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{{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>2012-06-17 19:03:25 UTC</tt>.<br>
: The original revision id was <tt>346022254</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 (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 [[xenharmonic/22edo|22edo]]'s 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.
== Theory ==
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 || Cents value || Ratios in 2.5.7.11.17 subgroup || Ratios with flat 3 || Ratios with sharp 3 || Ratios with patent 9 ||
{{Harmonics in equal |35}}
|| 0 || 0 || **1/1** || (see comma table) || || ||
|| 1 || 34.29 || **50/49**, **121/119**, 33/32 || **36/35** || 25/24 || **81/80** ||
|| 2 || 68.57 || 128/125 || **25/24** || 81/80 || ||
|| 3 || 102.86 || **17/16** || **15/14** || **16/15** || **18/17** ||
|| 4 || 137.14 || || **12/11**, 16/15 || || ||
|| 5 || 171.43 || **11/10** || || 12/11 || **10/9** ||
|| 6 || 205.71 || || || || **9/8** ||
|| 7 || 240 || **8/7** || || 7/6 || ||
|| 8 || 274.29 || **20/17** || **7/6** || || ||
|| 9 || 308.57 || || **6/5** || || ||
|| 10 || 342.86 || **17/14** || || 6/5 || **11/9** ||
|| 11 || 377.14 || **5/4** || || || ||
|| 12 || 411.43 || **14/11** || || || ||
|| 13 || 445.71 || **22/17**, 32/25 || || || **9/7** ||
|| 14 || 480 || || || 4/3 || ||
|| 15 || 514.29 || || **4/3** || || ||
|| 16 || 548.57 || **11/8** || || || ||
|| 17 || 582.86 || **7/5** || **24/17** || 17/12 || ||
|| 18 || 617.14 || **10/7** || **17/12** || 24/17 || ||
|| 19 || 651.43 || **16/11** || || || ||
|| 20 || 685.71 || || **3/2** || || ||
|| 21 || 720 || || || 3/2 || ||
|| 22 || 754.29 || **17/11**, 25/16 || || || **14/9** ||
|| 23 || 788.57 || **11/7** || || || ||
|| 24 || 822.86 || **8/5** || || || ||
|| 25 || 857.15 || || || 5/3 || **18/11** ||
|| 26 || 891.43 || || **5/3** || || ||
|| 27 || 925.71 || **17/10** || **12/7** || || ||
|| 28 || 960 || **7/4** || || || ||
|| 29 || 994.29 || || || || **16/9** ||
|| 30 || 1028.57 || **20/11** || || || **9/5** ||
|| 31 || 1062.86 || || **11/6**, 15/8 || || ||
|| 32 || 1097.14 || **32/17** || **28/15** || **15/8** || **17/9** ||
|| 33 || 1131.43 || || || || ||
|| 34 || 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 |||| Inconsistent 2.9'/7.5/3 [[Sensi]] ||
| unison
|| 1 || 16\35 || || ||
| 1
|| 1 || 17\35 || || ||
| D
|| 5 || 1\35 || || [[Blackwood]] (favoring 7/6) ||
| 1sn, prime
|| 5 || 2\35 || || [[Blackwood]] (favoring 6/5 and 20/17) ||
|-
|| 5 || 3\35 || || [[Blackwood]] (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 (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 <a class="wiki_link" href="http://xenharmonic.wikispaces.com/22edo">22edo</a>'s 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>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 patent 9<br />
</td>
</tr>
<tr>
<td>0<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>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>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>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>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>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>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>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>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>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>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>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>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>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>480<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>4/3<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>15<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>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>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>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>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>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>720<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>3/2<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>22<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>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>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>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>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>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>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>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>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>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>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>1131.43<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>34<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 colspan="2">Inconsistent 2.9'/7.5/3 <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> (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> (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> (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]]
Prime factorization
5 × 7
Step size
34.2857 ¢
Fifth
20\35 (685.714 ¢) (→ 4\7 )
Semitones (A1:m2)
0:5 (0 ¢ : 171.4 ¢)
Dual sharp fifth
21\35 (720 ¢) (→ 3\5 )
Dual flat fifth
20\35 (685.714 ¢) (→ 4\7 )
Dual major 2nd
6\35 (205.714 ¢)
Consistency limit
7
Distinct consistency limit
7
35 equal divisions of the octave (abbreviated 35edo or 35ed2 ), also called 35-tone equal temperament (35tet ) or 35 equal temperament (35et ) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 35 equal parts of about 34.3 ¢ each. Each step represents a frequency ratio of 21/35 , or the 35th root of 2.
Theory 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 ¢ and 5edo's wide fifth of 720 ¢. Because it includes 7edo, 35edo tunes the 29th harmonic with only 1 ¢ of error.
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.
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).
Odd harmonics
Approximation of odd harmonics in 35edo
Harmonic
3
5
7
9
11
13
15
17
19
21
23
Error
Absolute (¢ )
-16.2
-9.2
-8.8
+1.8
-2.7
+16.6
+8.9
-2.1
+11.1
+9.2
-11.1
Relative (% )
-47.4
-26.7
-25.7
+5.3
-8.0
+48.5
+25.9
-6.1
+32.3
+26.9
-32.5
Stepsreduced )
55
81
98
111
121
130
137
143
149
154
158
Notation 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.
