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{{Infobox ET
{{Infobox ET}}
| Prime factorization = 5 × 7
{{ED intro}}
| Step size = 34.2857¢
| Sharp fifth = 21\35 (720.0¢) (→[[5edo|3\5]])
| Flat fifth = 20\35 (685.7¢) (→[[7edo|4\7]])
| Major 2nd = 6\35 (205.7¢)
| Consistency = 7
}}


== Theory ==
== Theory ==
{{Odd harmonics in edo|edo=35}}
As 35 is 5 times 7, 35edo allows for mixing the two smallest xenharmonic [[macrotonal edos]]: [[5edo]] and [[7edo]]. A single degree of 35edo represents the difference between 7edo's narrow fifth of 685.71{{c}} and 5edo's wide fifth of 720{{c}}. Because it includes 7edo, 35edo tunes the 29th harmonic with only 1{{c}} of error.
35-tET or 35-[[EDO]] refers to a tuning system which divides the octave into 35 steps of approximately [[cent|34.29¢]] each.


As 35 is 5 times 7, 35edo allows for mixing the two smallest xenharmonic [[macrotonal edos]]: [[5edo]] and [[7edo]]. A single degree of 35edo represents the difference between 7edo's narrow fifth of 685.71¢ and 5edo's wide fifth of 720¢. Because it includes 7edo, 35edo tunes the 29th harmonic with +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]]'s more in-tune versions of 35edo MOS's and consistent representation of both subgroups. 35edo has the optimal patent val for [[greenwood]] and [[secund]] temperaments, as well as 11-limit [[muggles]], and the 35f val is an excellent tuning for 13-limit muggles. 35edo is the largest edo with a lack of a diatonic scale.
35edo can also represent the 2.3.5.7.11.17 [[subgroup]] and 2.9.5.7.11.17 subgroup, because of the accuracy of 9 and the flatness of all other subgroup generators (7/5 and 17/11 stand out, having less than 1 cent error). Therefore among [[whitewood]] tunings it is very versatile; you can switch between these different subgroups if you don't mind having to use two different 3/2s to reach the inconsistent 9 (a characteristic of whitewood tunings), and if you ignore [[22edo]]'s more in-tune versions of 35edo MOS's and consistent representation of both subgroups.  
 
35edo has the optimal [[patent val]] for [[greenwood]] and [[secund]] temperaments, as well as 11-limit [[muggles]], and the 35f val is an excellent tuning for 13-limit muggles. 35edo is the largest edo with a lack of a [[diatonic scale]] (unless 7edo is considered a diatonic scale).
 
