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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
{{interwiki
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| de = 34-EDO
: This revision was by author [[User:Kosmo|Kosmo]] and made on <tt>2010-08-20 17:30:35 UTC</tt>.<br>
| en = 34edo
: The original revision id was <tt>157561473</tt>.<br>
| es =
: The revision comment was: <tt></tt><br>
| ja =
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
}}
<h4>Original Wikitext content:</h4>
{{Infobox ET}}
<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">[[http://en.wikipedia.org/wiki/34_equal_temperament|Wikipedia article]] about 34edo
{{ED intro}}
{{Wikipedia| 34 equal temperament }}


== Theory ==
34edo contains two [[17edo]]'s and the half-octave tritone of 600 cents. It excels in approximating harmonics 3, 5, 13, 17, and 23 (2.3.5.13.17.23 [[subgroup]] a.k.a. the no-7's no-11's no-19's 23-limit), with tuning even more accurate than [[31edo]] in the 5-limit, but with a sharp tendency and fifth rather than a flat one, and ''not'' tempering out [[81/80]] unlike 31edo.


[[@http://www.archive.org/details/Ascension_105|Ascension]]
34edo's significance in regards to JI approximation comes from making many simple and natural equivalences between JI intervals. For example, a key characteristic of 34edo is that it splits the standard whole tone of [[9/8]] into six parts, such that three chromatic semitones of [[25/24]] or two diatonic semitones of [[16/15]] result in 9/8. Additionally, if you stack a five-step [[10/9]] interval four times, you reach the perfect fifth [[3/2]], supporting [[tetracot]]. This also means that the perfect fifth is mapped to 20 steps. Given that and the fact that the major third [[5/4]] is mapped to 11 steps, one can see that 34edo takes advantage of a natural logarithmic approximation of 5/4 as a portion of 3/2, or equivalently [[6/5]] as a portion of 5/4, resulting in [[gammic temperament]]. It also has the thirds from 17edo: "neogothic" minor and major thirds of about 282 and 424 cents, and a neutral third of 353 cents. For [[extraclassical tonality]], a tendo third of 459 cents and an arto third of 247 cents are also available, approximating 13/10 and 15/13 respectively.
Drums Bass and 34-tone guitar</pre></div>
 
<h4>Original HTML content:</h4>
34edo supports the [[diatonic scale]], both the simpler 5L 2s [[Moment-of-symmetry scale|moment-of-symmetry]] form and a more complex [[nicetone]] scale representing the [[zarlino]] diatonic. This can be extended into a 12-note chromatic scale of [[10L 2s]] by stacking the two different varieties of semitones, with an intuitive non-MOS form appearing at LLsLLLLLLsLL (created by first subdividing 34edo into the standard [[pentic]] scale and then splitting that into further smaller steps).
<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;34edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/34_equal_temperament" rel="nofollow"&gt;Wikipedia article&lt;/a&gt; about 34edo&lt;br /&gt;
 
&lt;br /&gt;
=== Odd harmonics ===
&lt;br /&gt;
{{Harmonics in equal|34|intervals=odd|columns=12}}
&lt;a class="wiki_link_ext" href="http://www.archive.org/details/Ascension_105" rel="nofollow" target="_blank"&gt;Ascension&lt;/a&gt;&lt;br /&gt;
 
