35edo: Difference between revisions

Revision as of 05:02, 26 December 2016

IMPORTED REVISION FROM WIKISPACES

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Original Wikitext content:

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, as well as 11-limit [[Magic family#Muggles-11-limit%7D|muggles]], and the 35f val is an excellent tuning for 13-limit muggles.

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.

=Notation= 

||= Degrees ||= Cents ||||||= [[xenharmonic/Ups and Downs Notation|Up/down ]][[xenharmonic/Ups and Downs Notation|Notation]] ||
||= 0 ||= 0 ||= unison ||= 1 ||= D ||
||= 1 ||= 34.29 ||= up unison ||= ^1 ||= D^ ||
||= 2 ||= 68.57 ||= double-up unison ||= ^^1 ||= D^^ ||
||= 3 ||= 102.86 ||= double-down 2nd ||= vv2 ||= Evv ||
||= 4 ||= 137.14 ||= down 2nd ||= v2 ||= Ev ||
||= 5 ||= 171.43 ||= 2nd ||= 2 ||= E ||
||= 6 ||= 205.71 ||= up 2nd ||= ^2 ||= E^ ||
||= 7 ||= 240 ||= double-up 2nd ||= ^^2 ||= E^^ ||
||= 8 ||= 274.29 ||= double-down 3rd ||= vv3 ||= Fvv ||
||= 9 ||= 308.57 ||= down 3rd ||= v3 ||= Fv ||
||= 10 ||= 342.86 ||= 3rd ||= 3 ||= F ||
||= 11 ||= 377.14 ||= up 3rd ||= ^3 ||= F^ ||
||= 12 ||= 411.43 ||= double-up 3rd ||= ^^3 ||= F^^ ||
||= 13 ||= 445.71 ||= double-down 4th ||= vv4 ||= Gvv ||
||= 14 ||= 480 ||= down 4th ||= v4 ||= Gv ||
||= 15 ||= 514.29 ||= 4th ||= 4 ||= G ||
||= 16 ||= 548.57 ||= up 4th ||= ^4 ||= G^ ||
||= 17 ||= 582.86 ||= double-up 4th ||= ^^4 ||= G^^ ||
||= 18 ||= 617.14 ||= double-downv 5th ||= vv5 ||= Avv ||
||= 19 ||= 651.43 ||= down 5th ||= v5 ||= Av ||
||= 20 ||= 685.71 ||= 5th ||= 5 ||= A ||
||= 21 ||= 720 ||= up 5th ||= ^5 ||= A^ ||
||= 22 ||= 754.29 ||= double-up 5th ||= ^^5 ||= A^^ ||
||= 23 ||= 788.57 ||= double-down 6th ||= vv6 ||= Bvv ||
||= 24 ||= 822.86 ||= down 6th ||= v6 ||= Bv ||
||= 25 ||= 857.15 ||= 6th ||= 6 ||= B ||
||= 26 ||= 891.43 ||= up 6th ||= ^6 ||= B^ ||
||= 27 ||= 925.71 ||= double-up 6th ||= ^^6 ||= B^^ ||
||= 28 ||= 960 ||= double-down 7th ||= vv7 ||= Cvv ||
||= 29 ||= 994.29 ||= down 7th ||= v7 ||= Cv ||
||= 30 ||= 1028.57 ||= 7th ||= 7 ||= C ||
||= 31 ||= 1062.86 ||= up 7th ||= ^7 ||= C^ ||
||= 32 ||= 1097.14 ||= double-up 7th ||= ^^7 ||= C^^ ||
||= 33 ||= 1131.43 ||= double-down 8ve ||= vv8 ||= Dvv ||
||= 34 ||= 1165.71 ||= down 8ve ||= v8 ||= Dv ||
||= 35 ||= 1200 ||= 8ve ||= 8 ||= D ||
= = 
=[[#Rank two temperaments]]= 
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.

0-10-20 = C E G = C = C or C perfect
0-9-20 = C Ev G = C(v3) = C down-three
0-11-20 = C E^ G = C(^3) = C up-three
0-10-19 = C E Gv = C(v5) = C down-five
0-11-21 = C E^ G^ = C(^3,^5) = C up-three up-five

0-10-20-30 = C E G B = C7 = C seven
0-10-20-29 = C E G Bv = C(v7) = C down-seven
0-9-20-30 = C Ev G B = C7(v3) = C seven down-three
0-9-20-29 = C Ev G Bv = C.v7 = C dot down seven

For a more complete list, see [[xenharmonic/Ups and Downs Notation#Chord%20names%20in%20other%20EDOs|Ups and Downs Notation - Chord names in other EDOs]].