Degrees
Cents
Ups and downs notation
Dual-fifth notation
based on closest 12edo interval
0
0.000
unison
1
D
1sn, prime
1
34.286
up unison
^1
^D
augmented 1sn
2
68.571
dup unison
^^1
^^D
diminished 2nd
3
102.857
dud 2nd
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
Sagittal notation Best fifth notation This notation uses the same sagittal sequence as EDOs 30b and 40 , and is a superset of the notation for 7-EDO .
Second-best fifth notation This notation uses the same sagittal sequence as 42-EDO , and is a superset of the notation for 5-EDO .
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.
0-10-20 = C E G = C = C or C perfect
0-9-20 = C vE G = Cv = C down
0-11-20 = C ^E G = C^ = C up
0-10-19 = C E vG = C(v5) = C down-five
0-11-21 = C ^E ^G = C^(^5) = C up up-five
0-10-20-30 = C E G B = C7 = C seven
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 .
JI Intervals (Bolded ratio indicates that the ratio is most accurately tuned by the given 35edo interval.)
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
The following tables show how 15-odd-limit intervals are represented in 35edo. Prime harmonics are in bold ; inconsistent intervals are in italics .
15-odd-limit intervals in 35edo (direct approximation, even if inconsistent)
Interval and complement
Error (abs, ¢ )
Error (rel, % )
1/1, 2/1
0.000
0.0
7/5, 10/7
0.345
1.0
13/12, 24/13 1.430 4.2
9/8, 16/9 1.804 5.3
11/8, 16/11 2.747 8.0
11/9, 18/11 4.551 13.3
11/7, 14/11
6.079
17.7
11/10, 20/11
6.424
18.7
5/3, 6/5
7.070
20.6
7/6, 12/7
7.415
21.6
15/13, 26/15 7.741 22.6
13/10, 20/13 8.500 24.8
7/4, 8/7 8.826 25.7
13/7, 14/13 8.845 25.8
15/8, 16/15 8.874 25.9
5/4, 8/5 9.171 26.7
9/7, 14/9 10.630 31.0
9/5, 10/9 10.975 32.0
15/11, 22/15 11.621 33.9
11/6, 12/11
13.494
39.4
13/9, 18/13 14.811 43.2
13/11, 22/13 14.924 43.5
3/2, 4/3 16.241 47.4
15/14, 28/15
16.586
48.4
13/8, 16/13 16.615 48.5
15-odd-limit intervals in 35edo (patent val mapping)
Interval and complement
Error (abs, ¢ )
Error (rel, % )
1/1, 2/1
0.000
0.0
7/5, 10/7
0.345
1.0
11/8, 16/11 2.747 8.0
11/7, 14/11
6.079
17.7
11/10, 20/11
6.424
18.7
5/3, 6/5
7.070
20.6
7/6, 12/7
7.415
21.6
7/4, 8/7 8.826 25.7
5/4, 8/5 9.171 26.7
11/6, 12/11
13.494
39.4
3/2, 4/3 16.241 47.4
15/14, 28/15
16.586
48.4
13/8, 16/13 16.615 48.5
13/11, 22/13 19.362 56.5
15/11, 22/15 22.665 66.1
9/5, 10/9 23.311 68.0
9/7, 14/9 23.656 69.0
15/8, 16/15 25.412 74.1
13/7, 14/13 25.441 74.2
13/10, 20/13 25.786 75.2
11/9, 18/11 29.735 86.7
9/8, 16/9 32.481 94.7
13/12, 24/13 32.856 95.8
15/13, 26/15 42.027 122.6
13/9, 18/13 49.097 143.2
Regular temperament properties Rank-2 temperaments
Periods
Generator
Temperaments with
Temperaments with sharp 3/2 (35b val)
Mos scales
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
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
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 tempers out the following commas . (Note: This assumes the val ⟨ 35 55 81 98 121 130]
Prime
Ratio [ 1] Monzo
Cents
Color name
Name(s)
3
2187/2048
[ -11 7⟩ 113.69
Lawa
Whitewood comma, apotome, Pythagorean chroma
5
6561/6250
[ -1 8 -5⟩ 84.07
Quingu
Ripple comma
5
(15 digits)
[ 9 9 -10⟩ 54.46
Quinbigu
Mynic comma
5
3125/3072
[ -10 -1 5⟩ 29.61
Laquinyo
Magic comma, small diesis
7
405/392
[ -3 4 1 -2⟩ 56.48
Ruruyo
Greenwoodma
7
16807/16384
[ -14 0 0 5⟩ 44.13
Laquinzo
Cloudy comma
7
525/512
[ -9 1 2 1⟩ 43.41
Lazoyoyo
Avicennma
7
126/125
[ 1 2 -3 1⟩ 13.79
Zotrigu
Septimal semicomma, starling comma
11
99/98
[ -1 2 0 -2 1⟩ 17.58
Loruru
Mothwellsma
13
66/65
[ 1 1 -1 0 1 -1⟩ 26.43
Thulogu
Winmeanma
↑ Ratios longer than 10 digits are presented by placeholders with informative hints
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 term , 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 E8 Heterotic G2 Manifold JUMBLE Chuckles McGee Claudi Meneghin No Clue Music 
