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Wikispaces>keenanpepper **Imported revision 313564534 - Original comment: ** |
Wikispaces>xenwolf **Imported revision 574999527 - Original comment: linked all occurences of Interseptimal: there are 4 ranges described on the target page** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User: | : This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2016-02-16 16:40:29 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>574999527</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : The revision comment was: <tt>linked all occurences of Interseptimal: there are 4 ranges described on the target page</tt><br> | ||
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<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> | <h4>Original Wikitext content:</h4> | ||
| Line 47: | Line 47: | ||
|| *middle || 400-423 || | || *middle || 400-423 || | ||
|| *large || 423-440 || | || *large || 423-440 || | ||
|| Interseptimal (Maj3-4) || 440-468 || | || [[Interseptimal]] (Maj3-4) || 440-468 || | ||
|| [[Perfect Fourth]]s || 468-528 || | || [[Perfect Fourth]]s || 468-528 || | ||
|| *small || 468-491 || | || *small || 468-491 || | ||
| Line 75: | Line 75: | ||
|| *middle || 900-920 || | || *middle || 900-920 || | ||
|| *large || 920-940 || | || *large || 920-940 || | ||
|| Interseptimal (Maj6-min7) || 940-960 || | || [[Interseptimal]] (Maj6-min7) || 940-960 || | ||
|| [[Minor Seventh]]s || 960-1025 || | || [[Minor Seventh]]s || 960-1025 || | ||
|| *small || 960-987 || | || *small || 960-987 || | ||
| Line 402: | Line 402: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>Interseptimal (Maj3-4)<br /> | <td><a class="wiki_link" href="/Interseptimal">Interseptimal</a> (Maj3-4)<br /> | ||
</td> | </td> | ||
<td>440-468<br /> | <td>440-468<br /> | ||
| Line 570: | Line 570: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>Interseptimal (Maj6-min7)<br /> | <td><a class="wiki_link" href="/Interseptimal">Interseptimal</a> (Maj6-min7)<br /> | ||
</td> | </td> | ||
<td>940-960<br /> | <td>940-960<br /> | ||
Revision as of 16:40, 16 February 2016
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author xenwolf and made on 2016-02-16 16:40:29 UTC.
- The original revision id was 574999527.
- The revision comment was: linked all occurences of Interseptimal: there are 4 ranges described on the target page
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
Original Wikitext content:
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==
[[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."//
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") ||
|| [[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
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
[[code]]Original HTML content:
<html><head><title>interval category</title></head><body>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 <a class="wiki_link" href="/Just%20Intonation">Just Intonation</a> and the irrational intervals of <a class="wiki_link" href="/EDO">EDO</a>s, <a class="wiki_link" href="/EDONOI">EDONOI</a>s, and other systems. However, it is helpful to consider interval categories, which there may be a finite number to consider.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:1:<h2> --><h2 id="toc0"><a name="x-The Schulter System"></a><!-- ws:end:WikiTextHeadingRule:1 -->The Schulter System</h2>