=Intervals= 

(Bolded ratio indicates that the ratio is most accurately tuned by the given 35-edo interval.)
|| Degrees || Cents value || Ratios in2.5.7.11.17 subgroup || Ratios with flat 3 || Ratios with sharp 3 || Ratios with patent 9 ||
|| 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,  **21/16** ||   ||
|| 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,  **32/21** ||   ||
|| 22 || 754.29 || **17/11**  , 25/16 ||   ||   || **14/9** ||
|| 23 || 788.57 || **11/7** ||   ||   ||   ||
|| 24 || 822.86 || **8/5** ||   ||   ||   ||
|| 25 || 857.14 || **28/17** ||   || 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]]= 
=Rank two temperaments= 

||~ Periods
per octave ||~ Generator ||~ Temperaments with
flat 3/2 (patent val) ||~ <span style="display: block; text-align: center;">Temperaments with sharp 3/2 (35b val)</span> ||
|| 1 || 1\35 ||   ||   ||
|| 1 || 2\35 ||   ||   ||
|| 1 || 3\35 ||   || [[Ripple]] ||
|| 1 || 4\35 || [[xenharmonic/Greenwoodmic temperaments#Secund|Secund]] ||   ||
|| 1 || 6\35 |||| Messed-up [[Chromatic pairs#Baldy|Baldy]] ||
|| 1 || 8\35 ||   || Messed-up [[Orwell]] ||
|| 1 || 9\35 || [[xenharmonic/Myna|Myna]] ||   ||
|| 1 || 11\35 || [[Magic family#Muggles|Muggles]] ||   ||
|| 1 || 12\35 ||   || [[Avicennmic temperaments#Roman|Roman]] ||
|| 1 || 13\35 |||| Inconsistent 2.9'/7.5/3 [[Sensi]] ||
|| 1 || 16\35 ||   ||   ||
|| 1 || 17\35 ||   ||   ||
|| 5 || 1\35 ||   || [[Blackwood]] (favoring 7/6) ||
|| 5 || 2\35 ||   || [[Blackwood]] (favoring 6/5 and 20/17) ||
|| 5 || 3\35 ||   || [[Blackwood]] (favoring 5/4 and 17/14) ||
|| 7 || 1\35 || [[xenharmonic/Apotome family|Whitewood]]/[[xenharmonic/Apotome family#Redwood|Redwood]] ||   ||
|| 7 || 2\35 || [[xenharmonic/Greenwoodmic temperaments#Greenwood|Greenwood]] ||   ||
=<span style="background-color: #ffffff;">Scales</span>= 
== == 
==<span style="background-color: #ffffff;">Commas</span>== 
35EDO tempers out the following commas. (Note: This assumes the val < 35 55 81 98 121/1 130|.)
||~ **Comma** ||~ **Monzo** ||~ **Value (Cents)** ||~ **Name 1** ||~ **Name 2** ||~ **Name 3** ||
||= 2187/2048 || | -11 7 > ||> 113.69 ||= Apotome ||= Whitewood comma ||   ||
||= 6561/6250 || | -1 8 -5 > ||> 84.07 ||= Ripple comma ||=   ||   ||
||=   || | 9 9 -10 > ||> 54.46 ||= Mynic comma ||=   ||   ||
||= 3125/3072 || | -10 -1 5 > ||> 29.61 ||= Small diesis ||= Magic comma ||   ||
||= 405/392 || | -3 4 1 -2 > ||> 56.48 ||= Greenwoodma ||=   ||   ||
||= 16807/16384 || | -14 0 0 5 > ||> 44.13 ||=   ||=   ||   ||
||= 525/512 || | -9 1 2 1 > ||> 43.41 ||= Avicenna ||=   ||   ||
||= 126/125 || | 1 2 -3 1 > ||> 13.79 ||= Starling comma ||= Septimal semicomma ||   ||
||= 99/98 || | -1 2 0 -2 1 > ||> 17.58 ||= Mothwellsma ||=   ||   ||
||= 66/65 || | 1 1 -1 0 1 -1 > ||> 26.43 ||=   ||=   ||   ||
== == 

==Music== 
[[@http://soonlabel.com/xenharmonic/archives/2348|Little Prelude & Fugue, "The Bijingle" by Claudi Meneghin]]
[[@http://www.archive.org/download/Transcendissonance/05Self-destructingMechanicalForest-CityOfTheAsleep.mp3|Self-Destructing Mechanical Forest]] by Chuckles McGee (in Secund[9])