Drums Bass and 34-tone guitar&lt;/body&gt;&lt;/html&gt;</pre></div>
== Intervals ==
{| class="wikitable center-all right-2 left-3 left-4 left-5"
|-
!
! Cents
! Approx. ratios<ref group="note">{{sg|limit=2.3.5.11.13.17.23 [[subgroup]]}}</ref>
! Ratios of 7<br />Using the 34 Val
! Ratios of 7<br />Using the 34d Val
! colspan="3" | [[Ups and downs notation]]
([[Enharmonic unisons in ups and downs notation|EUs]]: v<sup>4</sup>A1 and ^^d2)
! colspan="2" | [[Solfege|Solfeges]]
|-
| 0
| 0.000
| 1/1
|
|
| P1
| perfect unison
| D
| da
| do
|-
| 1
| 35.294
| [[81/80]], [[128/125]], [[51/50]]
| [[28/27]], [[64/63]]
| [[36/35]]
| ^1, vm2
| up 1sn, downminor 2nd
| ^D, vEb
| du/fro
| di
|-
| 2
| 70.588
| [[25/24]], [[26/25]], [[24/23]], [[27/26]], [[23/22]], [[648/625]], [[33/32]]
| [[21/20]], [[36/35]], [[50/49]]
| [[28/27]], [[49/48]]
| ^^1, m2
| dup 1sn, minor 2nd
| ^^D, Eb
| fra
| rih
|-
| 3
| 105.882
| [[17/16]], [[18/17]], [[16/15]]
| [[14/13]]
| [[15/14]], [[21/20]]
| vA1, ^m2
| downaug 1sn,<br />upminor 2nd
| vD#, ^Eb
| fru
| ra
|-
| 4
| 141.176
| [[13/12]], [[12/11]], [[25/23]]
| [[15/14]]
| [[14/13]]
| A1, ~2
| aug 1sn, mid 2nd
| D#, vvE
| ri
| ru
|-
| 5
| 176.471
| [[10/9]], [[11/10]]
|
|
| vM2
| downmajor 2nd
| vE
| ro
| reh
|-
| 6
| 211.765
| [[9/8]], [[17/15]], [[26/23]]
|
| [[8/7]]
| M2
| major 2nd
| E
| ra
| re
|-
| 7
| 247.059
| [[15/13]], [[23/20]]
| [[7/6]], [[8/7]]
|
| ^M2, vm3
| upmajor 2nd,<br />downminor 3rd
| ^E, vF
| ru/no
| raw
|-
| 8
| 282.353
| [[20/17]], [[75/64]], [[27/23]], [[13/11]]
|
| [[7/6]]
| m3
| minor 3rd
| F
| na
| meh
|-
| 9
| 317.647
| [[6/5]]
|
| 17/14
| ^m3
| upminor 3rd
| ^F
| nu
| me
|-
| 10
| 352.941
| [[16/13]], [[11/9]], [[27/22]]
| [[17/14]], [[21/17]]
|
| ~3
| mid 3rd
| ^^F
| mi
| mu
|-
| 11
| 388.235
| [[5/4]]
| [[14/11]]
| [[21/17]]
| vM3
| downmajor 3rd
| vF#
| mo
| mi
|-
| 12
| 423.529
| [[51/40]], [[32/25]], [[23/18]]
|
| [[9/7]], [[14/11]]
| M3
| major 3rd
| F#
| ma
| maa
|-
| 13
| 458.824
| [[13/10]], [[30/23]], [[17/13]], [[22/17]]
| [[9/7]], [[21/16]]
|
| ^M3, v4
| upmajor 3rd, down 4th
| ^F#, vG
| mu/fo
| maw
|-
| 14
| 494.118
| [[4/3]]
|
| [[21/16]]
| P4
| 4th
| G
| fa
| fa
|-
| 15
| 529.412
| [[27/20]], [[34/25]], [[15/11]], [[23/17]]
|
|
| ^4
| up 4th
| ^G
| fu
| fih
|-
| 16
| 564.706
| [[25/18]], [[18/13]], [[11/8]], [[32/23]]
| [[7/5]]
|
| ~4, d5
| mid 4th, dim 5th
| ^^G, Ab
| fi/sha
| fu
|-
| 17
| 600.000
| [[45/32]], [[64/45]], [[17/12]], [[24/17]]
|
| [[7/5]], [[10/7]]
| vA4, ^d5
| downaug 4th, updim 5th
| vG#, ^Ab
| po/shu
| fi/se
|-
| 18
| 635.294
| [[36/25]], [[13/9]], [[16/11]], [[23/16]]
| [[10/7]]
|
| A4, ~5
| aug 4th, mid 5th
| G#, vvA
| pa/si
| su
|-
| 19
| 670.588
| [[40/27]], [[25/17]], [[22/15]], [[34/23]]
|
|
| v5
| down 5th
| vA
| so
| sih
|-
| 20
| 705.882
| [[3/2]]
|
| [[32/21]]
| P5
| perfect 5th
| A
| sa
| sol
|-
| 21
| 741.176
| [[20/13]], [[23/15]], [[26/17]], [[17/11]]
| [[14/9]], [[32/21]]
|
| ^5, vm6
| up 5th, downminor 6th
| ^A, vBb
| su/flo
| saw
|-
| 22
| 776.471
| [[25/16]], [[80/51]], [[36/23]]
|
| [[14/9]], [[11/7]]
| m6
| minor 6th
| Bb
| fla
| leh
|-
| 23
| 811.765
| [[8/5]]
| [[11/7]]
| [[34/21]]
| ^m6
| upminor 6th
| ^Bb
| flu
| le
|-
| 24
| 847.059
| [[13/8]], [[18/11]], [[44/27]]
| [[28/17]], [[34/21]]
|
| ~6
| mid 6th
| vvB
| li
| lu
|-
| 25
| 882.353
| [[5/3]]
|
| [[28/17]]
| vM6
| downmajor 6th
| vB
| lo
| la
|-
| 26
| 917.647
| [[17/10]], [[128/75]], [[46/27]], [[22/13]]
|
| [[12/7]]
| M6
| major 6th
| B
| la
| laa
|-
| 27
| 952.941
| [[26/15]], [[40/23]]
| [[7/4]], [[12/7]]
|
| ^M6, vm7
| upmajor 6th,<br />downminor 7th
| ^B, vC
| lu/tho
| law
|-
| 28
| 988.235
| [[16/9]], [[30/17]], [[23/13]]
|
| [[7/4]]
| m7
| minor 7th
| C
| tha
| teh
|-
| 29
| 1023.529
| [[9/5]], [[20/11]]
|
|
| ^m7
| upminor 7th
| ^C
| thu
| te
|-
| 30
| 1058.824
| [[24/13]], [[11/6]], [[46/25]]
| [[28/15]]
| [[13/7]]
| ~7
| mid 7th
| ^^C
| ti
| tu
|-
| 31
| 1094.118
| [[32/17]], [[17/9]], [[15/8]]
| [[13/7]]
| [[28/15]], [[40/21]]
| vM7
| downmajor 7th
| vC#
| to
| ti
|-
| 32
| 1129.412
| [[48/25]], [[25/13]], [[23/12]], [[625/324]],  [[64/33]]
| [[40/21]], [[35/18]], [[49/25]]
| [[27/14]], [[96/49]]
| M7
| major 7th
| C#
| ta
| taa
|-
| 33
| 1164.706
| [[160/81]], [[125/64]], [[100/51]]
| [[27/14]], [[63/32]]
| [[35/18]]
| ^M7, v8
| upmajor 7th, down 8ve
| vD
| tu/do
| da
|-
| 34
| 1200.000
| [[2/1]]
|
|
| P8
| 8ve
| D
| da
| do
|}
 
