;a class="wiki_link" href="/Gallery%20of%20Just%20Intervals"&gt;Gallery of Just Intervals&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextCodeRule:0:
&amp;lt;pre class=&amp;quot;text&amp;quot;&amp;gt;Pure unison (1:1)          0 cents&amp;lt;br/&amp;gt;&amp;lt;br/&amp;gt;Commas                  0-30 cents        (Section 11)&amp;lt;br/&amp;gt;&amp;lt;br/&amp;gt;Dieses                  30-60 cents        (Section 11)&amp;lt;br/&amp;gt;&amp;lt;br/&amp;gt;Minor seconds          60-125 cents        (Section 5)&amp;lt;br/&amp;gt;        small              60-80 cents&amp;lt;br/&amp;gt;        middle            80-100 cents&amp;lt;br/&amp;gt;        large            100-125 cents&amp;lt;br/&amp;gt;&amp;lt;br/&amp;gt;Neutral seconds      125-170 cents        (Section 6)&amp;lt;br/&amp;gt;        small              125-135 cents&amp;lt;br/&amp;gt;        middle            135-160 cents&amp;lt;br/&amp;gt;        large              160-170 cents&amp;lt;br/&amp;gt;&amp;lt;br/&amp;gt;Equable heptatonic&amp;lt;br/&amp;gt;(heartland range)    160-182 cents        (Section 12)&amp;lt;br/&amp;gt;&amp;lt;br/&amp;gt;Major seconds&amp;lt;br/&amp;gt;(or tones)            180-240 cents        (Section 4)&amp;lt;br/&amp;gt;        small              180-200 cents&amp;lt;br/&amp;gt;        middle            200-220 cents&amp;lt;br/&amp;gt;        large              220-240 cents&amp;lt;br/&amp;gt;&amp;lt;br/&amp;gt;Interseptimal&amp;lt;br/&amp;gt;(Maj2-min3)          240-260 cents        (Section 9)&amp;lt;br/&amp;gt;&amp;lt;br/&amp;gt;Minor thirds          260-330 cents        (Section 2)&amp;lt;br/&amp;gt;        small              260-280 cents&amp;lt;br/&amp;gt;        middle            280-300 cents&amp;lt;br/&amp;gt;        large              300-330 cents&amp;lt;br/&amp;gt;&amp;lt;br/&amp;gt;Neutral thirds        330-372 cents        (Section 3)&amp;lt;br/&amp;gt;        small              330-342 cents&amp;lt;br/&amp;gt;        middle            342-360 cents&amp;lt;br/&amp;gt;        large              360-372 cents&amp;lt;br/&amp;gt;&amp;lt;br/&amp;gt;Major thirds          372-440 cents        (Section 2)&amp;lt;br/&amp;gt;        small              372-400 cents&amp;lt;br/&amp;gt;        middle            400-423 cents&amp;lt;br/&amp;gt;        large              423-440 cents&amp;lt;br/&amp;gt;&amp;lt;br/&amp;gt;Interseptimal        440-468 cents        (Section 9)&amp;lt;br/&amp;gt;(Maj3-4)&amp;lt;br/&amp;gt;&amp;lt;br/&amp;gt;Perfect fourths      468-528 cents        (Section 7)&amp;lt;br/&amp;gt;        small              468-491 cents&amp;lt;br/&amp;gt;        middle            491-505 cents&amp;lt;br/&amp;gt;        large              505-523 cents&amp;lt;br/&amp;gt;&amp;lt;br/&amp;gt;Superfourths          528-560 cents        (Section 10)&amp;lt;br/&amp;gt;&amp;lt;br/&amp;gt;Tritonic region      560-640 cents        (Section 8)&amp;lt;br/&amp;gt;        small              560-577 cents&amp;lt;br/&amp;gt;        middle            577-623 cents&amp;lt;br/&amp;gt;        large              623-640 cents&amp;lt;br/&amp;gt;&amp;lt;br/&amp;gt;Subfifths            640-672 cents        (Section 10)&amp;lt;br/&amp;gt;&amp;lt;br/&amp;gt;Perfect