|
|
| (92 intermediate revisions by 36 users not shown) |
| Line 1: |
Line 1: |
| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | {{Infobox ET}} |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| | {{ED intro}} |
| : This revision was by author [[User:phylingual|phylingual]] and made on <tt>2012-05-06 09:19:06 UTC</tt>.<br>
| |
| : The original revision id was <tt>330639234</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">35-tET or 35-[[xenharmonic/edo|EDO]] refers to a tuning system which divides the octave into 35 steps of approximately [[xenharmonic/cent|34.29¢]] each.
| |
|
| |
|
| As 35 is 5 times 7, 35edo allows for mixing the two smallest xenharmonic [[xenharmonic/macrotonal edos|macrotonal edos]]: [[xenharmonic/5edo|5edo]] and [[xenharmonic/7edo|7edo]]. A single degree of 35edo represents the difference between 7edo's narrow fifth of 685.71¢ and 5edo's wide fifth of 720¢. Because it includes 7edo, 35edo tunes the 29th harmonic with +1 cent of error. 35edo can also represent the 2.3.5.7.11.17 [[xenharmonic/Just intonation subgroups|subgroup]] and 2.9.5.7.11.17 subgroup, because of the accuracy of 9 and the flatness of all other subgroup generators. Therefore among whitewood tunings it is very versatile, you can switch between these different subgroups if you don't mind having to use two different 3/2s to reach the inconsistent 9 (a characteristic of whitewood tunings), and if you ignore [[xenharmonic/22edo|22edo]]'s | | == Theory == |
| more in-tune versions of 35edo MOS's and consistent representation of both subgroups. 35edo has the optimal patent val for [[xenharmonic/Greenwoodmic temperaments|greenwood]] and [[xenharmonic/Greenwoodmic temperaments#Secund|secund]] temperaments.
| | As 35 is 5 times 7, 35edo allows for mixing the two smallest xenharmonic [[macrotonal edos]]: [[5edo]] and [[7edo]]. A single degree of 35edo represents the difference between 7edo's narrow fifth of 685.71{{c}} and 5edo's wide fifth of 720{{c}}. Because it includes 7edo, 35edo tunes the 29th harmonic with only 1{{c}} of error. |
|
| |
|
| A good beginning for start to play 35-EDO is with the Sub-diatonic scale, that is a [[xenharmonic/MOS|MOS]] of 3L2s: 9 4 9 9 4.
| | 35edo can also represent the 2.3.5.7.11.17 [[subgroup]] and 2.9.5.7.11.17 subgroup, because of the accuracy of 9 and the flatness of all other subgroup generators (7/5 and 17/11 stand out, having less than 1 cent error). Therefore among [[whitewood]] tunings it is very versatile; you can switch between these different subgroups if you don't mind having to use two different 3/2s to reach the inconsistent 9 (a characteristic of whitewood tunings), and if you ignore [[22edo]]'s more in-tune versions of 35edo MOS's and consistent representation of both subgroups. |
|
| |
|
| =Intervals=
| | 35edo has the optimal [[patent val]] for [[greenwood]] and [[secund]] temperaments, as well as 11-limit [[muggles]], and the 35f val is an excellent tuning for 13-limit muggles. 35edo is the largest edo with a lack of a [[diatonic scale]] (unless 7edo is considered a diatonic scale). |
|
| |
|
| (Bolded ratio indicates that the ratio is most accurately tuned by the given 35-edo interval.)
| | === Odd harmonics === |
| || Degrees || Solfege || Cents value || Ratios in 2.5.7.11.17 subgroup || Ratios with flat 3 || Ratios with sharp 3 || Ratios with 9 ||
| | {{Harmonics in equal|35}} |
| || 0 || do || 0 || **1/1** || (see comma table) || || ||
| |
| || 1 || du || 34.29 || **50/49**, **121/119**, 33/32 || **36/35** || 25/24 || **81/80** ||
| |
| || 2 || di || 68.57 || 128/125 || **25/24** || 81/80 || ||
| |
| || 3 || ra || 102.86 || **17/16** || **15/14** || **16/15** || **18/17** ||
| |
| || 4 || ru || 137.14 || || **12/11**, 16/15 || || ||
| |
| || 5 || ro || 171.43 || **11/10** || || 12/11 || **10/9** ||
| |
| || 6 || re || 205.71 || || || || **9/8** ||
| |
| || 7 || ri || 240 || **8/7** || || 7/6 || ||
| |
| || 8 || ma || 274.29 || **20/17** || **7/6** || || ||
| |
| || 9 || me || 308.57 || || **6/5** || || ||
| |
| || 10 || mu || 342.86 || **17/14** || || 6/5 || **11/9** ||
| |
| || 11 || mi || 377.14 || **5/4** || || || ||
| |
| || 12 || mo || 411.43 || **14/11** || || || ||
| |
| || 13 || fe || 445.71 || **22/17**, 32/25 || || || **9/7** ||
| |
| || 14 || fo || 480 || || || 4/3 || ||
| |
| || 15 || fa || 514.29 || || **4/3** || || ||
| |
| || 16 || fu || 548.57 || **11/8** || || || ||
| |
| || 17 || fi || 582.86 || **7/5** || **24/17** || 17/12 || ||
| |
| || 18 || se || 617.14 || **10/7** || **17/12** || 24/17 || ||
| |
| || 19 || su || 651.43 || **16/11** || || || ||
| |
| || 20 || so || 685.71 || || **3/2** || || ||
| |
| || 21 || sa || 720 || || || 3/2 || ||
| |
| || 22 || si || 754.29 || **17/11**, 25/16 || || || **14/9** ||
| |
| || 23 || lo || 788.57 || **11/7** || || || ||
| |
| || 24 || le || 822.86 || **8/5** || || || ||
| |
| || 25 || lu || 857.15 || || || 5/3 || **18/11** ||
| |
| || 26 || la || 891.43 || || **5/3** || || ||
| |
| || 27 || li || 925.71 || **17/10** || **12/7** || || ||
| |
| || 28 || ta || 960 || **7/4** || || || ||
| |
| || 29 || te || 994.29 || || || || **16/9** ||
| |
| || 30 || to || 1028.57 || **20/11** || || || **9/5** ||
