Revision as of 00:00, 17 July 2018

The 5-limit consists of all justly tuned intervals whose numerators and denominators are both products of the primes 2, 3, and 5; these are sometimes called regular numbers. Some examples of 5-limit intervals are 5/4, 6/5, 10/9 and 81/80. The 5 odd-limit consists of intervals whose numerators and denominators, when all factors of two have been removed, are less than or equal to 5. Reduced to an octave, these are the ratios 1/1, 6/5, 5/4, 4/3, 3/2, 8/5, 5/3, 2/1. Approximating these ratios has been basic to Western common-practice music since the Renaissance.

The octave equivalence classes of 5-limit intervals can usefully be depicted on a lattice diagram, either as a hexagonal lattice or as a square lattice; this can be done automatically by Scala. If the intervals are depicted with maximum symmetry as a hexagonal lattice, then the corresponding 5-limit triads define a hexagonal tiling.

EDOs which do relatively well in approximating the 5-limit are 2edo, 3edo, 7edo, 9edo, 10edo, 12edo, 19edo, 22edo, 31edo, 34edo, 53edo, 118edo and 289edo.

Syntonic Comma Pairs

A significant interval in 5-limit JI is 81/80, the syntonic comma or Didymus' comma, which measures about 21.5¢. Although it rarely appears as an interval in a scale, it represents the difference between many 5-limit intervals and a nearby 3-limit (Pythagorean) interval. 81/80 is tempered out in 12edo, meantone, and many other related systems, meaning that those 5- and 3-limit distinctions are obliterated and one interval stands in for each. Living in a largely 12edo musical culture from birth, we are not accustomed to distinguishing two different major thirds, two different minor seconds, etc. Below is a list of some common intervals involving 3 and 5 which are distinguished by 81/80. The next column modifies intervals by another 81/80, for a total of 6561/6400 (43 cents). Bold fractions are simplest for this interval category.

3-limit interval		interval category		\|5-limit interval (81/80)		\|Another 5-limit (6561/6400)
ratio	cents value			ratio	cents value	ratio	cents value
1/1	0.000	unison	C	81/80	21.506	6561/6400	43.013
2187/2048	113.685	aug. unison	C#	135/128	92.179	25/24	70.672
256/243	90.225	minor 2nd	Db	16/15	111.731	27/25	133.238
9/8	203.910	major 2nd	D	10/9	182.404	800/729	160.897
19683/16384	317.595	aug. 2nd	D#	1215/1024	296.089	75/64	274.582
32/27	294.135	minor 3rd	Eb	6/5	315.641	243/200	337.148
81/64	407.820	major 3rd	E	5/4	386.314	100/81	364.807
8192/6561	384.360	dim. fourth	Fb	512/405	405.866	32/25	427.373
4/3	498.045	fourth	F	27/20	519.551	2187/1600	541.058
729/512	611.730	aug. fourth	F#	45/32	590.224	25/18	568.717
1024/729	588.270	dim. fifth	Gb	64/45	609.776	36/25	631.283
3/2	701.955	fifth	G	40/27	680.449	3200/2187	658.942
6561/4096	815.640	aug. fifth	G#	405/256	794.134	25/16	772.627
128/81	792.180	minor 6th	Ab	8/5	813.686	81/50	835.193
27/16	905.865	major 6th	A	5/3	884.359	400/243	862.852
32768/19683	882.405	dim. 7th	Bbb	2048/1215	903.911	128/75	925.418
16/9	996.090	minor 7th	Bb	9/5	1017.596	729/400	1039.103
243/128	1109.775	major 7th	B	15/8	1088.269	50/27	1066.762
4096/2187	1086.315	dim. octave	Cb	256/135	1107.821	48/25	1129.328
2/1	1200.000	octave	C	160/81	1178.494	12800/6561	1156.987

It is important to note that 5-limit music does not mean favoring intervals of 5 over intervals of 3. It means allowing for both 3's and 5's in generating harmonic material, and so it is an interplay between both. The 5-limit includes the 3-limit -- a work in 5-limit JI will utilize intervals from both sides of the chart above.

