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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | 35-tET or 35-[[EDO|EDO]] refers to a tuning system which divides the octave into 35 steps of approximately [[cent|34.29¢]] each. |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
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| : This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2016-12-30 15:40:33 UTC</tt>.<br>
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| : The original revision id was <tt>602918142</tt>.<br>
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| : The revision comment was: <tt></tt><br>
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| The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
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| <h4>Original Wikitext content:</h4>
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| <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.
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| 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. | | As 35 is 5 times 7, 35edo allows for mixing the two smallest xenharmonic [[macrotonal_edos|macrotonal edos]]: [[5edo|5edo]] and [[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 [[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 [[22edo|22edo]]'s more in-tune versions of 35edo MOS's and consistent representation of both subgroups. 35edo has the optimal patent val for [[Greenwoodmic_temperaments|greenwood]] and [[Greenwoodmic_temperaments#Secund|secund]] temperaments, as well as 11-limit [[Magic_family#Muggles-11-limit}|muggles]], and the 35f val is an excellent tuning for 13-limit muggles. |
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| 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. | | A good beginning for start to play 35-EDO is with the Sub-diatonic scale, that is a [[MOS|MOS]] of 3L2s: 9 4 9 9 4. |
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| =Notation= | | =Notation= |
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| ||= Degrees ||= Cents ||||||= [[xenharmonic/Ups and Downs Notation|Up/down ]][[xenharmonic/Ups and Downs Notation|Notation]] || | | {| class="wikitable" |
| ||= 0 ||= 0 ||= unison ||= 1 ||= D || | | |- |
| ||= 1 ||= 34.29 ||= up unison ||= ^1 ||= D^ || | | | style="text-align:center;" | Degrees |
| ||= 2 ||= 68.57 ||= double-up unison ||= ^^1 ||= D^^ || | | | style="text-align:center;" | Cents |
| ||= 3 ||= 102.86 ||= double-down 2nd ||= vv2 ||= Evv || | | | colspan="3" style="text-align:center;" | [[Ups_and_Downs_Notation|Up/down ]][[Ups_and_Downs_Notation|Notation]] |
| ||= 4 ||= 137.14 ||= down 2nd ||= v2 ||= Ev || | | |- |
| ||= 5 ||= 171.43 ||= 2nd ||= 2 ||= E || | | | style="text-align:center;" | 0 |
| ||= 6 ||= 205.71 ||= up 2nd ||= ^2 ||= E^ || | | | style="text-align:center;" | 0 |
| ||= 7 ||= 240 ||= double-up 2nd ||= ^^2 ||= E^^ || | | | style="text-align:center;" | unison |
| ||= 8 ||= 274.29 ||= double-down 3rd ||= vv3 ||= Fvv || | | | style="text-align:center;" | 1 |
| ||= 9 ||= 308.57 ||= down 3rd ||= v3 ||= Fv || | | | style="text-align:center;" | D |
| ||= 10 ||= 342.86 ||= 3rd ||= 3 ||= F || | | |- |
| ||= 11 ||= 377.14 ||= up 3rd ||= ^3 ||= F^ || | | | style="text-align:center;" | 1 |
| ||= 12 ||= 411.43 ||= double-up 3rd ||= ^^3 ||= F^^ || | | | style="text-align:center;" | 34.29 |
| ||= 13 ||= 445.71 ||= double-down 4th ||= vv4 ||= Gvv || | | | style="text-align:center;" | up unison |
