List of tritave reduced harmonics: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
The first few [[tritave]] reduced [[harmonic]]s, for the sake of convenient access. Feel free to add higher [[limit]] ones like [[29/27]]. I don't personally see that they're needed at this stage in musical development but someday they will be.
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-09-12 18:20:52 UTC</tt>.<br>
: The original revision id was <tt>591734018</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">The first few tritave reduced harmonics, for the sake of convenient access. Feel free to add higher limit ones like 29/27. I don't personally see that they're needed at this stage in musical development but someday they will be.


1/1...............0.000 unison, perfect prime
1/1...............0.000 unison, perfect prime
28/27...........&lt;span style="background-color: rgba(255,255,255,0);"&gt;62.961 septimal third tone&lt;/span&gt;
 
28/27...........<span style="background-color: rgba(255,255,255,0);">62.961 septimal third tone</span>
 
29/27...........123.721 undetrigesimal augmented semitone
29/27...........123.721 undetrigesimal augmented semitone
10/9.............182.404 minor whole tone
10/9.............182.404 minor whole tone
31/27...........239.171 tricesimoprimal major whole tone
31/27...........239.171 tricesimoprimal major whole tone
32/27...........294.135 &lt;span style="background-color: rgba(255,255,255,0);"&gt;Pythagorean minor third&lt;/span&gt;
 
32/27...........294.135 <span style="background-color: rgba(255,255,255,0);">Pythagorean minor third</span>
 
11/9.............347.408 lesser undecimal neutral third
11/9.............347.408 lesser undecimal neutral third
34/27...........399.09 quasi-equal tempered major third
34/27...........399.09 quasi-equal tempered major third
35/27...........449.275 5-7 third-fourth
35/27...........449.275 5-7 third-fourth
4/3...............498.045 perfect fourth
4/3...............498.045 perfect fourth
37/27...........545.479 tricesimoseptimal augmented fourth
37/27...........545.479 tricesimoseptimal augmented fourth
38/27...........591.648 &lt;span style="background-color: rgba(255,255,255,0);"&gt;undevicesimal tritone&lt;/span&gt;
 
38/27...........591.648 <span style="background-color: rgba(255,255,255,0);">undevicesimal tritone</span>
 
13/9.............636.618 tridecimal diminished fifth
13/9.............636.618 tridecimal diminished fifth
40/27...........680.449 classic wolf fifth
40/27...........680.449 classic wolf fifth
41/27...........723.197 quadricesimoprimal wolf fifth
41/27...........723.197 quadricesimoprimal wolf fifth
14/9.............764.916 septimal minor sixth
14/9.............764.916 septimal minor sixth
43/27...........805.653 quadricesimotertial minor sixth
43/27...........805.653 quadricesimotertial minor sixth
44/27...........845.453 lesser undecimal neutral sixth
44/27...........845.453 lesser undecimal neutral sixth
5/3...............884.359 major sixth, BP sixth
5/3...............884.359 major sixth, BP sixth
46/27...........922.409 &lt;span style="background-color: rgba(255,255,255,0);"&gt;vicesimotertial major sixth&lt;/span&gt;
 
&lt;span style="background-color: rgba(255,255,255,0);"&gt;47/27...........959.642 quadricesimoseptimal sixth-seventh&lt;/span&gt;
46/27...........922.409 <span style="background-color: rgba(255,255,255,0);">vicesimotertial major sixth</span>
 
<span style="background-color: rgba(255,255,255,0);">47/27...........959.642 quadricesimoseptimal sixth-seventh</span>
 
16/9.............996.090 Pythagorean minor seventh
16/9.............996.090 Pythagorean minor seventh
49/27...........1031.787 septimal augmented minor seventh
49/27...........1031.787 septimal augmented minor seventh
50/27...........1066.762 octave minus major limma
50/27...........1066.762 octave minus major limma
17/9.............1101.045 septendecimal major seventh
17/9.............1101.045 septendecimal major seventh
52/27...........1134.663 octave minus 26th partial chroma
52/27...........1134.663 octave minus 26th partial chroma
53/27...........1167.6395 octave minus quincesimotertial diesis
53/27...........1167.6395 octave minus quincesimotertial diesis
2/1...............1200.000 octave
2/1...............1200.000 octave
55/27...........1231.767 55th partial chroma + 1 octave
55/27...........1231.767 55th partial chroma + 1 octave
56/27...........12&lt;span style="background-color: rgba(255,255,255,0);"&gt;62.961 septimal third tone + 1 octave&lt;/span&gt;
 