See Harmonic Limit

Music

Duodene2 by Chris Vaisvil

Ariel's 12-tone JI by Chris Vaisvil

The Ballad of Jed Clampett by Paul Henning

Do Wah Diddy Diddy by Barry and Greenwich

Symphony 4, first movement by William Copper

Magnificat by William Copper

Catch for Woodwin Quintet by William Copper

5-limit: Difference between revisions

Revision as of 00:00, 17 July 2018

Syntonic Comma Pairs

Music

Navigation menu

@@ Line 1: / Line 1: @@
-<h2>IMPORTED REVISION FROM WIKISPACES</h2>
+The ''5-limit'' consists of all [[Just_intonation|justly tuned]] intervals whose numerators and denominators are both products of the primes 2, 3, and 5; these are sometimes called [http://en.wikipedia.org/wiki/Regular_number regular numbers]. Some examples of 5-limit intervals are [[5/4|5/4]], [[6/5|6/5]], [[10/9|10/9]] and [[81/80|81/80]]. The 5 odd-limit consists of intervals whose numerators and denominators, when all factors of two have been removed, are less than or equal to 5. Reduced to an octave, these are the ratios 1/1, 6/5, 5/4, [[4/3|4/3]], [[3/2|3/2]], [[8/5|8/5]], [[5/3|5/3]], 2/1. Approximating these ratios has been basic to Western common-practice music since the Renaissance.
-This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:PiotrGrochowski|PiotrGrochowski]] and made on <tt>2016-10-11 09:49:16 UTC</tt>.<br>
-: The original revision id was <tt>594912366</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 //5-limit// consists of all [[Just intonation|justly tuned]] intervals whose numerators and denominators are both products of the primes 2, 3, and 5; these are sometimes called [[http://en.wikipedia.org/wiki/Regular_number|regular numbers]]. Some examples of 5-limit intervals are [[5_4|5/4]], [[6_5|6/5]], [[10_9|10/9]] and [[81_80|81/80]]. The 5 odd-limit consists of intervals whose numerators and denominators, when all factors of two have been removed, are less than or equal to 5. Reduced to an octave, these are the ratios 1/1, 6/5, 5/4, [[4_3|4/3]], [[3_2|3/2]], [[8_5|8/5]], [[5_3|5/3]], 2/1. Approximating these ratios has been basic to Western common-practice music since the Renaissance.
-The octave equivalence classes of 5-limit intervals can usefully be depicted on a lattice diagram, either as a [[http://en.wikipedia.org/wiki/Hexagonal_lattice|hexagonal lattice]] or as a [[http://en.wikipedia.org/wiki/Square_lattice|square lattice]]; this can be done automatically by [[http://www.huygens-fokker.org/scala/|Scala]]. If the intervals are depicted with maximum symmetry as a hexagonal lattice, then the corresponding 5-limit triads define a [[http://en.wikipedia.org/wiki/Hexagonal_tiling|hexagonal tiling]].
+The octave equivalence classes of 5-limit intervals can usefully be depicted on a lattice diagram, either as a [http://en.wikipedia.org/wiki/Hexagonal_lattice hexagonal lattice] or as a [http://en.wikipedia.org/wiki/Square_lattice square lattice]; this can be done automatically by [http://www.huygens-fokker.org/scala/ Scala]. If the intervals are depicted with maximum symmetry as a hexagonal lattice, then the corresponding 5-limit triads define a [http://en.wikipedia.org/wiki/Hexagonal_tiling hexagonal tiling].
-[[EDO]]s which do relatively well in approximating the 5-limit are [[2edo]], [[3edo]], [[7edo]], [[9edo]], [[10edo]], [[12edo]], [[19edo]], [[22edo]], [[31edo]], [[34edo]], [[53edo]], [[118edo]] and [[289edo]].
+[[EDO|EDO]]s which do relatively well in approximating the 5-limit are [[2edo|2edo]], [[3edo|3edo]], [[7edo|7edo]], [[9edo|9edo]], [[10edo|10edo]], [[12edo|12edo]], [[19edo|19edo]], [[22edo|22edo]], [[31edo|31edo]], [[34edo|34edo]], [[53edo|53edo]], [[118edo|118edo]] and [[289edo|289edo]].
 ==Syntonic Comma Pairs==
-A significant interval in 5-limit JI is [[81_80|81/80]], the syntonic comma or Didymus' comma, which measures about 21.5¢. Although it rarely appears as an interval in a scale, it represents the difference between many 5-limit intervals and a nearby [[3-limit]] (Pythagorean) interval. 81/80 is tempered out in [[12edo]], [[meantone]], and many other related systems, meaning that those 5- and 3-limit distinctions are obliterated and one interval stands in for each. Living in a largely [[12edo]] musical culture from birth, we are not accustomed to distinguishing two different major thirds, two different minor seconds, etc. Below is a list of some common intervals involving 3 and 5 which are distinguished by 81/80. The next column modifies intervals by another 81/80, for a total of 6561/6400 (43 cents). **Bold** fractions are simplest for this interval category.
+A significant interval in 5-limit JI is [[81/80|81/80]], the syntonic comma or Didymus' comma, which measures about 21.5¢. Although it rarely appears as an interval in a scale, it represents the difference between many 5-limit intervals and a nearby [[3-limit|3-limit]] (Pythagorean) interval. 81/80 is tempered out in [[12edo|12edo]], [[Meantone|meantone]], and many other related systems, meaning that those 5- and 3-limit distinctions are obliterated and one interval stands in for each. Living in a largely [[12edo|12edo]] musical culture from birth, we are not accustomed to distinguishing two different major thirds, two different minor seconds, etc. Below is a list of some common intervals involving 3 and 5 which are distinguished by 81/80. The next column modifies intervals by another 81/80, for a total of 6561/6400 (43 cents). '''Bold''' fractions are simplest for this interval category.
