41edo: Difference between revisions
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
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: This revision was by author [[User:MasonGreen1|MasonGreen1]] and made on <tt>2016-04- | : This revision was by author [[User:MasonGreen1|MasonGreen1]] and made on <tt>2016-04-10 02:11:23 UTC</tt>.<br> | ||
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The 41-tET, 41-EDO, or 41-ET, is the scale derived by dividing the octave into 41 equally-sized steps. Each step represents a frequency ratio of 29.268 [[cent]]s, an [[interval]] close in size to [[64_63|64/63]], the [[Septimal comma|septimal comma]]. 41-ET can be seen as a tuning of the //[[Schismatic family#Garibaldi|Garibaldi temperament]]// <ref>[[http://x31eq.com/schismic.htm|"Schismic Temperaments"]] at x31eq.com the website of [[Graham Breed]]</ref> , <ref>[[http://x31eq.com/decimal_lattice.htm|"Lattices with Decimal Notation"]] at x31eq.com</ref> , <ref>[[http://en.wikipedia.org/wiki/Schismatic_temperament|Schismatic temperament]]</ref> the //[[Magic family|Magic temperament]]// <ref>[[http://en.wikipedia.org/wiki/Magic_temperament|Magic temperament]]</ref> and the superkleismic (41&26) temperament. It is the second smallest equal temperament (after [[29edo]]) whose perfect fifth is closer to just intonation than that of [[12edo|12-ET]], and is the seventh [[The Riemann Zeta Function and Tuning#Zeta%20EDO%20lists|zeta integral edo]] after 31; it is not, however, a [[The Riemann Zeta Function and Tuning#Zeta%20EDO%20lists|zeta gap edo]]. This has to do with the fact that it can deal with the [[11-limit]] fairly well, and the [[13-limit]] perhaps close enough for government work, though its [[13_10|13/10]] is 14 cents sharp. Various 13-limit [[magic extensions]] are supported by 41: 13-limit magic, and less successfully necromancy and witchcraft, all merge into one in 41edo tuning. The 41f val provides a superb tuning for sorcery, giving a less-complex version of the 13-limit, and the 41ef val likewise works well for telepathy; telepathy and sorcery merging into one however not in 41edo but in 22edo. | The 41-tET, 41-EDO, or 41-ET, is the scale derived by dividing the octave into 41 equally-sized steps. Each step represents a frequency ratio of 29.268 [[cent]]s, an [[interval]] close in size to [[64_63|64/63]], the [[Septimal comma|septimal comma]]. 41-ET can be seen as a tuning of the //[[Schismatic family#Garibaldi|Garibaldi temperament]]// <ref>[[http://x31eq.com/schismic.htm|"Schismic Temperaments"]] at x31eq.com the website of [[Graham Breed]]</ref> , <ref>[[http://x31eq.com/decimal_lattice.htm|"Lattices with Decimal Notation"]] at x31eq.com</ref> , <ref>[[http://en.wikipedia.org/wiki/Schismatic_temperament|Schismatic temperament]]</ref> the //[[Magic family|Magic temperament]]// <ref>[[http://en.wikipedia.org/wiki/Magic_temperament|Magic temperament]]</ref> and the superkleismic (41&26) temperament. It is the second smallest equal temperament (after [[29edo]]) whose perfect fifth is closer to just intonation than that of [[12edo|12-ET]], and is the seventh [[The Riemann Zeta Function and Tuning#Zeta%20EDO%20lists|zeta integral edo]] after 31; it is not, however, a [[The Riemann Zeta Function and Tuning#Zeta%20EDO%20lists|zeta gap edo]]. This has to do with the fact that it can deal with the [[11-limit]] fairly well, and the [[13-limit]] perhaps close enough for government work, though its [[13_10|13/10]] is 14 cents sharp. Various 13-limit [[magic extensions]] are supported by 41: 13-limit magic, and less successfully necromancy and witchcraft, all merge into one in 41edo tuning. The 41f val provides a superb tuning for sorcery, giving a less-complex version of the 13-limit, and the 41ef val likewise works well for telepathy; telepathy and sorcery merging into one however not in 41edo but in 22edo. | ||
41edo is consistent in the 15 odd limit. | 41edo is consistent in the 15 odd limit. In fact, //all// of its intervals between 100 and 1100 cents in size are 15-odd-limit consonances. (In comparison, [[31edo]] is only consistent up to the 11-limit, and the intervals 12/31 and 19/31 have no 11-limit approximations). | ||
41-ET forms the foundation of the [[http://www.h-pi.com/theory/huntsystem1.html|H-System]], which uses the scale degrees of 41-ET as the basic [[13-limit]] intervals requiring fine tuning +/- 1 [[http://www.h-pi.com/theory/huntsystem2.html|average JND]] from the 41-ET circle in [[205edo]]. | 41-ET forms the foundation of the [[http://www.h-pi.com/theory/huntsystem1.html|H-System]], which uses the scale degrees of 41-ET as the basic [[13-limit]] intervals requiring fine tuning +/- 1 [[http://www.h-pi.com/theory/huntsystem2.html|average JND]] from the 41-ET circle in [[205edo]]. | ||
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=Intervals= | =Intervals= | ||
||~ degrees of 41edo ||~ cents value ||~ Approximate Ratios in the [[11-limit]] ||~ Andrew's solfege syllable ||~ generator for ||~ some MOS and MODMOS Scales available || | ||~ degrees of 41edo ||~ cents value ||~ Approximate Ratios in the [[11-limit]] ||~ Proposed names ||~ Andrew's solfege syllable ||~ generator for ||~ some MOS and MODMOS Scales available || | ||
|| 0 || 0.00 || [[1_1|1/1]] || do || || || | || 0 || 0.00 || [[1_1|1/1]] || Unison || do || || || | ||