Chords can be named using ups and downs as C upminor, D downmajor seven, etc. See [[Ups and downs notation #Chord names in other EDOs]].
 
== Notation ==
=== Ups and downs notation ===
34edo can be notated with [[ups and downs]], spoken as up, dup, downsharp, sharp, upsharp etc. and down, dud, upflat etc. Note that dup is equivalent to dudsharp and dud is equivalent to dupflat.
{{Sharpness-sharp4a}}
 
[[Alternative symbols for ups and downs notation]] uses sharps and flats with arrows, borrowed from extended [[Helmholtz–Ellis notation]]:
{{Sharpness-sharp4}}
 
=== Sagittal notation ===
This notation uses the same sagittal sequence as [[41edo#Sagittal notation|41-EDO]], and is a superset of the notation for [[17edo#Sagittal notation|17-EDO]].
 
==== Evo flavor ====
<imagemap>
File:34-EDO_Evo_Sagittal.svg
desc none
rect 80 0 300 50 [[Sagittal_notation]]
rect 431 0 591 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
rect 20 80 120 106 [[81/80]]
rect 120 80 240 106 [[33/32]]
default [[File:34-EDO_Evo_Sagittal.svg]]
</imagemap>
 
==== Revo flavor ====
<imagemap>
File:34-EDO_Revo_Sagittal.svg
desc none
rect 80 0 300 50 [[Sagittal_notation]]
rect 423 0 583 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
rect 20 80 120 106 [[81/80]]
rect 120 80 240 106 [[33/32]]
default [[File:34-EDO_Revo_Sagittal.svg]]
</imagemap>
 
==== Evo-SZ flavor ====
<imagemap>
File:34-EDO_Evo-SZ_Sagittal.svg
desc none
rect 80 0 300 50 [[Sagittal_notation]]
rect 423 0 583 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
rect 20 80 120 106 [[81/80]]
rect 120 80 240 106 [[33/32]]
default [[File:34-EDO_Evo-SZ_Sagittal.svg]]
</imagemap>
 