-||||~ 3-limit interval ||||~ interval category ||||~ |5-limit interval (81/80) ||||~ |Another 5-limit (6561/6400) ||
+{| class="wikitable"
-||~ ratio ||~ cents value ||~   ||~   ||~ ratio ||~ cents value ||~ ratio ||~ cents value ||
+|-
-|| **[[1_1|1/1]]** || **0.000** || unison || C || [[81_80|81/80]] || 21.506 || [[6561_6400|6561/6400]] || 43.013 ||
+! colspan="2" | 3-limit interval
-|| [[2187_2048|2187/2048]] || 113.685 || aug. unison || C# || [[135_128|135/128]] || 92.179 || **[[25_24|25/24]]** || **70.672** ||
+! colspan="2" | interval category
-|| [[256_243|256/243]] || 90.225 || minor 2nd || Db || **[[16_15|16/15]]** || **111.731** || [[27_25|27/25]] || 133.238 ||
+! colspan="2" | |5-limit interval (81/80)
-|| **[[9_8|9/8]]** || **203.910** || major 2nd || D || [[10_9|10/9]] || 182.404 || [[800_729|800/729]] || 160.897 ||
+! colspan="2" | |Another 5-limit (6561/6400)
-|| [[19683_16384|19683/16384]] || 317.595 || aug. 2nd || D# || [[1215_1024|1215/1024]] || 296.089 || **[[75_64|75/64]]** || **274.582** ||
+|-
-|| [[32_27|32/27]] || 294.135 || minor 3rd || Eb || **[[6_5|6/5]]** || **315.641** || [[243_200|243/200]] || 337.148 ||
+! | ratio
-|| [[81_64|81/64]] || 407.820 || major 3rd || E || **[[5_4|5/4]]** || **386.314** || [[100_81|100/81]] || 364.807 ||
+! | cents value
-|| [[8192_6561|8192/6561]] || 384.360 || dim. fourth || Fb || [[512_405|512/405]] || 405.866 || **[[32_25|32/25]]** || **427.373** ||
+! |
-|| **[[4_3|4/3]]** || **498.045** || fourth || F || [[27_20|27/20]] || 519.551 || [[2187_1600|2187/1600]] || 541.058 ||
+! |
-|| [[729_512|729/512]] || 611.730 || aug. fourth || F# || [[45_32|45/32]] || 590.224 || **[[25_18|25/18]]** || **568.717** ||
+! | ratio
-|| [[1024_729|1024/729]] || 588.270 || dim. fifth || Gb || [[64_45|64/45]] || 609.776 || **[[36_25|36/25]]** || **631.283** ||
+! | cents value
-|| **[[3_2|3/2]]** || **701.955** || fifth || G || [[40_27|40/27]] || 680.449 || [[3200_2187|3200/2187]] || 658.942 ||
+! | ratio
-|| [[6561_4096|6561/4096]] || 815.640 || aug. fifth || G# || [[405_256|405/256]] || 794.134 || **[[25_16|25/16]]** || **772.627** ||
+! | cents value
-|| [[128_81|128/81]] || 792.180 || minor 6th || Ab || **[[8_5|8/5]]** || **813.686** || [[81_50|81/50]] || 835.193 ||
+|-
-|| [[27_16|27/16]] || 905.865 || major 6th || A || **[[5_3|5/3]]** || **884.359** || [[400_243|400/243]] || 862.852 ||
+| | '''[[1/1|1/1]]'''
-|| [[32768_19683|32768/19683]] || 882.405 || dim. 7th || Bbb || [[2048_1215|2048/1215]] || 903.911 || **[[128_75|128/75]]** || **925.418** ||
+| | '''0.000'''
-|| [[16_9|16/9]] || 996.090 || minor 7th || Bb || **[[9_5|9/5]]** || **1017.596** || [[729_400|729/400]] || 1039.103 ||
+| | unison
-|| [[243_128|243/128]] || 1109.775 || major 7th || B || **[[15_8|15/8]]** || **1088.269** || [[50_27|50/27]] || 1066.762 ||
+| | C
-|| [[4096_2187|4096/2187]] || 1086.315 || dim. octave || Cb || [[256_135|256/135]] || 1107.821 || **[[48_25|48/25]]** || **1129.328** ||
+| | [[81/80|81/80]]
-|| **[[2_1|2/1]]** || **1200.000** || octave || C || [[160_81|160/81]] || 1178.494 || [[12800_6561|12800/6561]] || 1156.987 ||
+| | 21.506
+| | [[6561/6400|6561/6400]]
+| | 43.013
+|-
+| | [[2187/2048|2187/2048]]
+| | 113.685
+| | aug. unison
+| | C#
+| | [[135/128|135/128]]
+| | 92.179
+| | '''[[25/24|25/24]]'''
+| | '''70.672'''
+|-
+| | [[256/243|256/243]]
+| | 90.225
+| | minor 2nd
+| | Db
+| | '''[[16/15|16/15]]'''
+| | '''111.731'''
+| | [[27/25|27/25]]
+| | 133.238
+|-
+| | '''[[9/8|9/8]]'''
+| | '''203.910'''
+| | major 2nd
+| | D
+| | [[10/9|10/9]]
+| | 182.404
+| | [[800/729|800/729]]
+| | 160.897
+|-
+| | [[19683/16384|19683/16384]]
+| | 317.595
+| | aug. 2nd
+| | D#
+| | [[1215/1024|1215/1024]]
+| | 296.089
+| | '''[[75/64|75/64]]'''
+| | '''274.582'''
+|-
+| | [[32/27|32/27]]
+| | 294.135
+| | minor 3rd
+| | Eb
+| | '''[[6/5|6/5]]'''
+| | '''315.641'''
+| | [[243/200|243/200]]
+| | 337.148
+|-
+| | [[81/64|81/64]]
+| | 407.820
+| | major 3rd
+| | E
+| | '''[[5/4|5/4]]'''
+| | '''386.314'''
+| | [[100/81|100/81]]
+| | 364.807
+|-
+| | [[8192/6561|8192/6561]]
+| | 384.360
+| | dim. fourth
+| | Fb
+| | [[512/405|512/405]]
+| | 405.866
+| | '''[[32/25|32/25]]'''
+| | '''427.373'''
+|-
+| | '''[[4/3|4/3]]'''
+| | '''498.045'''
+| | fourth
+| | F
+| | [[27/20|27/20]]
+| | 519.551
+| | [[2187/1600|2187/1600]]
+| | 541.058
+|-
+| | [[729/512|729/512]]
+| | 611.730
+| | aug. fourth
+| | F#
+| | [[45/32|45/32]]
+| | 590.224
+| | '''[[25/18|25/18]]'''
+| | '''568.717'''
+|-
+| | [[1024/729|1024/729]]
+| | 588.270
+| | dim. fifth
+| | Gb
+| | [[64/45|64/45]]
+| | 609.776
+| | '''[[36/25|36/25]]'''
+| | '''631.283'''
+|-
+| | '''[[3/2|3/2]]'''
+| | '''701.955'''
+| | fifth
+| | G
+| | [[40/27|40/27]]
+| | 680.449
+| | [[3200/2187|3200/2187]]