<br />
<a class="wiki_link" href="/Margo%20Schulter">Margo Schulter</a> describes her system for categorizing intervals in <a class="wiki_link_ext" href="http://www.bestii.com/%7Emschulter/IntervalSpectrumRegions.txt" rel="nofollow">Regions of the Interval Spectrum</a>, which begins:<br />
<br />
<em>"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."</em><br />
<br />
Schulter proposes the following categories and gives a tentative range of cents values for intervals that fall within those categories. In <em>Regions</em>, 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."<br />
<br />
<br />
<table class="wiki_table">
<tr>
<th>Interval Category<br />
</th>
<th>Associated Ranges of Cents Values (borders are "fuzzy")<br />
</th>
</tr>
<tr>
<td><a class="wiki_link" href="/Unison">Pure Unison</a> (1:1)<br />
</td>
<td>0<br />
</td>
</tr>
<tr>
<td><a class="wiki_link" href="/Comma">Comma</a>s<br />
</td>
<td>0-30<br />
</td>
</tr>
<tr>
<td><a class="wiki_link" href="/Diesis">Dieses</a><br />
</td>
<td>30-60<br />
</td>
</tr>
<tr>
<td><a class="wiki_link" href="/Minor%20Second">Minor Second</a>s<br />
</td>
<td>60-125<br />
</td>
</tr>
<tr>
<td>*small<br />
</td>
<td>60-80<br />
</td>
</tr>
<tr>
<td>*middle<br />
</td>
<td>80-100<br />
</td>
</tr>
<tr>
<td>*large<br />
</td>
<td>100-125<br />
</td>
</tr>
<tr>
<td><a class="wiki_link" href="/Neutral%20Second">Neutral Second</a>s<br />
</td>
<td>125-170<br />
</td>
</tr>
<tr>
<td>*small<br />
</td>
<td>125-135<br />
</td>
</tr>
<tr>
<td>*middle<br />
</td>
<td>135-160<br />
</td>
</tr>
<tr>
<td>*large<br />
</td>
<td>160-170<br />
</td>
</tr>
<tr>
<td>Equable Heptatonic<br />
</td>
<td>160-182<br />
</td>
</tr>
<tr>
<td><a class="wiki_link" href="/Major%20Second">Major Second</a>s<br />
</td>
<td>180-240<br />
</td>
</tr>
<tr>
<td>*small<br />
</td>
<td>180-200<br />
</td>
</tr>
<tr>
<td>*middle<br />
</td>
<td>200-220<br />
</td>
</tr>
<tr>
<td>*large<br />
</td>
<td>220-240<br />
</td>
</tr>
<tr>
<td><a class="wiki_link" href="/Interseptimal">Interseptimal</a> (Maj2-min3)<br />
</td>
<td>240-260<br />
</td>
</tr>
<tr>
<td><a class="wiki_link" href="/Minor%20Third">Minor Third</a>s<br />
</td>
<td>260-330<br />
</td>
</tr>
<tr>
<td>*small<br />
</td>
<td>260-280<br />
</td>
</tr>
<tr>
<td>*middle<br />
</td>
<td>280-300<br />
</td>
</tr>
<tr>
<td>*large<br />
</td>
<td>300-330<br />
</td>
</tr>
<tr>
<td><a class="wiki_link" href="/Neutral%20Third">Neutral Third</a>s<br />
</td>
<td>330-372<br />
</td>
</tr>
<tr>
<td>*small<br />
</td>
<td>330-342<br />
</td>
</tr>
<tr>
<td>*middle<br />
</td>
<td>342-360<br />
</td>
</tr>
<tr>
<td>*large<br />
</td>
<td>360-372<br />
</td>
</tr>
<tr>
<td><a class="wiki_link" href="/Major%20Third">Major Third</a>s<br />
</td>
<td>372-440<br />
</td>
</tr>
<tr>
<td>*small<br />
</td>
<td>372-400<br />
</td>
</tr>
<tr>
<td>*middle<br />
</td>
<td>400-423<br />
</td>
</tr>
<tr>
<td>*large<br />
</td>
<td>423-440<br />
</td>
</tr>
<tr>
<td><a class="wiki_link" href="/Interseptimal">Interseptimal</a> (Maj3-4)<br />
</td>
<td>440-468<br />
</td>
</tr>
<tr>