=== Odd harmonics ===
{{Harmonics in equal|35}}


== Notation ==
== Notation ==
The 7edo fifth is preferred as the diatonic generator for ups and downs notation due to being much easier to notate than the 5edo fifth (which involves E and F being enharmonic), as well as being closer to 3/2.
{| class="wikitable"
{| class="wikitable"
|-
|-
Line 39: Line 38:
| 2
| 2
| 68.571
| 68.571
| double-up unison
| dup unison
| ^^1
| ^^1
| ^^D
| ^^D
Line 46: Line 45:
| 3
| 3
| 102.857
| 102.857
| double-down 2nd
| dud 2nd
| vv2
| vv2
| vvE
| vvE
Line 74: Line 73:
| 7
| 7
| 240
| 240
| double-up 2nd
| dup 2nd
| ^^2
| ^^2
| ^^E
| ^^E
Line 81: Line 80:
| 8
| 8
| 274.286
| 274.286
| double-down 3rd
| dud 3rd
| vv3
| vv3
| vvF
| vvF
Line 109: Line 108:
| 12
| 12
| 411.429
| 411.429
| double-up 3rd
| dup 3rd
| ^^3
| ^^3
| ^^F
| ^^F
Line 116: Line 115:
| 13
| 13
| 445.714
| 445.714
| double-down 4th
| dud 4th
| vv4
| vv4
| vvG
| vvG
Line 144: Line 143:
| 17
| 17
| 582.857
| 582.857
| double-up 4th
| dup 4th
| ^^4
| ^^4
| ^^G
| ^^G
Line 151: Line 150:
| 18
| 18
| 617.143
| 617.143
| double-down 5th
| dud 5th
| vv5
| vv5
| vvA
| vvA
Line 179: Line 178:
| 22
| 22
| 754.286
| 754.286
| double-up 5th
| dup 5th
| ^^5
| ^^5
| ^^A
| ^^A
Line 186: Line 185:
| 23
| 23
| 788.571
| 788.571
| double-down 6th
| dud 6th
| vv6
| vv6
| vvB
| vvB
Line 214: Line 213:
| 27
| 27
| 925.714
| 925.714
| double-up 6th
| dup 6th
| ^^6
| ^^6
| ^^B
| ^^B
Line 221: Line 220:
| 28
| 28
| 960
| 960
| double-down 7th
| dud 7th
| vv7
| vv7
| vvC
| vvC
Line 249: Line 248:
| 32
| 32
| 1097.143
| 1097.143
| double-up 7th
| dup 7th
| ^^7
| ^^7
| ^^C
| ^^C
Line 256: Line 255:
| 33
| 33
| 1131.429
| 1131.429
| double-down 8ve
| dud 8ve
| vv8
| vv8
| vvD
| vvD
Line 275: Line 274:
| 8ve
| 8ve
|}
|}
===Sagittal notation===
====Best fifth notation====
This notation uses the same sagittal sequence as EDOs [[30edo#Second-best fifth notation|30b]] and [[40edo#Sagittal notation|40]], and is a superset of the notation for [[7edo#Sagittal notation|7-EDO]].
<imagemap>
File:35-EDO_Sagittal.svg
desc none
rect 80 0 300 50 [[Sagittal_notation]]
rect 415 0 575 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
rect 20 80 415 106 [[Fractional_3-limit_notation#Bad-fifths_limma-fraction_notation | limma-fraction notation]]
default [[File:35-EDO_Sagittal.svg]]
</imagemap>
====Second-best fifth notation====
This notation uses the same sagittal sequence as [[42edo#Sagittal notation|42-EDO]], and is a superset of the notation for [[5edo#Sagittal notation|5-EDO]].
<imagemap>
File:35b_Sagittal.svg
desc none
rect 80 0 300 50 [[Sagittal_notation]]
rect 391 0 551 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
rect 20 80 391 106 [[Fractional_3-limit_notation#Bad-fifths_apotome-fraction_notation | apotome-fraction notation]]
default [[File:35b_Sagittal.svg]]
</imagemap>


=== Chord Names ===
=== Chord Names ===
Line 297: Line 321:
0-9-20-29 = C vE G vB = Cv7 = C down seven
0-9-20-29 = C vE G vB = Cv7 = C down seven


For a more complete list, see [[Ups and Downs Notation#Chords and Chord Progressions|Ups and Downs Notation - Chords and Chord Progressions]].
For a more complete list, see [[Ups and downs notation#Chords and Chord Progressions|Ups and downs notation - Chords and Chord Progressions]].