|| 1 || 29.27 || [[81_80|81/80]] || di || || || | || 1 || 29.27 || [[81_80|81/80]] || Red unison || di || || || | ||
|| 2 || 58.54 || [[25_24|25/24]], [[28_27|28/27]], [[33_32|33/32]] || ro || [[Hemimiracle]] || || | || 2 || 58.54 || [[25_24|25/24]], [[28_27|28/27]], [[33_32|33/32]] || Blue minor second || ro || [[Hemimiracle]] || || | ||
|| 3 || 87.80 || [[21_20|21/20]], [[22_21|22/21]] || rih || 88cET (approx) / [[octacot]] || || | || 3 || 87.80 || [[21_20|21/20]], [[22_21|22/21]] || Gray minor second || rih || 88cET (approx) / [[octacot]] || || | ||
|| 4 || 117.07 || [[16_15|16/15]], [[15_14|15/14]] || ra || [[Miracle]] || || | || 4 || 117.07 || [[16_15|16/15]], [[15_14|15/14]] || Red minor second || ra || [[Miracle]] || || | ||
|| 5 || 146.34 || [[12_11|12/11]] || ru || [[Bohlen-Pierce]]/[[bohpier]] || || | || 5 || 146.34 || [[12_11|12/11]] || Neutral second || ru || [[Bohlen-Pierce]]/[[bohpier]] || || | ||
|| 6 || 175.61 || [[10_9|10/9]], [[11_10|11/10]] || reh || [[Tetracot]]/[[bunya]]/[[monkey]] || 13-tone MOS: 1 5 1 5 1 5 1 5 5 1 5 1 5 || | || 6 || 175.61 || [[10_9|10/9]], [[11_10|11/10]] || Blue major second || reh || [[Tetracot]]/[[bunya]]/[[monkey]] || 13-tone MOS: 1 5 1 5 1 5 1 5 5 1 5 1 5 || | ||
|| 7 || 204.88 || [[9_8|9/8]] || re || [[Baldy]] || 11-tone MOS: 6 1 6 6 1 6 1 6 1 6 1 || | || 7 || 204.88 || [[9_8|9/8]] || Gray major second || re || [[Baldy]] || 11-tone MOS: 6 1 6 6 1 6 1 6 1 6 1 || | ||
|| 8 || 234.15 || [[8_7|8/7]] || ri || [[Rodan]]/[[guiron]] || 11-tone MOS: 7 1 7 1 7 1 7 1 1 7 1 || | || 8 || 234.15 || [[8_7|8/7]] || Red major second || ri || [[Rodan]]/[[guiron]] || 11-tone MOS: 7 1 7 1 7 1 7 1 1 7 1 || | ||
|| 9 || 263.41 || [[7_6|7/6]], [[32_25|32/25]] || ma || [[Septimin]] || 9-tone MOS: 5 4 5 5 4 5 4 5 4 || | || 9 || 263.41 || [[7_6|7/6]], [[32_25|32/25]] || Blue minor third || ma || [[Septimin]] || 9-tone MOS: 5 4 5 5 4 5 4 5 4 || | ||
|| 10 || 292.68 || [[32_27|32/27]] || meh || [[Quasitemp]] || || | || 10 || 292.68 || [[32_27|32/27]] || Gray minor third || meh || [[Quasitemp]] || || | ||
|| 11 || 321.95 || [[6_5|6/5]] || me || [[Superkleismic]] || 11-tone MOS: 5 3 5 3 3 5 3 3 5 3 3 || | || 11 || 321.95 || [[6_5|6/5]] || Red minor third || me || [[Superkleismic]] || 11-tone MOS: 5 3 5 3 3 5 3 3 5 3 3 || | ||
|| 12 || 351.22 || [[11_9|11/9]],[[27_22|27/22]] || | || 12 || 351.22 || [[11_9|11/9]],[[27_22|27/22]] || Neutral third || mu || [[Hemififths]]/[[karadeniz]] || 10-tone MOS: 5 2 5 5 2 5 5 5 2 5 || | ||
|| 13 || 380.49 || [[5_4|5/4]] || mi || [[Magic]]/[[witchcraft]] || 10-tone MOS: 2 9 2 2 9 2 2 9 2 2 || | || 13 || 380.49 || [[5_4|5/4]] || Blue major third || mi || [[Magic]]/[[witchcraft]] || 10-tone MOS: 2 9 2 2 9 2 2 9 2 2 || | ||
|| 14 || 409.76 || [[14_11|14/11]], [[81_64|81/64]] || maa || [[Hocus]] || || | || 14 || 409.76 || [[14_11|14/11]], [[81_64|81/64]] || Gray major third || maa || [[Hocus]] || || | ||
|| 15 || 439.02 || [[9_7|9/7]] || mo || || 11-tone MOS: 4 3 4 4 4 3 4 4 3 4 4 || | || 15 || 439.02 || [[9_7|9/7]] || Red major third || mo || || 11-tone MOS: 4 3 4 4 4 3 4 4 3 4 4 || | ||
|| 16 || 468.29 || [[21_16|21/16]] || fe || [[Barbad]] || || | || 16 || 468.29 || [[21_16|21/16]] || Blue fourth || fe || [[Barbad]] || || | ||
|| 17 || 497.56 || [[4_3|4/3]] || fa || [[Schismatic]] ([[helmholtz]], [[Garibaldi temperament|garibaldi]], [[cassandra]]) || || | || 17 || 497.56 || [[4_3|4/3]] || Perfect fourth || fa || [[Schismatic]] ([[helmholtz]], [[Garibaldi temperament|garibaldi]], [[cassandra]]) || || | ||
|| 18 || 526.83 || [[15_11|15/11]], [[27_20|27/20]] || fih || [[Trismegistus]] || 9-tone MOS: 5 5 3 5 5 5 5 3 5 || | || 18 || 526.83 || [[15_11|15/11]], [[27_20|27/20]] || Red fourth || fih || [[Trismegistus]] || 9-tone MOS: 5 5 3 5 5 5 5 3 5 || | ||
|| 19 || 556.10 || [[11_8|11/8]] || fu || || || | || 19 || 556.10 || [[11_8|11/8]] || Blue minor tritone || fu || || || | ||
|| 20 || 585.37 || [[7_5|7/5]] || fi || [[Pluto]] || || | || 20 || 585.37 || [[7_5|7/5]] || Minor tritone / diminished fifth || fi || [[Pluto]] || || | ||
|| 21 || 614.63 || [[10_7|10/7]] || se || || || | || 21 || 614.63 || [[10_7|10/7]] || Major tritone / augmented fourth || se || || || | ||
|| 22 || 643.90 || [[16_11|16/11]] || su || || || | || 22 || 643.90 || [[16_11|16/11]] || Red major tritone || su || || || | ||
|| 23 || 673.17 || [[22_15|22/15]], [[40_27|40/27]] || sih || || || | || 23 || 673.17 || [[22_15|22/15]], [[40_27|40/27]] || Blue fifth || sih || || || | ||
|| 24 || 702.44 || [[3_2|3/2]] || | || 24 || 702.44 || [[3_2|3/2]] || Perfect fifth || sol || || || | ||
|| 25 || 731.71 || [[32_21|32/21]] || si || || || | || 25 || 731.71 || [[32_21|32/21]] || Red fifth || si || || || | ||
|| 26 || 760.98 || [[14_9|14/9]], [[25_16|25/16]] || lo || || || | || 26 || 760.98 || [[14_9|14/9]], [[25_16|25/16]] || Blue minor sixth || lo || || || | ||
|| 27 || 790.24 || [[11_7|11/7]], [[128_81|128/81]] || leh || || || | || 27 || 790.24 || [[11_7|11/7]], [[128_81|128/81]] || Gray minor sixth || leh || || || | ||
|| 28 || 819.51 || [[8_5|8/5]] || le || || || | || 28 || 819.51 || [[8_5|8/5]] || Red minor sixth || le || || || | ||
|| 29 || 848.78 || [[18_11|18/11]], [[44_27|44/27]] || lu || || || | || 29 || 848.78 || [[18_11|18/11]], [[44_27|44/27]] || Neutral sixth || lu || || || | ||
|| 30 || 878.05 || [[5_3|5/3]] || la || || || | || 30 || 878.05 || [[5_3|5/3]] || Blue major sixth || la || || || | ||
