Porcupine intervals: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
These are the intervals found in porcupine temperament.
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>2012-07-19 18:25:19 UTC</tt>.<br>
: The original revision id was <tt>354010786</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]], 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]], 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 right-3 center-5"
||||||||~ Unisons ||~  ||
|-
|| Perfect unison (P1) || 0 || 1/1 || 0 ||   ||
! Name ([[Pergen|ups and downs]])
|| Augmented unison (A1) || 61.1 || 81/80~36/35~33/32~25/24 || -7 || [[Cluster temperament#porcupine%28fish%29|And other ratios, of course]] ||
! Name (1L 6s (onyx))
||||||||~ Seconds ||~  ||
! Size*
|| Diminished second (d2) || 101.6 || 21/20~16/15 || 8 ||   ||
! Ratio
|| Minor second (m2) || 162.7 || 12/11~11/10~10/9 || 1 ||   ||
! [[Fifthspan #Rank-2 temperaments|Genspan]]
|| Major second (M2) || 223.8 || 9/8~8/7 || -6 ||   ||
! Comments
|| Augmented second (A2) || 284.9 || Close to 13/11 || -13 || Also "subminor third" ||
|-
||||||||~ Thirds ||~  ||
! colspan="6" | Unisons
|| 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 ||
| Perfect unison (P1)
|| Augmented third (A3) || 447.6 || 9/7 (close to 13/10) || -12 || Also "subminor fourth" ||
| 0.0
||||||||~ Fourths ||~  ||
| 1/1
|| Diminished fourth (d4) || 427.0 || 14/11 || 10 || Also "supermajor third" ||
| 0
|| 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" ||
| Up unison (^1)
||||||||~ Fifths ||~  ||
| Augmented unison (A1)
|| Diminished fifth (d5) || 589.7 || 7/5 || 11 || Also "supermajor fourth" ||
| 61.1
|| Minor fifth (m5) || 650.8 || 16/11 || 4 ||   ||
| 81/80~36/35~33/32~25/24
|| Major fifth (M5) || 711.9 || 3/2 || -3 || Rather than "perfect fifth" ||
| -7
|| Augmented fifth (A5) || 773.0 || 11/7 || -10 || Also "subminor sixth" ||
| [[Cluster temperament #porcupine(fish)|Among other ratios]]
||||||||~ Sixths ||~  ||
|-
|| Diminished sixth (d6) || 752.4 || 14/9 (close to 20/13) || 12 || Also "supermajor fifth" ||
! colspan="6" | Seconds
|| Minor sixth (m6) || 813.5 || 8/5 || 5 || Coincidentally familiar ||
|-
|| Major sixth (M6) || 874.6 || 5/3 || -2 || Coincidentally familiar ||
| Upminor second (^m2)
|| Augmented sixth (A6) || 935.7 || 12/7 || -9 || Also "subminor seventh" ||
| Diminished second (d2)
||||||||~ Sevenths ||~  ||
| 101.6
|| Diminished seventh (d7) || 915.1 || Close to 22/13 || 13 || Also "supermajor sixth" ||
| 21/20~16/15
|| Minor seventh (m7) || 976.2 || 7/4~16/9 || 6 ||   ||
| 8
|| Major seventh (M7) || 1037.3 || 9/5~11/6 || -3 ||   ||
|  
|| Augmented seventh (A7) || 1098.4 || 15/8 || -8 ||   ||
|-