== JI Intervals ==
== JI Intervals ==
Line 564: Line 588:
|}
|}


{| class="wikitable" style="text-align:center;"
{{15-odd-limit|35}}
|-
! Interval, complement
! Error (abs., in [[cent]]s)
|-
|[[7/5]] [[10/7]]
|0.3448
|-
|[[13/12]] [[24/13]]
|1.4296
|-
|[[9/8]] [[16/9]]
|1.8039
|-
|[[17/16]] [[32/17]]
|2.0984
|-
|[[11/8]] [[16/11]]
|2.7469
|-
|[[18/17]] [[17/9]]
|3.9024
|-
|[[11/9]] [[18/11]]
|4.5509
|-
|[[11/10]] [[20/11]]
|6.4247
|-
|[[14/11]] [[11/7]]
|6.0789
|-
|[[6/5]] [[5/3]]
|7.0703
|-
|[[7/6]] [[12/7]]
|7.4151
|-
|[[8/7]] [[7/4]]
|8.8259
|-
|[[14/13]] [[13/7]]
|8.8447
|-
|[[16/15]] [[15/8]]
|8.8742
|-
|[[5/4]] [[8/5]]
|9.1707
|-
|[[10/9]] [[9/5]]
|10.9747
|-
|[[12/11]] [[11/6]]
|13.494
|-
|[[3/2]] [[4/3]]
|16.241
|-
|[[15/14]] [[28/15]]
|16.5858
|-
|
|
|}


== Rank-2 temperaments ==
== Regular temperament properties ==
=== Rank-2 temperaments ===
{| class="wikitable"
{| class="wikitable"
|-
|-
! | Periods
! Periods<br>per 8ve
 
! Generator
per octave
! Temperaments with<br>flat 3/2 (patent val)
! | Generator
! Temperaments with sharp 3/2 (35b val)
! | Temperaments with
! [[Mos scale]]s
 
flat 3/2 (patent val)
! | <span style="display: block; text-align: center;">Temperaments with sharp 3/2 (35b val)</span>
|-
|-
| | 1
| 1
| | 1\35
| 1\35
| |  
|  
| |  
|  
|  
|-
|-
| | 1
| 1
| | 2\35
| 2\35
| |  
|  
| |
|  
| [[1L 16s]], [[17L 1s]]
|-
|-
| | 1
| 1
| | 3\35
| 3\35
| |  
|  
| | [[Ripple|Ripple]]
| [[Ripple]]
| [[1L 10s]], [[11L 1s]], [[12L 11s]]
|-
|-
| | 1
| 1
| | 4\35
| 4\35
| | [[Greenwoodmic_temperaments#Secund|Secund]]
| [[Secund]]
| |  
|  
| [[1L 7s]], [[8L 1s]], [[9L 8s]], [[9L 17s]]
|-
|-
| | 1
| 1
| | 6\35
| 6\35
| colspan="2" | Messed-up [[Chromatic_pairs#Baldy|Baldy]]
| colspan="2" | [[Baldy]] (messed-up)
| [[1L 4s]], [[5L 1s]], [[6L 5s]], [[6L 11s]], [[6L 17s]], [[6L 23s]]
|-
|-
| | 1
| 1
| | 8\35
| 8\35
| |  
|  
| | Messed-up [[Orwell]]