|| 31 || 907.32 || [[27_16|27/16]] || laa || || || | || 31 || 907.32 || [[27_16|27/16]] || Gray major sixth || laa || || || | ||
|| 32 || 936.59 || [[12_7|12/7]] || li || || || | || 32 || 936.59 || [[12_7|12/7]] || Red major sixth || li || || || | ||
|| 33 || 965.85 || [[7_4|7/4]] || ta || || || | || 33 || 965.85 || [[7_4|7/4]] || Blue minor seventh || ta || || || | ||
|| 34 || 995.12 || [[16_9|16/9]] || teh || || || | || 34 || 995.12 || [[16_9|16/9]] || Gray minor seventh || teh || || || | ||
|| 35 || 1024.39 || [[9_5|9/5]], [[20_11|20/11]] || te || || || | || 35 || 1024.39 || [[9_5|9/5]], [[20_11|20/11]] || Red minor seventh || te || || || | ||
|| 36 || 1053.66 || [[11_6|11/6]] || tu || || || | || 36 || 1053.66 || [[11_6|11/6]] || Neutral seventh || tu || || || | ||
|| 37 || 1082.93 || [[15_8|15/8]] || ti || || || | || 37 || 1082.93 || [[15_8|15/8]] || Blue major seventh || ti || || || | ||
|| 38 || 1112.20 || [[40_21|40/21]], [[21_11|21/11]] || taa || || || | || 38 || 1112.20 || [[40_21|40/21]], [[21_11|21/11]] || Gray major seventh || taa || || || | ||
|| 39 || 1141.46 || [[48_25|48/25]], [[27_14|27/14]], [[64_33|64/33]] || to || || || | || 39 || 1141.46 || [[48_25|48/25]], [[27_14|27/14]], [[64_33|64/33]] || Red major seventh || to || || || | ||
|| 40 || 1170.73 || [[160_81|160/81]] || da || || || | || 40 || 1170.73 || [[160_81|160/81]] || Blue octave || da || || || | ||
==Selected just intervals by error== | ==Selected just intervals by error== | ||
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||= 38 ||= 40 ||= ||= 1112.2 ||= ||= 24 ||= 38 || | ||= 38 ||= 40 ||= ||= 1112.2 ||= ||= 24 ||= 38 || | ||
==Notation== | |||
A red-note/blue-note system, similar to the one proposed for [[36edo]], is one option for notating 41edo. We have the "white key" albitonic notes A-G (7 in total), the "black key" sharps and flats (10 in total), a "red" and "blue" version of each albitonic note (14 in total), a "red" (dark red?) version of each sharp and a "blue" (dark blue?) version of each flat (10 in total), adding up to 41. This would result in quite a colorful keyboard! Note that there are no red flats or blue sharps. Using this nomenclature the notes are: | |||
A, red A, blue Bb, Bb, A#, red A#, blue B, B, red B, blue C, C, red C, blue Db, Db, C#, red C#, blue D, D, red D, blue Eb, Eb, D#, red D#, blue E, E, red E, blue F, F, red F, blue Gb, Gb, F#, red F#, blue G, G, red G, blue Ab, Ab, G#, red G#, blue A, A. | |||
Interval classes could also be named by analogy. The natural, colorless, or gray interval classes are the Pythagorean ones (which show up in the standard diatonic scale), while "red" and "blue" versions are one step higher or lower. Gray thirds, sixths, and sevenths are usually more dissonant than their colorful counterparts, but the reverse is true of fourths and fifths. | |||
=Music= | =Music= | ||
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<h4>Original HTML content:</h4> | <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"><html><head><title>41edo</title></head><body><span style="color: #004d25; font-family: 'Times New Roman',Times,serif; font-size: 20px;"><strong>41 Tone Equal Temperament</strong></span><br /> | <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"><html><head><title>41edo</title></head><body><span style="color: #004d25; font-family: 'Times New Roman',Times,serif; font-size: 20px;"><strong>41 Tone Equal Temperament</strong></span><br /> | ||
<!-- ws:start:WikiTextTocRule: | <!-- ws:start:WikiTextTocRule:31:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:31 --><!-- ws:start:WikiTextTocRule:32: --><a href="#Introduction">Introduction</a><!-- ws:end:WikiTextTocRule:32 --><!-- ws:start:WikiTextTocRule:33: --> | <a href="#Commas">Commas</a><!-- ws:end:WikiTextTocRule:33 --><!-- ws:start:WikiTextTocRule:34: --> | <a href="#Temperaments">Temperaments</a><!-- ws:end:WikiTextTocRule:34 --><!-- ws:start:WikiTextTocRule:35: --> | <a href="#Intervals">Intervals</a><!-- ws:end:WikiTextTocRule:35 --><!-- ws:start:WikiTextTocRule:36: --><!-- ws:end:WikiTextTocRule:36 --><!-- ws:start:WikiTextTocRule:37: --> | <a href="#Instruments">Instruments</a><!-- ws:end:WikiTextTocRule:37 --><!-- ws:start:WikiTextTocRule:38: --> | <a href="#Harmonic Scale">Harmonic Scale</a><!-- ws:end:WikiTextTocRule:38 --><!-- ws:start:WikiTextTocRule:39: --> | <a href="#Nonoctave Temperaments">Nonoctave Temperaments</a><!-- ws:end:WikiTextTocRule:39 --><!-- ws:start:WikiTextTocRule:40: --><!-- ws:end:WikiTextTocRule:40 --><!-- ws:start:WikiTextTocRule:41: --> | <a href="#Music">Music</a><!-- ws:end:WikiTextTocRule:41 --><!-- ws:start:WikiTextTocRule:42: --> | <a href="#Links">Links</a><!-- ws:end:WikiTextTocRule:42 --><!-- ws:start:WikiTextTocRule:43: --> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:43 --><!-- ws:start:WikiTextHeadingRule:9:&lt;h1&gt; --><h1 id="toc0"><a name="Introduction"></a><!-- ws:end:WikiTextHeadingRule:9 -->Introduction</h1> | ||
