36edo: Difference between revisions

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That 36edo contains 12edo as a subset makes it compatible with traditional instruments tuned to 12edo. By tuning one 12-edo instrument up or down about 33{{c}}, one can arrive at a 24-tone subset of 36edo (see, for instance, Jacob Barton's piece for two clarinets, [http://www.jacobbarton.net/2010/02/de-quinin-for-two-clarinets/ De-quinin']{{Dead link}}). Three 12edo instruments could play the entire gamut.

=== ~~Harmonics~~ ===

=== Odd harmonics ===

In the 5-limit, 36edo offers no improvement over 12edo, since its nearest approximation to [[5/4]] is the overly-familiar 400{{c}} major third. However, it excels at the 7th harmonic and intervals involving 7. As a 3 and 7 tuning, or in other words as a tuning for the 2.3.7 [[subgroup]], 36edo's single degree of around 33{{c}} serves a double function as [[49/48]], the so-called [https://en.wikipedia.org/wiki/Septimal_diesis Slendro diesis] of around 36{{c}}, and as [[64/63]], the so-called [https://en.wikipedia.org/wiki/Septimal_comma septimal comma] of around 27{{c}}. Meanwhile, its second degree functions as [[28/27]], the so-called [https://en.wikipedia.org/wiki/Septimal_third-tone Septimal third-tone] (since {{nowrap|28/27 {{=}} 49/48 × 64/63}}). The 2.3.7 subgroup can be extended to the [[k*N_subgroups|2*36 subgroup]] 2.3.25.7.55.13.17, and on this subgroup it tempers out the same commas as [[72edo]] does in the full [[17-limit]].

In the 5-limit, 36edo offers no improvement over 12edo, since its nearest approximation to [[5/4]] is the overly-familiar 400{{c}} major third. However, it excels at the 7th harmonic and intervals involving 7. As a 3 and 7 tuning, or in other words as a tuning for the 2.3.7 [[subgroup]], 36edo's single degree of around 33{{c}} serves a double function as [[49/48]], the so-called [https://en.wikipedia.org/wiki/Septimal_diesis Slendro diesis] of around 36{{c}}, and as [[64/63]], the so-called [https://en.wikipedia.org/wiki/Septimal_comma septimal comma] of around 27{{c}}. Meanwhile, its second degree functions as [[28/27]], the so-called [https://en.wikipedia.org/wiki/Septimal_third-tone Septimal third-tone] (since {{nowrap|28/27 {{=}} [[49/48]] × 64/63}}). The 2.3.7 subgroup can be extended to the [[k*N_subgroups|2*36 subgroup]] 2.3.25.7.55.13.17 (since the 25th harmonic is more accurate than the 5th harmonic, and the 55th harmonic is more accurate than the 5th and 11th harmonics), and on this subgroup it tempers out the same commas as [[72edo]] does in the full [[17-limit]].

36edo is also notable for being the smallest multiple of 12edo to be [[distinctly consistent]] in the [[7-odd-limit]] (that is, all 7-odd-limit just intervals are represented by different steps).

36edo has almost 50% relative error on harmonics 5/1 and 11/1. This means that whether one [[octave stretch|stretches]] or [[octave shrinking|compresses]] the octave, either way it will improve 36edo's approximations of [[JI]], but in opposite directions, as long as it is done by the right amount, as discussed in more detail in [[36edo#Octave_stretch_or_compression|octave stretch or compression]].

{{Harmonics in equal|36|intervals=odd|columns=14|prec=2|start=15|collapsed=true|title=Approximation of odd harmonics in 36edo (continued)}}

=== Mappings ===

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=== Additional properties ===

36edo ~~also~~ offers a good approximation to the [[acoustic phi|acoustic golden ratio]], as 25\36. [[Heinz Bohlen]] proposed 36edo as a suitable temperament for approximating his 833-cents scale. The 13th harmonic (octave reduced) is so closely mapped on [[acoustic phi]] that 36edo could be treated as a 2.3.7.ϕ.17 temperament.

36edo offers a good approximation to the [[acoustic phi|acoustic golden ratio]], as 25\36. [[Heinz Bohlen]] proposed 36edo as a suitable temperament for approximating his 833-cents scale. The 13th harmonic (octave reduced) is so closely mapped on [[acoustic phi]] that 36edo could be treated as a 2.3.7.ϕ.17 temperament.

The [[edonoi]] scales of [[57edt]] and [[101ed7]] are almost exactly the same as 36edo. It is 36edo with the [[stretched octave|octave stretched]] by less than 1{{c}}. Its main usage is to optimise 36edo for use as a [[dual-n|dual-5]] tuning, while also making slight improvements to 3/1 and 7/1 as well. So if one intends to use both 36edo’s vals for 5/1 at once, 101ed7 may be worth considering.