| ||= 14 ||= 480 ||= down 4th ||= v4 ||= Gv || | | | style="text-align:center;" | ^1 |
| ||= 15 ||= 514.29 ||= 4th ||= 4 ||= G || | | | style="text-align:center;" | D^ |
| ||= 16 ||= 548.57 ||= up 4th ||= ^4 ||= G^ || | | |- |
| ||= 17 ||= 582.86 ||= double-up 4th ||= ^^4 ||= G^^ || | | | style="text-align:center;" | 2 |
| ||= 18 ||= 617.14 ||= double-downv 5th ||= vv5 ||= Avv || | | | style="text-align:center;" | 68.57 |
| ||= 19 ||= 651.43 ||= down 5th ||= v5 ||= Av || | | | style="text-align:center;" | double-up unison |
| ||= 20 ||= 685.71 ||= 5th ||= 5 ||= A || | | | style="text-align:center;" | ^^1 |
| ||= 21 ||= 720 ||= up 5th ||= ^5 ||= A^ || | | | style="text-align:center;" | D^^ |
| ||= 22 ||= 754.29 ||= double-up 5th ||= ^^5 ||= A^^ || | | |- |
| ||= 23 ||= 788.57 ||= double-down 6th ||= vv6 ||= Bvv || | | | style="text-align:center;" | 3 |
| ||= 24 ||= 822.86 ||= down 6th ||= v6 ||= Bv || | | | style="text-align:center;" | 102.86 |
| ||= 25 ||= 857.15 ||= 6th ||= 6 ||= B || | | | style="text-align:center;" | double-down 2nd |
| ||= 26 ||= 891.43 ||= up 6th ||= ^6 ||= B^ || | | | style="text-align:center;" | vv2 |
| ||= 27 ||= 925.71 ||= double-up 6th ||= ^^6 ||= B^^ || | | | style="text-align:center;" | Evv |
| ||= 28 ||= 960 ||= double-down 7th ||= vv7 ||= Cvv || | | |- |
| ||= 29 ||= 994.29 ||= down 7th ||= v7 ||= Cv || | | | style="text-align:center;" | 4 |
| ||= 30 ||= 1028.57 ||= 7th ||= 7 ||= C || | | | style="text-align:center;" | 137.14 |
| ||= 31 ||= 1062.86 ||= up 7th ||= ^7 ||= C^ || | | | style="text-align:center;" | down 2nd |
| ||= 32 ||= 1097.14 ||= double-up 7th ||= ^^7 ||= C^^ || | | | style="text-align:center;" | v2 |
| ||= 33 ||= 1131.43 ||= double-down 8ve ||= vv8 ||= Dvv || | | | style="text-align:center;" | Ev |
| ||= 34 ||= 1165.71 ||= down 8ve ||= v8 ||= Dv || | | |- |
| ||= 35 ||= 1200 ||= 8ve ||= 8 ||= D || | | | style="text-align:center;" | 5 |
| = = | | | style="text-align:center;" | 171.43 |
| =[[#Rank two temperaments]]= | | | style="text-align:center;" | 2nd |
| | | style="text-align:center;" | 2 |
| | | style="text-align:center;" | E |
| | |- |
| | | style="text-align:center;" | 6 |
| | | style="text-align:center;" | 205.71 |
| | | style="text-align:center;" | up 2nd |
| | | style="text-align:center;" | ^2 |
| | | style="text-align:center;" | E^ |
| | |- |
| | | style="text-align:center;" | 7 |
| | | style="text-align:center;" | 240 |
| | | style="text-align:center;" | double-up 2nd |
| | | style="text-align:center;" | ^^2 |
| | | style="text-align:center;" | E^^ |
| | |- |
| | | style="text-align:center;" | 8 |
| | | style="text-align:center;" | 274.29 |
| | | style="text-align:center;" | double-down 3rd |
| | | style="text-align:center;" | vv3 |
| | | style="text-align:center;" | Fvv |
| | |- |
| | | style="text-align:center;" | 9 |
| | | style="text-align:center;" | 308.57 |
| | | style="text-align:center;" | down 3rd |
| | | style="text-align:center;" | v3 |
| | | style="text-align:center;" | Fv |
| | |- |
| | | style="text-align:center;" | 10 |
| | | style="text-align:center;" | 342.86 |
| | | style="text-align:center;" | 3rd |
| | | style="text-align:center;" | 3 |
| | | style="text-align:center;" | F |
| | |- |
| | | style="text-align:center;" | 11 |
| | | style="text-align:center;" | 377.14 |
| | | style="text-align:center;" | up 3rd |
| | | style="text-align:center;" | ^3 |
| | | style="text-align:center;" | F^ |
| | |- |
| | | style="text-align:center;" | 12 |