| [[Orwell]] (messed-up)
| [[1L 3s]], [[4L 1s]], [[4L 5s]], [[9L 4s]], [[13L 9s]]
|-
|-
| | 1
| 1
| | 9\35
| 9\35
| | [[Myna|Myna]]
| [[Myna]]
| |  
|  
| [[1L 3s]], [[4L 3s]], [[4L 7s]], [[4L 11s]], [[4L 15s]], …, [[4L 27s]]
|-
|-
| | 1
| 1
| | 11\35
| 11\35
| | [[Muggles]]
| [[Muggles]]
| |  
|  
| [[3L 1s]], [[3L 4s]], [[3L 7s]] [[3L 10s]], [[3L 13s]], [[16L 3s]]
|-
|-
| | 1
| 1
| | 12\35
| 12\35
| |  
|  
| | [[Avicennmic_temperaments#Roman|Roman]]
| [[Roman]]
| [[2L 1s]], [[3L 2s]], [[3L 5s]], [[3L 8s]], [[3L 11s]], [[3L 14s]], [[3L 17s]], [[3L 20s]], …, [[3L 29s]]
|-
|-
| | 1
| 1
| | 13\35
| 13\35
| colspan="2" | Inconsistent 2.9'/7.5/3 [[Sensi]]
| colspan="2" | Inconsistent 2.9'/7.5/3 [[sensi]]
| [[2L 1s]], [[3L 2s]], [[3L 5s]], [[8L 3s]], [[8L 11s]], [[8L 19s]]
|-
|-
| | 1
| 1
| | 16\35
| 16\35
| |  
|  
| |
|  
| [[2L 1s]], [[2L 3s]], [[2L 5s]], [[2L 7s]], [[2L 9s]], [[11L 2s]], [[11L 13s]]
|-
|-
| | 1
| 1
| | 17\35
| 17\35
| |  
|  
| |
|  
| [[2L 1s]], [[2L 3s]], [[2L 5s]], [[2L 7s]], [[2L 9s]], [[2L 11s]], [[2L 13s]], [[2L 15s]], [[2L 17s]], [[2L 19s]], …, [[2L 31s]]
|-
|-
| | 5
| 5
| | 1\35
| 1\35
| |  
|  
| | [[Blackwood]] (favoring 7/6)
| [[Blackwood]] (favoring 7/6)
| [[5L 5s]], [[5L 10s]], [[5L 15s]], [[5L 20s]], [[5L 25s]]
|-
|-
| | 5
| 5
| | 2\35
| 2\35
| |  
|  
| | [[Blackwood]] (favoring 6/5 and 20/17)
| [[Blackwood]] (favoring 6/5 and 20/17)
| [[5L 5s]], [[5L 10s]], [[15L 5s]]
|-
|-
| | 5
| 5
| | 3\35
| 3\35
| |  
|  
| | [[Blackwood]] (favoring 5/4 and 17/14)
| [[Blackwood]] (favoring 5/4 and 17/14)
| [[5L 5s]], [[10L 5s]], [[10L 15s]]
|-
|-
| | 7
| 7
| | 1\35
| 1\35
| | [[Apotome_family|Whitewood]]/[[Apotome_family#Redwood|Redwood]]
| [[Whitewood]] / [[redwood]]
| |  
|  
| [[7L 7s]], [[7L 14s]], [[7L 21s]]
|-
|-
| | 7
| 7
| | 2\35
| 2\35
| | [[Greenwoodmic_temperaments#Greenwood|Greenwood]]
| [[Greenwood]]
| |  
|  
| [[7L 7s]], [[14L 7s]]
|}
|}