Thanks to its sevenths, 36edo is an ideal tuning for its size for [[metallic harmony]].

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! Additional ratios of 2.3.7.13.17.19<ref group="note" name="subg" />

! Additional ratios of 2.3.5.7<ref group="note" name="incons">Inconsistent intervals are in ''italics.''</ref>

! colspan="3" | [[Ups and ~~Downs Notation|Ups~~ and downs ~~notation]]~~

! colspan="3" | [[Ups and downs notation]]

([[Enharmonic unisons in ups and downs notation|EUs]]: v3A1 and d2)

|-

| 0

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| D

|}

Chords can be named using ups and downs as C upminor, D downmajor seven, etc. See [[Ups and downs notation #Chords and chord progressions]].

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== Approximation to JI ==

~~=== Interval mappings ===~~

~~{{Q-odd-limit intervals|36}}~~

~~{{Q-odd-limit intervals|35.98|apx=val|header=none|tag=none|title=15-odd-limit intervals by 36e val mapping}}~~

=== 3-limit (Pythagorean) approximations (same as 12edo): ===

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63/32 = 1172.736... cents; 35 degrees of 36edo = 1166.666... cents.

=== 15-odd-limit approximations ===

{{Q-odd-limit intervals|35.98|apx=val|header=none|tag=none|title=15-odd-limit intervals by 36e val mapping}}

~~=== Zeta peak index ===~~

~~{{ZPI~~

~~| zpi = 155~~

~~| steps = 35.9823877000425~~

~~| step size = 33.3496490006021~~

~~| tempered height = 6.027497~~

~~| pure height = 5.885059~~

~~| integral = 1.028887~~

~~| gap = 14.706508~~

~~| octave = 1200.58736402167~~

~~| consistent = 8~~

~~| distinct = 8~~

}}

== Regular temperament properties ==

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=== Uniform maps ===

=== Commas ===

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| Go comma

|}

=== Rank-2 temperaments ===

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Line 1,014:

|}

<nowiki/>* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct

== Octave stretch or compression ==

What follows is a comparison of stretched- and compressed-octave 36edo tunings.

; [[21edf]]

* Step size: 33.426{{c}}, octave size: 1203.351{{c}}

Stretching the octave of 36edo by a little over 3{{c}} results in improved primes 5, 11, and 13, but worse primes 2, 3, and 7. This approximates all harmonics up to 16 within 13.4{{c}}. The tuning 21edf does this.

{{Harmonics in equal|21|3|2|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 21edf (continued)}}

; [[57edt]]

* Step size: 33.368{{c}}, octave size: 1201.235{{c}}

If one intends to use both 36edo's vals for 5/1 at once, stretching the octave of 36edo by about 1{{c}} optimises 36edo for that dual-5 usage, while also making slight improvements to primes 3, 7, 11, and 13. This approximates all harmonics up to 16 within 16.6{{c}}. Several almost-identical tunings do this: 57edt, [[93ed6]], [[101ed7]], [[zpi|155zpi]], and the 2.3.7.13-subgroup [[TE]] and [[WE]] tunings of 36et.

{{Harmonics in equal|57|3|1|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 57edt (continued)}}

; 36edo

* Step size: 33.333{{c}}, octave size: 1200.000{{c}}

Pure-octaves 36edo approximates all harmonics up to 16 within 15.3{{c}}.

{{Harmonics in equal|36|2|1|intervals=integer|columns=11|collapsed=true}}

{{Harmonics in equal|36|2|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 36edo (continued)}}

; [[TE|36et, 13-limit TE tuning]]

* Step size: 33.304{{c}}, octave size: 1198.929{{c}}

Compressing the octave of 36edo by about 2{{c}} results in much improved primes 5 and 11, but much worse primes 7 and 13. This approximates all harmonics up to 16 within 11.6{{c}}. The 11- and 13-limit TE tunings of 36et both do this, as do their respective WE tunings.

{{Harmonics in cet|33.303596|columns=11|collapsed=true|title=Approximation of harmonics in 13-limit TE tuning of 36et}}

{{Harmonics in cet|33.303596|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 13-limit TE tuning of 36et (continued)}}

{| class="wikitable sortable center-all mw-collapsible mw-collapsed"

|+ style="white-space: nowrap;" | Comparison of stretched and compressed tunings

|-

! rowspan="2" | Tuning !! rowspan="2" | Octave size (cents) !! colspan="6" | Prime error (cents)