56/27...........12<span style="background-color: rgba(255,255,255,0);">62.961 septimal third tone + 1 octave</span>
 
19/9.............1293.603 undevicesimal semitone +1 octave
19/9.............1293.603 undevicesimal semitone +1 octave
58/27&lt;span style="background-color: rgba(255,255,255,0);"&gt;...........1323.721 undetrigesimal augmented semitone + 1 octave&lt;/span&gt;
 
58/27<span style="background-color: rgba(255,255,255,0);">...........1323.721 undetrigesimal augmented semitone + 1 octave</span>
 
59/27...........1353.307 undesexagesimal neutral ninth
59/27...........1353.307 undesexagesimal neutral ninth
20/9.............1382.404 classical major ninth
20/9.............1382.404 classical major ninth
61/27...........1411.020 sexacesimoprimal major ninth
61/27...........1411.020 sexacesimoprimal major ninth
&lt;span style="background-color: rgba(255,255,255,0);"&gt;62/27...........1439.171 tricesimoprimal maximal ninth&lt;/span&gt;
 
<span style="background-color: rgba(255,255,255,0);">62/27...........1439.171 tricesimoprimal maximal ninth</span>
 
7/3...............1466.871 minimal tenth, BP tenth
7/3...............1466.871 minimal tenth, BP tenth
64/27...........1494.135 &lt;span style="background-color: rgba(255,255,255,0);"&gt;Pythagorean minor tenth&lt;/span&gt;
 
64/27...........1494.135 <span style="background-color: rgba(255,255,255,0);">Pythagorean minor tenth</span>
 
65/27...........1520.976 65th partial minor tenth
65/27...........1520.976 65th partial minor tenth
22/9.............1547.408 lesser undecimal neutral tenth
22/9.............1547.408 lesser undecimal neutral tenth
67/27...........1573.442 &lt;span style="background-color: rgba(255,255,255,0);"&gt;sexacesimoseptimal perde segah + 1 octave&lt;/span&gt;
 
&lt;span style="background-color: rgba(255,255,255,0);"&gt;68/27...........1599.09 quasi-equal tempered major tenth&lt;/span&gt;
67/27...........1573.442 <span style="background-color: rgba(255,255,255,0);">sexacesimoseptimal perde segah + 1 octave</span>
 
<span style="background-color: rgba(255,255,255,0);">68/27...........1599.09 quasi-equal tempered major tenth</span>


23/9.............1624.364 vicesimotertial major tenth
23/9.............1624.364 vicesimotertial major tenth
70/27...........164&lt;span style="background-color: rgba(255,255,255,0);"&gt;9.275 3-5-7 tenth-eleventh&lt;/span&gt;
 
&lt;span style="background-color: rgba(255,255,255,0);"&gt;71/27...........1673.8315 septuacesimoprimal tenth-eleventh&lt;/span&gt;
70/27...........164<span style="background-color: rgba(255,255,255,0);">9.275 3-5-7 tenth-eleventh</span>
 
<span style="background-color: rgba(255,255,255,0);">71/27...........1673.8315 septuacesimoprimal tenth-eleventh</span>


8/3...............1698.045 perfect 11th
8/3...............1698.045 perfect 11th
73/27...........1721.9245 &lt;span style="background-color: rgba(255,255,255,0);"&gt;septuacesimotertial wolf eleventh&lt;/span&gt;
 
&lt;span style="background-color: rgba(255,255,255,0);"&gt;74/27...........1745.479 tricesimoseptimal augmented eleventh&lt;/span&gt;
73/27...........1721.9245 <span style="background-color: rgba(255,255,255,0);">septuacesimotertial wolf eleventh</span>
 
