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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
This is one possible naming and organization system for intervals of [[Porcupine|porcupine]] temperament. It's based on the porcupine[7] scale, or equivalently on the [[val|val]] &lt;7 11 16|.
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2012-07-25 23:09:10 UTC</tt>.<br>
: The original revision id was <tt>354850834</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">This is one possible naming and organization system for intervals of [[porcupine]] temperament. It's based on the porcupine[7] scale, or equivalently on the [[val]] &lt;7 11 16|.


In [[22edo]], all the neighboring intervals on this chart that are shown as about 20 cents apart are actually the same. For example, the augmented third (9/7) and the diminished fourth (14/11) are both the same interval (8\22) in 22edo. This corresponds to 99/98 being tempered out in 22edo.
In [[22edo|22edo]], all the neighboring intervals on this chart that are shown as about 20 cents apart are actually the same. For example, the augmented third (9/7) and the diminished fourth (14/11) are both the same interval (8\22) in 22edo. This corresponds to 99/98 being tempered out in 22edo.


In [[15edo]], on the other hand, the intervals that are shown as about 40 cents apart are actually the same. For example, the augmented third (9/7), is now the same as a **minor** fourth (4/3) rather than a diminished one. That is because 28/27 is tempered out in 15edo.
In [[15edo|15edo]], on the other hand, the intervals that are shown as about 40 cents apart are actually the same. For example, the augmented third (9/7), is now the same as a '''minor''' fourth (4/3) rather than a diminished one. That is because 28/27 is tempered out in 15edo.