=== Kosmorsky's thoughts ===
The chain of fifths gives you the seven naturals, and their sharps and flats. The sharp or flat of a note is (what is commonly called) a neutral second away – the double-sharp means a minor third away from the natural. This has led certain "complainers", in seeking to notate 17 edo, to create an extra character to raise something a small step of which. To render this symbol philosophically harmonious with 34 tone equal temperament, a symbol indicating an adjustment of 1/34 up or down serves the purpose by using two of it, doubled laterally or vertically as composer. This however emphasizes certain aspects of 34edo which ''may not be most efficient expressions of some musical purposes.'' Users can construct their own notation to the needs of the music and performer. As an example, a system with 15 "nominals" like A, B, C … F, instead of seven, might be waste – of paper, or space, or memory if they aren't used consecutively frequently. The system spelled out here has familiarity as an advantage and disadvantage. The spacing of the nominals and lines is the same. Dense chords of certain types would be very impossible to notate. Finally, the table uses ^ and v for "up" and "down", but these might be reserved for adjustments of 1/68th of an octave, being hollow, and filled in triangles are recommended.
 
== Approximation to JI ==
[[File:34ed2.svg|250px|thumb|right|alt=alt : Your browser has no SVG support.|Selected 19-limit intervals approximated in 34edo]]
Like [[17edo]], 34edo contains good approximations of just intervals involving 3, 11, and 13 – specifically, 13/8, 13/12, 13/11, 13/9, 11/9 and their inversions – while failing to closely approximate ratios of 7 given its step size. 34edo adds ratios of 5 into the mix – including 5/4, 6/5, 9/5, 15/8, 13/10, 15/13, and their inversions – as well as 17 – including 17/16, 18/17, 17/12, 17/11, 17/10, 17/13, 17/15 and their inversions. Since it distinguishes between 9/8 and 10/9 (exaggerating the difference between them, the [[syntonic comma]] of 81/80, from 21.5 cents to 35.3 cents), it is suitable for quasi-5-limit JI but is not a [[meantone]] system. While no number of fifths (3/2) land on major or minor thirds, an even number of major or minor thirds will be the same pitch as a pitch somewhere in the circle of seventeen fifths.
 
The sharpening of ~13{{c}} of 11/8 can fit with the 9/8 and 13/8 which both are about 7 cents sharp. This is the basis of a subtle trick: the guitarist tunes the high 'E' string flat by several cents, enough to be imperceptible in many contexts, but which makes chords/harmonies against those several intervals tuned more justly.
 
Likewise the 16{{c}} flat 27\34 approximate 7/4 can be musically useful especially in [[kleismic]] or [[4L&nbsp;3s]] contexts (with generator a 9\34 minor third). On the other hand, the slightly worse and sharper 7/4, 28\34, sounds more like the "dominant seventh" found in blues and jazz – which some listeners are accustomed to. ([[68edo]] contains a copy of 34edo and has the intervals 7/4 and 11/8 tuned nearly just.)
 
=== Interval mappings ===
{{Q-odd-limit intervals|34}}
{{Q-odd-limit intervals|34.1|apx=val|header=none|tag=none|title=15-odd-limit intervals by 34d val mapping}}
 
Of particular interest is the fact that the 34d val allows all 15-odd-limit intervals to be mapped consistently except for 7/4 and 8/7.
 
== Tuning by ear ==
In principle, one can approximate 34edo by ear using only 5-limit intervals, using the fact that 17edo is very close to a circle of seventeen [[25/24]] chromatic semitones to within 1.5{{c}}, and using a pure 5/4 which is less than 2{{c}} off for the second chain. The overall tuning error, assuming everything is tuned perfectly, will be less than 3.5{{c}}, or a relative error of less than 10%.
 
== Approximation to irrational intervals ==
As a Fibonacci number, 34edo contains a fraction of an octave which is a close approximation to the [[logarithmic phi]] – 21 degrees of 34edo, approximately 741.2{{c}}. Repeated iterations of this interval generates [[moment of symmetry]] scales with near-phi relationships between the step sizes. As a 2.3.5.13 temperament, the 21\34 generator is an approximate 20/13, and the temperament tempers out 512/507 and {{monzo| -6 2 6 0 0 -13 }}. From the tempering of 512/507, two 16/13 neutral thirds are an approximate 3/2, defining an essentially tempered neutral triad with a sharp rather than a flat fifth. (On the other hand, the frequency ratio phi is ~ 833{{c}}, and the equal divisions of octave approximating this interval closely are 13edo and [[36edo]].)
 
=== Counterpoint ===
34edo has such an excellent [[sqrt(25/24)]] that the next edo to have a better one is [[441edo|441]]. Every sequence of intervals available in [[17edo]] are reachable by [[strict contrary motion]] in 34edo.
 