| |
| || 31 || tu || 1062.86 || || **11/6**, 15/8 || || ||
| |
| || 32 || ti || 1097.14 || **32/17** || **28/15** || **15/8** || **17/9** ||
| |
| || 33 || de || 1131.43 || || || || ||
| |
| || 34 || da || 1165.71 || || || || ||
| |
| =Rank two temperaments=
| |
|
| |
|
| ||~ Periods
| | == Notation == |
| per octave ||~ Generator ||~ Temperaments with
| | The 7edo fifth is preferred as the diatonic generator for ups and downs notation due to being much easier to notate than the 5edo fifth (which involves E and F being enharmonic), as well as being closer to 3/2. |
| flat 3/2 (patent val) ||~ <span style="display: block; text-align: center;">Temperaments with</span><span style="display: block; text-align: center;">sharp 3/2 (35b val)</span> ||
| | {| class="wikitable" |
| || 1 || 1\35 || || ||
| | |- |
| || 1 || 2\35 || || ||
| | ! Degrees |
| || 1 || 3\35 || || [[Ripple]] ||
| | ! Cents |
| || 1 || 4\35 || [[xenharmonic/Greenwoodmic temperaments#Secund|Secund]] || ||
| | ! colspan="3" | [[Ups and downs notation]] |
| || 1 || 6\35 |||| Messed-up [[Chromatic pairs#Baldy|Baldy]] ||
| | ! [[Dual-fifth tuning|Dual-fifth]] notation |
| || 1 || 8\35 || || Messed-up [[Orwell]] ||
| | <small>based on closest 12edo interval</small> |
| || 1 || 9\35 || [[xenharmonic/Myna|Myna]] || || | | |- |
| || 1 || 11\35 || [[Magic family#Muggles|Muggles]] || || | | | 0 |
| || 1 || 12\35 || || [[Avicennmic temperaments#Roman|Roman]] || | | | 0.000 |
| || 1 || 13\35 || || [[xenharmonic/Sensipent family|Sensipent]] but //not// [[Sensi]] || | | | unison |
| || 1 || 16\35 || || || | | | 1 |
| || 1 || 17\35 || || || | | | D |
| || 5 || 1\35 || || [[Blackwood]] (very unfair, favoring 7/6) || | | | 1sn, prime |
| || 5 || 2\35 || || [[Blackwood]] (unfair, favoring 6/5 and 20/17) || | | |- |
| || 5 || 3\35 || || [[Blackwood]] (fair, favoring 5/4 and 17/14) || | | | 1 |
| || 7 || 1\35 || [[xenharmonic/Apotome family|Whitewood]]/[[xenharmonic/Apotome family#Redwood|Redwood]] || || | | | 34.286 |
| || 7 || 2\35 || [[xenharmonic/Greenwoodmic temperaments#Greenwood|Greenwood]] || || | | | up unison |
| =<span style="background-color: #ffffff;">Scales</span>=
| | | ^1 |
| == ==
| | | ^D |
| ==<span style="background-color: #ffffff;">Commas</span>==
| | | augmented 1sn |
| 35EDO tempers out the following commas. (Note: This assumes the val <35 55 81 98 121 130|.)
| | |- |
| ||~ **Comma** ||~ **Monzo** ||~ **Value (Cents)** ||~ **Name 1** ||~ **Name 2** ||~ **Name 3** || | | | 2 |
| ||= 2187/2048 || | -11 7 > ||> 113.69 ||= Apotome ||= Whitewood comma || || | | | 68.571 |
| ||= 6561/6250 || | -1 8 -5 > ||> 84.07 ||= Ripple comma ||= || ||
| | | dup unison |
| ||= 10077696/9765625 || | 9 9 -10 > ||> 54.46 ||= Mynic comma ||= || || | | | ^^1 |
| ||= 3125/3072 || | -10 -1 5 > ||> 29.61 ||= Small diesis ||= Magic comma || || | | | ^^D |
| ||= 405/392 || | -3 4 1 -2 > ||> 56.48 ||= Greenwoodma ||= || || | | | diminished 2nd |
| ||= 16807/16384 || | -14 0 0 5 > ||> 44.13 ||= ||= || ||
| | |- |
| ||= 525/512 || | -9 1 2 1 > ||> 43.41 ||= Avicennma ||= || || | | | 3 |
| ||= 126/125 || | 1 2 -3 1 > ||> 13.79 ||= Starling comma ||= Septimal semicomma || || | | | 102.857 |
| ||= 99/98 || | -1 2 0 -2 1 > ||> 17.58 ||= Mothwellsma ||= || || | | | dud 2nd |
| ||= 66/65 || | 1 1 -1 0 1 -1 > ||> 26.43 ||= ||= || || | | | vv2 |
| == ==
| | | vvE |
| | | minor 2nd |
| | |- |
| | | 4 |
| | | 137.143 |
| | | down 2nd |
| | | v2 |
| | | vE |
| | | neutral 2nd |
| | |- |
| | | 5 |
| | | 171.429 |
| | | 2nd |
| | | 2 |
| | | E |
| | | submajor 2nd |
| | |- |
| | | 6 |
| | | 205.714 |
| | | up 2nd |
| | | ^2 |
| | | ^E |
| | | major 2nd |
| | |- |
| | | 7 |
| | | 240 |
| | | dup 2nd |
| | | ^^2 |
| | | ^^E |
| | | supermajor 2nd |
| | |- |
| | | 8 |
| | | 274.286 |
| | | dud 3rd |
| | | vv3 |
| | | vvF |
| | | diminished 3rd |
| | |- |
| | | 9 |
| | | 308.571 |
| | | down 3rd |
| | | v3 |
| | | vF |
| | | minor 3rd |
| | |- |
| | | 10 |
| | | 342.857 |
| | | 3rd |
| | | 3 |
| | | F |
| | | neutral 3rd |
| | |- |
| | | 11 |
| | | 377.143 |
| | | up 3rd |
| | | ^3 |
| | | ^F |
| | | major 3rd |
| | |- |
| | | 12 |
| | | 411.429 |
| | | dup 3rd |
| | | ^^3 |
| | | ^^F |
| | | augmented 3rd |
| | |- |
| | | 13 |
| | | 445.714 |
| | | dud 4th |
| | | vv4 |
| | | vvG |
| | | diminished 4th |
| | |- |
| | | 14 |
| | | 480 |
| | | down 4th |
| | | v4 |
| | | vG |
| | | minor 4th |
| | |- |
| | | 15 |
| | | 514.286 |
| | | 4th |
| | | 4 |
| | | G |
| | | major 4th |
| | |- |
| | | 16 |
| | | 548.571 |
| | | up 4th |
| | | ^4 |
| | | ^G |
| | | augmented 4th |
| | |- |
| | | 17 |
| | | 582.857 |
| | | dup 4th |
| | | ^^4 |
| | | ^^G |
| | | minor tritone |
| | |- |
| | | 18 |
| | | 617.143 |
| | | dud 5th |
| | | vv5 |
| | | vvA |
| | | major tritone |
| | |- |
| | | 19 |
| | | 651.429 |
| | | down 5th |
| | | v5 |
| | | vA |
| | | diminished 5th |
| | |- |
| | | 20 |
| | | 685.714 |
| | | 5th |
| | | 5 |
| | | A |
| | | minor 5th |
| | |- |
| | | 21 |
| | | 720 |
| | | up 5th |
| | | ^5 |
| | | ^A |
| | | major 5th |
| | |- |
| | | 22 |
| | | 754.286 |
| | | dup 5th |
| | | ^^5 |
| | | ^^A |
| | | augmented 5th |
| | |- |
| | | 23 |
| | | 788.571 |