||~ Name ||~ Size* ||~ Ratio ||~ No. of Porcupine Generators(~162.7¢) ||~ Comments ||
{| class="wikitable"
||||||||~ Unisons ||~  ||
|-
|| Perfect unison (P1) || 0 || 1/1 || 0 ||   ||
! | Name
|| Augmented unison (A1) || 61.1 || 81/80~36/35~33/32~25/24 || -7 || [[Cluster temperament#porcupine%28fish%29|And other ratios, of course]] ||
! | Size*
||||||||~ Seconds ||~  ||
! | Ratio
|| Diminished second (d2) || 101.6 || 21/20~16/15 || 8 ||   ||
! | No. of Porcupine Generators(~162.7¢)
|| Minor second (m2) || 162.7 || 12/11~11/10~10/9~35/32 || 1 ||   ||
! | Comments
|| Major second (M2) || 223.8 || 9/8~8/7 || -6 ||   ||
|-
|| Augmented second (A2) || 284.9 || Close to 13/11 || -13 || Also "subminor third" ||
! colspan="4" | Unisons
||||||||~ Thirds ||~  ||
! |  
|| Diminished third (d3) || 264.3 || 7/6 || 9 || Also "supermajor second" ||
|-
|| Minor third (m3) || 325.4 || 6/5~11/9 || 2 || Coincidentally familiar ||
| | Perfect unison (P1)
|| Major third (M3) || 386.5 || 5/4 || -5 || Coincidentally familiar ||
| | 0
|| Augmented third (A3) || 447.6 || 9/7 (close to 13/10) || -12 || Also "subminor fourth" ||
| | 1/1
||||||||~ Fourths ||~  ||
| | 0
|| Diminished fourth (d4) || 427.0 || 14/11 || 10 || Also "supermajor third" ||
| |  
|| Minor fourth (m4) || 488.1 || 4/3 || 3 || Rather than "perfect fourth" ||
|-
|| Major fourth (M4) || 549.2 || 11/8 || -4 ||   ||
| | Augmented unison (A1)
|| Augmented fourth (A4) || 610.3 || 10/7 || -11 || Also "subminor fifth" ||
| | 61.1
||||||||~ Fifths ||~  ||
| | 81/80~36/35~33/32~25/24
|| Diminished fifth (d5) || 589.7 || 7/5 || 11 || Also "supermajor fourth" ||
| | -7
|| Minor fifth (m5) || 650.8 || 16/11 || 4 ||   ||
| | [[Cluster_temperament#porcupine(fish)|And other ratios, of course]]
|| Major fifth (M5) || 711.9 || 3/2 || -3 || Rather than "perfect fifth" ||
|-
|| Augmented fifth (A5) || 773.0 || 11/7 || -10 || Also "subminor sixth" ||
! colspan="4" | Seconds
||||||||~ Sixths ||~  ||
! |  
|| Diminished sixth (d6) || 752.4 || 14/9 (close to 20/13) || 12 || Also "supermajor fifth" ||
|-
|| Minor sixth (m6) || 813.5 || 8/5 || 5 || Coincidentally familiar ||
| | Diminished second (d2)
|| Major sixth (M6) || 874.6 || 5/3 || -2 || Coincidentally familiar ||
| | 101.6
|| Augmented sixth (A6) || 935.7 || 12/7 || -9 || Also "subminor seventh" ||
| | 21/20~16/15
||||||||~ Sevenths ||~  ||
| | 8
|| Diminished seventh (d7) || 915.1 || Close to 22/13 || 13 || Also "supermajor sixth" ||
| |  
|| Minor seventh (m7) || 976.2 || 7/4~16/9 || 6 ||   ||
|-
|| Major seventh (M7) || 1037.3 || 9/5~11/6 || -3 ||   ||
| | Minor second (m2)
|| Augmented seventh (A7) || 1098.4 || 15/8 || -8 ||   ||
| | 162.7
||||||||~ Octaves ||~  ||
| | 12/11~11/10~10/9~35/32
|| Diminished octave (d8) || 1138.9 || 21/11~35/18~160/81 || 7 ||   ||
| | 1
|| Perfect octave (P8) || 1200 || 2/1 || 0 ||   ||
| |  
|| Augmented octave (A8) || 1261.1 || 81/40~45/22~33/16~25/12 || -7 ||   ||
|-
``*`` In POTE 11-limit porcupine
| | Major second (M2)
| | 223.8
| | 9/8~8/7
| | -6
| |  
|-
| | Augmented second (A2)
| | 284.9
| | Close to 13/11
| | -13
| | Also "subminor third"
|-
! colspan="4" | Thirds
! |  
|-
| | Diminished third (d3)
| | 264.3
| | 7/6
| | 9
| | Also "supermajor second"
|-
| | Minor third (m3)
| | 325.4
| | 6/5~11/9
| | 2
| | Coincidentally familiar
|-
| | Major third (M3)
| | 386.5
| | 5/4
| | -5
| | Coincidentally familiar
|-
| | Augmented third (A3)
| | 447.6
| | 9/7 (close to 13/10)
| | -12
| | Also "subminor fourth"
|-
! colspan="4" | Fourths
! |  
|-
| | Diminished fourth (d4)
| | 427.0
| | 14/11
| | 10
| | Also "supermajor third"
|-
| | Minor fourth (m4)
| | 488.1
| | 4/3
| | 3
| | Rather than "perfect fourth"
|-
| | Major fourth (M4)
| | 549.2
| | 11/8
| | -4
| |  
|-
| | Augmented fourth (A4)
| | 610.3
| | 10/7
| | -11
| | Also "subminor fifth"
|-
! colspan="4" | Fifths
! |  
|-
| | Diminished fifth (d5)
| | 589.7
| | 7/5
| | 11
| | Also "supermajor fourth"
|-
| | Minor fifth (m5)
| | 650.8
| | 16/11
| | 4
| |  
|-
| | Major fifth (M5)
| | 711.9
| | 3/2
| | -3
| | Rather than "perfect fifth"
|-
| | Augmented fifth (A5)
| | 773.0
| | 11/7
| | -10
| | Also "subminor sixth"
|-
! colspan="4" | Sixths
! |  
|-
| | Diminished sixth (d6)
| | 752.4
| | 14/9 (close to 20/13)
| | 12
| | Also "supermajor fifth"
|-
| | Minor sixth (m6)
| | 813.5
| | 8/5
| | 5
| | Coincidentally familiar
|-
| | Major sixth (M6)
| | 874.6
| | 5/3
| | -2
| | Coincidentally familiar
|-
| | Augmented sixth (A6)
| | 935.7
| | 12/7
| | -9
| | Also "subminor seventh"
|-
! colspan="4" | Sevenths
! |  
|-
| | Diminished seventh (d7)
| | 915.1
| | Close to 22/13
| | 13
| | Also "supermajor sixth"
|-
| | Minor seventh (m7)
| | 976.2
| | 7/4~16/9
| | 6
| |  
|-
| | Major seventh (M7)
| | 1037.3
| | 9/5~11/6
| | -3
| |  
|-
| | Augmented seventh (A7)
| | 1098.4
| | 15/8
| | -8
| |  
|-
! colspan="4" | Octaves
! |  
|-
| | Diminished octave (d8)
| | 1138.9
| | 21/11~35/18~160/81
| | 7
| |  
|-
| | Perfect octave (P8)
| | 1200
| | 2/1
| | 0
| |  
|-
| | Augmented octave (A8)
| | 1261.1
| | 81/40~45/22~33/16~25/12
| | -7
| |  
|}
* In POTE 11-limit porcupine