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
|-
! rowspan="2" | [[Subgroup]]
! rowspan="2" | [[Comma list]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br />8ve stretch (¢)
! colspan="2" | Tuning error
|-
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
| 2.3.5
| 2048/2025, 15625/15552
| {{mapping| 34 54 79 }}
| −1.10
| 1.03
| 2.92
|-
| 2.3.5.7
| 50/49, 64/63, 4375/4374
| {{mapping| 34 54 79 96 }} (34d)
| −2.56
| 2.66
| 7.57
|-
| 2.3.5.7.11
| 50/49, 64/63, 99/98, 243/242
| {{mapping| 34 54 79 96 118 }} (34d)
| −2.82
| 2.44
| 6.93
|-
| 2.3.5.7.11.13
| 50/49, 64/63, 78/77, 99/98, 144/143
| {{mapping| 34 54 79 96 118 126 }} (34d)
| −2.64
| 2.26
| 6.42
|-
| 2.3.5.7.11.13.17
| 50/49, 64/63, 78/77, 85/84, 99/98, 144/143
| {{mapping| 34 54 79 96 118 126 139 }} (34d)
| −2.30
| 2.26
| 6.41
|}
 
In the 5-limit, 34edo [[support]]s [[hanson]], [[srutal]], [[tetracot]], [[würschmidt]], and [[vishnu]] temperaments. It does less well in the [[7-limit]], with two mappings possible for [[7/4]]: a flat one from the [[patent val]], and a sharp one from the 34d val. By way of the patent val 34 supports [[keemun]] temperament, and 34d is an excellent alternative to [[22edo]] for 7-limit [[pajara]] temperament. In the [[11-limit]], 34de supports 11-limit [[pajaric]], and in fact is quite close to the [[POTE tuning]]; it adds [[4375/4374]] to the commas of 11-limit pajaric. On the other hand, the 34d val supports pajara, vishnu and würschmidt, adding 4375/4374 to the commas of pajara. Among subgroup temperaments, the patent val supports [[semaphore]] on the 2.3.7 subgroup.
 
=== Uniform maps ===
{{Uniform map|edo=34}}
 
=== Rank-2 temperaments ===
* [[List of 34edo rank two temperaments by badness]]
* [[List of edo-distinct 34d rank two temperaments]]
 
{| class="wikitable"
|+ style="font-size: 105%;" | Rank-2 temperaments by period and generator
|-
! Periods<br />per 8ve
! Generator
! Cents
! Mosses
! Temperaments
|-
| rowspan="8" style="text-align: center;" | 1
| 1\34
| 35.294
|
| [[Gammic]]
|-
| 3\34
| 105.88
| [[11L&nbsp;1s]]<br />[[11L&nbsp;12s]]
|
|-
| 5\34
| 176.471
| [[6L&nbsp;1s]]<br />[[7L&nbsp;6s]]<br />[[7L&nbsp;13s]]
| [[Tetracot]], [[bunya]] (34d), [[modus]] (34d), [[monkey]] (34), [[wollemia]] (34)
|-
| 7\34
| 247.059
| [[5L&nbsp;4s]]<br />[[5L&nbsp;9s]]<br />[[5L&nbsp;14s]]<br />[[5L&nbsp;19s]]
| [[Immunity]] (34), [[immunized]] (34d)
|-
| 9\34
| 317.647
| [[4L&nbsp;3s]]<br />[[4L&nbsp;7s]]<br />[[4L&nbsp;11s]]<br />[[15L&nbsp;4s]]
| [[Hanson]], [[keemun]] (34), [[catalan]] (34d), [[catakleismic]] (34d)
|-
| 11\34
| 388.235
| [[3L&nbsp;7s]]<br />[[3L&nbsp;10s]]<br />[[3L&nbsp;13s]]<br />[[3L&nbsp;16s]]<br />[[3L&nbsp;19s]]<br />[[3L&nbsp;22s]]<br />
| [[Würschmidt]] (34d), [[worschmidt]] (34)
|-
| 13\34
| 458.824
| [[3L&nbsp;2s]]<br />[[5L&nbsp;3s]]<br />[[8L&nbsp;5s]]<br />[[13L&nbsp;8s]]
| [[Petrtri]]
|-
| 15\34
| 529.412
| [[2L&nbsp;3s]]<br />[[2L&nbsp;5s]]<br />[[7L&nbsp;2s]]<br />[[9L&nbsp;7s]]
| [[Mabila]]
|-
| rowspan="8" style="text-align: center;" | 2
| 2\34
| 70.588
| [[16L&nbsp;2s]]
| [[Vishnu]]
|-
| 3\34
| 105.882
| [[2L&nbsp;6s]]<br />[[2L&nbsp;8s]]<br />[[10L&nbsp;2s]]<br />[[12L&nbsp;10s]]
| [[Srutal]] (34d), [[pajara]] (34d), [[diaschismic]] (34)
|-
| 4\34
| 141.176
| [[2L&nbsp;6s]]<br />[[8L&nbsp;2s]]<br />[[8L&nbsp;10s]]
| [[Fifive]], [[crepuscular]] (34d), [[fifives]] (34)
|-
| 5\34
| 176.471
| [[6L&nbsp;2s]]<br />[[6L&nbsp;8s]]<br />[[14L&nbsp;6s]]
| [[Stratosphere]]
|-
| 6\34
| 211.765
| [[4L&nbsp;2s]]<br />[[6L&nbsp;4s]]<br />[[6L&nbsp;10s]]<br />[[6L&nbsp;16s]]
| [[Antikythera]]
|-
| 7\34
| 247.059
| [[4L&nbsp;2s]]<br />[[4L&nbsp;6s]]<br />[[10L&nbsp;4s]]
| [[Tobago]]
|-
| 8\34
| 282.353
| [[2L&nbsp;2s]]<br />[[4L&nbsp;2s]]<br />[[4L&nbsp;6s]]<br />[[4L&nbsp;10s]]<br />[[4L&nbsp;14s]]
| [[Bikleismic]]
|}
 