fifths        672-732 cents        (Section 7)&amp;lt;br/&amp;gt;        small              672-695 cents&amp;lt;br/&amp;gt;        middle            695-709 cents&amp;lt;br/&amp;gt;        large              709-732 cents&amp;lt;br/&amp;gt;&amp;lt;br/&amp;gt;Interseptimal        732-760 cents        (Section 9)&amp;lt;br/&amp;gt;(5-min6)&amp;lt;br/&amp;gt;&amp;lt;br/&amp;gt;Minor sixths          760-828 cents        (Section 2)&amp;lt;br/&amp;gt;        small              760-777 cents&amp;lt;br/&amp;gt;        middle            777-800 cents&amp;lt;br/&amp;gt;        large              800-828 cents&amp;lt;br/&amp;gt;&amp;lt;br/&amp;gt;Neutral sixths        828-870 cents        (Section 3)&amp;lt;br/&amp;gt;        small              828-840 cents&amp;lt;br/&amp;gt;        middle            840-858 cents&amp;lt;br/&amp;gt;        large              858-870 cents&amp;lt;br/&amp;gt;&amp;lt;br/&amp;gt;Major sixths          870-940 cents        (Section 2)&amp;lt;br/&amp;gt;        small              870-900 cents&amp;lt;br/&amp;gt;        middle            900-920 cents&amp;lt;br/&amp;gt;        large              920-940 cents&amp;lt;br/&amp;gt;&amp;lt;br/&amp;gt;Interseptimal        940-960 cents        (Section 9)&amp;lt;br/&amp;gt;(Maj6-min7)&amp;lt;br/&amp;gt;&amp;lt;br/&amp;gt;Minor sevenths      960-1025 cents        (Section 4)&amp;lt;br/&amp;gt;        small              960-987 cents&amp;lt;br/&amp;gt;        middle            987-1000 cents&amp;lt;br/&amp;gt;        large            1000-1025 cents&amp;lt;br/&amp;gt;&amp;lt;br/&amp;gt;Equable heptatonic  1018-1040 cents        (Section 12)&amp;lt;br/&amp;gt;(heartland range)&amp;lt;br/&amp;gt;&amp;lt;br/&amp;gt;Neutral sevenths    1030-1075 cents        (Section 6)&amp;lt;br/&amp;gt;        small            1030-1043 cents&amp;lt;br/&amp;gt;        middle          1043-1065 cents&amp;lt;br/&amp;gt;        large            1065-1075 cents&amp;lt;br/&amp;gt;&amp;lt;br/&amp;gt;Major sevenths      1075-1140 cents        (Section 5)&amp;lt;br/&amp;gt;        small            1075-1100 cents&amp;lt;br/&amp;gt;        middle          1100-1120 cents&amp;lt;br/&amp;gt;        large            1120-1140 cents&amp;lt;br/&amp;gt;&amp;lt;br/&amp;gt;Octave less diesis  1140-1170 cents        (Section 11)&amp;lt;br/&amp;gt;&amp;lt;br/&amp;gt;Octave less comma  1170-1200 cents        (Section 11)&amp;lt;br/&amp;gt;&amp;lt;br/&amp;gt;Pure octave (2:1)        1200 cents&amp;lt;/pre&amp;gt;
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&lt;/style&gt;&lt;pre class="text"&gt;Pure unison (1:1)          0 cents
&amp;nbsp;
Commas                  0-30 cents        (Section 11)
&amp;nbsp;
Dieses                  30-60 cents        (Section 11)
&amp;nbsp;
Minor seconds          60-125 cents        (Section 5)
        small              60-80 cents
        middle            80-100 cents
        large            100-125 cents
&amp;nbsp;
Neutral seconds      125-170 cents        (Section 6)
        small              125-135 cents
        middle            135-160 cents
        large              160-170 cents
&amp;nbsp;
Equable heptatonic
(heartland range)    160-182 cents        (Section 12)