<span style="background-color: rgba(255,255,255,0);">74/27...........1745.479 tricesimoseptimal augmented eleventh</span>


25/9.............1768.717 classic augmented eleventh, BP twelfth
25/9.............1768.717 classic augmented eleventh, BP twelfth
76/27...........17&lt;span style="background-color: rgba(255,255,255,0);"&gt;91.648 undevicesimal tritone + 1 octave&lt;/span&gt;
 
&lt;span style="background-color: rgba(255,255,255,0);"&gt;77/27...........1814.279 7-11 tritone + 1 octave&lt;/span&gt;
76/27...........17<span style="background-color: rgba(255,255,255,0);">91.648 undevicesimal tritone + 1 octave</span>
26/9.............1836.618 tridecimal &lt;span style="background-color: rgba(255,255,255,0);"&gt;diminished twelfth&lt;/span&gt;
 
79/27...........1858.672 undeoctogesimal &lt;span style="background-color: rgba(255,255,255,0);"&gt;diminished twelfth&lt;/span&gt;
<span style="background-color: rgba(255,255,255,0);">77/27...........1814.279 7-11 tritone + 1 octave</span>
80/27...........18&lt;span style="background-color: rgba(255,255,255,0);"&gt;80.449 classic wolf twelfth&lt;/span&gt;
 
26/9.............1836.618 tridecimal <span style="background-color: rgba(255,255,255,0);">diminished twelfth</span>
 
79/27...........1858.672 undeoctogesimal <span style="background-color: rgba(255,255,255,0);">diminished twelfth</span>
 
80/27...........18<span style="background-color: rgba(255,255,255,0);">80.449 classic wolf twelfth</span>
 
3/1...............1901.955 tritave
3/1...............1901.955 tritave


--
--


Other useful tritave based intervals: (to be filled in as people see fit)</pre></div>
Other useful tritave based [[interval]]s: (to be filled in as people see fit)
<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;Tritave Reduced Harmonics&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The first few tritave reduced harmonics, for the sake of convenient access. Feel free to add higher limit ones like 29/27. I don't personally see that they're needed at this stage in musical development but someday they will be.&lt;br /&gt;
== See also ==
&lt;br /&gt;
* [[Pentave Reduced Harmonics]]
1/1...............0.000 unison, perfect prime&lt;br /&gt;
* [[List of octave-reduced harmonics]]
28/27...........&lt;span style="background-color: rgba(255,255,255,0);"&gt;62.961 septimal third tone&lt;/span&gt;&lt;br /&gt;
 