+| | 658.942
+|-
+| | [[6561/4096|6561/4096]]
+| | 815.640
+| | aug. fifth
+| | G#
+| | [[405/256|405/256]]
+| | 794.134
+| | '''[[25/16|25/16]]'''
+| | '''772.627'''
+|-
+| | [[128/81|128/81]]
+| | 792.180
+| | minor 6th
+| | Ab
+| | '''[[8/5|8/5]]'''
+| | '''813.686'''
+| | [[81/50|81/50]]
+| | 835.193
+|-
+| | [[27/16|27/16]]
+| | 905.865
+| | major 6th
+| | A
+| | '''[[5/3|5/3]]'''
+| | '''884.359'''
+| | [[400/243|400/243]]
+| | 862.852
+|-
+| | [[32768/19683|32768/19683]]
+| | 882.405
+| | dim. 7th
+| | Bbb
+| | [[2048/1215|2048/1215]]
+| | 903.911
+| | '''[[128/75|128/75]]'''
+| | '''925.418'''
+|-
+| | [[16/9|16/9]]
+| | 996.090
+| | minor 7th
+| | Bb
+| | '''[[9/5|9/5]]'''
+| | '''1017.596'''
+| | [[729/400|729/400]]
+| | 1039.103
+|-
+| | [[243/128|243/128]]
+| | 1109.775
+| | major 7th
+| | B
+| | '''[[15/8|15/8]]'''
+| | '''1088.269'''
+| | [[50/27|50/27]]
+| | 1066.762
+|-
+| | [[4096/2187|4096/2187]]
+| | 1086.315
+| | dim. octave
+| | Cb
+| | [[256/135|256/135]]
+| | 1107.821
+| | '''[[48/25|48/25]]'''
+| | '''1129.328'''
+|-
+| | '''[[2/1|2/1]]'''
+| | '''1200.000'''
+| | octave
+| | C
+| | [[160/81|160/81]]
+| | 1178.494
+| | [[12800/6561|12800/6561]]
+| | 1156.987
+|}
-It is important to note that 5-limit music does not mean favoring intervals of 5 over intervals of 3. It means allowing for //both// 3's and 5's in generating harmonic material, and so it is an interplay between both. The 5-limit //includes// the 3-limit -- a work in 5-limit JI will utilize intervals from both sides of the chart above.
+It is important to note that 5-limit music does not mean favoring intervals of 5 over intervals of 3. It means allowing for ''both'' 3's and 5's in generating harmonic material, and so it is an interplay between both. The 5-limit ''includes'' the 3-limit -- a work in 5-limit JI will utilize intervals from both sides of the chart above.
-See [[Harmonic Limit]]
+See [[Harmonic_Limit|Harmonic Limit]]
 =Music=
-[[http://clones.soonlabel.com/public/micro/just/Duodene/duodene2.mp3|Duodene2]] by [[Chris Vaisvil]]
+[http://clones.soonlabel.com/public/micro/just/Duodene/duodene2.mp3 Duodene2] by [[Chris_Vaisvil|Chris Vaisvil]]
-[[http://micro.soonlabel.com/just/Ariels-JI/ariels-12-tone-ji.mp3|Ariel's 12-tone JI]] by Chris Vaisvil
-[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/5limit/The%20Ballad%20of%20Jed%20Clampett.mp3|The Ballad of Jed Clampett]] by [[http://en.wikipedia.org/wiki/Paul_Henning|Paul Henning]]
-[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/5limit/Do%20Wah%20Diddy.mp3|Do Wah Diddy Diddy]] by [[http://en.wikipedia.org/wiki/Jeff_Barry|Barry]] and [[http://en.wikipedia.org/wiki/Ellie_Greenwich|Greenwich]]
-[[https://soundcloud.com/williamcopper/0511_1|Symphony 4, first movement]] by [[http://www.williamcopper.com|William Copper]]
-[[http://micro.soonlabel.com/gene_ward_smith/Others/Copper/Magnificat0465.mp3|Magnificat]] by [[http://www.williamcopper.com|William Copper]]
-[[http://micro.soonlabel.com/gene_ward_smith/Others/Copper/Catch%20for%20Woodwind%20Quintet-0570.mp3|Catch for Woodwin Quintet]] by [[http://www.hartenshield.com/william_copper.html|William Copper]]</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;5-limit&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The &lt;em&gt;5-limit&lt;/em&gt; consists of all &lt;a class="wiki_link" href="/Just%20intonation"&gt;justly tuned&lt;/a&gt; intervals whose numerators and denominators are both products of the primes 2, 3, and 5; these are sometimes called &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Regular_number" rel="nofollow"&gt;regular numbers&lt;/a&gt;. Some examples of 5-limit intervals are &lt;a class="wiki_link" href="/5_4"&gt;5/4&lt;/a&gt;, &lt;a class="wiki_link" href="/6_5"&gt;6/5&lt;/a&gt;, &lt;a class="wiki_link" href="/10_9"&gt;10/9&lt;/a&gt; and &lt;a class="wiki_link" href="/81_80"&gt;81/80&lt;/a&gt;. The 5 odd-limit consists of intervals whose numerators and denominators, when all factors of two have been removed, are less than or equal to 5. Reduced to an octave, these are the ratios 1/1, 6/5, 5/4, &lt;a class="wiki_link" href="/4_3"&gt;4/3&lt;/a&gt;, &lt;a class="wiki_link" href="/3_2"&gt;3/2&lt;/a&gt;, &lt;a class="wiki_link" href="/8_5"&gt;8/5&lt;/a&gt;, &lt;a class="wiki_link" href="/5_3"&gt;5/3&lt;/a&gt;, 2/1. Approximating these ratios has been basic to Western common-practice music since the Renaissance.&lt;br /&gt;
-&lt;br /&gt;
-The octave equivalence classes of 5-limit intervals can usefully be depicted on a lattice diagram, either as a &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Hexagonal_lattice" rel="nofollow"&gt;hexagonal lattice&lt;/a&gt; or as a &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Square_lattice" rel="nofollow"&gt;square lattice&lt;/a&gt;; this can be done automatically by &lt;a class="wiki_link_ext" href="http://www.huygens-fokker.org/scala/" rel="nofollow"&gt;Scala&lt;/a&gt;. If the intervals are depicted with maximum symmetry as a hexagonal lattice, then the corresponding 5-limit triads define a &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Hexagonal_tiling" rel="nofollow"&gt;hexagonal tiling&lt;/a&gt;.&lt;br /&gt;