Original HTML content:

<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 />
<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, as well as 11-limit <a class="wiki_link" href="/Magic%20family#Muggles-11-limit%7D">muggles</a>, and the 35f val is an excellent tuning for 13-limit muggles.<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="Notation"></a><!-- ws:end:WikiTextHeadingRule:0 -->Notation</h1>
 <br />


<table class="wiki_table">
    <tr>
        <td style="text-align: center;">Degrees<br />
</td>
        <td style="text-align: center;">Cents<br />
</td>
        <td colspan="3" style="text-align: center;"><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation">Up/down </a><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation">Notation</a><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">0<br />
</td>
        <td style="text-align: center;">0<br />
</td>
        <td style="text-align: center;">unison<br />
</td>
        <td style="text-align: center;">1<br />
</td>
        <td style="text-align: center;">D<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">1<br />
</td>
        <td style="text-align: center;">34.29<br />
</td>
        <td style="text-align: center;">up unison<br />
</td>
        <td style="text-align: center;">^1<br />
</td>
        <td style="text-align: center;">D^<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">2<br />
</td>
        <td style="text-align: center;">68.57<br />
</td>
        <td style="text-align: center;">double-up unison<br />
</td>
        <td style="text-align: center;">^^1<br />
</td>
        <td style="text-align: center;">D^^<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">3<br />
</td>
        <td style="text-align: center;">102.86<br />
</td>
        <td style="text-align: center;">double-down 2nd<br />
</td>
        <td style="text-align: center;">vv2<br />
</td>
        <td style="text-align: center;">Evv<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">4<br />
</td>
        <td style="text-align: center;">137.14<br />
</td>
        <td style="text-align: center;">down 2nd<br />
</td>
        <td style="text-align: center;">v2<br />
</td>
        <td style="text-align: center;">Ev<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">5<br />
</td>
        <td style="text-align: center;">171.43<br />
</td>
        <td style="text-align: center;">2nd<br />
</td>
        <td style="text-align: center;">2<br />
</td>
        <td style="text-align: center;">E<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">6<br />
</td>
        <td style="text-align: center;">205.71<br />
</td>
        <td style="text-align: center;">up 2nd<br />
</td>
        <td style="text-align: center;">^2<br />
</td>
        <td style="text-align: center;">E^<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">7<br />
</td>
        <td style="text-align: center;">240<br />
</td>
        <td style="text-align: center;">double-up 2nd<br />
</td>
        <td style="text-align: center;">^^2<br />
</td>
        <td style="text-align: center;">E^^<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">8<br />
</td>
        <td style="text-align: center;">274.29<br />
</td>
        <td style="text-align: center;">double-down 3rd<br />
</td>
        <td style="text-align: center;">vv3<br />
</td>
        <td style="text-align: center;">Fvv<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">9<br />
</td>
        <td style="text-align: center;">308.57<br />
</td>
        <td style="text-align: center;">down 3rd<br />
</td>
        <td style="text-align: center;">v3<br />
</td>
        <td style="text-align: center;">Fv<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">10<br />
</td>
        <td style="text-align: center;">342.86<br />
</td>
        <td style="text-align: center;">3rd<br />
</td>
        <td style="text-align: center;">3<br />
</td>
        <td style="text-align: center;">F<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">11<br />
</td>
        <td style="text-align: center;">377.14<br />
</td>
        <td style="text-align: center;">up 3rd<br />
</td>
        <td style="text-align: center;">^3<br />
</td>
        <td style="text-align: center;">F^<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">12<br />
</td>
        <td style="text-align: center;">411.43<br />
</td>
        <td style="text-align: center;">double-up 3rd<br />
</td>
        <td style="text-align: center;">^^3<br />
</td>
        <td style="text-align: center;">F^^<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">13<br />
</td>
        <td style="text-align: center;">445.71<br />
</td>
        <td style="text-align: center;">double-down 4th<br />
</td>
        <td style="text-align: center;">vv4<br />
</td>
        <td style="text-align: center;">Gvv<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">14<br />
</td>
        <td style="text-align: center;">480<br />
</td>
        <td style="text-align: center;">down 4th<br />
</td>
        <td style="text-align: center;">v4<br />
</td>
        <td style="text-align: center;">Gv<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">15<br />
</td>
        <td style="text-align: center;">514.29<br />
</td>
        <td style="text-align: center;">4th<br />
</td>
        <td style="text-align: center;">4<br />
</td>
        <td style="text-align: center;">G<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">16<br />
</td>
        <td style="text-align: center;">548.57<br />
</td>
        <td style="text-align: center;">up 4th<br />
</td>
        <td style="text-align: center;">^4<br />