=== Commas ===
34et [[tempering out|tempers out]] the following [[comma]]s. This assumes the [[patent val]] {{val| 34 54 79 95 118 126 }}.
 
{| class="commatable wikitable center-all left-3 right-4 left-6"
|-
! [[Harmonic limit|Prime<br />limit]]
! [[Ratio]]<ref group="note">{{rd}}</ref>
! [[Monzo]]
! [[Cents]]
! [[Color name]]
! Name
|-
| 3
| <abbr title="134217728/129140163">(18 digits)</abbr>
| {{monzo| 27 -17 }}
| 66.765
| Sasawa
| [[17-comma]]
|-
| 5
| [[20000/19683]]
| {{monzo| 5 -9 4 }}
| 27.660
| Saquadyo
| Tetracot comma
|-
| 5
| [[2048/2025]]
| {{monzo| 11 -4 -2 }}
| 19.553
| Sagugu
| Diaschisma
|-
| 5
| <abbr title="393216/390625">(12 digits)</abbr>
| {{monzo| 17 1 -8 }}
| 11.445
| Saquadbigu
| [[Würschmidt comma]]
|-
| 5
| [[15625/15552]]
| {{monzo| -6 -5 6 }}
| 8.107
| Tribiyo
| Kleisma
|-
| 5
| <abbr title="6115295232/6103515625">(20 digits)</abbr>
| {{monzo| 23 6 -14 }}
| 3.338
| Sasepbigu
| [[Vishnuzma]]
|-
| 7
| [[1029/1000]]
| {{monzo| -3 1 -3 3 }}
| 49.492
| Trizogu
| Keega
|-
| 7
| [[49/48]]
| {{monzo| -4 -1 0 2 }}
| 35.697
| Zozo
| Semaphoresma, slendro diesis
|-
| 7
| [[875/864]]
| {{monzo| -5 -3 3 1 }}
| 21.902
| Zotriyo
| Keema
|-
| 7
| [[126/125]]
| {{monzo| 1 2 -3 1 }}
| 13.795
| Zotrigu
| Starling comma
|-
| 11
| [[100/99]]
| {{monzo| 2 -2 2 0 -1 }}
| 17.399
| Luyoyo
| Ptolemisma
|-
| 11
| [[243/242]]
| {{monzo| -1 5 0 0 -2 }}
| 7.139
| Lulu
| Rastma
|-
| 11
| [[385/384]]
| {{monzo| -7 -1 1 1 1 }}
| 4.503
| Lozoyo
| Keenanisma
|-
| 13
| [[91/90]]
| {{monzo| -1 -2 -1 1 0 1 }}
| 19.120
| Thozogu
| Superleap
|}
 