The 41-tET, 41-EDO, or 41-ET, is the scale derived by dividing the octave into 41 equally-sized steps. Each step represents a frequency ratio of 29.268 <a class="wiki_link" href="/cent">cent</a>s, an <a class="wiki_link" href="/interval">interval</a> close in size to <a class="wiki_link" href="/64_63">64/63</a>, the <a class="wiki_link" href="/Septimal%20comma">septimal comma</a>. 41-ET can be seen as a tuning of the <em><a class="wiki_link" href="/Schismatic%20family#Garibaldi">Garibaldi temperament</a></em> <!-- ws:start:WikiTextRefRule:2:&amp;lt;ref&amp;gt;&lt;a class=&quot;wiki_link_ext&quot; href=&quot;http://x31eq.com/schismic.htm&quot; rel=&quot;nofollow&quot;&gt;&amp;quot;Schismic Temperaments&amp;quot;&lt;/a&gt; at x31eq.com the website of &lt;a class=&quot;wiki_link&quot; href=&quot;/Graham%20Breed&quot;&gt;Graham Breed&lt;/a&gt;&amp;lt;/ref&amp;gt; --><sup id="cite_ref-1" class="reference"><a href="#cite_note-1">[1]</a></sup><!-- ws:end:WikiTextRefRule:2 --> , <!-- ws:start:WikiTextRefRule:4:&amp;lt;ref&amp;gt;&lt;a class=&quot;wiki_link_ext&quot; href=&quot;http://x31eq.com/decimal_lattice.htm&quot; rel=&quot;nofollow&quot;&gt;&amp;quot;Lattices with Decimal Notation&amp;quot;&lt;/a&gt; at x31eq.com&amp;lt;/ref&amp;gt; --><sup id="cite_ref-2" class="reference"><a href="#cite_note-2">[2]</a></sup><!-- ws:end:WikiTextRefRule:4 --> , <!-- ws:start:WikiTextRefRule:6:&amp;lt;ref&amp;gt;&lt;a class=&quot;wiki_link_ext&quot; href=&quot;http://en.wikipedia.org/wiki/Schismatic_temperament&quot; rel=&quot;nofollow&quot;&gt;Schismatic temperament&lt;/a&gt;&amp;lt;/ref&amp;gt; --><sup id="cite_ref-3" class="reference"><a href="#cite_note-3">[3]</a></sup><!-- ws:end:WikiTextRefRule:6 --> the <em><a class="wiki_link" href="/Magic%20family">Magic temperament</a></em> <!-- ws:start:WikiTextRefRule:8:&amp;lt;ref&amp;gt;&lt;a class=&quot;wiki_link_ext&quot; href=&quot;http://en.wikipedia.org/wiki/Magic_temperament&quot; rel=&quot;nofollow&quot;&gt;Magic temperament&lt;/a&gt;&amp;lt;/ref&amp;gt; --><sup id="cite_ref-4" class="reference"><a href="#cite_note-4">[4]</a></sup><!-- ws:end:WikiTextRefRule:8 --> and the superkleismic (41&amp;26) temperament. It is the second smallest equal temperament (after <a class="wiki_link" href="/29edo">29edo</a>) whose perfect fifth is closer to just intonation than that of <a class="wiki_link" href="/12edo">12-ET</a>, and is the seventh <a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta%20EDO%20lists">zeta integral edo</a> after 31; it is not, however, a <a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta%20EDO%20lists">zeta gap edo</a>. This has to do with the fact that it can deal with the <a class="wiki_link" href="/11-limit">11-limit</a> fairly well, and the <a class="wiki_link" href="/13-limit">13-limit</a> perhaps close enough for government work, though its <a class="wiki_link" href="/13_10">13/10</a> is 14 cents sharp. Various 13-limit <a class="wiki_link" href="/magic%20extensions">magic extensions</a> are supported by 41: 13-limit magic, and less successfully necromancy and witchcraft, all merge into one in 41edo tuning. The 41f val provides a superb tuning for sorcery, giving a less-complex version of the 13-limit, and the 41ef val likewise works well for telepathy; telepathy and sorcery merging into one however not in 41edo but in 22edo.<br /> | The 41-tET, 41-EDO, or 41-ET, is the scale derived by dividing the octave into 41 equally-sized steps. Each step represents a frequency ratio of 29.268 <a class="wiki_link" href="/cent">cent</a>s, an <a class="wiki_link" href="/interval">interval</a> close in size to <a class="wiki_link" href="/64_63">64/63</a>, the <a class="wiki_link" href="/Septimal%20comma">septimal comma</a>. 41-ET can be seen as a tuning of the <em><a class="wiki_link" href="/Schismatic%20family#Garibaldi">Garibaldi temperament</a></em> <!-- ws:start:WikiTextRefRule:2:&amp;lt;ref&amp;gt;&lt;a class=&quot;wiki_link_ext&quot; href=&quot;http://x31eq.com/schismic.htm&quot; rel=&quot;nofollow&quot;&gt;&amp;quot;Schismic Temperaments&amp;quot;&lt;/a&gt; at x31eq.com the website of &lt;a class=&quot;wiki_link&quot; href=&quot;/Graham%20Breed&quot;&gt;Graham Breed&lt;/a&gt;&amp;lt;/ref&amp;gt; --><sup id="cite_ref-1" class="reference"><a href="#cite_note-1">[1]</a></sup><!-- ws:end:WikiTextRefRule:2 --> , <!-- ws:start:WikiTextRefRule:4:&amp;lt;ref&amp;gt;&lt;a class=&quot;wiki_link_ext&quot; href=&quot;http://x31eq.com/decimal_lattice.htm&quot; rel=&quot;nofollow&quot;&gt;&amp;quot;Lattices with Decimal Notation&amp;quot;&lt;/a&gt; at x31eq.com&amp;lt;/ref&amp;gt; --><sup id="cite_ref-2" class="reference"><a href="#cite_note-2">[2]</a></sup><!-- ws:end:WikiTextRefRule:4 --> , <!-- ws:start:WikiTextRefRule:6:&amp;lt;ref&amp;gt;&lt;a class=&quot;wiki_link_ext&quot; href=&quot;http://en.wikipedia.org/wiki/Schismatic_temperament&quot; rel=&quot;nofollow&quot;&gt;Schismatic temperament&lt;/a&gt;&amp;lt;/ref&amp;gt; --><sup id="cite_ref-3" class="reference"><a href="#cite_note-3">[3]</a></sup><!-- ws:end:WikiTextRefRule:6 --> the <em><a class="wiki_link" href="/Magic%20family">Magic temperament</a></em> <!-- ws:start:WikiTextRefRule:8:&amp;lt;ref&amp;gt;&lt;a class=&quot;wiki_link_ext&quot; href=&quot;http://en.wikipedia.org/wiki/Magic_temperament&quot; rel=&quot;nofollow&quot;&gt;Magic temperament&lt;/a&gt;&amp;lt;/ref&amp;gt; --><sup id="cite_ref-4" class="reference"><a href="#cite_note-4">[4]</a></sup><!