| | | style="text-align:center;" | 411.43 |
| | | style="text-align:center;" | double-up 3rd |
| | | style="text-align:center;" | ^^3 |
| | | style="text-align:center;" | F^^ |
| | |- |
| | | style="text-align:center;" | 13 |
| | | style="text-align:center;" | 445.71 |
| | | style="text-align:center;" | double-down 4th |
| | | style="text-align:center;" | vv4 |
| | | style="text-align:center;" | Gvv |
| | |- |
| | | style="text-align:center;" | 14 |
| | | style="text-align:center;" | 480 |
| | | style="text-align:center;" | down 4th |
| | | style="text-align:center;" | v4 |
| | | style="text-align:center;" | Gv |
| | |- |
| | | style="text-align:center;" | 15 |
| | | style="text-align:center;" | 514.29 |
| | | style="text-align:center;" | 4th |
| | | style="text-align:center;" | 4 |
| | | style="text-align:center;" | G |
| | |- |
| | | style="text-align:center;" | 16 |
| | | style="text-align:center;" | 548.57 |
| | | style="text-align:center;" | up 4th |
| | | style="text-align:center;" | ^4 |
| | | style="text-align:center;" | G^ |
| | |- |
| | | style="text-align:center;" | 17 |
| | | style="text-align:center;" | 582.86 |
| | | style="text-align:center;" | double-up 4th |
| | | style="text-align:center;" | ^^4 |
| | | style="text-align:center;" | G^^ |
| | |- |
| | | style="text-align:center;" | 18 |
| | | style="text-align:center;" | 617.14 |
| | | style="text-align:center;" | double-downv 5th |
| | | style="text-align:center;" | vv5 |
| | | style="text-align:center;" | Avv |
| | |- |
| | | style="text-align:center;" | 19 |
| | | style="text-align:center;" | 651.43 |
| | | style="text-align:center;" | down 5th |
| | | style="text-align:center;" | v5 |
| | | style="text-align:center;" | Av |
| | |- |
| | | style="text-align:center;" | 20 |
| | | style="text-align:center;" | 685.71 |
| | | style="text-align:center;" | 5th |
| | | style="text-align:center;" | 5 |
| | | style="text-align:center;" | A |
| | |- |
| | | style="text-align:center;" | 21 |
| | | style="text-align:center;" | 720 |
| | | style="text-align:center;" | up 5th |
| | | style="text-align:center;" | ^5 |
| | | style="text-align:center;" | A^ |
| | |- |
| | | style="text-align:center;" | 22 |
| | | style="text-align:center;" | 754.29 |
| | | style="text-align:center;" | double-up 5th |
| | | style="text-align:center;" | ^^5 |
| | | style="text-align:center;" | A^^ |
| | |- |
| | | style="text-align:center;" | 23 |
| | | style="text-align:center;" | 788.57 |
| | | style="text-align:center;" | double-down 6th |
| | | style="text-align:center;" | vv6 |
| | | style="text-align:center;" | Bvv |
| | |- |
| | | style="text-align:center;" | 24 |
| | | style="text-align:center;" | 822.86 |
| | | style="text-align:center;" | down 6th |
| | | style="text-align:center;" | v6 |
| | | style="text-align:center;" | Bv |
| | |- |
| | | style="text-align:center;" | 25 |
| | | style="text-align:center;" | 857.15 |
| | | style="text-align:center;" | 6th |
| | | style="text-align:center;" | 6 |
| | | style="text-align:center;" | B |
| | |- |
| | | style="text-align:center;" | 26 |
| | | style="text-align:center;" | 891.43 |
| | | style="text-align:center;" | up 6th |
| | | style="text-align:center;" | ^6 |
| | | style="text-align:center;" | B^ |
| | |- |
| | | style="text-align:center;" | 27 |
| | | style="text-align:center;" | 925.71 |
| | | style="text-align:center;" | double-up 6th |
| | | style="text-align:center;" | ^^6 |
| | | style="text-align:center;" | B^^ |
| | |- |