<td><a class="wiki_link" href="/Perfect%20Fourth">Perfect Fourth</a>s<br />
</td>
<td>468-528<br />
</td>
</tr>
<tr>
<td>*small<br />
</td>
<td>468-491<br />
</td>
</tr>
<tr>
<td>*middle<br />
</td>
<td>491-505<br />
</td>
</tr>
<tr>
<td>*large<br />
</td>
<td>505-528<br />
</td>
</tr>
<tr>
<td><a class="wiki_link" href="/Superfourth">Superfourth</a>s<br />
</td>
<td>528-560<br />
</td>
</tr>
<tr>
<td><a class="wiki_link" href="/Tritone">Tritonic Region</a><br />
</td>
<td>560-640<br />
</td>
</tr>
<tr>
<td>*small<br />
</td>
<td>560-577<br />
</td>
</tr>
<tr>
<td>*middle<br />
</td>
<td>577-623<br />
</td>
</tr>
<tr>
<td>*large<br />
</td>
<td>623-640<br />
</td>
</tr>
<tr>
<td><a class="wiki_link" href="/Subfifth">Subfifth</a>s<br />
</td>
<td>640-672<br />
</td>
</tr>
<tr>
<td><a class="wiki_link" href="/Perfect%20Fifth">Perfect Fifth</a>s<br />
</td>
<td>672-732<br />
</td>
</tr>
<tr>
<td>*small<br />
</td>
<td>672-695<br />
</td>
</tr>
<tr>
<td>*middle<br />
</td>
<td>695-709<br />
</td>
</tr>
<tr>
<td>*large<br />
</td>
<td>709-732<br />
</td>
</tr>
<tr>
<td>Interseptimal (5-min6)<br />
</td>
<td>732-760<br />
</td>
</tr>
<tr>
<td><a class="wiki_link" href="/Minor%20Sixth">Minor Sixth</a>s<br />
</td>
<td>760-828<br />
</td>
</tr>
<tr>
<td>*small<br />
</td>
<td>760-777<br />
</td>
</tr>
<tr>
<td>*middle<br />
</td>
<td>777-800<br />
</td>
</tr>
<tr>
<td>*large<br />
</td>
<td>800-828<br />
</td>
</tr>
<tr>
<td><a class="wiki_link" href="/Neutral%20Sixth">Neutral Sixth</a>s<br />
</td>
<td>828-870<br />
</td>
</tr>
<tr>
<td>*small<br />
</td>
<td>828-840<br />
</td>
</tr>
<tr>
<td>*middle<br />
</td>
<td>840-858<br />
</td>
</tr>
<tr>
<td>*large<br />
</td>
<td>858-870<br />
</td>
</tr>
<tr>
<td><a class="wiki_link" href="/Major%20Sixth">Major Sixth</a>s<br />
</td>
<td>870-940<br />
</td>
</tr>
<tr>
<td>*small<br />
</td>
<td>870-900<br />
</td>
</tr>
<tr>
<td>*middle<br />
</td>
<td>900-920<br />
</td>
</tr>
<tr>
<td>*large<br />
</td>
<td>920-940<br />
</td>
</tr>
<tr>
<td><a class="wiki_link" href="/Interseptimal">Interseptimal</a> (Maj6-min7)<br />
</td>
<td>940-960<br />
</td>
</tr>
<tr>
<td><a class="wiki_link" href="/Minor%20Seventh">Minor Seventh</a>s<br />
</td>
<td>960-1025<br />
</td>
</tr>
<tr>
<td>*small<br />
</td>
<td>960-987<br />
</td>
</tr>
<tr>
<td>*middle<br />
</td>
<td>987-1000<br />
</td>
</tr>
<tr>
<td>*large<br />
</td>
<td>1000-1025<br />
</td>
</tr>
<tr>
<td>Equable Heptatonic<br />
</td>
<td>1018-1040<br />
</td>
</tr>
<tr>
<td><a class="wiki_link" href="/Neutral%20Seventh">Neutral Seventh</a>s<br />
</td>
<td>1030-1075<br />
</td>
</tr>
<tr>
<td>*small<br />
</td>
<td>1030-1043<br />
</td>
</tr>
<tr>
<td>*middle<br />
</td>
<td>1043-1065<br />
</td>
</tr>
<tr>
<td>*large<br />
</td>
<td>1065-1075<br />
</td>
</tr>
<tr>
<td><a class="wiki_link" href="/Major%20Seventh">Major Seventh</a>s<br />
</td>
<td>1075-1140<br />
</td>
</tr>
<tr>
<td>*small<br />
</td>
<td>1075-1100<br />
</td>
</tr>
<tr>
<td>*middle<br />
</td>
<td>1100-1120<br />
</td>
</tr>
<tr>
<td>*large<br />
</td>
<td>1120-1140<br />
</td>
</tr>
<tr>
<td>Octave less diesis<br />
</td>
<td>1140-1170<br />
</td>
</tr>
<tr>
<td>Octave less comma<br />
</td>
<td>1170-1200<br />
</td>
</tr>
<tr>