-- ws:end:WikiTextRefRule:8 --> and the superkleismic (41&amp;26) temperament. It is the second smallest equal temperament (after <a class="wiki_link" href="/29edo">29edo</a>) whose perfect fifth is closer to just intonation than that of <a class="wiki_link" href="/12edo">12-ET</a>, and is the seventh <a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta%20EDO%20lists">zeta integral edo</a> after 31; it is not, however, a <a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta%20EDO%20lists">zeta gap edo</a>. This has to do with the fact that it can deal with the <a class="wiki_link" href="/11-limit">11-limit</a> fairly well, and the <a class="wiki_link" href="/13-limit">13-limit</a> perhaps close enough for government work, though its <a class="wiki_link" href="/13_10">13/10</a> is 14 cents sharp. Various 13-limit <a class="wiki_link" href="/magic%20extensions">magic extensions</a> are supported by 41: 13-limit magic, and less successfully necromancy and witchcraft, all merge into one in 41edo tuning. The 41f val provides a superb tuning for sorcery, giving a less-complex version of the 13-limit, and the 41ef val likewise works well for telepathy; telepathy and sorcery merging into one however not in 41edo but in 22edo.<br /> | ||
<br /> | <br /> | ||
41edo is consistent in the 15 odd limit.<br /> | 41edo is consistent in the 15 odd limit. In fact, <em>all</em> of its intervals between 100 and 1100 cents in size are 15-odd-limit consonances. (In comparison, <a class="wiki_link" href="/31edo">31edo</a> is only consistent up to the 11-limit, and the intervals 12/31 and 19/31 have no 11-limit approximations).<br /> | ||
<br /> | <br /> | ||
41-ET forms the foundation of the <a class="wiki_link_ext" href="http://www.h-pi.com/theory/huntsystem1.html" rel="nofollow">H-System</a>, which uses the scale degrees of 41-ET as the basic <a class="wiki_link" href="/13-limit">13-limit</a> intervals requiring fine tuning +/- 1 <a class="wiki_link_ext" href="http://www.h-pi.com/theory/huntsystem2.html" rel="nofollow">average JND</a> from the 41-ET circle in <a class="wiki_link" href="/205edo">205edo</a>.<br /> | 41-ET forms the foundation of the <a class="wiki_link_ext" href="http://www.h-pi.com/theory/huntsystem1.html" rel="nofollow">H-System</a>, which uses the scale degrees of 41-ET as the basic <a class="wiki_link" href="/13-limit">13-limit</a> intervals requiring fine tuning +/- 1 <a class="wiki_link_ext" href="http://www.h-pi.com/theory/huntsystem2.html" rel="nofollow">average JND</a> from the 41-ET circle in <a class="wiki_link" href="/205edo">205edo</a>.<br /> | ||
| Line 875: | Line 882: | ||
</th> | </th> | ||
<th>Approximate Ratios in the <a class="wiki_link" href="/11-limit">11-limit</a><br /> | <th>Approximate Ratios in the <a class="wiki_link" href="/11-limit">11-limit</a><br /> | ||
</th> | |||
<th>Proposed names<br /> | |||
</th> | </th> | ||
<th>Andrew's solfege syllable<br /> | <th>Andrew's solfege syllable<br /> | ||
| Line 889: | Line 898: | ||
</td> | </td> | ||
<td><a class="wiki_link" href="/1_1">1/1</a><br /> | <td><a class="wiki_link" href="/1_1">1/1</a><br /> | ||
</td> | |||
<td>Unison<br /> | |||
</td> | </td> | ||
<td>do<br /> | <td>do<br /> | ||
| Line 903: | Line 914: | ||
</td> | </td> | ||
<td><a class="wiki_link" href="/81_80">81/80</a><br /> | <td><a class="wiki_link" href="/81_80">81/80</a><br /> | ||
</td> | |||
<td>Red unison<br /> | |||
</td> | </td> | ||
<td>di<br /> | <td>di<br /> | ||
| Line 917: | Line 930: | ||
</td> | </td> | ||
<td><a class="wiki_link" href="/25_24">25/24</a>, <a class="wiki_link" href="/28_27">28/27</a>, <a class="wiki_link" href="/33_32">33/32</a><br /> | <td><a class="wiki_link" href="/25_24">25/24</a>, <a class="wiki_link" href="/28_27">28/27</a>, <a class="wiki_link" href="/33_32">33/32</a><br /> | ||
</td> | |||
<td>Blue minor second<br /> | |||
</td> | </td> | ||
<td>ro<br /> | <td>ro<br /> | ||
| Line 931: | Line 946: | ||
</td> | </td> | ||
<td><a class="wiki_link" href="/21_20">21/20</a>, <a class="wiki_link" href="/22_21">22/21</a><br /> | <td><a class="wiki_link" href="/21_20">21/20</a>, <a class="wiki_link" href="/22_21">22/21</a><br /> | ||
</td> | |||
<td>Gray minor second<br /> | |||
</td> | </td> | ||
<td>rih<br /> | <td>rih<br /> | ||
| Line 945: | Line 962: | ||
</td> | </td> | ||
<td><a class="wiki_link" href="/16_15">16/15</a>, <a class="wiki_link" href="/15_14">15/14</a><br /> | <td><a class="wiki_link" href="/16_15">16/15</a>, <a class="wiki_link" href="/15_14">15/14</a><br /> | ||
</td> | |||
<td>Red minor second<br /> | |||
</td> | </td> | ||
<td>ra<br /> | <td>ra<br /> | ||
| Line 959: | Line 978: | ||
</td> | </td> | ||
<td><a class="wiki_link" href="/12_11">12/11</a><br /> | <td><a class="wiki_link" href="/12_11">12/11</a><br /> | ||
</td> | |||
<td>Neutral second<br /> | |||
</td> | </td> | ||
<td>ru<br /> | <td>ru<br /> | ||
| Line 973: | Line 994: | ||
</td> | </td> | ||
<td><a class="wiki_link" href="/10_9">10/9</a>, <a class="wiki_link" href="/11_10">11/10</a><br /> | <td><a class="wiki_link" href="/10_9">10/9</a>, <a class="wiki_link" href="/11_10">11/10</a><br /> | ||
</td> | |||
<td>Blue major second<br /> | |||
</td> | </td> | ||
<td>reh<br /> | <td>reh<br /> | ||
| Line 987: | Line 1,010: | ||
</td> | </td> | ||
<td><a class="wiki_link" href="/9_8">9/8</a><br /> | <td><a class="wiki_link" href="/9_8">9/8</a><br /> | ||
</td> | |||
<td>Gray major second<br /> | |||
</td> | </td> | ||
<td>re<br /> | <td>re<br /> | ||
| Line 1,001: | Line 1,026: | ||
</td> | </td> | ||
<td><a class="wiki_link" href="/8_7">8/7</a><br /> | <td><a class="wiki_link" href="/8_7">8/7</a><br /> | ||