| | | style="text-align:center;" | 28 |
| | | style="text-align:center;" | 960 |
| | | style="text-align:center;" | double-down 7th |
| | | style="text-align:center;" | vv7 |
| | | style="text-align:center;" | Cvv |
| | |- |
| | | style="text-align:center;" | 29 |
| | | style="text-align:center;" | 994.29 |
| | | style="text-align:center;" | down 7th |
| | | style="text-align:center;" | v7 |
| | | style="text-align:center;" | Cv |
| | |- |
| | | style="text-align:center;" | 30 |
| | | style="text-align:center;" | 1028.57 |
| | | style="text-align:center;" | 7th |
| | | style="text-align:center;" | 7 |
| | | style="text-align:center;" | C |
| | |- |
| | | style="text-align:center;" | 31 |
| | | style="text-align:center;" | 1062.86 |
| | | style="text-align:center;" | up 7th |
| | | style="text-align:center;" | ^7 |
| | | style="text-align:center;" | C^ |
| | |- |
| | | style="text-align:center;" | 32 |
| | | style="text-align:center;" | 1097.14 |
| | | style="text-align:center;" | double-up 7th |
| | | style="text-align:center;" | ^^7 |
| | | style="text-align:center;" | C^^ |
| | |- |
| | | style="text-align:center;" | 33 |
| | | style="text-align:center;" | 1131.43 |
| | | style="text-align:center;" | double-down 8ve |
| | | style="text-align:center;" | vv8 |
| | | style="text-align:center;" | Dvv |
| | |- |
| | | style="text-align:center;" | 34 |
| | | style="text-align:center;" | 1165.71 |
| | | style="text-align:center;" | down 8ve |
| | | style="text-align:center;" | v8 |
| | | style="text-align:center;" | Dv |
| | |- |
| | | style="text-align:center;" | 35 |
| | | style="text-align:center;" | 1200 |
| | | style="text-align:center;" | 8ve |
| | | style="text-align:center;" | 8 |
| | | style="text-align:center;" | D |
| | |} |
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| | = = |
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| 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. | | 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. |
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| 0-10-20 = C E G = C = C or C perfect | | 0-10-20 = C E G = C = C or C perfect |
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| 0-9-20 = C Ev G = C(v3) = C down-three | | 0-9-20 = C Ev G = C(v3) = C down-three |
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| 0-11-20 = C E^ G = C(^3) = C up-three | | 0-11-20 = C E^ G = C(^3) = C up-three |
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| 0-10-19 = C E Gv = C(v5) = C down-five | | 0-10-19 = C E Gv = C(v5) = C down-five |
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| 0-11-21 = C E^ G^ = C(^3,^5) = C up-three up-five | | 0-11-21 = C E^ G^ = C(^3,^5) = C up-three up-five |
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| 0-10-20-30 = C E G B = C7 = C seven | | 0-10-20-30 = C E G B = C7 = C seven |
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| 0-10-20-29 = C E G Bv = C(v7) = C down-seven | | 0-10-20-29 = C E G Bv = C(v7) = C down-seven |
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| 0-9-20-30 = C Ev G B = C7(v3) = C seven down-three | | 0-9-20-30 = C Ev G B = C7(v3) = C seven down-three |
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| 0-9-20-29 = C Ev G Bv = C.v7 = C dot down seven | | 0-9-20-29 = C Ev G Bv = C.v7 = C dot down seven |
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| 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]]. | | For a more complete list, see [[Ups_and_Downs_Notation#Chord names in other EDOs|Ups and Downs Notation - Chord names in other EDOs]]. |