||||||||~ Octaves ||~  ||
| Downmajor second (vM2)
|| Diminished octave (d8) || 1138.9 || 21/11~35/18~160/81 || 7 ||   ||
| Perfect second (P2)
|| Perfect octave (P8) || 1200 || 2/1 || 0 ||   ||
| 162.7
|| Augmented octave (A8) || 1261.1 || 81/40~45/22~33/16~25/12 || -7 ||   ||
| 12/11~11/10~10/9~35/32
``*`` In POTE 11-limit porcupine
| 1
|  
|-
| Major second (M2)
| Augmented second (A2)
| 223.8
| 9/8~8/7
| -6
|  
|-
| Upmajor second (^M2)
| Double-augmented second (AA2)
| 284.9
| Close to 13/11
| -13
| Also "subminor third"
|-
! colspan="6" | Thirds
|-
| Minor third (m3)
| Diminished third (d3)
| 264.3
| 7/6
| 9
| Also "supermajor second"
|-
| Upminor third (^m3)
| Minor third (m3)
| 325.4
| 6/5~11/9
| 2
|  
|-
| Downmajor third (vM3)
| Major third (M3)
| 386.5
| 5/4
| -5
|  
|-
| Major third (M3)
| Augmented third (A3)
| 447.6
| 9/7 (close to 13/10)
| -12
| Also "subminor fourth"
|-
! colspan="6" | Fourths
|-
| Down fourth (v4)
| Diminished fourth (d4)
| 427.0
| 14/11
| 10
| Also "supermajor third"
|-
| Perfect fourth (P4)
| Minor fourth (m4)
| 488.1
| 4/3
| 3
|  
|-
| Upfourth (^4)
| Major fourth (M4)
| 549.2
| 11/8
| -4
|  
|-
| Downaugmented fourth (vA4)
| Augmented fourth (A4)
| 610.3
| 10/7
| -11
| Also "subminor fifth"
|-
! colspan="6" | Fifths
|-
| Updiminished fifth (^d5)
| Diminished fifth (d5)
| 589.7
| 7/5
| 11
| Also "supermajor fourth"
|-
| Down fifth (v5)
| Minor fifth (m5)
| 650.8
| 16/11
| 4
|  
|-
| Perfect fifth (P5)
| Major fifth (M5)
| 711.9
| 3/2
| -3
|  
|-
| Up fifth (^5)
| Augmented fifth (A5)
| 773.0
| 11/7
| -10
| Also "subminor sixth"
|-
! colspan="6" | Sixths
|-
| Minor sixth (m6)
| Diminished sixth (d6)
| 752.4
| 14/9 (close to 20/13)
| 12
| Also "supermajor fifth"
|-
| Upminor sixth (^m6)
| Minor sixth (m6)
| 813.5
| 8/5
| 5
|  
|-
| Downmajor sixth (vM6)
| Major sixth (M6)
| 874.6
| 5/3
| -2
|  
|-
| Major sixth (M6)
| Augmented sixth (A6)
| 935.7
| 12/7
| -9
| Also "subminor seventh"
|-
! colspan="6" | Sevenths
|-
| Downminor seventh (vm7)
| Double-diminished seventh (dd7)
| 915.1
| Close to 22/13
| 13
| Also "supermajor sixth"
|-
| Minor seventh (m7)
| Diminished seventh (d7)
| 976.2
| 7/4~16/9
| 6
|  
|-
| Upminor seventh (^m7)
| Perfect seventh (P7)
| 1037.3
| 9/5~11/6
| -1
|  
|-
| Downmajor seventh (vM7)
| Augmented seventh (A7)
| 1098.4
| 15/8
| -8
|  
|-
! colspan="6" | Octaves
|-
| Down octave (v8)
| Diminished octave (d8)
| 1138.9
| 21/11~35/18~160/81
| 7
|  
|-
| Perfect octave (P8)
| Perfect octave (P8)
| 1200.0
| 2/1
| 0
|  
|-
| Up octave (^8)
| Augmented octave (A8)
| 1261.1
| 81/40~45/22~33/16~25/12
| -7
|  
|}
* In cents, 11-limit POTE tuning of porcupine, where the generator is ~162.7¢.