</td> | |||
<td>Red major second<br /> | |||
</td> | </td> | ||
<td>ri<br /> | <td>ri<br /> | ||
| Line 1,015: | Line 1,042: | ||
</td> | </td> | ||
<td><a class="wiki_link" href="/7_6">7/6</a>, <a class="wiki_link" href="/32_25">32/25</a><br /> | <td><a class="wiki_link" href="/7_6">7/6</a>, <a class="wiki_link" href="/32_25">32/25</a><br /> | ||
</td> | |||
<td>Blue minor third<br /> | |||
</td> | </td> | ||
<td>ma<br /> | <td>ma<br /> | ||
| Line 1,029: | Line 1,058: | ||
</td> | </td> | ||
<td><a class="wiki_link" href="/32_27">32/27</a><br /> | <td><a class="wiki_link" href="/32_27">32/27</a><br /> | ||
</td> | |||
<td>Gray minor third<br /> | |||
</td> | </td> | ||
<td>meh<br /> | <td>meh<br /> | ||
| Line 1,043: | Line 1,074: | ||
</td> | </td> | ||
<td><a class="wiki_link" href="/6_5">6/5</a><br /> | <td><a class="wiki_link" href="/6_5">6/5</a><br /> | ||
</td> | |||
<td>Red minor third<br /> | |||
</td> | </td> | ||
<td>me<br /> | <td>me<br /> | ||
| Line 1,057: | Line 1,090: | ||
</td> | </td> | ||
<td><a class="wiki_link" href="/11_9">11/9</a>,<a class="wiki_link" href="/27_22">27/22</a><br /> | <td><a class="wiki_link" href="/11_9">11/9</a>,<a class="wiki_link" href="/27_22">27/22</a><br /> | ||
</td> | |||
<td>Neutral third<br /> | |||
</td> | </td> | ||
<td>mu<br /> | <td>mu<br /> | ||
| Line 1,071: | Line 1,106: | ||
</td> | </td> | ||
<td><a class="wiki_link" href="/5_4">5/4</a><br /> | <td><a class="wiki_link" href="/5_4">5/4</a><br /> | ||
</td> | |||
<td>Blue major third<br /> | |||
</td> | </td> | ||
<td>mi<br /> | <td>mi<br /> | ||
| Line 1,085: | Line 1,122: | ||
</td> | </td> | ||
<td><a class="wiki_link" href="/14_11">14/11</a>, <a class="wiki_link" href="/81_64">81/64</a><br /> | <td><a class="wiki_link" href="/14_11">14/11</a>, <a class="wiki_link" href="/81_64">81/64</a><br /> | ||
</td> | |||
<td>Gray major third<br /> | |||
</td> | </td> | ||
<td>maa<br /> | <td>maa<br /> | ||
| Line 1,099: | Line 1,138: | ||
</td> | </td> | ||
<td><a class="wiki_link" href="/9_7">9/7</a><br /> | <td><a class="wiki_link" href="/9_7">9/7</a><br /> | ||
</td> | |||
<td>Red major third<br /> | |||
</td> | </td> | ||
<td>mo<br /> | <td>mo<br /> | ||
| Line 1,113: | Line 1,154: | ||
</td> | </td> | ||
<td><a class="wiki_link" href="/21_16">21/16</a><br /> | <td><a class="wiki_link" href="/21_16">21/16</a><br /> | ||
</td> | |||
<td>Blue fourth<br /> | |||
</td> | </td> | ||
<td>fe<br /> | <td>fe<br /> | ||
| Line 1,127: | Line 1,170: | ||
</td> | </td> | ||
<td><a class="wiki_link" href="/4_3">4/3</a><br /> | <td><a class="wiki_link" href="/4_3">4/3</a><br /> | ||
</td> | |||
<td>Perfect fourth<br /> | |||
</td> | </td> | ||
<td>fa<br /> | <td>fa<br /> | ||
| Line 1,141: | Line 1,186: | ||
</td> | </td> | ||
<td><a class="wiki_link" href="/15_11">15/11</a>, <a class="wiki_link" href="/27_20">27/20</a><br /> | <td><a class="wiki_link" href="/15_11">15/11</a>, <a class="wiki_link" href="/27_20">27/20</a><br /> | ||
</td> | |||
<td>Red fourth<br /> | |||
</td> | </td> | ||
<td>fih<br /> | <td>fih<br /> | ||
| Line 1,155: | Line 1,202: | ||
</td> | </td> | ||
<td><a class="wiki_link" href="/11_8">11/8</a><br /> | <td><a class="wiki_link" href="/11_8">11/8</a><br /> | ||
</td> | |||
<td>Blue minor tritone<br /> | |||
</td> | </td> | ||
<td>fu<br /> | <td>fu<br /> | ||
| Line 1,169: | Line 1,218: | ||
</td> | </td> | ||
<td><a class="wiki_link" href="/7_5">7/5</a><br /> | <td><a class="wiki_link" href="/7_5">7/5</a><br /> | ||
</td> | |||
<td>Minor tritone / diminished fifth<br /> | |||
</td> | </td> | ||
<td>fi<br /> | <td>fi<br /> | ||
| Line 1,183: | Line 1,234: | ||
</td> | </td> | ||
<td><a class="wiki_link" href="/10_7">10/7</a><br /> | <td><a class="wiki_link" href="/10_7">10/7</a><br /> | ||
</td> | |||
<td>Major tritone / augmented fourth<br /> | |||
</td> | </td> | ||
<td>se<br /> | <td>se<br /> | ||
| Line 1,197: | Line 1,250: | ||
</td> | </td> | ||
<td><a class="wiki_link" href="/16_11">16/11</a><br /> | <td><a class="wiki_link" href="/16_11">16/11</a><br /> | ||
</td> | |||
<td>Red major tritone<br /> | |||
</td> | </td> | ||
<td>su<br /> | <td>su<br /> | ||
| Line 1,211: | Line 1,266: | ||
</td> | </td> | ||
<td><a class="wiki_link" href="/22_15">22/15</a>, <a class="wiki_link" href="/40_27">40/27</a><br /> | <td><a class="wiki_link" href="/22_15">22/15</a>, <a class="wiki_link" href="/40_27">40/27</a><br /> | ||
</td> | |||
<td>Blue fifth<br /> | |||
</td> | </td> | ||
<td>sih<br /> | <td>sih<br /> | ||
| Line 1,225: | Line 1,282: | ||
</td> | </td> | ||
<td><a class="wiki_link" href="/3_2">3/2</a><br /> | <td><a class="wiki_link" href="/3_2">3/2</a><br /> | ||
</td> | |||
<td>Perfect fifth<br /> | |||
</td> | </td> | ||
<td>sol<br /> | <td>sol<br /> | ||
| Line 1,239: | Line 1,298: | ||
</td> | </td> | ||
<td><a class="wiki_link" href="/32_21">32/21</a><br /> | <td><a class="wiki_link" href="/32_21">32/21</a><br /> | ||
</td> | |||
<td>Red fifth<br /> | |||
</td> | </td> | ||
<td>si<br /> | <td>si<br /> | ||
| Line 1,253: | Line 1,314: | ||
</td> | </td> | ||
<td><a class="wiki_link" href="/14_9">14/9</a>, <a class="wiki_link" href="/25_16">25/16</a><br /> | <td><a class="wiki_link" href="/14_9">14/9</a>, <a class="wiki_link" href="/25_16">25/16</a><br /> | ||
</td> | |||
<td>Blue minor sixth<br /> | |||
</td> | </td> | ||