| | | dud 6th |
| | | vv6 |
| | | vvB |
| | | diminished 6th |
| | |- |
| | | 24 |
| | | 822.857 |
| | | down 6th |
| | | v6 |
| | | vB |
| | | minor 6th |
| | |- |
| | | 25 |
| | | 857.143 |
| | | 6th |
| | | 6 |
| | | B |
| | | neutral 6th |
| | |- |
| | | 26 |
| | | 891.429 |
| | | up 6th |
| | | ^6 |
| | | ^B |
| | | major 6th |
| | |- |
| | | 27 |
| | | 925.714 |
| | | dup 6th |
| | | ^^6 |
| | | ^^B |
| | | augmented 6th |
| | |- |
| | | 28 |
| | | 960 |
| | | dud 7th |
| | | vv7 |
| | | vvC |
| | | diminished 7th |
| | |- |
| | | 29 |
| | | 994.286 |
| | | down 7th |
| | | v7 |
| | | vC |
| | | minor 7th |
| | |- |
| | | 30 |
| | | 1028.571 |
| | | 7th |
| | | 7 |
| | | C |
| | | superminor 7th |
| | |- |
| | | 31 |
| | | 1062.857 |
| | | up 7th |
| | | ^7 |
| | | ^C |
| | | neutral 7th |
| | |- |
| | | 32 |
| | | 1097.143 |
| | | dup 7th |
| | | ^^7 |
| | | ^^C |
| | | major 7th |
| | |- |
| | | 33 |
| | | 1131.429 |
| | | dud 8ve |
| | | vv8 |
| | | vvD |
| | | augmented 7th |
| | |- |
| | | 34 |
| | | 1165.714 |
| | | down 8ve |
| | | v8 |
| | | vD |
| | | diminished 8ve |
| | |- |
| | | 35 |
| | | 1200 |
| | | 8ve |
| | | 8 |
| | | D |
| | | 8ve |
| | |} |
|
| |
|
| == == </pre></div> | | ===Sagittal notation=== |
| <h4>Original HTML content:</h4>
| | ====Best fifth notation==== |
| <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>35edo</title></head><body>35-tET or 35-<a class="wiki_link" href="http://xenharmonic.wikispaces.com/edo">EDO</a> refers to a tuning system which divides the octave into 35 steps of approximately <a class="wiki_link" href="http://xenharmonic.wikispaces.com/cent">34.29¢</a> each.<br />
| | This notation uses the same sagittal sequence as EDOs [[30edo#Second-best fifth notation|30b]] and [[40edo#Sagittal notation|40]], and is a superset of the notation for [[7edo#Sagittal notation|7-EDO]]. |
| <br />
| |
| As 35 is 5 times 7, 35edo allows for mixing the two smallest xenharmonic <a class="wiki_link" href="http://xenharmonic.wikispaces.com/macrotonal%20edos">macrotonal edos</a>: <a class="wiki_link" href="http://xenharmonic.wikispaces.com/5edo">5edo</a> and <a class="wiki_link" href="http://xenharmonic.wikispaces.com/7edo">7edo</a>. A single degree of 35edo represents the difference between 7edo's narrow fifth of 685.71¢ and 5edo's wide fifth of 720¢. Because it includes 7edo, 35edo tunes the 29th harmonic with +1 cent of error. 35edo can also represent the 2.3.5.7.11.17 <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Just%20intonation%20subgroups">subgroup</a> and 2.9.5.7.11.17 subgroup, because of the accuracy of 9 and the flatness of all other subgroup generators. Therefore among whitewood tunings it is very versatile, you can switch between these different subgroups if you don't mind having to use two different 3/2s to reach the inconsistent 9 (a characteristic of whitewood tunings), and if you ignore <a class="wiki_link" href="http://xenharmonic.wikispaces.com/22edo">22edo</a>'s<br />
| |
| more in-tune versions of 35edo MOS's and consistent representation of both subgroups. 35edo has the optimal patent val for <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Greenwoodmic%20temperaments">greenwood</a> and <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Greenwoodmic%20temperaments#Secund">secund</a> temperaments.<br />
| |
| <br />
| |
| A good beginning for start to play 35-EDO is with the Sub-diatonic scale, that is a <a class="wiki_link" href="http://xenharmonic.wikispaces.com/MOS">MOS</a> of 3L2s: 9 4 9 9 4.<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Intervals"></a><!-- ws:end:WikiTextHeadingRule:0 -->Intervals</h1>
| |
| <br />
| |
| (Bolded ratio indicates that the ratio is most accurately tuned by the given 35-edo interval.)<br />
| |
|
| |
|
| | <imagemap> |
| | File:35-EDO_Sagittal.svg |
| | desc none |
| | rect 80 0 300 50 [[Sagittal_notation]] |
| | rect 415 0 575 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation] |
| | rect 20 80 415 106 [[Fractional_3-limit_notation#Bad-fifths_limma-fraction_notation | limma-fraction notation]] |
| | default [[File:35-EDO_Sagittal.svg]] |
| | </imagemap> |
|
| |
|
| <table class="wiki_table">
| | ====Second-best fifth notation==== |
| <tr>
| | This notation uses the same sagittal sequence as [[42edo#Sagittal notation|42-EDO]], and is a superset of the notation for [[5edo#Sagittal notation|5-EDO]]. |
| <td>Degrees<br />
| |
| </td>
| |
| <td>Solfege<br />
| |
| </td>
| |
| <td>Cents value<br />
| |
| </td>
| |
| <td>Ratios in 2.5.7.11.17 subgroup<br />
| |
| </td>
| |
| <td>Ratios with flat 3<br />
| |
| </td>
| |
| <td>Ratios with sharp 3<br />
| |
| </td>
| |
| <td>Ratios with 9<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>0<br />
| |
| </td>
| |
| <td>do<br />
| |
| </td>
| |
| <td>0<br />
| |
| </td>
| |
| <td><strong>1/1</strong><br />
| |
| </td>
| |
| <td>(see comma table)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>1<br />
| |
| </td>
| |
| <td>du<br />
| |
| </td>
| |
| <td>34.29<br />
| |
| </td>
| |
| <td><strong>50/49</strong>, <strong>121/119</strong>, 33/32<br />
| |
| </td>
| |
| <td><strong>36/35</strong><br />
| |
| </td>
| |
| <td>25/24<br />