29/27...........123.721 undetrigesimal augmented semitone&lt;br /&gt;
[[Category:Lists of intervals]]
10/9.............182.404 minor whole tone&lt;br /&gt;
[[Category:Tritave]]
31/27...........239.171 tricesimoprimal major whole tone&lt;br /&gt;
32/27...........294.135 &lt;span style="background-color: rgba(255,255,255,0);"&gt;Pythagorean minor third&lt;/span&gt;&lt;br /&gt;
11/9.............347.408 lesser undecimal neutral third&lt;br /&gt;
34/27...........399.09 quasi-equal tempered major third&lt;br /&gt;
35/27...........449.275 5-7 third-fourth&lt;br /&gt;
4/3...............498.045 perfect fourth&lt;br /&gt;
37/27...........545.479 tricesimoseptimal augmented fourth&lt;br /&gt;
38/27...........591.648 &lt;span style="background-color: rgba(255,255,255,0);"&gt;undevicesimal tritone&lt;/span&gt;&lt;br /&gt;
13/9.............636.618 tridecimal diminished fifth&lt;br /&gt;
40/27...........680.449 classic wolf fifth&lt;br /&gt;
41/27...........723.197 quadricesimoprimal wolf fifth&lt;br /&gt;
14/9.............764.916 septimal minor sixth&lt;br /&gt;
43/27...........805.653 quadricesimotertial minor sixth&lt;br /&gt;
44/27...........845.453 lesser undecimal neutral sixth&lt;br /&gt;
5/3...............884.359 major sixth, BP sixth&lt;br /&gt;
46/27...........922.409 &lt;span style="background-color: rgba(255,255,255,0);"&gt;vicesimotertial major sixth&lt;/span&gt;&lt;br /&gt;
&lt;span style="background-color: rgba(255,255,255,0);"&gt;47/27...........959.642 quadricesimoseptimal sixth-seventh&lt;/span&gt;&lt;br /&gt;
16/9.............996.090 Pythagorean minor seventh&lt;br /&gt;
49/27...........1031.787 septimal augmented minor seventh&lt;br /&gt;
50/27...........1066.762 octave minus major limma&lt;br /&gt;
17/9.............1101.045 septendecimal major seventh&lt;br /&gt;
52/27...........1134.663 octave minus 26th partial chroma&lt;br /&gt;
53/27...........1167.6395 octave minus quincesimotertial diesis&lt;br /&gt;
2/1...............1200.000 octave&lt;br /&gt;
55/27...........1231.767 55th partial chroma + 1 octave&lt;br /&gt;
56/27...........12&lt;span style="background-color: rgba(255,255,255,0);"&gt;62.961 septimal third tone + 1 octave&lt;/span&gt;&lt;br /&gt;
19/9.............1293.603 undevicesimal semitone +1 octave&lt;br /&gt;
58/27&lt;span style="background-color: rgba(255,255,255,0);"&gt;...........1323.721 undetrigesimal augmented semitone + 1 octave&lt;/span&gt;&lt;br /&gt;
59/27...........1353.307 undesexagesimal neutral ninth&lt;br /&gt;
20/9.............1382.404 classical major ninth&lt;br /&gt;
61/27...........1411.020 sexacesimoprimal major ninth&lt;br /&gt;
&lt;span style="background-color: rgba(255,255,255,0);"&gt;62/27...........1439.171 tricesimoprimal maximal ninth&lt;/span&gt;&lt;br /&gt;
7/3...............1466.871 minimal tenth, BP tenth&lt;br /&gt;
64/27...........1494.135 &lt;span style="background-color: rgba(255,255,255,0);"&gt;Pythagorean minor tenth&lt;/span&gt;&lt;br /&gt;
65/27...........1520.976 65th partial minor tenth&lt;br /&gt;
22/9.............1547.408 lesser undecimal neutral tenth&lt;br /&gt;
67/27...........1573.442 &lt;span style="background-color: rgba(255,255,255,0);"&gt;sexacesimoseptimal perde segah + 1 octave&lt;/span&gt;&lt;br /&gt;
&lt;span style="background-color: rgba(255,255,255,0);"&gt;68/27...........1599.09 quasi-equal tempered major tenth&lt;/span&gt;&lt;br /&gt;
&lt;br /&gt;
23/9.............1624.364 vicesimotertial major tenth&lt;br /&gt;
70/27...........164&lt;span style="background-color: rgba(255,255,255,0);"&gt;9.275 3-5-7 tenth-eleventh&lt;/span&gt;&lt;br /&gt;
&lt;span style="background-color: rgba(255,255,255,0);"&gt;71/27...........1673.8315 septuacesimoprimal tenth-eleventh&lt;/span&gt;&lt;br /&gt;
&lt;br /&gt;
8/3...............1698.045 perfect 11th&lt;br /&gt;
73/27...........1721.9245 &lt;span style="background-color: rgba(255,255,255,0);"&gt;septuacesimotertial wolf eleventh&lt;/span&gt;&lt;br /&gt;
&lt;span style="background-color: rgba(255,255,255,0);"&gt;74/27...........1745.479 tricesimoseptimal augmented eleventh&lt;/span&gt;&lt;br /&gt;
&lt;br /&gt;
25/9.............1768.717 classic augmented eleventh, BP twelfth&lt;br /&gt;
76/27...........17&lt;span style="background-color: rgba(255,255,255,0);"&gt;91.648 undevicesimal tritone + 1 octave&lt;/span&gt;&lt;br /&gt;
&lt;span style="background-color: rgba(255,255,255,0);"&gt;77/27...........1814.279 7-11 tritone + 1 octave&lt;/span&gt;&lt;br /&gt;
26/9.............1836.618 tridecimal &lt;span style="background-color: rgba(255,255,255,0);"&gt;diminished twelfth&lt;/span&gt;&lt;br /&gt;
79/27...........1858.672 undeoctogesimal &lt;span style="background-color: rgba(255,255,255,0);"&gt;diminished twelfth&lt;/span&gt;&lt;br /&gt;
80/27...........18&lt;span style="background-color: rgba(255,255,255,0);"&gt;80.449 classic wolf twelfth&lt;/span&gt;&lt;br /&gt;
3/1...............1901.955 tritave&lt;br /&gt;
&lt;br /&gt;
--&lt;br /&gt;
&lt;br /&gt;
Other useful tritave based intervals: (to be filled in as people see fit)&lt;/body&gt;&lt;/html&gt;</pre></div>