</td>
        <td style="text-align: center;">G^<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">17<br />
</td>
        <td style="text-align: center;">582.86<br />
</td>
        <td style="text-align: center;">double-up 4th<br />
</td>
        <td style="text-align: center;">^^4<br />
</td>
        <td style="text-align: center;">G^^<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">18<br />
</td>
        <td style="text-align: center;">617.14<br />
</td>
        <td style="text-align: center;">double-downv 5th<br />
</td>
        <td style="text-align: center;">vv5<br />
</td>
        <td style="text-align: center;">Avv<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">19<br />
</td>
        <td style="text-align: center;">651.43<br />
</td>
        <td style="text-align: center;">down 5th<br />
</td>
        <td style="text-align: center;">v5<br />
</td>
        <td style="text-align: center;">Av<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">20<br />
</td>
        <td style="text-align: center;">685.71<br />
</td>
        <td style="text-align: center;">5th<br />
</td>
        <td style="text-align: center;">5<br />
</td>
        <td style="text-align: center;">A<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">21<br />
</td>
        <td style="text-align: center;">720<br />
</td>
        <td style="text-align: center;">up 5th<br />
</td>
        <td style="text-align: center;">^5<br />
</td>
        <td style="text-align: center;">A^<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">22<br />
</td>
        <td style="text-align: center;">754.29<br />
</td>
        <td style="text-align: center;">double-up 5th<br />
</td>
        <td style="text-align: center;">^^5<br />
</td>
        <td style="text-align: center;">A^^<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">23<br />
</td>
        <td style="text-align: center;">788.57<br />
</td>
        <td style="text-align: center;">double-down 6th<br />
</td>
        <td style="text-align: center;">vv6<br />
</td>
        <td style="text-align: center;">Bvv<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">24<br />
</td>
        <td style="text-align: center;">822.86<br />
</td>
        <td style="text-align: center;">down 6th<br />
</td>
        <td style="text-align: center;">v6<br />
</td>
        <td style="text-align: center;">Bv<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">25<br />
</td>
        <td style="text-align: center;">857.15<br />
</td>
        <td style="text-align: center;">6th<br />
</td>
        <td style="text-align: center;">6<br />
</td>
        <td style="text-align: center;">B<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">26<br />
</td>
        <td style="text-align: center;">891.43<br />
</td>
        <td style="text-align: center;">up 6th<br />
</td>
        <td style="text-align: center;">^6<br />
</td>
        <td style="text-align: center;">B^<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">27<br />
</td>
        <td style="text-align: center;">925.71<br />
</td>
        <td style="text-align: center;">double-up 6th<br />
</td>
        <td style="text-align: center;">^^6<br />
</td>
        <td style="text-align: center;">B^^<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">28<br />
</td>
        <td style="text-align: center;">960<br />
</td>
        <td style="text-align: center;">double-down 7th<br />
</td>
        <td style="text-align: center;">vv7<br />
</td>
        <td style="text-align: center;">Cvv<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">29<br />
</td>
        <td style="text-align: center;">994.29<br />
</td>
        <td style="text-align: center;">down 7th<br />
</td>
        <td style="text-align: center;">v7<br />
</td>
        <td style="text-align: center;">Cv<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">30<br />
</td>
        <td style="text-align: center;">1028.57<br />
</td>
        <td style="text-align: center;">7th<br />
</td>
        <td style="text-align: center;">7<br />
</td>
        <td style="text-align: center;">C<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">31<br />
</td>
        <td style="text-align: center;">1062.86<br />
</td>
        <td style="text-align: center;">up 7th<br />
</td>
        <td style="text-align: center;">^7<br />
</td>
        <td style="text-align: center;">C^<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">32<br />
</td>
        <td style="text-align: center;">1097.14<br />
</td>
        <td style="text-align: center;">double-up 7th<br />
</td>
        <td style="text-align: center;">^^7<br />
</td>
        <td style="text-align: center;">C^^<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">33<br />
</td>
        <td style="text-align: center;">1131.43<br />
</td>
        <td style="text-align: center;">double-down 8ve<br />
</td>
        <td style="text-align: center;">vv8<br />
</td>
        <td style="text-align: center;">Dvv<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">34<br />
</td>
        <td style="text-align: center;">1165.71<br />
</td>
        <td style="text-align: center;">down 8ve<br />
</td>
        <td style="text-align: center;">v8<br />
</td>
        <td style="text-align: center;">Dv<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">35<br />
</td>
        <td style="text-align: center;">1200<br />
</td>
        <td style="text-align: center;">8ve<br />
</td>
        <td style="text-align: center;">8<br />
</td>
        <td style="text-align: center;">D<br />
</td>
    </tr>
</table>