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| =Intervals= | | =Intervals= |
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| (Bolded ratio indicates that the ratio is most accurately tuned by the given 35-edo interval.) | | (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 ||
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| || 0 || 0 || **1/1** || (see comma table) || || ||
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| || 1 || 34.29 || **50/49** , **121/119** , 33/32 || **36/35** || 25/24 || **81/80** ||
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| || 2 || 68.57 || 128/125 || **25/24** || 81/80 || ||
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| || 3 || 102.86 || **17/16** || **15/14** || **16/15** || **18/17** ||
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| || 4 || 137.14 || || **12/11** , 16/15 || || ||
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| || 5 || 171.43 || **11/10** || || 12/11 || **10/9** ||
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| || 6 || 205.71 || || || || **9/8** ||
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| || 7 || 240 || **8/7** || || 7/6 || ||
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| || 8 || 274.29 || **20/17** || **7/6** || || ||
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| || 9 || 308.57 || || **6/5** || || ||
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| || 10 || 342.86 || **17/14** || || 6/5 || **11/9** ||
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| || 11 || 377.14 || **5/4** || || || ||
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| || 12 || 411.43 || **14/11** || || || ||
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| || 13 || 445.71 || **22/17** , 32/25 || || || **9/7** ||
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| || 14 || 480 || || || 4/3, **21/16** || ||
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| || 15 || 514.29 || || **4/3** || || ||
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| || 16 || 548.57 || **11/8** || || || ||
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| || 17 || 582.86 || **7/5** || **24/17** || 17/12 || ||
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| || 18 || 617.14 || **10/7** || **17/12** || 24/17 || ||
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| || 19 || 651.43 || **16/11** || || || ||
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| || 20 || 685.71 || || **3/2** || || ||
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| || 21 || 720 || || || 3/2, **32/21** || ||
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| || 22 || 754.29 || **17/11** , 25/16 || || || **14/9** ||
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| || 23 || 788.57 || **11/7** || || || ||
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| || 24 || 822.86 || **8/5** || || || ||
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| || 25 || 857.14 || **28/17** || || 5/3 || **18/11** ||
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| || 26 || 891.43 || || **5/3** || || ||
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| || 27 || 925.71 || **17/10** || **12/7** || || ||
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| || 28 || 960 || **7/4** || || || ||
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| || 29 || 994.29 || || || || **16/9** ||