-&lt;br /&gt;
-&lt;a class="wiki_link" href="/EDO"&gt;EDO&lt;/a&gt;s which do relatively well in approximating the 5-limit are &lt;a class="wiki_link" href="/2edo"&gt;2edo&lt;/a&gt;, &lt;a class="wiki_link" href="/3edo"&gt;3edo&lt;/a&gt;, &lt;a class="wiki_link" href="/7edo"&gt;7edo&lt;/a&gt;, &lt;a class="wiki_link" href="/9edo"&gt;9edo&lt;/a&gt;, &lt;a class="wiki_link" href="/10edo"&gt;10edo&lt;/a&gt;, &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt;, &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt;, &lt;a class="wiki_link" href="/22edo"&gt;22edo&lt;/a&gt;, &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt;, &lt;a class="wiki_link" href="/34edo"&gt;34edo&lt;/a&gt;, &lt;a class="wiki_link" href="/53edo"&gt;53edo&lt;/a&gt;, &lt;a class="wiki_link" href="/118edo"&gt;118edo&lt;/a&gt; and &lt;a class="wiki_link" href="/289edo"&gt;289edo&lt;/a&gt;.&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-Syntonic Comma Pairs"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Syntonic Comma Pairs&lt;/h2&gt;
- &lt;br /&gt;
-A significant interval in 5-limit JI is &lt;a class="wiki_link" href="/81_80"&gt;81/80&lt;/a&gt;, the syntonic comma or Didymus' comma, which measures about 21.5¢. Although it rarely appears as an interval in a scale, it represents the difference between many 5-limit intervals and a nearby &lt;a class="wiki_link" href="/3-limit"&gt;3-limit&lt;/a&gt; (Pythagorean) interval. 81/80 is tempered out in &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt;, &lt;a class="wiki_link" href="/meantone"&gt;meantone&lt;/a&gt;, and many other related systems, meaning that those 5- and 3-limit distinctions are obliterated and one interval stands in for each. Living in a largely &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt; musical culture from birth, we are not accustomed to distinguishing two different major thirds, two different minor seconds, etc. Below is a list of some common intervals involving 3 and 5 which are distinguished by 81/80. The next column modifies intervals by another 81/80, for a total of 6561/6400 (43 cents). &lt;strong&gt;Bold&lt;/strong&gt; fractions are simplest for this interval category.&lt;br /&gt;
-&lt;br /&gt;
+[http://micro.soonlabel.com/just/Ariels-JI/ariels-12-tone-ji.mp3 Ariel's 12-tone JI] by Chris Vaisvil
-&lt;table class="wiki_table"&gt;
+[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/5limit/The%20Ballad%20of%20Jed%20Clampett.mp3 The Ballad of Jed Clampett] by [http://en.wikipedia.org/wiki/Paul_Henning Paul Henning]
-    &lt;tr&gt;
-        &lt;th colspan="2"&gt;3-limit interval&lt;br /&gt;
-&lt;/th&gt;
-        &lt;th colspan="2"&gt;interval category&lt;br /&gt;
-&lt;/th&gt;
-        &lt;th colspan="2"&gt;|5-limit interval (81/80)&lt;br /&gt;
-&lt;/th&gt;
-        &lt;th colspan="2"&gt;|Another 5-limit (6561/6400)&lt;br /&gt;
-&lt;/th&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;th&gt;ratio&lt;br /&gt;
-&lt;/th&gt;
-        &lt;th&gt;cents value&lt;br /&gt;
-&lt;/th&gt;
-        &lt;th&gt;&lt;br /&gt;
-&lt;/th&gt;
-        &lt;th&gt;&lt;br /&gt;
-&lt;/th&gt;
-        &lt;th&gt;ratio&lt;br /&gt;
-&lt;/th&gt;
-        &lt;th&gt;cents value&lt;br /&gt;
-&lt;/th&gt;
-        &lt;th&gt;ratio&lt;br /&gt;
-&lt;/th&gt;
-        &lt;th&gt;cents value&lt;br /&gt;
-&lt;/th&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;&lt;strong&gt;&lt;a class="wiki_link" href="/1_1"&gt;1/1&lt;/a&gt;&lt;/strong&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;strong&gt;0.000&lt;/strong&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;unison&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;C&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;a class="wiki_link" href="/81_80"&gt;81/80&lt;/a&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;21.506&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;a class="wiki_link" href="/6561_6400"&gt;6561/6400&lt;/a&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;43.013&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;&lt;a class="wiki_link" href="/2187_2048"&gt;2187/2048&lt;/a&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;113.685&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;aug. unison&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;C#&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;a class="wiki_link" href="/135_128"&gt;135/128&lt;/a&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;92.179&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;strong&gt;&lt;a class="wiki_link" href="/25_24"&gt;25/24&lt;/a&gt;&lt;/strong&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;strong&gt;70.672&lt;/strong&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;&lt;a class="wiki_link" href="/256_243"&gt;256/243&lt;/a&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;90.225&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;minor 2nd&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;Db&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;strong&gt;&lt;a