<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><!-- ws:end:WikiTextHeadingRule:2 --> </h1>
 <!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><!-- ws:end:WikiTextHeadingRule:4 --><!-- ws:start:WikiTextAnchorRule:22:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@Rank two temperaments&quot; title=&quot;Anchor: Rank two temperaments&quot;/&gt; --><a name="Rank two temperaments"></a><!-- ws:end:WikiTextAnchorRule:22 --></h1>
 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.<br />
<br />
0-10-20 = C E G = C = C or C perfect<br />
0-9-20 = C Ev G = C(v3) = C down-three<br />
0-11-20 = C E^ G = C(^3) = C up-three<br />
0-10-19 = C E Gv = C(v5) = C down-five<br />
0-11-21 = C E^ G^ = C(^3,^5) = C up-three up-five<br />
<br />
0-10-20-30 = C E G B = C7 = C seven<br />
0-10-20-29 = C E G Bv = C(v7) = C down-seven<br />
0-9-20-30 = C Ev G B = C7(v3) = C seven down-three<br />
0-9-20-29 = C Ev G Bv = C.v7 = C dot down seven<br />
<br />
For a more complete list, see <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation#Chord%20names%20in%20other%20EDOs">Ups and Downs Notation - Chord names in other EDOs</a>.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name="Intervals"></a><!-- ws:end:WikiTextHeadingRule:6 -->Intervals</h1>
 <br />
(Bolded ratio indicates that the ratio is most accurately tuned by the given 35-edo interval.)<br />


<table class="wiki_table">
    <tr>
        <td>Degrees<br />
</td>
        <td>Cents value<br />
</td>
        <td>Ratios in2.5.7.11.17 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,  <strong>21/16</strong><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,  <strong>32/21</strong><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>857.14<br />
</td>
        <td><strong>28/17</strong><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:8:&lt;h1&gt; --><h1 id="toc4"><!-- ws:end:WikiTextHeadingRule:8 --><!-- ws:start:WikiTextAnchorRule:23:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@Rank two temperaments&quot; title=&quot;Anchor: Rank two temperaments&quot;/&gt; --><a name="Rank two temperaments"></a><!-- ws:end:WikiTextAnchorRule:23 --></h1>
 <!-- ws:start:WikiTextHeadingRule:10:&lt;h1&gt; --><h1 id="toc5"><a name="Rank two temperaments"></a><!-- ws:end:WikiTextHeadingRule:10 -->Rank two temperaments</h1>
 <br />


<table class="wiki_table">
    <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 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:12:&lt;h1&gt; --><h1 id="toc6"><a name="Scales"></a><!-- ws:end:WikiTextHeadingRule:12 --><span style="background-color: #ffffff;">Scales</span></h1>
 <!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><!-- ws:end:WikiTextHeadingRule:14 --> </h2>
 <!-- ws:start:WikiTextHeadingRule:16:&lt;h2&gt; --><h2 id="toc8"><a name="Scales-Commas"></a><!-- ws:end:WikiTextHeadingRule:16 --><span style="background-color: #ffffff;">Commas</span></h2>
 35EDO tempers out the following commas. (Note: This assumes the val &lt; 35 55 81 98 121/1 130|.)<br />


<table class="wiki_table">
    <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;"><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;">Avicenna<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:18:&lt;h2&gt; --><h2 id="toc9"><!-- ws:end:WikiTextHeadingRule:18 --> </h2>
 <br />
<!-- ws:start:WikiTextHeadingRule:20:&lt;h2&gt; --><h2 id="toc10"><a name="Scales-Music"></a><!-- ws:end:WikiTextHeadingRule:20 -->Music</h2>
 <a class="wiki_link_ext" href="http://soonlabel.com/xenharmonic/archives/2348" rel="nofollow" target="_blank">Little Prelude &amp; Fugue, &quot;The Bijingle&quot; by Claudi Meneghin</a><br />
<a class="wiki_link_ext" href="http://www.archive.org/download/Transcendissonance/05Self-destructingMechanicalForest-CityOfTheAsleep.mp3" rel="nofollow" target="_blank">Self-Destructing Mechanical Forest</a> by Chuckles McGee (in Secund[9])</body></html>

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