| |
| </td>
| |
| <td><strong>81/80</strong><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>2<br />
| |
| </td>
| |
| <td>di<br />
| |
| </td>
| |
| <td>68.57<br />
| |
| </td>
| |
| <td>128/125<br />
| |
| </td>
| |
| <td><strong>25/24</strong><br />
| |
| </td>
| |
| <td>81/80<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>3<br />
| |
| </td>
| |
| <td>ra<br />
| |
| </td>
| |
| <td>102.86<br />
| |
| </td>
| |
| <td><strong>17/16</strong><br />
| |
| </td>
| |
| <td><strong>15/14</strong><br />
| |
| </td>
| |
| <td><strong>16/15</strong><br />
| |
| </td>
| |
| <td><strong>18/17</strong><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>4<br />
| |
| </td>
| |
| <td>ru<br />
| |
| </td>
| |
| <td>137.14<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><strong>12/11</strong>, 16/15<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>5<br />
| |
| </td>
| |
| <td>ro<br />
| |
| </td>
| |
| <td>171.43<br />
| |
| </td>
| |
| <td><strong>11/10</strong><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>12/11<br />
| |
| </td>
| |
| <td><strong>10/9</strong><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>6<br />
| |
| </td>
| |
| <td>re<br />
| |
| </td>
| |
| <td>205.71<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><strong>9/8</strong><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>7<br />
| |
| </td>
| |
| <td>ri<br />
| |
| </td>
| |
| <td>240<br />
| |
| </td>
| |
| <td><strong>8/7</strong><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>7/6<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>8<br />
| |
| </td>
| |
| <td>ma<br />
| |
| </td>
| |
| <td>274.29<br />
| |
| </td>
| |
| <td><strong>20/17</strong><br />
| |
| </td>
| |
| <td><strong>7/6</strong><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>9<br />
| |
| </td>
| |
| <td>me<br />
| |
| </td>
| |
| <td>308.57<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><strong>6/5</strong><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>10<br />
| |
| </td>
| |
| <td>mu<br />
| |
| </td>
| |
| <td>342.86<br />
| |
| </td>
| |
| <td><strong>17/14</strong><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>6/5<br />
| |
| </td>
| |
| <td><strong>11/9</strong><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>11<br />
| |
| </td>
| |
| <td>mi<br />
| |
| </td>
| |
| <td>377.14<br />
| |
| </td>
| |
| <td><strong>5/4</strong><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>12<br />
| |
| </td>
| |
| <td>mo<br />
| |
| </td>
| |
| <td>411.43<br />
| |
| </td>
| |
| <td><strong>14/11</strong><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>13<br />
| |
| </td>
| |
| <td>fe<br />
| |
| </td>
| |
| <td>445.71<br />
| |
| </td>
| |
| <td><strong>22/17</strong>, 32/25<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><strong>9/7</strong><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>14<br />
| |
| </td>
| |
| <td>fo<br />
| |
| </td>
| |
| <td>480<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>4/3<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>15<br />
| |
| </td>
| |
| <td>fa<br />
| |
| </td>
| |
| <td>514.29<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><strong>4/3</strong><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>16<br />
| |
| </td>
| |
| <td>fu<br />
| |
| </td>
| |
| <td>548.57<br />
| |
| </td>
| |
| <td><strong>11/8</strong><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>17<br />
| |
| </td>
| |
| <td>fi<br />
| |
| </td>
| |
| <td>582.86<br />
| |
| </td>
| |
| <td><strong>7/5</strong><br />
| |
| </td>
| |
| <td><strong>24/17</strong><br />
| |
| </td>
| |
| <td>17/12<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>18<br />
| |
| </td>
| |
| <td>se<br />
| |
| </td>
| |
| <td>617.14<br />
| |
| </td>
| |
| <td><strong>10/7</strong><br />
| |
| </td>
| |
| <td><strong>17/12</strong><br />
| |
| </td>
| |
| <td>24/17<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>19<br />
| |
| </td>
| |
| <td>su<br />
| |
| </td>
| |
| <td>651.43<br />
| |
| </td>
| |
| <td><strong>16/11</strong><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>20<br />
| |
| </td>
| |
| <td>so<br />
| |
| </td>
| |
| <td>685.71<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><strong>3/2</strong><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>21<br />
| |
| </td>
| |
| <td>sa<br />
| |
| </td>
| |
| <td>720<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>3/2<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>22<br />
| |
| </td>
| |
| <td>si<br />
| |
| </td>
| |
| <td>754.29<br />
| |
| </td>
| |
| <td><strong>17/11</strong>, 25/16<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><strong>14/9</strong><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>23<br />
| |
| </td>
| |
| <td>lo<br />
| |
| </td>
| |
| <td>788.57<br />
| |
| </td>
| |
| <td><strong>11/7</strong><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>24<br />
| |
| </td>
| |
| <td>le<br />
| |
| </td>
| |
| <td>822.86<br />
| |
| </td>
| |
| <td><strong>8/5</strong><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>25<br />
| |
| </td>
| |
| <td>lu<br />
| |
| </td>
| |