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| || 30 || 1028.57 || **20/11** || || || **9/5** ||
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| || 31 || 1062.86 || || **11/6** , 15/8 || || ||
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| || 32 || 1097.14 || **32/17** || **28/15** || **15/8** || **17/9** ||
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| || 33 || 1131.43 || || || || ||
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| || 34 || 1165.71 || || || || ||
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| =[[#Rank two temperaments]]=
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| =Rank two temperaments=
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| ||~ Periods | | {| class="wikitable" |
| 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> || | | | | Degrees |
| || 1 || 1\35 || || || | | | | Cents value |
| || 1 || 2\35 || || || | | | | Ratios in2.5.7.11.17 subgroup |
| || 1 || 3\35 || || [[Ripple]] || | | | | Ratios with flat 3 |
| || 1 || 4\35 || [[xenharmonic/Greenwoodmic temperaments#Secund|Secund]] || || | | | | Ratios with sharp 3 |
| || 1 || 6\35 |||| Messed-up [[Chromatic pairs#Baldy|Baldy]] || | | | | Ratios with patent 9 |
| || 1 || 8\35 || || Messed-up [[Orwell]] || | | |- |
| || 1 || 9\35 || [[xenharmonic/Myna|Myna]] || || | | | | 0 |
| || 1 || 11\35 || [[Magic family#Muggles|Muggles]] || || | | | | 0 |
| || 1 || 12\35 || || [[Avicennmic temperaments#Roman|Roman]] || | | | | '''1/1''' |
| || 1 || 13\35 |||| Inconsistent 2.9'/7.5/3 [[Sensi]] || | | | | (see comma table) |
| || 1 || 16\35 || || || | | | | |
| || 1 || 17\35 || || || | | | | |
| || 5 || 1\35 || || [[Blackwood]] (favoring 7/6) || | | |- |
| || 5 || 2\35 || || [[Blackwood]] (favoring 6/5 and 20/17) || | | | | 1 |
| || 5 || 3\35 || || [[Blackwood]] (favoring 5/4 and 17/14) || | | | | 34.29 |
| || 7 || 1\35 || [[xenharmonic/Apotome family|Whitewood]]/[[xenharmonic/Apotome family#Redwood|Redwood]] || || | | | | '''50/49''' , '''121/119''' , 33/32 |
| || 7 || 2\35 || [[xenharmonic/Greenwoodmic temperaments#Greenwood|Greenwood]] || || | | | | '''36/35''' |
| =<span style="background-color: #ffffff;">Scales</span>=
| | | | 25/24 |
| == ==
| | | | '''81/80''' |
| ==<span style="background-color: #ffffff;">Commas</span>==
| | |- |
| 35EDO tempers out the following commas. (Note: This assumes the val < 35 55 81 98 121 130|.)
| | | | 2 |
| ||~ **Comma** ||~ **Monzo** ||~ **Value (Cents)** ||~ **Name 1** ||~ **Name 2** ||~ **Name 3** || | | | | 68.57 |
| ||= 2187/2048 || | -11 7 > ||> 113.69 ||= Apotome ||= Whitewood comma || || | | | | 128/125 |
| ||= 6561/6250 || | -1 8 -5 > ||> 84.07 ||= Ripple comma ||= || || | | | | '''25/24''' |
| ||= 10077696/9765625 || | 9 9 -10 > ||> 54.46 ||= Mynic comma ||= || || | | | | 81/80 |
| ||= 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 ||= ||= || || | | | | 3 |
| ||= 525/512 || | -9 1 2 1 > ||> 43.41 ||= Avicenna ||= || || | | | | 102.86 |
| ||= 126/125 || | 1 2 -3 1 > ||> 13.79 ||= Starling comma ||= Septimal semicomma || || | | | | '''17/16''' |
| ||= 99/98 || | -1 2 0 -2 1 > ||> 17.58 ||= Mothwellsma ||= || || | | | | '''15/14''' |
| ||= 66/65 || | 1 1 -1 0 1 -1 > ||> 26.43 ||= ||= || || | | | | '''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 |
| | | | |
| | | | |
| | | | |
| | | | |
| | |} |
|
| |
|
| ==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])</pre></div>
| |
| <h4>Original HTML content:</h4>
| |