== Scales ==
=== MOS scales ===
{{main|List of MOS scales in 34edo}}
=== Ternary scales ===
* [[Blackdye]] (5:3:1)
* [[Diachrome]] (5:2:1)
* [[Cthon5m]] (4:2:1)
 
== Instruments ==
=== Lumatone ===
* [[Lumatone mapping for 34edo]]
 
=== Skip fretting ===
* [[Skip fretting system 34 2 9]]
* [[Skip fretting system 34 2 11]]
 
== Music ==
=== Modern renderings ===
; {{W|Johann Sebastian Bach}}
* [https://www.youtube.com/watch?v=Mni0bsUVgHk "Ricercar a 6" from ''The Musical Offering'', BWV 1079] (1747) – with syntonic-comma adjustment, rendered by Claudi Meneghin (2025)
 
; {{W|Scott Joplin}}
* [https://www.youtube.com/watch?v=CwMem5p1R6Y ''Maple Leaf Rag''] (1899) – rendered by Claudi Meneghin (2024)
 
; {{W|Marco Uccellini}}
* [https://www.youtube.com/watch?v=AOPOHIOgqhQ ''Aria Sopra La Bergamasca''] – arranged for Organ and rendered by Claudi Meneghin (2024)
 
=== 21st century ===
; [[Flora Canou]]
* [https://soundcloud.com/floracanou/october-dieting-plan?in=floracanou/sets/totmc-suite-vol-1 "October Dieting Plan"] from [https://soundcloud.com/floracanou/sets/totmc-suite-vol-1 ''TOTMC Suite Vol. 1''] (2023) – [[modus]] in 34edo tuning
 
; [[E8 Heterotic]]
* [https://youtu.be/8vyiBt-LyR4?si=eCqiwSY6rftnAiFN ''Kythira's Wake''] (2019)
* [https://youtu.be/cp9kxB1N8FI?si=6gQzx0og8PyAao_k ''Septendecimal Samsara''] (2019) – synthwave
* [https://youtu.be/WsC4y7eG8aw?si=cwuySPEyBGJapFXX ''Dodecahedron''] (2019) – contemporary jazz
* [https://youtu.be/SoMEMYpRV4w?si=0COl0PwuPo-eQG8K ''No Threes For You''] (2019)
* [https://youtu.be/_dOIyByMTfU?si=DsWUSQnERSKi0zbu "Elements - Water"] from ''Elements'' (2019–2020)
 
; [[Francium]]
* "Travel To Stay" from ''Mysteries'' (2023) – [https://open.spotify.com/track/2S2UlMKNNL5yB3280KpgvK Spotify] | [https://francium223.bandcamp.com/track/travel-to-stay Bandcamp] | [https://www.youtube.com/watch?v=fDkW1SnMcdw YouTube]
* "Locksmiths" from ''The Decatonic Album'' (2024) – [https://open.spotify.com/track/2Hzun107B8bxcZaMOClN6T Spotify] | [https://francium223.bandcamp.com/track/locksmiths Bandcamp] | [https://www.youtube.com/watch?v=pQLbtF0Obhc YouTube]
* [https://www.youtube.com/watch?v=HG0kJBHjuZ4 ''Plane Sonatina No. 2''] (2025)
* [https://www.youtube.com/watch?v=ZrjbxQbdVw4 ''cucumber service''] (2025)
 
; [[Adam Freese]]
* [https://www.youtube.com/watch?v=lfdHBBPHvLc ''Austice''] (2023)
 
; [[Hideya]]
* [https://www.youtube.com/watch?v=wT6v8dlUFWo ''Like refracted light''] (2023)
 
; [[Peter Kosmorsky]]
* [https://www.archive.org/details/Ascension_105 ''Ascension''] (2010)
 
; [[luphoria]]
* ''[https://www.youtube.com/watch?v=Dcpkrci64Ms look]'' (2023)
 
; [[Claudi Meneghin]]
* [https://www.youtube.com/watch?v=O_7w4KoaOY4 ''Semitone-Canon on The Mother's Malison Theme, for Cor Anglais & Violin''] (2022)
 
; [[Ray Perlner]]
* [[:File:A stroll through some retuned maqams.mp3|''A stroll through some retuned maqams'']] (2020)
 
; [[Robin Perry]]
* [https://www.youtube.com/watch?v=FXTM0HeuExk ''Uncomfortable In Crowds'' (extended)] (2013)
 
; [[Tapeworm Saga]]
* [https://www.youtube.com/watch?v=BhgxwP9_cSw ''A 3/4 piece in 34edo on 12/31/23''] (2023)
 