| <td>857.15<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>5/3<br />
| |
| </td>
| |
| <td><strong>18/11</strong><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>26<br />
| |
| </td>
| |
| <td>la<br />
| |
| </td>
| |
| <td>891.43<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><strong>5/3</strong><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>27<br />
| |
| </td>
| |
| <td>li<br />
| |
| </td>
| |
| <td>925.71<br />
| |
| </td>
| |
| <td><strong>17/10</strong><br />
| |
| </td>
| |
| <td><strong>12/7</strong><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>28<br />
| |
| </td>
| |
| <td>ta<br />
| |
| </td>
| |
| <td>960<br />
| |
| </td>
| |
| <td><strong>7/4</strong><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>29<br />
| |
| </td>
| |
| <td>te<br />
| |
| </td>
| |
| <td>994.29<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><strong>16/9</strong><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>30<br />
| |
| </td>
| |
| <td>to<br />
| |
| </td>
| |
| <td>1028.57<br />
| |
| </td>
| |
| <td><strong>20/11</strong><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><strong>9/5</strong><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>31<br />
| |
| </td>
| |
| <td>tu<br />
| |
| </td>
| |
| <td>1062.86<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><strong>11/6</strong>, 15/8<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>32<br />
| |
| </td>
| |
| <td>ti<br />
| |
| </td>
| |
| <td>1097.14<br />
| |
| </td>
| |
| <td><strong>32/17</strong><br />
| |
| </td>
| |
| <td><strong>28/15</strong><br />
| |
| </td>
| |
| <td><strong>15/8</strong><br />
| |
| </td>
| |
| <td><strong>17/9</strong><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>33<br />
| |
| </td>
| |
| <td>de<br />
| |
| </td>
| |
| <td>1131.43<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>34<br />
| |
| </td>
| |
| <td>da<br />
| |
| </td>
| |
| <td>1165.71<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| <!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Rank two temperaments"></a><!-- ws:end:WikiTextHeadingRule:2 -->Rank two temperaments</h1>
| | <imagemap> |
| <br />
| | File:35b_Sagittal.svg |
| | desc none |
| | rect 80 0 300 50 [[Sagittal_notation]] |
| | rect 391 0 551 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation] |
| | rect 20 80 391 106 [[Fractional_3-limit_notation#Bad-fifths_apotome-fraction_notation | apotome-fraction notation]] |
| | default [[File:35b_Sagittal.svg]] |
| | </imagemap> |
|
| |
|
| | === Chord Names === |
| | Ups and downs can be used to name 35edo chords. Because every interval is perfect, the quality can be omitted, and the words major, minor, augmented and diminished are never used. An up or down immediately after the chord root affects the 3rd, 6th, 7th, and/or the 11th (every other note of a stacked-3rds chord 6-1-3-5-7-9-11-13). Alterations are always enclosed in parentheses, additions never are. |
|
| |
|
| <table class="wiki_table">
| | 0-10-20 = C E G = C = C or C perfect |
| <tr>
| |
| <th>Periods<br />
| |
| per octave<br />
| |
| </th>
| |
| <th>Generator<br />
| |
| </th>
| |
| <th>Temperaments with<br />
| |
| flat 3/2 (patent val)<br />
| |
| </th>
| |
| <th><span style="display: block; text-align: center;">Temperaments with</span><span style="display: block; text-align: center;">sharp 3/2 (35b val)</span><br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td>1<br />
| |
| </td>
| |
| <td>1\35<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>1<br />
| |
| </td>
| |
| <td>2\35<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>1<br />
| |
| </td>
| |
| <td>3\35<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/Ripple">Ripple</a><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>1<br />
| |
| </td>
| |
| <td>4\35<br />
| |
| </td>
| |
| <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Greenwoodmic%20temperaments#Secund">Secund</a><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>1<br />
| |
| </td>
| |
| <td>6\35<br />
| |
| </td>
| |
| <td colspan="2">Messed-up <a class="wiki_link" href="/Chromatic%20pairs#Baldy">Baldy</a><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>1<br />
| |
| </td>
| |
| <td>8\35<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>Messed-up <a class="wiki_link" href="/Orwell">Orwell</a><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>1<br />
| |
| </td>
| |
| <td>9\35<br />
| |
| </td>
| |
| <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Myna">Myna</a><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>1<br />
| |
| </td>
| |
| <td>11\35<br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/Magic%20family#Muggles">Muggles</a><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>1<br />
| |
| </td>
| |
| <td>12\35<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/Avicennmic%20temperaments#Roman">Roman</a><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>1<br />
| |
| </td>
| |
| <td>13\35<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Sensipent%20family">Sensipent</a> but <em>not</em> <a class="wiki_link" href="/Sensi">Sensi</a><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>1<br />
| |
| </td>
| |