class="wiki_link" href="/16_15"&gt;16/15&lt;/a&gt;&lt;/strong&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;strong&gt;111.731&lt;/strong&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;a class="wiki_link" href="/27_25"&gt;27/25&lt;/a&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;133.238&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;&lt;strong&gt;&lt;a class="wiki_link" href="/9_8"&gt;9/8&lt;/a&gt;&lt;/strong&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;strong&gt;203.910&lt;/strong&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;major 2nd&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;D&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;a class="wiki_link" href="/10_9"&gt;10/9&lt;/a&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;182.404&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;a class="wiki_link" href="/800_729"&gt;800/729&lt;/a&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;160.897&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;&lt;a class="wiki_link" href="/19683_16384"&gt;19683/16384&lt;/a&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;317.595&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;aug. 2nd&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;D#&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;a class="wiki_link" href="/1215_1024"&gt;1215/1024&lt;/a&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;296.089&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;strong&gt;&lt;a class="wiki_link" href="/75_64"&gt;75/64&lt;/a&gt;&lt;/strong&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;strong&gt;274.582&lt;/strong&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;&lt;a class="wiki_link" href="/32_27"&gt;32/27&lt;/a&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;294.135&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;minor 3rd&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;Eb&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;strong&gt;&lt;a class="wiki_link" href="/6_5"&gt;6/5&lt;/a&gt;&lt;/strong&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;strong&gt;315.641&lt;/strong&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;a class="wiki_link" href="/243_200"&gt;243/200&lt;/a&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;337.148&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;&lt;a class="wiki_link" href="/81_64"&gt;81/64&lt;/a&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;407.820&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;major 3rd&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;E&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;strong&gt;&lt;a class="wiki_link" href="/5_4"&gt;5/4&lt;/a&gt;&lt;/strong&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;strong&gt;386.314&lt;/strong&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;a class="wiki_link" href="/100_81"&gt;100/81&lt;/a&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;364.807&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;&lt;a class="wiki_link" href="/8192_6561"&gt;8192/6561&lt;/a&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;384.360&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;dim. fourth&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;Fb&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;a class="wiki_link" href="/512_405"&gt;512/405&lt;/a&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;405.866&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;strong&gt;&lt;a class="wiki_link" href="/32_25"&gt;32/25&lt;/a&gt;&lt;/strong&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;strong&gt;427.373&lt;/strong&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;&lt;strong&gt;&lt;a class="wiki_link" href="/4_3"&gt;4/3&lt;/a&gt;&lt;/strong&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;strong&gt;498.045&lt;/strong&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;fourth&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;F&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;a class="wiki_link" href="/27_20"&gt;27/20&lt;/a&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;519.551&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;a class="wiki_link" href="/2187_1600"&gt;2187/1600&lt;/a&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;541.058&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;&lt;a class="wiki_link" href="/729_512"&gt;729/512&lt;/a&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;611.730&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;aug. fourth&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;F#&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;a class="wiki_link" href="/45_32"&gt;45/32&lt;/a&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;590.224&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;strong&gt;&lt;a class="wiki_link" href="/25_18"&gt;25/18&lt;/a&gt;&lt;/strong&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;strong&gt;568.717&lt;/strong&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;&lt;a