<td><a class="wiki_link" href="/Octave">Pure Octave</a> (2:1)<br />
</td>
<td>1200<br />
</td>
</tr>
</table>
<br />
See: <a class="wiki_link" href="/interval%20size%20measure">interval size measure</a>, <a class="wiki_link" href="/Gallery%20of%20Just%20Intervals">Gallery of Just Intervals</a><br />
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<pre class="text">Pure unison (1:1) 0 cents<br/><br/>Commas 0-30 cents (Section 11)<br/><br/>Dieses 30-60 cents (Section 11)<br/><br/>Minor seconds 60-125 cents (Section 5)<br/> small 60-80 cents<br/> middle 80-100 cents<br/> large 100-125 cents<br/><br/>Neutral seconds 125-170 cents (Section 6)<br/> small 125-135 cents<br/> middle 135-160 cents<br/> large 160-170 cents<br/><br/>Equable heptatonic<br/>(heartland range) 160-182 cents (Section 12)<br/><br/>Major seconds<br/>(or tones) 180-240 cents (Section 4)<br/> small 180-200 cents<br/> middle 200-220 cents<br/> large 220-240 cents<br/><br/>Interseptimal<br/>(Maj2-min3) 240-260 cents (Section 9)<br/><br/>Minor thirds 260-330 cents (Section 2)<br/> small 260-280 cents<br/> middle 280-300 cents<br/> large 300-330 cents<br/><br/>Neutral thirds 330-372 cents (Section 3)<br/> small 330-342 cents<br/> middle 342-360 cents<br/> large 360-372 cents<br/><br/>Major thirds 372-440 cents (Section 2)<br/> small 372-400 cents<br/> middle 400-423 cents<br/> large 423-440 cents<br/><br/>Interseptimal 440-468 cents (Section 9)<br/>(Maj3-4)<br/><br/>Perfect fourths 468-528 cents (Section 7)<br/> small 468-491 cents<br/> middle 491-505 cents<br/> large 505-523 cents<br/><br/>Superfourths 528-560 cents (Section 10)<br/><br/>Tritonic region 560-640 cents (Section 8)<br/> small 560-577 cents<br/> middle 577-623 cents<br/> large 623-640 cents<br/><br/>Subfifths 640-672 cents (Section 10)<br/><br/>Perfect fifths 672-732 cents (Section 7)<br/> small 672-695 cents<br/> middle 695-709 cents<br/> large 709-732 cents<br/><br/>Interseptimal 732-760 cents (Section 9)<br/>(5-min6)<br/><br/>Minor sixths 760-828 cents (Section 2)<br/> small 760-777 cents<br/> middle 777-800 cents<br/> large 800-828 cents<br/><br/>Neutral sixths 828-870 cents (Section 3)<br/> small 828-840 cents<br/> middle 840-858 cents<br/> large 858-870 cents<br/><br/>Major sixths 870-940 cents (Section 2)<br/> small 870-900 cents<br/> middle 900-920 cents<br/> large 920-940 cents<br/><br/>Interseptimal 940-960 cents (Section 9)<br/>(Maj6-min7)<br/><br/>Minor sevenths 960-1025 cents (Section 4)<br/> small 960-987 cents<br/> middle 987-1000 cents<br/> large 1000-1025 cents<br/><br/>Equable heptatonic 1018-1040 cents (Section 12)<br/>(heartland range)<br/><br/>Neutral sevenths 1030-1075 cents (Section 6)<br/> small 1030-1043 cents<br/> middle 1043-1065 cents<br/> large 1065-1075 cents<br/><br/>Major sevenths 1075-1140 cents (Section 5)<br/> small 1075-1100 cents<br/> middle 1100-1120 cents<br/> large 1120-1140 cents<br/><br/>Octave less diesis 1140-1170 cents (Section 11)<br/><br/>Octave less comma 1170-1200 cents (Section 11)<br/><br/>Pure octave (2:1) 1200 cents</pre>
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</style><pre class="text">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</pre>
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