<td>lo<br /> | <td>lo<br /> | ||
| Line 1,267: | Line 1,330: | ||
</td> | </td> | ||
<td><a class="wiki_link" href="/11_7">11/7</a>, <a class="wiki_link" href="/128_81">128/81</a><br /> | <td><a class="wiki_link" href="/11_7">11/7</a>, <a class="wiki_link" href="/128_81">128/81</a><br /> | ||
</td> | |||
<td>Gray minor sixth<br /> | |||
</td> | </td> | ||
<td>leh<br /> | <td>leh<br /> | ||
| Line 1,281: | Line 1,346: | ||
</td> | </td> | ||
<td><a class="wiki_link" href="/8_5">8/5</a><br /> | <td><a class="wiki_link" href="/8_5">8/5</a><br /> | ||
</td> | |||
<td>Red minor sixth<br /> | |||
</td> | </td> | ||
<td>le<br /> | <td>le<br /> | ||
| Line 1,295: | Line 1,362: | ||
</td> | </td> | ||
<td><a class="wiki_link" href="/18_11">18/11</a>, <a class="wiki_link" href="/44_27">44/27</a><br /> | <td><a class="wiki_link" href="/18_11">18/11</a>, <a class="wiki_link" href="/44_27">44/27</a><br /> | ||
</td> | |||
<td>Neutral sixth<br /> | |||
</td> | </td> | ||
<td>lu<br /> | <td>lu<br /> | ||
| Line 1,309: | Line 1,378: | ||
</td> | </td> | ||
<td><a class="wiki_link" href="/5_3">5/3</a><br /> | <td><a class="wiki_link" href="/5_3">5/3</a><br /> | ||
</td> | |||
<td>Blue major sixth<br /> | |||
</td> | </td> | ||
<td>la<br /> | <td>la<br /> | ||
| Line 1,323: | Line 1,394: | ||
</td> | </td> | ||
<td><a class="wiki_link" href="/27_16">27/16</a><br /> | <td><a class="wiki_link" href="/27_16">27/16</a><br /> | ||
</td> | |||
<td>Gray major sixth<br /> | |||
</td> | </td> | ||
<td>laa<br /> | <td>laa<br /> | ||
| Line 1,337: | Line 1,410: | ||
</td> | </td> | ||
<td><a class="wiki_link" href="/12_7">12/7</a><br /> | <td><a class="wiki_link" href="/12_7">12/7</a><br /> | ||
</td> | |||
<td>Red major sixth<br /> | |||
</td> | </td> | ||
<td>li<br /> | <td>li<br /> | ||
| Line 1,351: | Line 1,426: | ||
</td> | </td> | ||
<td><a class="wiki_link" href="/7_4">7/4</a><br /> | <td><a class="wiki_link" href="/7_4">7/4</a><br /> | ||
</td> | |||
<td>Blue minor seventh<br /> | |||
</td> | </td> | ||
<td>ta<br /> | <td>ta<br /> | ||
| Line 1,365: | Line 1,442: | ||
</td> | </td> | ||
<td><a class="wiki_link" href="/16_9">16/9</a><br /> | <td><a class="wiki_link" href="/16_9">16/9</a><br /> | ||
</td> | |||
<td>Gray minor seventh<br /> | |||
</td> | </td> | ||
<td>teh<br /> | <td>teh<br /> | ||
| Line 1,379: | Line 1,458: | ||
</td> | </td> | ||
<td><a class="wiki_link" href="/9_5">9/5</a>, <a class="wiki_link" href="/20_11">20/11</a><br /> | <td><a class="wiki_link" href="/9_5">9/5</a>, <a class="wiki_link" href="/20_11">20/11</a><br /> | ||
</td> | |||
<td>Red minor seventh<br /> | |||
</td> | </td> | ||
<td>te<br /> | <td>te<br /> | ||
| Line 1,393: | Line 1,474: | ||
</td> | </td> | ||
<td><a class="wiki_link" href="/11_6">11/6</a><br /> | <td><a class="wiki_link" href="/11_6">11/6</a><br /> | ||
</td> | |||
<td>Neutral seventh<br /> | |||
</td> | </td> | ||
<td>tu<br /> | <td>tu<br /> | ||
| Line 1,407: | Line 1,490: | ||
</td> | </td> | ||
<td><a class="wiki_link" href="/15_8">15/8</a><br /> | <td><a class="wiki_link" href="/15_8">15/8</a><br /> | ||
</td> | |||
<td>Blue major seventh<br /> | |||
</td> | </td> | ||
<td>ti<br /> | <td>ti<br /> | ||
| Line 1,421: | Line 1,506: | ||
</td> | </td> | ||
<td><a class="wiki_link" href="/40_21">40/21</a>, <a class="wiki_link" href="/21_11">21/11</a><br /> | <td><a class="wiki_link" href="/40_21">40/21</a>, <a class="wiki_link" href="/21_11">21/11</a><br /> | ||
</td> | |||
<td>Gray major seventh<br /> | |||
</td> | </td> | ||
<td>taa<br /> | <td>taa<br /> | ||
| Line 1,435: | Line 1,522: | ||
</td> | </td> | ||
<td><a class="wiki_link" href="/48_25">48/25</a>, <a class="wiki_link" href="/27_14">27/14</a>, <a class="wiki_link" href="/64_33">64/33</a><br /> | <td><a class="wiki_link" href="/48_25">48/25</a>, <a class="wiki_link" href="/27_14">27/14</a>, <a class="wiki_link" href="/64_33">64/33</a><br /> | ||
</td> | |||
<td>Red major seventh<br /> | |||
</td> | </td> | ||
<td>to<br /> | <td>to<br /> | ||
| Line 1,449: | Line 1,538: | ||
</td> | </td> | ||
<td><a class="wiki_link" href="/160_81">160/81</a><br /> | <td><a class="wiki_link" href="/160_81">160/81</a><br /> | ||
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<td>Blue octave<br /> | |||
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<td>da<br /> | <td>da<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:19:&lt;h1&gt; --><h1 id="toc5"><a name="Instruments"></a><!-- ws:end:WikiTextHeadingRule:19 -->Instruments</h1> | <!-- ws:start:WikiTextHeadingRule:19:&lt;h1&gt; --><h1 id="toc5"><a name="Instruments"></a><!-- ws:end:WikiTextHeadingRule:19 -->Instruments</h1> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:2530:&lt;img src=&quot;/file/view/Ron_Sword_with_a_41ET_Guitar.jpg/221056094/Ron_Sword_with_a_41ET_Guitar.jpg&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/Ron_Sword_with_a_41ET_Guitar.jpg/221056094/Ron_Sword_with_a_41ET_Guitar.jpg" alt="Ron_Sword_with_a_41ET_Guitar.jpg" title="Ron_Sword_with_a_41ET_Guitar.jpg" /><!-- ws:end:WikiTextLocalImageRule:2530 --><br /> | ||
<em>41-EDO Classical guitar, by Ron Sword.</em><br /> | <em>41-EDO Classical guitar, by Ron Sword.</em><br /> | ||
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<!-- ws:start:WikiTextHeadingRule:25:&lt;h2&gt; --><h2 id="toc8"><a name="Nonoctave Temperaments-Notation"></a><!-- ws:end:WikiTextHeadingRule:25 -->Notation</h2> | |||