&amp;nbsp;
Major seconds
(or tones)            180-240 cents        (Section 4)
        small              180-200 cents
        middle            200-220 cents
        large              220-240 cents
&amp;nbsp;
Interseptimal
(Maj2-min3)          240-260 cents        (Section 9)
&amp;nbsp;
Minor thirds          260-330 cents        (Section 2)
        small              260-280 cents
        middle            280-300 cents
        large              300-330 cents
&amp;nbsp;
Neutral thirds        330-372 cents        (Section 3)
        small              330-342 cents
        middle            342-360 cents
        large              360-372 cents
&amp;nbsp;
Major thirds          372-440 cents        (Section 2)
        small              372-400 cents
        middle            400-423 cents
        large              423-440 cents
&amp;nbsp;
Interseptimal        440-468 cents        (Section 9)
(Maj3-4)
&amp;nbsp;
Perfect fourths      468-528 cents        (Section 7)
        small              468-491 cents
        middle            491-505 cents
        large              505-523 cents
&amp;nbsp;
Superfourths          528-560 cents        (Section 10)
&amp;nbsp;
Tritonic region      560-640 cents        (Section 8)
        small              560-577 cents
        middle            577-623 cents
        large              623-640 cents
&amp;nbsp;
Subfifths            640-672 cents        (Section 10)
&amp;nbsp;
Perfect fifths        672-732 cents        (Section 7)
        small              672-695 cents
        middle            695-709 cents
        large              709-732 cents
&amp;nbsp;
Interseptimal        732-760 cents        (Section 9)
(5-min6)
&amp;nbsp;
Minor sixths          760-828 cents        (Section 2)
        small              760-777 cents
        middle            777-800 cents
        large              800-828 cents
&amp;nbsp;
Neutral sixths        828-870 cents        (Section 3)
        small              828-840 cents
        middle            840-858 cents
        large              858-870 cents
&amp;nbsp;
Major sixths          870-940 cents        (Section 2)
        small              870-900 cents
        middle            900-920 cents
        large              920-940 cents
&amp;nbsp;
Interseptimal        940-960 cents        (Section 9)
(Maj6-min7)
&amp;nbsp;
Minor sevenths      960-1025 cents        (Section 4)
        small              960-987 cents
        middle            987-1000 cents
        large            1000-1025 cents
&amp;nbsp;
Equable heptatonic  1018-1040 cents        (Section 12)
(heartland range)
&amp;nbsp;
Neutral sevenths    1030-1075 cents        (Section 6)
        small            1030-1043 cents
        middle          1043-1065 cents
        large            1065-1075 cents
&amp;nbsp;
Major sevenths      1075-1140 cents        (Section 5)
        small            1075-1100 cents
        middle          1100-1120 cents
        large            1120-1140 cents
&amp;nbsp;
Octave less diesis  1140-1170 cents        (Section 11)
&amp;nbsp;
Octave less comma  1170-1200 cents        (Section 11)
&amp;nbsp;
Pure octave (2:1)        1200 cents&lt;/pre&gt;
 