[[image:porcupine_interval_matrix_pote.png]]
[[File:porcupine_interval_matrix_pote.png|alt=porcupine_interval_matrix_pote.png|porcupine_interval_matrix_pote.png]]
[[image:porcupine_interval_matrix_22edo.png]]


See also: [[Porcupine Notation]]</pre></div>
[[File:porcupine_interval_matrix_22edo.png|alt=porcupine_interval_matrix_22edo.png|porcupine_interval_matrix_22edo.png]]
<h4>Original HTML 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;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Porcupine intervals&lt;/title&gt;&lt;/head&gt;&lt;body&gt;This is one possible naming and organization system for intervals of &lt;a class="wiki_link" href="/porcupine"&gt;porcupine&lt;/a&gt; temperament. It's based on the porcupine[7] scale, or equivalently on the &lt;a class="wiki_link" href="/val"&gt;val&lt;/a&gt; &amp;lt;7 11 16|.&lt;br /&gt;
&lt;br /&gt;
In &lt;a class="wiki_link" href="/22edo"&gt;22edo&lt;/a&gt;, all the neighboring intervals on this chart that are shown as about 20 cents apart are actually the same. For example, the augmented third (9/7) and the diminished fourth (14/11) are both the same interval (8\22) in 22edo. This corresponds to 99/98 being tempered out in 22edo.&lt;br /&gt;
&lt;br /&gt;
In &lt;a class="wiki_link" href="/15edo"&gt;15edo&lt;/a&gt;, on the other hand, the intervals that are shown as about 40 cents apart are actually the same. For example, the augmented third (9/7), is now the same as a &lt;strong&gt;minor&lt;/strong&gt; fourth (4/3) rather than a diminished one. That is because 28/27 is tempered out in 15edo.&lt;br /&gt;
&lt;br /&gt;


 
See also: [[Porcupine_Notation|Porcupine Notation]]
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;th&gt;Name&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Size*&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Ratio&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;No. of Porcupine Generators(~162.7¢)&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Comments&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;th colspan="4"&gt;Unisons&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Perfect unison (P1)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1/1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Augmented unison (A1)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;61.1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;81/80~36/35~33/32~25/24&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/Cluster%20temperament#porcupine%28fish%29"&gt;And other ratios, of course&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;th colspan="4"&gt;Seconds&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Diminished second (d2)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;101.6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;21/20~16/15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Minor second (m2)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;162.7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;12/11~11/10~10/9~35/32&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Major second (M2)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;223.8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9/8~8/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Augmented second (A2)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;284.9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Close to 13/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Also &amp;quot;subminor third&amp;quot;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;th colspan="4"&gt;Thirds&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Diminished third (d3)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;264.3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7/6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Also &amp;quot;supermajor second&amp;quot;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Minor third (m3)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;325.4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;6/5~11/9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Coincidentally familiar&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Major third (M3)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;386.5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5/4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Coincidentally familiar&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Augmented third (A3)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;447.6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9/7 (close to 13/10)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-12&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Also &amp;quot;subminor fourth&amp;quot;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;th colspan="4"&gt;Fourths&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Diminished fourth (d4)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;427.0&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;14/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Also &amp;quot;supermajor third&amp;quot;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Minor fourth (m4)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;488.1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;4/3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Rather than &amp;quot;perfect fourth&amp;quot;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Major fourth (M4)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;549.2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Augmented fourth (A4)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;610.3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;10/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Also &amp;quot;subminor fifth&amp;quot;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;th colspan="4"&gt;Fifths&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Diminished fifth (d5)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;589.7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Also &amp;quot;supermajor fourth&amp;quot;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Minor fifth (m5)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;650.8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;16/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Major fifth (M5)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;711.9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Rather than &amp;quot;perfect fifth&amp;quot;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Augmented fifth (A5)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;773.0&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Also &amp;quot;subminor sixth&amp;quot;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;th colspan="4"&gt;Sixths&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Diminished sixth (d6)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;752.4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;14/9 (close to 20/13)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;12&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Also &amp;quot;supermajor fifth&amp;quot;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Minor sixth (m6)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;813.5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;8/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Coincidentally familiar&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Major sixth (M6)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;874.6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5/3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Coincidentally familiar&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Augmented sixth (A6)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;935.7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;12/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Also &amp;quot;subminor seventh&amp;quot;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;th colspan="4"&gt;Sevenths&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Diminished seventh (d7)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;915.1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Close to 22/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Also &amp;quot;supermajor sixth&amp;quot;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Minor seventh (m7)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;976.2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7/4~16/9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Major seventh (M7)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1037.3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9/5~11/6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Augmented seventh (A7)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1098.4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;15/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;th colspan="4"&gt;Octaves&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Diminished octave (d8)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1138.9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;21/11~35/18~160/81&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Perfect octave (P8)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1200&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;2/1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Augmented octave (A8)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1261.1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;81/40~45/22~33/16~25/12&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;!-- ws:start:WikiTextRawRule:00:``*`` --&gt;*&lt;!-- ws:end:WikiTextRawRule:00 --&gt; In POTE 11-limit porcupine&lt;br /&gt;
&lt;br /&gt;
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&lt;!-- ws:start:WikiTextLocalImageRule:412:&amp;lt;img src=&amp;quot;/file/view/porcupine_interval_matrix_22edo.png/354850800/porcupine_interval_matrix_22edo.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/porcupine_interval_matrix_22edo.png/354850800/porcupine_interval_matrix_22edo.png" alt="porcupine_interval_matrix_22edo.png" title="porcupine_interval_matrix_22edo.png" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:412 --&gt;&lt;br /&gt;
&lt;br /&gt;
See also: &lt;a class="wiki_link" href="/Porcupine%20Notation"&gt;Porcupine Notation&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>