| <td>16\35<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>1<br />
| |
| </td>
| |
| <td>17\35<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>5<br />
| |
| </td>
| |
| <td>1\35<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/Blackwood">Blackwood</a> (very unfair, favoring 7/6)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>5<br />
| |
| </td>
| |
| <td>2\35<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/Blackwood">Blackwood</a> (unfair, favoring 6/5 and 20/17)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>5<br />
| |
| </td>
| |
| <td>3\35<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/Blackwood">Blackwood</a> (fair, favoring 5/4 and 17/14)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>7<br />
| |
| </td>
| |
| <td>1\35<br />
| |
| </td>
| |
| <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Apotome%20family">Whitewood</a>/<a class="wiki_link" href="http://xenharmonic.wikispaces.com/Apotome%20family#Redwood">Redwood</a><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>7<br />
| |
| </td>
| |
| <td>2\35<br />
| |
| </td>
| |
| <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Greenwoodmic%20temperaments#Greenwood">Greenwood</a><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| <!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="Scales"></a><!-- ws:end:WikiTextHeadingRule:4 --><span style="background-color: #ffffff;">Scales</span></h1>
| | 0-9-20 = C vE G = Cv = C down |
| <!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><!-- ws:end:WikiTextHeadingRule:6 --> </h2>
| |
| <!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="Scales-Commas"></a><!-- ws:end:WikiTextHeadingRule:8 --><span style="background-color: #ffffff;">Commas</span></h2>
| |
| 35EDO tempers out the following commas. (Note: This assumes the val &lt;35 55 81 98 121 130|.)<br />
| |
|
| |
|
| | 0-11-20 = C ^E G = C^ = C up |
|
| |
|
| <table class="wiki_table">
| | 0-10-19 = C E vG = C(v5) = C down-five |
| <tr>
| |
| <th><strong>Comma</strong><br />
| |
| </th>
| |
| <th><strong>Monzo</strong><br />
| |
| </th>
| |
| <th><strong>Value (Cents)</strong><br />
| |
| </th>
| |
| <th><strong>Name 1</strong><br />
| |
| </th>
| |
| <th><strong>Name 2</strong><br />
| |
| </th>
| |
| <th><strong>Name 3</strong><br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">2187/2048<br />
| |
| </td>
| |
| <td>| -11 7 &gt;<br />
| |
| </td>
| |
| <td style="text-align: right;">113.69<br />
| |
| </td>
| |
| <td style="text-align: center;">Apotome<br />
| |
| </td>
| |
| <td style="text-align: center;">Whitewood comma<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">6561/6250<br />
| |
| </td>
| |
| <td>| -1 8 -5 &gt;<br />
| |
| </td>
| |
| <td style="text-align: right;">84.07<br />
| |
| </td>
| |
| <td style="text-align: center;">Ripple comma<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">10077696/9765625<br />
| |
| </td>
| |
| <td>| 9 9 -10 &gt;<br />
| |
| </td>
| |
| <td style="text-align: right;">54.46<br />
| |
| </td>
| |
| <td style="text-align: center;">Mynic comma<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">3125/3072<br />
| |
| </td>
| |
| <td>| -10 -1 5 &gt;<br />
| |
| </td>
| |
| <td style="text-align: right;">29.61<br />
| |
| </td>
| |
| <td style="text-align: center;">Small diesis<br />
| |
| </td>
| |
| <td style="text-align: center;">Magic comma<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">405/392<br />
| |
| </td>
| |
| <td>| -3 4 1 -2 &gt;<br />
| |
| </td>
| |
| <td style="text-align: right;">56.48<br />
| |
| </td>
| |
| <td style="text-align: center;">Greenwoodma<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">16807/16384<br />
| |
| </td>
| |
| <td>| -14 0 0 5 &gt;<br />
| |
| </td>
| |
| <td style="text-align: right;">44.13<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">525/512<br />
| |
| </td>
| |
| <td>| -9 1 2 1 &gt;<br />
| |
| </td>
| |
| <td style="text-align: right;">43.41<br />
| |
| </td>
| |
| <td style="text-align: center;">Avicennma<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">126/125<br />
| |
| </td>
| |
| <td>| 1 2 -3 1 &gt;<br />
| |
| </td>
| |
| <td style="text-align: right;">13.79<br />
| |
| </td>
| |
| <td style="text-align: center;">Starling comma<br />
| |
| </td>
| |
| <td style="text-align: center;">Septimal semicomma<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">99/98<br />
| |
| </td>
| |
| <td>| -1 2 0 -2 1 &gt;<br />
| |
| </td>
| |
| <td style="text-align: right;">17.58<br />
| |
| </td>
| |
| <td style="text-align: center;">Mothwellsma<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">66/65<br />
| |
| </td>
| |
| <td>| 1 1 -1 0 1 -1 &gt;<br />
| |
| </td>
| |
| <td style="text-align: right;">26.43<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| <!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><!-- ws:end:WikiTextHeadingRule:10 --> </h2>
| | 0-11-21 = C ^E ^G = C^(^5) = C up up-five |
| <br />
| | |
| <!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><!-- ws:end:WikiTextHeadingRule:12 --> </h2>
| | 0-10-20-30 = C E G B = C7 = C seven |
| </body></html></pre></div>
| | |
| | 0-10-20-29 = C E G vB = C,v7 = C add down-seven |