Latest revision as of 10:08, 4 December 2024

The first few tritave reduced harmonics, for the sake of convenient access. Feel free to add higher limit ones like 29/27. I don't personally see that they're needed at this stage in musical development but someday they will be.

1/1...............0.000 unison, perfect prime

28/27...........62.961 septimal third tone

29/27...........123.721 undetrigesimal augmented semitone

10/9.............182.404 minor whole tone

31/27...........239.171 tricesimoprimal major whole tone

32/27...........294.135 Pythagorean minor third

11/9.............347.408 lesser undecimal neutral third

34/27...........399.09 quasi-equal tempered major third

35/27...........449.275 5-7 third-fourth

4/3...............498.045 perfect fourth

37/27...........545.479 tricesimoseptimal augmented fourth

38/27...........591.648 undevicesimal tritone

13/9.............636.618 tridecimal diminished fifth

40/27...........680.449 classic wolf fifth

41/27...........723.197 quadricesimoprimal wolf fifth

14/9.............764.916 septimal minor sixth

43/27...........805.653 quadricesimotertial minor sixth

44/27...........845.453 lesser undecimal neutral sixth

5/3...............884.359 major sixth, BP sixth

46/27...........922.409 vicesimotertial major sixth

47/27...........959.642 quadricesimoseptimal sixth-seventh

16/9.............996.090 Pythagorean minor seventh

49/27...........1031.787 septimal augmented minor seventh

50/27...........1066.762 octave minus major limma

17/9.............1101.045 septendecimal major seventh

52/27...........1134.663 octave minus 26th partial chroma

53/27...........1167.6395 octave minus quincesimotertial diesis

2/1...............1200.000 octave

55/27...........1231.767 55th partial chroma + 1 octave

56/27...........1262.961 septimal third tone + 1 octave

19/9.............1293.603 undevicesimal semitone +1 octave

58/27...........1323.721 undetrigesimal augmented semitone + 1 octave

59/27...........1353.307 undesexagesimal neutral ninth

20/9.............1382.404 classical major ninth

61/27...........1411.020 sexacesimoprimal major ninth

62/27...........1439.171 tricesimoprimal maximal ninth

7/3...............1466.871 minimal tenth, BP tenth

64/27...........1494.135 Pythagorean minor tenth

65/27...........1520.976 65th partial minor tenth

22/9.............1547.408 lesser undecimal neutral tenth

67/27...........1573.442 sexacesimoseptimal perde segah + 1 octave

68/27...........1599.09 quasi-equal tempered major tenth

23/9.............1624.364 vicesimotertial major tenth

70/27...........1649.275 3-5-7 tenth-eleventh

71/27...........1673.8315 septuacesimoprimal tenth-eleventh

8/3...............1698.045 perfect 11th

73/27...........1721.9245 septuacesimotertial wolf eleventh

74/27...........1745.479 tricesimoseptimal augmented eleventh

25/9.............1768.717 classic augmented eleventh, BP twelfth

76/27...........1791.648 undevicesimal tritone + 1 octave

77/27...........1814.279 7-11 tritone + 1 octave

26/9.............1836.618 tridecimal diminished twelfth

79/27...........1858.672 undeoctogesimal diminished twelfth

80/27...........1880.449 classic wolf twelfth

3/1...............1901.955 tritave

--

Other useful tritave based intervals: (to be filled in as people see fit)

See also

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