== Scales ==
=== Commas ===
A good beginning for start to play 35-EDO is with the Sub-diatonic scale, that is a [[MOS]] of 3L2s: 9 4 9 9 4.
35et [[tempering out|tempers out]] the following [[comma]]s. (Note: This assumes the [[val]] {{val| 35 55 81 98 121 130 }}.)
 
== Commas ==
35 EDO [[tempers out]] the following [[comma]]s. (Note: This assumes the [[val]] {{val| 35 55 81 98 121 130 }}.)


{| class="commatable wikitable center-1 center-2 right-4 center-5"
{| class="commatable wikitable center-1 center-2 right-4 center-5"
|-
|-
! [[Harmonic limit|Prime <br> limit]]
! [[Harmonic limit|Prime<br>limit]]
! [[Ratio]]<ref>Ratios longer than 10 digits are presented by placeholders with informative hints</ref>
! [[Ratio]]<ref>Ratios longer than 10 digits are presented by placeholders with informative hints</ref>
! [[Monzo]]
! [[Monzo]]
Line 746: Line 718:
| 113.69
| 113.69
| Lawa
| Lawa
| Apotome, Whitewood comma
| Whitewood comma, apotome, Pythagorean chroma
|-
|-
| 5
| 5
Line 767: Line 739:
| 29.61
| 29.61
| Laquinyo
| Laquinyo
| Small diesis, Magic comma
| Magic comma, small diesis
|-
|-
| 7
| 7
Line 781: Line 753:
| 44.13
| 44.13
| Laquinzo
| Laquinzo
| Cloudy
| Cloudy comma
|-
|-
| 7
| 7
Line 788: Line 760:
| 43.41
| 43.41
| Lazoyoyo
| Lazoyoyo
| Avicenna
| Avicennma
|-
|-
| 7
| 7
Line 795: Line 767:
| 13.79
| 13.79
| Zotrigu
| Zotrigu
| Starling comma, Septimal semicomma
| Septimal semicomma, starling comma
|-
|-
| 11
| 11
Line 812: Line 784:
|}
|}
<references/>
<references/>
== Scales ==
* A good place to start using 35-EDO is with the sub-diatonic scale, that is a [[MOS]] of 3L2s: 9 4 9 9 4.
* Also available is the amulet scale{{idiosyncratic}}, approximated from [[magic]] in [[25edo]]: 3 1 3 3 1 3 4 3 3 1 3 4 3
* Approximations of [[gamelan]] scales:
** 5-tone pelog: 3 5 12 3 12
** 7-tone pelog: 3 5 7 5 3 8 4
** 5-tone slendro: 7 7 7 7 7
== Instruments ==
=== Lumatone ===
35edo can be played on the [[Lumatone]]. See [[Lumatone mapping for 35edo]]
=== Skip fretting ===
'''Skip fretting system 35 3 8''' is a [[skip fretting]] system for [[35edo]]. All examples on this page are for 7-string [[guitar]].
; Prime harmonics
1/1: string 2 open
2/1: string 3 fret 9 and string 6 fret 1
3/2: string 3 fret 4 and string 4 fret 13
5/4: string 3 fret 1, string 4 fret 10, and string 7 fret 2
7/4: string 4 fret 4
11/8: string 1 fret 8, string 4 open, and string 5 fret 9
13/8: string 1 fret 11, string 4 fret 3, and string 5 fret 12
17/16: string 2 fret 1 and string 3 fret 10


== Music ==
== Music ==
* [http://soonlabel.com/xenharmonic/archives/2348 Little Prelude &amp; Fugue, "The Bijingle" by Claudi Meneghin]
; [[dotuXil]]
* [http://www.archive.org/download/Transcendissonance/05Self-destructingMechanicalForest-CityOfTheAsleep.mp3 Self-Destructing Mechanical Forest] by Chuckles McGee (in Secund[9])
* [https://www.youtube.com/watch?v=61ssLv9H6rk "Icebound Gallery of Refractions"] from [https://dotuxil.bandcamp.com/album/collected-refractions ''Collected Refractions''] (2024)
* [https://youtu.be/07-wj6BaTOw "G2 Manifold"] by E8 Heterotic (uses a combination of 5-EDO and 7-EDO, which can be classified as a 35-EDO subset.)
 
; [[E8 Heterotic]]
* [https://youtu.be/07-wj6BaTOw ''G2 Manifold''] (2020) – uses a combination of 5edo and 7edo, which can be classified as a 35edo subset.
 
; [[JUMBLE]]
* [https://www.youtube.com/watch?v=2qpsI26JfjY ''Penguins...?''] (2024)
 
; [[Chuckles McGee]]
* [https://www.archive.org/download/Transcendissonance/05Self-destructingMechanicalForest-CityOfTheAsleep.mp3 Self-Destructing Mechanical Forest] (in Secund[9])
 
; [[Claudi Meneghin]]
* [https://web.archive.org/web/20190412163316/http://soonlabel.com/xenharmonic/archives/2348'' Little Prelude &amp; Fugue, "The Bijingle"''] (2014)
* [https://www.youtube.com/watch?v=JPie2YDwA8I ''MicroFugue on Happy Birthday for Baroque Ensemble''] (2023)
 
; [[No Clue Music]]
* [https://www.youtube.com/watch?v=zMUQWdFRGao ''DarkSciFiThing''] (2024)


[[Category:35edo]]
[[Category:Equal divisions of the octave|##]] <!-- 2-digit number -->
[[Category:Listen]]
[[Category:Listen]]
Retrieved from "https://en.xen.wiki/w/35edo"