| <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><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 />
| |
|
| |
|
| | =Rank two temperaments= |
|
| |
|
| <table class="wiki_table">
| | {| class="wikitable" |
| <tr>
| | |- |
| <td style="text-align: center;">Degrees<br />
| | ! | Periods |
| </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>
| | per octave |
| <!-- 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>
| | ! | Generator |
| 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 />
| | ! | Temperaments with |
| <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 />
| |
|
| |
|
| | 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|Ripple]] |
| | |- |
| | | | 1 |
| | | | 4\35 |
| | | | [[Greenwoodmic_temperaments#Secund|Secund]] |
| | | | |
| | |- |
| | | | 1 |
| | | | 6\35 |
| | | colspan="2" | Messed-up [[Chromatic_pairs#Baldy|Baldy]] |
| | |- |
| | | | 1 |
| | | | 8\35 |
| | | | |
| | | | Messed-up [[Orwell|Orwell]] |
| | |- |
| | | | 1 |
| | | | 9\35 |
| | | | [[Myna|Myna]] |
| | | | |
| | |- |
| | | | 1 |
| | | | 11\35 |
| | | | [[Magic_family#Muggles|Muggles]] |
| | | | |
| | |- |
| | | | 1 |
| | | | 12\35 |
| | | | |
| | | | [[Avicennmic_temperaments#Roman|Roman]] |
| | |- |
| | | | 1 |
| | | | 13\35 |
| | | colspan="2" | Inconsistent 2.9'/7.5/3 [[Sensi|Sensi]] |
| | |- |
| | | | 1 |
| | | | 16\35 |
| | | | |
| | | | |
| | |- |
| | | | 1 |
| | | | 17\35 |
| | | | |
| | | | |
| | |- |
| | | | 5 |
| | | | 1\35 |
| | | | |
| | | | [[Blackwood|Blackwood]] (favoring 7/6) |
| | |- |
| | | | 5 |
| | | | 2\35 |
| | | | |
| | | | [[Blackwood|Blackwood]] (favoring 6/5 and 20/17) |
| | |- |
| | | | 5 |
| | | | 3\35 |
| | | | |
| | | | [[Blackwood|Blackwood]] (favoring 5/4 and 17/14) |
| | |- |
| | | | 7 |
| | | | 1\35 |
| | | | [[Apotome_family|Whitewood]]/[[Apotome_family#Redwood|Redwood]] |
| | | | |
| | |- |
| | | | 7 |
| | | | 2\35 |
| | | | [[Greenwoodmic_temperaments#Greenwood|Greenwood]] |
| | | | |
| | |} |
|
| |
|
| <table class="wiki_table">
| | =<span style="background-color: #ffffff;">Scales</span>= |
| <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 />
| |
|
| |
|
| | ==<span style="background-color: #ffffff;">Commas</span>== |
| | 35EDO tempers out the following commas. (Note: This assumes the val < 35 55 81 98 121 130|.) |
|
| |
|
| <table class="wiki_table">
| | {| class="wikitable" |
| <tr>
| | |- |
| <th>Periods<br />
| | ! | '''Comma''' |
| per octave<br />
| | ! | '''Monzo''' |
| </th>
| | ! | '''Value (Cents)''' |
| <th>Generator<br />
| | ! | '''Name 1''' |
| </th>
| | ! | '''Name 2''' |
| <th>Temperaments with<br />
| | ! | '''Name 3''' |
| flat 3/2 (patent val)<br />
| | |- |
| </th>
| | | style="text-align:center;" | 2187/2048 |
| <th><span style="display: block; text-align: center;">Temperaments with sharp 3/2 (35b val)</span><br />
| | | | | -11 7 > |
| </th>
| | | style="text-align:right;" | 113.69 |
| </tr>
| | | style="text-align:center;" | Apotome |
| <tr>
| | | style="text-align:center;" | Whitewood comma |
| <td>1<br />
| | | | |
| </td>
| | |- |
| <td>1\35<br />
| | | style="text-align:center;" | 6561/6250 |
| </td>
| | | | | -1 8 -5 > |
| <td><br />
| | | style="text-align:right;" | 84.07 |
| </td>
| | | style="text-align:center;" | Ripple comma |
| <td><br />
| | | style="text-align:center;" | |
| </td>
| | | | |
| </tr>
| | |- |
| <tr>
| | | style="text-align:center;" | 10077696/9765625 |
| <td>1<br />
| | | | | 9 9 -10 > |
| </td>
| | | style="text-align:right;" | 54.46 |
| <td>2\35<br />