class="wiki_link" href="/1024_729"&gt;1024/729&lt;/a&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;588.270&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;dim. fifth&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;Gb&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;a class="wiki_link" href="/64_45"&gt;64/45&lt;/a&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;609.776&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;strong&gt;&lt;a class="wiki_link" href="/36_25"&gt;36/25&lt;/a&gt;&lt;/strong&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;strong&gt;631.283&lt;/strong&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;&lt;strong&gt;&lt;a class="wiki_link" href="/3_2"&gt;3/2&lt;/a&gt;&lt;/strong&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;strong&gt;701.955&lt;/strong&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;fifth&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;G&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;a class="wiki_link" href="/40_27"&gt;40/27&lt;/a&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;680.449&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;a class="wiki_link" href="/3200_2187"&gt;3200/2187&lt;/a&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;658.942&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;&lt;a class="wiki_link" href="/6561_4096"&gt;6561/4096&lt;/a&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;815.640&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;aug. fifth&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;G#&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;a class="wiki_link" href="/405_256"&gt;405/256&lt;/a&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;794.134&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;strong&gt;&lt;a class="wiki_link" href="/25_16"&gt;25/16&lt;/a&gt;&lt;/strong&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;strong&gt;772.627&lt;/strong&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;&lt;a class="wiki_link" href="/128_81"&gt;128/81&lt;/a&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;792.180&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;minor 6th&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;Ab&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;strong&gt;&lt;a class="wiki_link" href="/8_5"&gt;8/5&lt;/a&gt;&lt;/strong&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;strong&gt;813.686&lt;/strong&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;a class="wiki_link" href="/81_50"&gt;81/50&lt;/a&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;835.193&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;&lt;a class="wiki_link" href="/27_16"&gt;27/16&lt;/a&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;905.865&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;major 6th&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;A&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;strong&gt;&lt;a class="wiki_link" href="/5_3"&gt;5/3&lt;/a&gt;&lt;/strong&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;strong&gt;884.359&lt;/strong&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;a class="wiki_link" href="/400_243"&gt;400/243&lt;/a&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;862.852&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;&lt;a class="wiki_link" href="/32768_19683"&gt;32768/19683&lt;/a&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;882.405&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;dim. 7th&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;Bbb&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;a class="wiki_link" href="/2048_1215"&gt;2048/1215&lt;/a&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;903.911&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;strong&gt;&lt;a class="wiki_link" href="/128_75"&gt;128/75&lt;/a&gt;&lt;/strong&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;strong&gt;925.418&lt;/strong&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;&lt;a class="wiki_link" href="/16_9"&gt;16/9&lt;/a&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;996.090&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;minor 7th&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;Bb&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;strong&gt;&lt;a class="wiki_link" href="/9_5"&gt;9/5&lt;/a&gt;&lt;/strong&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;strong&gt;1017.596&lt;/strong&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;a class="wiki_link" href="/729_400"&gt;729/400&lt;/a&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;1039.103&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;&lt;a class="wiki_link" href="/243_128"&gt;243/128&lt;/a&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;1109.775&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;major 7th&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;B&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;strong&gt;&lt;a class="wiki_link" href="/15_8"&gt;15/8&lt;/a&gt;&lt;/strong&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;strong&gt;1088.269&lt;/strong&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;a