| | |
| | 0-9-20-30 = C vE G B = Cv,7 = C down add-seven |
| | |
| | 0-9-20-29 = C vE G vB = Cv7 = C down seven |
| | |
| | For a more complete list, see [[Ups and downs notation#Chords and Chord Progressions|Ups and downs notation - Chords and Chord Progressions]]. |
| | |
| | == JI Intervals == |
| | (Bolded ratio indicates that the ratio is most accurately tuned by the given 35edo interval.) |
| | |
| | {| class="wikitable" |
| | |- |
| | | Degrees |
| | | Cents value |
| | | Ratios in 2.5.7.11.17 subgroup |
| | | Ratios with flat 3 |
| | | Ratios with sharp 3 |
| | | Ratios with best 9 |
| | |- |
| | | 0 |
| | | 0.000 |
| | | '''1/1''' |
| | | (see comma table) |
| | | |
| | | |
| | |- |
| | | 1 |
| | | 34.286 |
| | | '''50/49''', '''121/119''', 33/32 |
| | | '''36/35''' |
| | | 25/24 |
| | | '''81/80''' |
| | |- |
| | | 2 |
| | | 68.571 |
| | | 128/125 |
| | | '''25/24''' |
| | | 81/80 |
| | | |
| | |- |
| | | 3 |
| | | 102.857 |
| | | '''17/16''' |
| | | '''15/14''' |
| | | '''16/15''' |
| | | '''18/17''' |
| | |- |
| | | 4 |
| | | 137.143 |
| | | |
| | | '''12/11''', 16/15 |
| | | |
| | | |
| | |- |
| | | 5 |
| | |171.429 |
| | | '''11/10''' |
| | | |
| | | 12/11 |
| | | '''10/9''' |
| | |- |
| | | 6 |
| | | 205.714 |
| | | |
| | | |
| | | |
| | | '''9/8''' |
| | |- |
| | | 7 |
| | | 240 |
| | | '''8/7''' |
| | | |
| | | 7/6 |
| | | |
| | |- |
| | | 8 |
| | | 274.286 |
| | | '''20/17''' |
| | | '''7/6''' |
| | | |
| | | |
| | |- |
| | | 9 |
| | | 308.571 |
| | | |
| | | '''6/5''' |
| | | |
| | | |
| | |- |
| | | 10 |
| | |342.857 |
| | | '''17/14''' |
| | | |
| | | 6/5 |
| | | '''11/9''' |
| | |- |
| | | 11 |
| | | 377.143 |
| | | '''5/4''' |
| | | |
| | | |
| | | |
| | |- |
| | | 12 |
| | | 411.429 |
| | | '''14/11''' |
| | | |
| | | |
| | | |
| | |- |
| | | 13 |
| | | 445.714 |
| | | '''22/17''', 32/25 |
| | | |
| | | |
| | | '''9/7''' |
| | |- |
| | | 14 |
| | | 480 |
| | | |
| | | |
| | | 4/3, '''21/16''' |
| | | |
| | |- |
| | | 15 |
| | |514.286 |
| | | |
| | | '''4/3''' |
| | | |
| | | |
| | |- |
| | | 16 |
| | | 548.571 |
| | | '''11/8''' |
| | | |
| | | |
| | | |
| | |- |
| | | 17 |
| | | 582.857 |
| | | '''7/5''' |
| | | '''24/17''' |
| | | 17/12 |
| | | |
| | |- |
| | | 18 |
| | | 617.143 |
| | | '''10/7''' |
| | | '''17/12''' |
| | | 24/17 |
| | | |
| | |- |
| | | 19 |
| | | 651.429 |
| | | '''16/11''' |
| | | |
| | | |
| | | |
| | |- |
| | | 20 |
| | |685.714 |
| | | |
| | | '''3/2''' |
| | | |
| | | |
| | |- |
| | | 21 |
| | | 720 |
| | | |
| | | |
| | | 3/2, '''32/21''' |
| | | |
| | |- |
| | | 22 |
| | | 754.286 |
| | | '''17/11''', 25/16 |
| | | |
| | | |
| | | '''14/9''' |
| | |- |
| | | 23 |
| | | 788.571 |
| | | '''11/7''' |
| | | |
| | | |
| | | |
| | |- |
| | | 24 |
| | | 822.857 |
| | | '''8/5''' |
| | | |
| | | |
| | | |
| | |- |
| | | 25 |
| | |857.143 |
| | | '''28/17''' |
| | | |
| | | 5/3 |
| | | '''18/11''' |
| | |- |
| | | 26 |
| | | 891.429 |
| | | |
| | | '''5/3''' |
| | | |
| | | |
| | |- |
| | | 27 |
| | | 925.714 |
| | | '''17/10''' |
| | | '''12/7''' |
| | | |
| | | |
| | |- |
| | | 28 |
| | | 960 |
| | | '''7/4''' |
| | | |
| | | |
| | | |
| | |- |
| | | 29 |
| | | 994.286 |
| | | |
| | | |
| | | |
| | | '''16/9''' |
| | |- |
| | | 30 |
| | |1028.571 |
| | | '''20/11''' |
| | | |
| | | |
| | | '''9/5''' |
| | |- |
| | | 31 |
| | | 1062.857 |
| | | |
| | | '''11/6''', 15/8 |
| | | |
| | | |
| | |- |
| | | 32 |
| | | 1097.143 |
| | | '''32/17''' |
| | | '''28/15''' |
| | | '''15/8''' |
| | | '''17/9''' |
| | |- |
| | | 33 |
| | | 1131.429 |
| | | |
| | | |
| | | |
| | | |
| | |- |
| | | 34 |
| | | 1165.714 |
| | | |
| | | |
| | | |
| | | |
| | |- |
| | |3 |
| | |1200 |
| | | |
| | | |
| | | |
| | | |
| | |} |
| | |
| | {{15-odd-limit|35}} |
| | |
| | == Regular temperament properties == |
| | === Rank-2 temperaments === |
| | {| class="wikitable" |
| | |- |
| | ! Periods<br>per 8ve |
| | ! Generator |
| | ! Temperaments with<br>flat 3/2 (patent val) |
| | ! Temperaments with sharp 3/2 (35b val) |
| | ! [[Mos scale]]s |
| | |- |
| | | 1 |
| | | 1\35 |
| | | |
| | | |
| | | |
| | |- |
| | | 1 |
| | | 2\35 |
| | | |
| | | |
| | | [[1L 16s]], [[17L 1s]] |
| | |- |
| | | 1 |
| | | 3\35 |
| | | |
| | | [[Ripple]] |
| | | [[1L 10s]], [[11L 1s]], [[12L 11s]] |
| | |- |
| | | 1 |
| | | 4\35 |
| | | [[Secund]] |
| | | |
| | | [[1L 7s]], [[8L 1s]], [[9L 8s]], [[9L 17s]] |
| | |- |
| | | 1 |
| | | 6\35 |
| | | colspan="2" | [[Baldy]] (messed-up) |
| | | [[1L 4s]], [[5L 1s]], [[6L 5s]], [[6L 11s]], [[6L 17s]], [[6L 23s]] |
| | |- |
| | | 1 |
| | | 8\35 |
| | | |
| | | [[Orwell]] (messed-up) |
| | | [[1L 3s]], [[4L 1s]], [[4L 5s]], [[9L 4s]], [[13L 9s]] |
| | |- |
| | | 1 |
| | | 9\35 |
| | | [[Myna]] |
| | | |
| | | [[1L 3s]], [[4L 3s]], [[4L 7s]], [[4L 11s]], [[4L 15s]], …, [[4L 27s]] |
| | |- |
| | | 1 |
| | | 11\35 |
| | | [[Muggles]] |
| | | |
| | | [[3L 1s]], [[3L 4s]], [[3L 7s]] [[3L 10s]], [[3L 13s]], [[16L 3s]] |
| | |- |
| | | 1 |
| | | 12\35 |
| | | |
| | | [[Roman]] |
| | | [[2L 1s]], [[3L 2s]], [[3L 5s]], [[3L 8s]], [[3L 11s]], [[3L 14s]], [[3L 17s]], [[3L 20s]], …, [[3L 29s]] |
| | |- |
| | | 1 |
| | | 13\35 |
| | | colspan="2" | Inconsistent 2.9'/7.5/3 [[sensi]] |