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Revision as of 00:00, 17 July 2018

It is well-known that there are infinite possible intervals, even if one confines one's view to a single octave. This includes the rational intervals of Just Intonation and the irrational intervals of EDOs, EDONOIs, and other systems. However, it is helpful to consider interval categories, which there may be a finite number to consider.

The Schulter System

Margo Schulter describes her system for categorizing intervals in Regions of the Interval Spectrum, which begins:

"In naming categories of intervals, or regions of the spectrum in which they are found, there may be many valid and desirable schemes reflecting the diversity of viewpoints and styles to be found in world musics. What I describe here is merely one possible solution, and one influenced by my own musicmaking experience and philosophy which seeks an equitable and inclusive balance between intervals at or near simple integer ratios, and those having a more complex or active nature."

Schulter proposes the following categories and gives a tentative range of cents values for intervals that fall within those categories. In Regions, she points out, "A main caution is that the borders are inevitably 'fuzzy,' so that one region shades into another and suggested values in cents are more illustrative than definitive."

Interval Category Associated Ranges of Cents Values (borders are "fuzzy")
Pure Unison (1:1) 0
Commas 0-30
Dieses 30-60
Minor Seconds 60-125
*small 60-80
*middle 80-100
*large 100-125
Neutral Seconds 125-170
*small 125-135
*middle 135-160
*large 160-170
Equable Heptatonic 160-182
Major Seconds 180-240
*small 180-200
*middle 200-220
*large 220-240
Interseptimal (Maj2-min3) 240-260
Minor Thirds 260-330
*small 260-280
*middle 280-300
*large 300-330
Neutral Thirds 330-372
*small 330-342
*middle 342-360
*large 360-372
Major Thirds 372-440
*small 372-400
*middle 400-423
*large 423-440
Interseptimal (Maj3-4) 440-468
Perfect Fourths 468-528
*small 468-491
*middle 491-505
*large 505-528
Superfourths 528-560
Tritonic Region 560-640
*small 560-577
*middle 577-623
*large 623-640
Subfifths 640-672
Perfect Fifths 672-732
*small 672-695
*middle 695-709
*large 709-732
Interseptimal (5-min6) 732-760
Minor Sixths 760-828
*small 760-777
*middle 777-800
*large 800-828
Neutral Sixths 828-870
*small 828-840
*middle 840-858
*large 858-870
Major Sixths 870-940
*small 870-900
*middle 900-920
*large 920-940
Interseptimal (Maj6-min7) 940-960
Minor Sevenths 960-1025
*small 960-987
*middle 987-1000
*large 1000-1025
Equable Heptatonic 1018-1040
Neutral Sevenths 1030-1075
*small 1030-1043
*middle 1043-1065
*large 1065-1075
Major Sevenths 1075-1140
*small 1075-1100
*middle 1100-1120
*large 1120-1140
Octave less diesis 1140-1170
Octave less comma 1170-1200
Pure Octave (2:1) 1200

See: interval size measure, Gallery of Just Intervals 

Pure unison (1:1)           0 cents
 
Commas                   0-30 cents        (Section 11)
 
Dieses                  30-60 cents        (Section 11)
 
Minor seconds          60-125 cents        (Section 5)
        small              60-80 cents
        middle             80-100 cents
        large             100-125 cents
 
Neutral seconds       125-170 cents        (Section 6)
        small              125-135 cents
        middle             135-160 cents
        large              160-170 cents
 
Equable heptatonic
(heartland range)     160-182 cents        (Section 12)
 
Major seconds
(or tones)            180-240 cents        (Section 4)
        small              180-200 cents
        middle             200-220 cents
        large              220-240 cents
 
Interseptimal
(Maj2-min3)           240-260 cents        (Section 9)
 
Minor thirds          260-330 cents        (Section 2)
        small              260-280 cents
        middle             280-300 cents
        large              300-330 cents
 
Neutral thirds        330-372 cents        (Section 3)
        small              330-342 cents
        middle             342-360 cents
        large              360-372 cents
 
Major thirds          372-440 cents        (Section 2)
        small              372-400 cents
        middle             400-423 cents
        large              423-440 cents
 
Interseptimal         440-468 cents        (Section 9)
(Maj3-4)
 
Perfect fourths       468-528 cents        (Section 7)
        small              468-491 cents
        middle             491-505 cents
        large              505-523 cents
 
Superfourths          528-560 cents        (Section 10)
 
Tritonic region       560-640 cents        (Section 8)
        small              560-577 cents
        middle             577-623 cents
        large              623-640 cents
 
Subfifths             640-672 cents        (Section 10)
 
Perfect fifths        672-732 cents        (Section 7)
        small              672-695 cents
        middle             695-709 cents
        large              709-732 cents
 
Interseptimal         732-760 cents        (Section 9)
(5-min6)
 
Minor sixths          760-828 cents        (Section 2)
        small              760-777 cents
        middle             777-800 cents
        large              800-828 cents
 
Neutral sixths        828-870 cents        (Section 3)
        small              828-840 cents
        middle             840-858 cents
        large              858-870 cents
 
Major sixths          870-940 cents        (Section 2)
        small              870-900 cents
        middle             900-920 cents
        large              920-940 cents
 
Interseptimal         940-960 cents        (Section 9)
(Maj6-min7)
 
Minor sevenths       960-1025 cents        (Section 4)
        small              960-987 cents
        middle            987-1000 cents
        large            1000-1025 cents
 
Equable heptatonic  1018-1040 cents        (Section 12)
(heartland range)
 
Neutral sevenths    1030-1075 cents        (Section 6)
        small            1030-1043 cents
        middle           1043-1065 cents
        large            1065-1075 cents
 
Major sevenths      1075-1140 cents        (Section 5)
        small            1075-1100 cents
        middle           1100-1120 cents
        large            1120-1140 cents
 
Octave less diesis  1140-1170 cents        (Section 11)
 
Octave less comma   1170-1200 cents        (Section 11)
 
Pure octave (2:1)        1200 cents
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