| | | style="text-align:center;" | Mynic comma |
| </td>
| | | style="text-align:center;" | |
| <td><br />
| | | | |
| </td>
| | |- |
| <td><br />
| | | style="text-align:center;" | 3125/3072 |
| </td>
| | | | | -10 -1 5 > |
| </tr>
| | | style="text-align:right;" | 29.61 |
| <tr>
| | | style="text-align:center;" | Small diesis |
| <td>1<br />
| | | style="text-align:center;" | Magic comma |
| </td>
| | | | |
| <td>3\35<br />
| | |- |
| </td>
| | | style="text-align:center;" | 405/392 |
| <td><br />
| | | | | -3 4 1 -2 > |
| </td>
| | | style="text-align:right;" | 56.48 |
| <td><a class="wiki_link" href="/Ripple">Ripple</a><br />
| | | style="text-align:center;" | Greenwoodma |
| </td>
| | | style="text-align:center;" | |
| </tr>
| | | | |
| <tr>
| | |- |
| <td>1<br />
| | | style="text-align:center;" | 16807/16384 |
| </td>
| | | | | -14 0 0 5 > |
| <td>4\35<br />
| | | style="text-align:right;" | 44.13 |
| </td>
| | | style="text-align:center;" | |
| <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Greenwoodmic%20temperaments#Secund">Secund</a><br />
| | | style="text-align:center;" | |
| </td>
| | | | |
| <td><br />
| | |- |
| </td>
| | | style="text-align:center;" | 525/512 |
| </tr>
| | | | | -9 1 2 1 > |
| <tr>
| | | style="text-align:right;" | 43.41 |
| <td>1<br />
| | | style="text-align:center;" | Avicenna |
| </td>
| | | style="text-align:center;" | |
| <td>6\35<br />
| | | | |
| </td>
| | |- |
| <td colspan="2">Messed-up <a class="wiki_link" href="/Chromatic%20pairs#Baldy">Baldy</a><br />
| | | style="text-align:center;" | 126/125 |
| </td>
| | | | | 1 2 -3 1 > |
| </tr>
| | | style="text-align:right;" | 13.79 |
| <tr>
| | | style="text-align:center;" | Starling comma |
| <td>1<br />
| | | style="text-align:center;" | Septimal semicomma |
| </td>
| | | | |
| <td>8\35<br />
| | |- |
| </td>
| | | style="text-align:center;" | 99/98 |
| <td><br />
| | | | | -1 2 0 -2 1 > |
| </td>
| | | style="text-align:right;" | 17.58 |
| <td>Messed-up <a class="wiki_link" href="/Orwell">Orwell</a><br />
| | | style="text-align:center;" | Mothwellsma |
| </td>
| | | style="text-align:center;" | |
| </tr>
| | | | |
| <tr>
| | |- |
| <td>1<br />
| | | style="text-align:center;" | 66/65 |
| </td>
| | | | | 1 1 -1 0 1 -1 > |
| <td>9\35<br />
| | | style="text-align:right;" | 26.43 |
| </td>
| | | style="text-align:center;" | |
| <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Myna">Myna</a><br />
| | | style="text-align:center;" | |
| </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 98 121 130|.)<br />
| |
|
| |
|
| | == == |
|
| |
|
| <table class="wiki_table">
| | ==Music== |
| <tr>
| | [http://soonlabel.com/xenharmonic/archives/2348 Little Prelude & Fugue, "The Bijingle" by Claudi Meneghin] |
| <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;">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>
| | [http://www.archive.org/download/Transcendissonance/05Self-destructingMechanicalForest-CityOfTheAsleep.mp3 Self-Destructing Mechanical Forest] by Chuckles McGee (in Secund[9]) |
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| | [[Category:35edo]] |
| <!-- ws:start:WikiTextHeadingRule:20:&lt;h2&gt; --><h2 id="toc10"><a name="Scales-Music"></a><!-- ws:end:WikiTextHeadingRule:20 -->Music</h2>
| | [[Category:edo]] |
| <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 />
| | [[Category:listen]] |
| <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></pre></div>
| | [[Category:theory]] |