| | | [[2L 1s]], [[3L 2s]], [[3L 5s]], [[8L 3s]], [[8L 11s]], [[8L 19s]] |
| | |- |
| | | 1 |
| | | 16\35 |
| | | |
| | | |
| | | [[2L 1s]], [[2L 3s]], [[2L 5s]], [[2L 7s]], [[2L 9s]], [[11L 2s]], [[11L 13s]] |
| | |- |
| | | 1 |
| | | 17\35 |
| | | |
| | | |
| | | [[2L 1s]], [[2L 3s]], [[2L 5s]], [[2L 7s]], [[2L 9s]], [[2L 11s]], [[2L 13s]], [[2L 15s]], [[2L 17s]], [[2L 19s]], …, [[2L 31s]] |
| | |- |
| | | 5 |
| | | 1\35 |
| | | |
| | | [[Blackwood]] (favoring 7/6) |
| | | [[5L 5s]], [[5L 10s]], [[5L 15s]], [[5L 20s]], [[5L 25s]] |
| | |- |
| | | 5 |
| | | 2\35 |
| | | |
| | | [[Blackwood]] (favoring 6/5 and 20/17) |
| | | [[5L 5s]], [[5L 10s]], [[15L 5s]] |
| | |- |
| | | 5 |
| | | 3\35 |
| | | |
| | | [[Blackwood]] (favoring 5/4 and 17/14) |
| | | [[5L 5s]], [[10L 5s]], [[10L 15s]] |
| | |- |
| | | 7 |
| | | 1\35 |
| | | [[Whitewood]] / [[redwood]] |
| | | |
| | | [[7L 7s]], [[7L 14s]], [[7L 21s]] |
| | |- |
| | | 7 |
| | | 2\35 |
| | | [[Greenwood]] |
| | | |
| | | [[7L 7s]], [[14L 7s]] |
| | |} |
| | |
| | === Commas === |
| | 35et [[tempering out|tempers out]] the following [[comma]]s. (Note: This assumes the [[val]] {{val| 35 55 81 98 121 130 }}.) |
| | |
| | {| class="commatable wikitable center-1 center-2 right-4 center-5" |
| | |- |
| | ! [[Harmonic limit|Prime<br>limit]] |
| | ! [[Ratio]]<ref>Ratios longer than 10 digits are presented by placeholders with informative hints</ref> |
| | ! [[Monzo]] |
| | ! [[Cent]]s |
| | ! [[Color name]] |
| | ! Name(s) |
| | |- |
| | | 3 |
| | | [[2187/2048]] |
| | | {{monzo| -11 7 }} |
| | | 113.69 |
| | | Lawa |
| | | Whitewood comma, apotome, Pythagorean chroma |
| | |- |
| | | 5 |
| | | [[6561/6250]] |
| | | {{monzo| -1 8 -5 }} |
| | | 84.07 |
| | | Quingu |
| | | Ripple comma |
| | |- |
| | | 5 |
| | | <abbr title="10077696/9765625">(15 digits)</abbr> |
| | | {{monzo| 9 9 -10 }} |
| | | 54.46 |
| | | Quinbigu |
| | | [[Mynic comma]] |
| | |- |
| | | 5 |
| | | [[3125/3072]] |
| | | {{monzo| -10 -1 5 }} |
| | | 29.61 |
| | | Laquinyo |
| | | Magic comma, small diesis |
| | |- |
| | | 7 |
| | | [[405/392]] |
| | | {{monzo| -3 4 1 -2 }} |
| | | 56.48 |
| | | Ruruyo |
| | | Greenwoodma |
| | |- |
| | | 7 |
| | | [[16807/16384]] |
| | | {{monzo| -14 0 0 5 }} |
| | | 44.13 |
| | | Laquinzo |
| | | Cloudy comma |
| | |- |
| | | 7 |
| | | [[525/512]] |
| | | {{monzo| -9 1 2 1 }} |
| | | 43.41 |
| | | Lazoyoyo |
| | | Avicennma |
| | |- |
| | | 7 |
| | | [[126/125]] |
| | | {{monzo| 1 2 -3 1 }} |
| | | 13.79 |
| | | Zotrigu |
| | | Septimal semicomma, starling comma |
| | |- |
| | | 11 |
| | | [[99/98]] |
| | | {{monzo| -1 2 0 -2 1 }} |
| | | 17.58 |
| | | Loruru |
| | | Mothwellsma |
| | |- |
| | | 13 |
| | | [[66/65]] |
| | | {{monzo| 1 1 -1 0 1 -1 }} |
| | | 26.43 |
| | | Thulogu |
| | | Winmeanma |
| | |} |
| | <references/> |
| | |
| | == Scales == |
| | * A good place to start using 35-EDO is with the sub-diatonic scale, that is a [[MOS]] of 3L2s: 9 4 9 9 4. |
| | * Also available is the amulet scale{{idiosyncratic}}, approximated from [[magic]] in [[25edo]]: 3 1 3 3 1 3 4 3 3 1 3 4 3 |
| | * Approximations of [[gamelan]] scales: |
| | ** 5-tone pelog: 3 5 12 3 12 |
| | ** 7-tone pelog: 3 5 7 5 3 8 4 |
| | ** 5-tone slendro: 7 7 7 7 7 |
| | |
| | == Instruments == |
| | === Lumatone === |
| | 35edo can be played on the [[Lumatone]]. See [[Lumatone mapping for 35edo]] |
| | |
| | === Skip fretting === |
| | '''Skip fretting system 35 3 8''' is a [[skip fretting]] system for [[35edo]]. All examples on this page are for 7-string [[guitar]]. |
| | |
| | ; Prime harmonics |
| | 1/1: string 2 open |
| | |
| | 2/1: string 3 fret 9 and string 6 fret 1 |
| | |
| | 3/2: string 3 fret 4 and string 4 fret 13 |
| | |
| | 5/4: string 3 fret 1, string 4 fret 10, and string 7 fret 2 |
| | |
| | 7/4: string 4 fret 4 |
| | |
| | 11/8: string 1 fret 8, string 4 open, and string 5 fret 9 |
| | |
| | 13/8: string 1 fret 11, string 4 fret 3, and string 5 fret 12 |
| | |
| | 17/16: string 2 fret 1 and string 3 fret 10 |
| | |
| | == Music == |
| | ; [[dotuXil]] |
| | * [https://www.youtube.com/watch?v=61ssLv9H6rk "Icebound Gallery of Refractions"] from [https://dotuxil.bandcamp.com/album/collected-refractions ''Collected Refractions''] (2024) |
| | |
| | ; [[E8 Heterotic]] |
| | * [https://youtu.be/07-wj6BaTOw ''G2 Manifold''] (2020) – uses a combination of 5edo and 7edo, which can be classified as a 35edo subset. |
| | |
| | ; [[JUMBLE]] |
| | * [https://www.youtube.com/watch?v=2qpsI26JfjY ''Penguins...?''] (2024) |
| | |
| | ; [[Chuckles McGee]] |
| | * [https://www.archive.org/download/Transcendissonance/05Self-destructingMechanicalForest-CityOfTheAsleep.mp3 Self-Destructing Mechanical Forest] (in Secund[9]) |
| | |
| | ; [[Claudi Meneghin]] |
| | * [https://web.archive.org/web/20190412163316/http://soonlabel.com/xenharmonic/archives/2348'' Little Prelude & Fugue, "The Bijingle"''] (2014) |
| | * [https://www.youtube.com/watch?v=JPie2YDwA8I ''MicroFugue on Happy Birthday for Baroque Ensemble''] (2023) |
| | |
| | ; [[No Clue Music]] |
| | * [https://www.youtube.com/watch?v=zMUQWdFRGao ''DarkSciFiThing''] (2024) |
| | |
| | [[Category:Listen]] |