class="wiki_link" href="/50_27"&gt;50/27&lt;/a&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;1066.762&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;&lt;a class="wiki_link" href="/4096_2187"&gt;4096/2187&lt;/a&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;1086.315&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;dim. octave&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;Cb&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;a class="wiki_link" href="/256_135"&gt;256/135&lt;/a&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;1107.821&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;strong&gt;&lt;a class="wiki_link" href="/48_25"&gt;48/25&lt;/a&gt;&lt;/strong&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;strong&gt;1129.328&lt;/strong&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;&lt;strong&gt;&lt;a class="wiki_link" href="/2_1"&gt;2/1&lt;/a&gt;&lt;/strong&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;strong&gt;1200.000&lt;/strong&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;octave&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;C&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;a class="wiki_link" href="/160_81"&gt;160/81&lt;/a&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;1178.494&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;a class="wiki_link" href="/12800_6561"&gt;12800/6561&lt;/a&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;1156.987&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-&lt;/table&gt;
-&lt;br /&gt;
+[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/5limit/Do%20Wah%20Diddy.mp3 Do Wah Diddy Diddy] by [http://en.wikipedia.org/wiki/Jeff_Barry Barry] and [http://en.wikipedia.org/wiki/Ellie_Greenwich Greenwich]
-It is important to note that 5-limit music does not mean favoring intervals of 5 over intervals of 3. It means allowing for &lt;em&gt;both&lt;/em&gt; 3's and 5's in generating harmonic material, and so it is an interplay between both. The 5-limit &lt;em&gt;includes&lt;/em&gt; the 3-limit -- a work in 5-limit JI will utilize intervals from both sides of the chart above.&lt;br /&gt;
-&lt;br /&gt;
+[https://soundcloud.com/williamcopper/0511_1 Symphony 4, first movement] by [http://www.williamcopper.com William Copper]
-See &lt;a class="wiki_link" href="/Harmonic%20Limit"&gt;Harmonic Limit&lt;/a&gt;&lt;br /&gt;
-&lt;br /&gt;
+[http://micro.soonlabel.com/gene_ward_smith/Others/Copper/Magnificat0465.mp3 Magnificat] by [http://www.williamcopper.com William Copper]
-&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Music"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Music&lt;/h1&gt;
- &lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/just/Duodene/duodene2.mp3" rel="nofollow"&gt;Duodene2&lt;/a&gt; by &lt;a class="wiki_link" href="/Chris%20Vaisvil"&gt;Chris Vaisvil&lt;/a&gt;&lt;br /&gt;
+[http://micro.soonlabel.com/gene_ward_smith/Others/Copper/Catch%20for%20Woodwind%20Quintet-0570.mp3 Catch for Woodwin Quintet] by [http://www.hartenshield.com/william_copper.html William Copper]      [[Category:5-limit]]
-&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/just/Ariels-JI/ariels-12-tone-ji.mp3" rel="nofollow"&gt;Ariel's 12-tone JI&lt;/a&gt; by Chris Vaisvil&lt;br /&gt;
+[[Category:example]]
-&lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/5limit/The%20Ballad%20of%20Jed%20Clampett.mp3" rel="nofollow"&gt;The Ballad of Jed Clampett&lt;/a&gt; by &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Paul_Henning" rel="nofollow"&gt;Paul Henning&lt;/a&gt;&lt;br /&gt;
+[[Category:interval]]
-&lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/5limit/Do%20Wah%20Diddy.mp3" rel="nofollow"&gt;Do Wah Diddy Diddy&lt;/a&gt; by &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Jeff_Barry" rel="nofollow"&gt;Barry&lt;/a&gt; and &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Ellie_Greenwich" rel="nofollow"&gt;Greenwich&lt;/a&gt;&lt;br /&gt;
+[[Category:lattice]]
-&lt;a class="wiki_link_ext" href="https://soundcloud.com/williamcopper/0511_1" rel="nofollow"&gt;Symphony 4, first movement&lt;/a&gt; by &lt;a class="wiki_link_ext" href="http://www.williamcopper.com" rel="nofollow"&gt;William Copper&lt;/a&gt;&lt;br /&gt;
+[[Category:limit]]
-&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Copper/Magnificat0465.mp3" rel="nofollow"&gt;Magnificat&lt;/a&gt; by &lt;a class="wiki_link_ext" href="http://www.williamcopper.com" rel="nofollow"&gt;William Copper&lt;/a&gt;&lt;br /&gt;
+[[Category:listen]]
-&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Copper/Catch%20for%20Woodwind%20Quintet-0570.mp3" rel="nofollow"&gt;Catch for Woodwin Quintet&lt;/a&gt; by &lt;a class="wiki_link_ext" href="http://www.hartenshield.com/william_copper.html" rel="nofollow"&gt;William Copper&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
+[[Category:prime_limit]]
+[[Category:rank_3]]

5-limit: Difference between revisions

Revision as of 00:00, 17 July 2018

Syntonic Comma Pairs

Music

Navigation menu

Search