; [[Sintel]]
* [https://www.youtube.com/watch?v=hM7p_VVyeQ0 ''Diversion in 34edo''] (2021) – [https://www.youtube.com/watch?v=yTG0z4Znimw transcription by Stephen Weigel]
 
; [[Cam Taylor]]
* [https://www.youtube.com/watch?v=fbrXu7ls5tI ''34-equal Luma: a little sentimental''] (2023)
* [https://www.youtube.com/watch?v=9ORQlBmu_60 ''34 equal: classic triads''] (2023)
* [https://www.youtube.com/watch?v=zojGuuJqGQk&t=2s ''Diaschismatic/Srutal<nowiki>[12]</nowiki> in 34-equal on the harpsichord''] (2024)
 
; [[Userminusone]]
* [https://www.youtube.com/watch?v=5M_Kh94_t1Q ''Perspective''] (2021)
 
; [[Randy Wells]]
* [https://www.youtube.com/watch?v=o2FVaCPJk1k 傘がなくても嬉しい ''(The Puddle Song)''] (2021)
 
; [[Xotla]]
* from ''Lesser Groove'' (2020)
** "Apparatus" – [https://open.spotify.com/track/4pqelsaCnLZrjniGVt3jbN Spotify] | [https://xotla.bandcamp.com/track/apparatus-34edo Bandcamp] | [https://www.youtube.com/watch?v=A6bkzYtsLas YouTube] – sci-fi electro
** "Electrostat" – [https://open.spotify.com/track/5LIPr8n6uQySeLUfM11U2W Spotify] | [https://xotla.bandcamp.com/track/electrostat-tetracot-13 Bandcamp] | [https://www.youtube.com/watch?v=5SAuoyDwpgc YouTube] – ambient electro, tetracot[13] in 34edo tuning
** "Dreams Of Ambience" – [https://open.spotify.com/track/2J5wCauw4aY96DsIEuaDZh Spotify] | [https://xotla.bandcamp.com/track/dreams-of-ambience-34edo Bandcamp] | [https://www.youtube.com/watch?v=jkDA6lhqOYM YouTube] – ambient electro
* from ''Xotla's Microtonal Funk & Blues Vol. 2'' (2020)
** "Chaparral" – [https://open.spotify.com/track/6aOBS6z1Yadj8jUiFcl8l7 Spotify] | [https://xotla.bandcamp.com/track/chaparral Bandcamp] | [https://www.youtube.com/watch?v=k73ktCHq-ac YouTube] – space rock
** "Lull" – [https://open.spotify.com/track/7fDmfyAGNYJ79rkqcnxERm Spotify] | [https://xotla.bandcamp.com/track/lull Bandcamp] | [https://www.youtube.com/watch?v=9-RG2TDESK0 YouTube] – ambient
** "Vortices" – [https://open.spotify.com/track/3MJLNBVL6lMjUxnHeqQc6B Spotify] | [https://xotla.bandcamp.com/track/vortices Bandcamp] | [https://www.youtube.com/watch?v=xGPASo79vZc YouTube] – electro-rock
** "Escapade" – [https://open.spotify.com/track/5An9IJRQSG43gKtLnAUpOY Spotify] | [https://xotla.bandcamp.com/track/escapade Bandcamp] | [https://www.youtube.com/watch?v=3dRQy9hvWaU YouTube] – electronic rock
* [https://www.youtube.com/watch?v=56HuAL1jC8E ''Between Space''] (2022) – ambient sci-fi
 
; [[Zhea Erose]]
* [https://www.youtube.com/watch?v=xYZwye9PWSo ''Modal Studies in Tetracot''] (2021)
 
== See also ==
* [[Diaschismic-tetracot equivalence continuum]]
 
== External links ==
* [http://microstick.net/products/34-equal-guitar-by-larry-a-hanson/ 34 Equal Guitar] by [[Larry Hanson]] {{dead link}}
* [https://microstick.net Websites of Neil Haverstick]
* [https://myspace.com/microstick] – somehow broken (if you scroll to right, you'll find the songs, playing them, you can't hear anything)
 
== Notes ==
<references group="note" />
 
[[Category:Diaschismic]]
[[Category:Keemun]]
[[Category:Kleismic]]
[[Category:Pajara]]
[[Category:Oneirotonic]]
[[Category:Listen]]
[[Category:Würschmidt]]
[[Category:Tetracot]]
Retrieved from "https://en.xen.wiki/w/34edo"