! rowspan="2" | Mapping of primes 2–13 (steps)

|-

! 2 !! 3 !! 5 !! 7 !! 11 !! 13

|-

! 21edf

| 1203.351

| +3.3 || +3.3 || −12.0 || +7.2 || −6.5 || +5.1

| 36, 57, 83, 101, 124, 133

|-

! 57edt

| 1201.235

| +1.2 || 0.0 || +16.6 || +1.3 || −13.7 || −2.6

| 36, 57, 84, 101, 124, 133

|-

! 155zpi

| 1200.587

| +0.6 || −1.0 || +15.1 || −0.5 || −16.0|| −5.0

| 36, 57, 83, 101, 124, 133

|-

! 36edo

| '''1200.000'''

| '''0.0''' || '''−2.0''' || '''+13.7''' || '''−2.2''' || '''+15.3''' || '''−7.2'''

| '''36, 57, 84, 101, 125, 133'''

|-

! 13-limit TE

| 1198.929

| −1.1 || −3.7 || +11.2 || −5.2 || +11.6 || −11.1

| 36, 57, 84, 101, 125, 133

|-

! 11-limit TE

| 1198.330

| −1.7 || −4.6 || +9.8 || −6.8 || +9.5 || −13.4

| 36, 57, 84, 101, 125, 133

|}

== Scales ==

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'''Catler'''

* [[Lost spirit]] (approximated from [[Meantone]] in [[31edo]]): '''9 6 2 4 7 2 6'''

* [[Lost spirit]]{{idio}} (approximated from [[Meantone]] in [[31edo]]): '''9 6 2 4 7 2 6'''

'''Hedgehog'''

* [[Hedgehog]][14] MOS: '''3 2 3 2 3 2 3 3 2 3 2 3 2 3'''

* Palace (subset of Hedgehog[14]): '''5 5 5 6 5 5 5'''

* Palace{{idio}} (subset of Hedgehog[14]): '''5 5 5 6 5 5 5'''

[[833 Cent Golden Scale (Bohlen)]]: '''3 4 4 3 4 4 3'''

Line 1,057:

Line 1,112:

; [[Ivan Bratt]]

* [http://micro.soonlabel.com/gene_ward_smith/36edo/boomers.mp3 ''Boomers'']

; [[Bryan Deister]]

* [https://www.youtube.com/watch?v=psvrsa10-Wo ''36edo jam''] (2025)

; [[E8 Heterotic]]

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; [[NullPointerException Music]]

* [https://www.youtube.com/watch?v=i5Pa5R7PKu4 ''Jungle Hillocks''] (2020)

; [[Chris Orphal]]

* [https://www.youtube.com/watch?v=qbOOzC4360M ''Vademecum - Vadetecum (36-EDO) - Perf. New Music New Mexico''] (2023) (Saxophone: Edwin Anthony; Horn: Samuel Lutz; Trumpet: Doug Falk; Guitar: Carlos Arellano; Guitar tuned -31¢: Chris Orphal; Piano: Axel Retif)

; {{W|Henri Pousseur}}

Line 1,090:

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; [[Stephen Weigel]]

* [https://soundcloud.com/overtoneshock/exponentially-more-lost-and-forgetful-36-edo ''Exponentially More Lost and Forgetful''] (2017) played by flautists Orlando Cela and Wei Zhao

~~== Notes ==~~

~~<references group="note" />~~

[[Category:Listen]]