Revision as of 00:00, 17 July 2018

This is one possible naming and organization system for intervals of porcupine temperament. It's based on the porcupine[7] scale, or equivalently on the val <7 11 16|.

In 22edo, all the neighboring intervals on this chart that are shown as about 20 cents apart are actually the same. For example, the augmented third (9/7) and the diminished fourth (14/11) are both the same interval (8\22) in 22edo. This corresponds to 99/98 being tempered out in 22edo.

In 15edo, on the other hand, the intervals that are shown as about 40 cents apart are actually the same. For example, the augmented third (9/7), is now the same as a minor fourth (4/3) rather than a diminished one. That is because 28/27 is tempered out in 15edo.

Name Size* Ratio No. of Porcupine Generators(~162.7¢) Comments
Unisons
Perfect unison (P1) 0 1/1 0
Augmented unison (A1) 61.1 81/80~36/35~33/32~25/24 -7 And other ratios, of course
Seconds
Diminished second (d2) 101.6 21/20~16/15 8
Minor second (m2) 162.7 12/11~11/10~10/9~35/32 1
Major second (M2) 223.8 9/8~8/7 -6
Augmented second (A2) 284.9 Close to 13/11 -13 Also "subminor third"
Thirds
Diminished third (d3) 264.3 7/6 9 Also "supermajor second"
Minor third (m3) 325.4 6/5~11/9 2 Coincidentally familiar
Major third (M3) 386.5 5/4 -5 Coincidentally familiar
Augmented third (A3) 447.6 9/7 (close to 13/10) -12 Also "subminor fourth"
Fourths
Diminished fourth (d4) 427.0 14/11 10 Also "supermajor third"
Minor fourth (m4) 488.1 4/3 3 Rather than "perfect fourth"
Major fourth (M4) 549.2 11/8 -4
Augmented fourth (A4) 610.3 10/7 -11 Also "subminor fifth"
Fifths
Diminished fifth (d5) 589.7 7/5 11 Also "supermajor fourth"
Minor fifth (m5) 650.8 16/11 4
Major fifth (M5) 711.9 3/2 -3 Rather than "perfect fifth"
Augmented fifth (A5) 773.0 11/7 -10 Also "subminor sixth"
Sixths
Diminished sixth (d6) 752.4 14/9 (close to 20/13) 12 Also "supermajor fifth"
Minor sixth (m6) 813.5 8/5 5 Coincidentally familiar
Major sixth (M6) 874.6 5/3 -2 Coincidentally familiar
Augmented sixth (A6) 935.7 12/7 -9 Also "subminor seventh"
Sevenths
Diminished seventh (d7) 915.1 Close to 22/13 13 Also "supermajor sixth"
Minor seventh (m7) 976.2 7/4~16/9 6
Major seventh (M7) 1037.3 9/5~11/6 -3
Augmented seventh (A7) 1098.4 15/8 -8
Octaves
Diminished octave (d8) 1138.9 21/11~35/18~160/81 7
Perfect octave (P8) 1200 2/1 0
Augmented octave (A8) 1261.1 81/40~45/22~33/16~25/12 -7
  • In POTE 11-limit porcupine

porcupine_interval_matrix_pote.png

porcupine_interval_matrix_22edo.png

See also: Porcupine Notation

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