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A red-note/blue-note system, similar to the one proposed for <a class="wiki_link" href="/36edo">36edo</a>, is one option for notating 41edo. We have the &quot;white key&quot; albitonic notes A-G (7 in total), the &quot;black key&quot; sharps and flats (10 in total), a &quot;red&quot; and &quot;blue&quot; version of each albitonic note (14 in total), a &quot;red&quot; (dark red?) version of each sharp and a &quot;blue&quot; (dark blue?) version of each flat (10 in total), adding up to 41. This would result in quite a colorful keyboard! Note that there are no red flats or blue sharps. Using this nomenclature the notes are:<br /> | |||
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A, red A, blue Bb, Bb, A#, red A#, blue B, B, red B, blue C, C, red C, blue Db, Db, C#, red C#, blue D, D, red D, blue Eb, Eb, D#, red D#, blue E, E, red E, blue F, F, red F, blue Gb, Gb, F#, red F#, blue G, G, red G, blue Ab, Ab, G#, red G#, blue A, A.<br /> | |||
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Interval classes could also be named by analogy. The natural, colorless, or gray interval classes are the Pythagorean ones (which show up in the standard diatonic scale), while &quot;red&quot; and &quot;blue&quot; versions are one step higher or lower. Gray thirds, sixths, and sevenths are usually more dissonant than their colorful counterparts, but the reverse is true of fourths and fifths.<br /> | |||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:27:&lt;h1&gt; --><h1 id="toc9"><a name="Music"></a><!-- ws:end:WikiTextHeadingRule:27 -->Music</h1> | ||
<a class="wiki_link_ext" href="http://soundcloud.com/cameron-bobro/eveninghorizon-cbobro" rel="nofollow">EveningHorizon</a> <a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Bobro/EveningHorizon_CBobro.mp3" rel="nofollow">play</a> by Cameron Bobro<br /> | <a class="wiki_link_ext" href="http://soundcloud.com/cameron-bobro/eveninghorizon-cbobro" rel="nofollow">EveningHorizon</a> <a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Bobro/EveningHorizon_CBobro.mp3" rel="nofollow">play</a> by Cameron Bobro<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:29:&lt;h1&gt; --><h1 id="toc10"><a name="Links"></a><!-- ws:end:WikiTextHeadingRule:29 -->Links</h1> | ||
<ul><li><a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/41_equal_temperament" rel="nofollow">Wikipedia article on 41edo</a></li><li><a class="wiki_link" href="/Magic22%20as%20srutis#magic22assrutis">Magic22 as srutis</a> describes a possible use of 41edo for <a class="wiki_link" href="/indian">indian</a> music.</li><li>see also <a class="wiki_link" href="/Magic%20family">Magic family</a></li><li>Sword, Ron. <a class="wiki_link_ext" href="http://www.ronsword.com" rel="nofollow" target="_blank">&quot;Tetracontamonophonic Scales for Guitar&quot;</a></li></ul><!-- ws:start:WikiTextReferencesRule: | <ul><li><a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/41_equal_temperament" rel="nofollow">Wikipedia article on 41edo</a></li><li><a class="wiki_link" href="/Magic22%20as%20srutis#magic22assrutis">Magic22 as srutis</a> describes a possible use of 41edo for <a class="wiki_link" href="/indian">indian</a> music.</li><li>see also <a class="wiki_link" href="/Magic%20family">Magic family</a></li><li>Sword, Ron. <a class="wiki_link_ext" href="http://www.ronsword.com" rel="nofollow" target="_blank">&quot;Tetracontamonophonic Scales for Guitar&quot;</a></li></ul><!-- ws:start:WikiTextReferencesRule:3807: --><hr class="references" /><ol class="references"> | ||
<li id="cite_note-1"><a href="#cite_ref-1">^</a> <a class="wiki_link_ext" href="http://x31eq.com/schismic.htm" rel="nofollow">&quot;Schismic Temperaments&quot;</a> at x31eq.com the website of <a class="wiki_link" href="/Graham%20Breed">Graham Breed</a></li> | <li id="cite_note-1"><a href="#cite_ref-1">^</a> <a class="wiki_link_ext" href="http://x31eq.com/schismic.htm" rel="nofollow">&quot;Schismic Temperaments&quot;</a> at x31eq.com the website of <a class="wiki_link" href="/Graham%20Breed">Graham Breed</a></li> | ||
<li id="cite_note-2"><a href="#cite_ref-2">^</a> <a class="wiki_link_ext" href="http://x31eq.com/decimal_lattice.htm" rel="nofollow">&quot;Lattices with Decimal Notation&quot;</a> at x31eq.com</li> | <li id="cite_note-2"><a href="#cite_ref-2">^</a> <a class="wiki_link_ext" href="http://x31eq.com/decimal_lattice.htm" rel="nofollow">&quot;Lattices with Decimal Notation&quot;</a> at x31eq.com</li> | ||
<li id="cite_note-3"><a href="#cite_ref-3">^</a> <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Schismatic_temperament" rel="nofollow">Schismatic temperament</a></li> | <li id="cite_note-3"><a href="#cite_ref-3">^</a> <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Schismatic_temperament" rel="nofollow">Schismatic temperament</a></li> | ||
<li id="cite_note-4"><a href="#cite_ref-4">^</a> <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Magic_temperament" rel="nofollow">Magic temperament</a></li> | <li id="cite_note-4"><a href="#cite_ref-4">^</a> <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Magic_temperament" rel="nofollow">Magic temperament</a></li> | ||
</ol><!-- ws:end:WikiTextReferencesRule: | </ol><!-- ws:end:WikiTextReferencesRule:3807 --></body></html></pre></div> | ||