[[image:porcupine interval matrix pote.png]]
[[File:porcupine_interval_matrix_pote.png|alt=porcupine_interval_matrix_pote.png|porcupine_interval_matrix_pote.png]]
See also: [[Porcupine Notation]]</pre></div>
<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;


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


&lt;table class="wiki_table"&gt;
== See also ==
    &lt;tr&gt;
* [[Porcupine notation]]
        &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&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;
[[Category:Porcupine]]
&lt;br /&gt;
[[Category:Todo:cleanup]]
&lt;!-- ws:start:WikiTextLocalImageRule:411:&amp;lt;img src=&amp;quot;/file/view/porcupine%20interval%20matrix%20pote.png/354010706/porcupine%20interval%20matrix%20pote.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/porcupine%20interval%20matrix%20pote.png/354010706/porcupine%20interval%20matrix%20pote.png" alt="porcupine interval matrix pote.png" title="porcupine interval matrix pote.png" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:411 --&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>

Latest revision as of 07:26, 3 June 2025

These are the intervals found in porcupine temperament.

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 (ups and downs) Name (1L 6s (onyx)) Size* Ratio Genspan Comments
Unisons
Perfect unison (P1) Perfect unison (P1) 0.0 1/1 0
Up unison (^1) Augmented unison (A1) 61.1 81/80~36/35~33/32~25/24 -7 Among other ratios
Seconds
Upminor second (^m2) Diminished second (d2) 101.6 21/20~16/15 8
Downmajor second (vM2) Perfect second (P2) 162.7 12/11~11/10~10/9~35/32 1
Major second (M2) Augmented second (A2) 223.8 9/8~8/7 -6
Upmajor second (^M2) Double-augmented second (AA2) 284.9 Close to 13/11 -13 Also "subminor third"
Thirds
Minor third (m3) Diminished third (d3) 264.3 7/6 9 Also "supermajor second"
Upminor third (^m3) Minor third (m3) 325.4 6/5~11/9 2
Downmajor third (vM3) Major third (M3) 386.5 5/4 -5
Major third (M3) Augmented third (A3) 447.6 9/7 (close to 13/10) -12 Also "subminor fourth"
Fourths
Down fourth (v4) Diminished fourth (d4) 427.0 14/11 10 Also "supermajor third"
Perfect fourth (P4) Minor fourth (m4) 488.1 4/3 3
Upfourth (^4) Major fourth (M4) 549.2 11/8 -4
Downaugmented fourth (vA4) Augmented fourth (A4) 610.3 10/7 -11 Also "subminor fifth"
Fifths
Updiminished fifth (^d5) Diminished fifth (d5) 589.7 7/5 11 Also "supermajor fourth"
Down fifth (v5) Minor fifth (m5) 650.8 16/11 4
Perfect fifth (P5) Major fifth (M5) 711.9 3/2 -3
Up fifth (^5) Augmented fifth (A5) 773.0 11/7 -10 Also "subminor sixth"
Sixths
Minor sixth (m6) Diminished sixth (d6) 752.4 14/9 (close to 20/13) 12 Also "supermajor fifth"
Upminor sixth (^m6) Minor sixth (m6) 813.5 8/5 5
Downmajor sixth (vM6) Major sixth (M6) 874.6 5/3 -2
Major sixth (M6) Augmented sixth (A6) 935.7 12/7 -9 Also "subminor seventh"
Sevenths
Downminor seventh (vm7) Double-diminished seventh (dd7) 915.1 Close to 22/13 13 Also "supermajor sixth"
Minor seventh (m7) Diminished seventh (d7) 976.2 7/4~16/9 6
Upminor seventh (^m7) Perfect seventh (P7) 1037.3 9/5~11/6 -1
Downmajor seventh (vM7) Augmented seventh (A7) 1098.4 15/8 -8
Octaves
Down octave (v8) Diminished octave (d8) 1138.9 21/11~35/18~160/81 7
Perfect octave (P8) Perfect octave (P8) 1200.0 2/1 0
Up octave (^8) Augmented octave (A8) 1261.1 81/40~45/22~33/16~25/12 -7
  • In cents, 11-limit POTE tuning of porcupine, where the generator is ~162.7¢.

porcupine_interval_matrix_pote.png

porcupine_interval_matrix_22edo.png

See also

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