@@ Line 8: / Line 8: @@
 That 36edo contains 12edo as a subset makes it compatible with traditional instruments tuned to 12edo. By tuning one 12-edo instrument up or down about 33{{c}}, one can arrive at a 24-tone subset of 36edo (see, for instance, Jacob Barton's piece for two clarinets, [http://www.jacobbarton.net/2010/02/de-quinin-for-two-clarinets/ De-quinin']{{Dead link}}). Three 12edo instruments could play the entire gamut.
-=== Harmonics ===
+=== Odd harmonics ===
-In the 5-limit, 36edo offers no improvement over 12edo, since its nearest approximation to [[5/4]] is the overly-familiar 400{{c}} major third. However, it excels at the 7th harmonic and intervals involving 7. As a 3 and 7 tuning, or in other words as a tuning for the 2.3.7 [[subgroup]], 36edo's single degree of around 33{{c}} serves a double function as [[49/48]], the so-called [https://en.wikipedia.org/wiki/Septimal_diesis Slendro diesis] of around 36{{c}}, and as [[64/63]], the so-called [https://en.wikipedia.org/wiki/Septimal_comma septimal comma] of around 27{{c}}. Meanwhile, its second degree functions as [[28/27]], the so-called [https://en.wikipedia.org/wiki/Septimal_third-tone Septimal third-tone] (since {{nowrap|28/27 {{=}} 49/48 × 64/63}}). The 2.3.7 subgroup can be extended to the [[k*N_subgroups|2*36 subgroup]] 2.3.25.7.55.13.17, and on this subgroup it tempers out the same commas as [[72edo]] does in the full [[17-limit]].
+In the 5-limit, 36edo offers no improvement over 12edo, since its nearest approximation to [[5/4]] is the overly-familiar 400{{c}} major third. However, it excels at the 7th harmonic and intervals involving 7. As a 3 and 7 tuning, or in other words as a tuning for the 2.3.7 [[subgroup]], 36edo's single degree of around 33{{c}} serves a double function as [[49/48]], the so-called [https://en.wikipedia.org/wiki/Septimal_diesis Slendro diesis] of around 36{{c}}, and as [[64/63]], the so-called [https://en.wikipedia.org/wiki/Septimal_comma septimal comma] of around 27{{c}}. Meanwhile, its second degree functions as [[28/27]], the so-called [https://en.wikipedia.org/wiki/Septimal_third-tone Septimal third-tone] (since {{nowrap|28/27 {{=}} [[49/48]] × 64/63}}). The 2.3.7 subgroup can be extended to the [[k*N_subgroups|2*36 subgroup]] 2.3.25.7.55.13.17 (since the 25th harmonic is more accurate than the 5th harmonic, and the 55th harmonic is more accurate than the 5th and 11th harmonics), and on this subgroup it tempers out the same commas as [[72edo]] does in the full [[17-limit]].
 edo is also notable for being the smallest multiple of 12edo to be [[distinctly consistent]] in the [[7-odd-limit]] (that is, all 7-odd-limit just intervals are represented by different steps).
-{{harmonics in equal|36|prec=2}}
+edo has almost 50% relative error on harmonics 5/1 and 11/1. This means that whether one [[octave stretch|stretches]] or [[octave shrinking|compresses]] the octave, either way it will improve 36edo's approximations of [[JI]], but in opposite directions, as long as it is done by the right amount, as discussed in more detail in [[36edo#Octave_stretch_or_compression|octave stretch or compression]].
+{{Harmonics in equal|36|intervals=odd|prec=2|columns=14}}
+{{Harmonics in equal|36|intervals=odd|columns=14|prec=2|start=15|collapsed=true|title=Approximation of odd harmonics in 36edo (continued)}}
 === Mappings ===
@@ Line 21: / Line 24: @@
 === Additional properties ===
-edo also offers a good approximation to the [[acoustic phi|acoustic golden ratio]], as 25\36. [[Heinz Bohlen]] proposed 36edo as a suitable temperament for approximating his 833-cents scale. The 13th harmonic (octave reduced) is so closely mapped on [[acoustic phi]] that 36edo could be treated as a 2.3.7.ϕ.17 temperament.
+edo offers a good approximation to the [[acoustic phi|acoustic golden ratio]], as 25\36. [[Heinz Bohlen]] proposed 36edo as a suitable temperament for approximating his 833-cents scale. The 13th harmonic (octave reduced) is so closely mapped on [[acoustic phi]] that 36edo could be treated as a 2.3.7.ϕ.17 temperament.
-The [[edonoi]] scales of [[57edt]] and [[101ed7]] are almost exactly the same as 36edo. It is 36edo with the [[stretched octave|octave stretched]] by less than 1{{c}}. Its main usage is to optimise 36edo for use as a [[dual-n|dual-5]] tuning, while also making slight improvements to 3/1 and 7/1 as well. So if one intends to use both 36edo’s vals for 5/1 at once, 101ed7 may be worth considering.
 Thanks to its sevenths, 36edo is an ideal tuning for its size for [[metallic harmony]].
@@ Line 38: / Line 39: @@
 ! Additional ratios<br>of 2.3.7.13.17.19<ref group="note" name="subg" />
 ! Additional ratios<br>of 2.3.5.7<ref group="note" name="incons">Inconsistent intervals are in ''italics.''</ref>
-! colspan="3" | [[Ups and Downs Notation|Ups and downs<br />notation]]
+! colspan="3" | [[Ups and downs notation]]
+([[Enharmonic unisons in ups and downs notation|EUs]]: v<sup>3</sup>A1 and d2)
 |-
 | 0
@@ Line 373: / Line 375: @@
 | D
 |}
+<references group="note" />
 Chords can be named using ups and downs as C upminor, D downmajor seven, etc. See [[Ups and downs notation #Chords and chord progressions]].
@@ Line 427: / Line 430: @@
 == Approximation to JI ==
-[[File:36ed2.svg|250px|thumb|right|alt=alt : Your browser has no SVG support.|Selected 29-limit intervals approximated in 36edo]]
+[[File:36ed2.svg|250px|thumb|right|alt=alt : Your browser has no SVG support.|Selected 19-limit intervals approximated in 36edo]]
-=== Interval mappings ===
-{{Q-odd-limit intervals|36}}
-{{Q-odd-limit intervals|35.98|apx=val|header=none|tag=none|title=15-odd-limit intervals by 36e val mapping}}
 === 3-limit (Pythagorean) approximations (same as 12edo): ===
@@ Line 488: / Line 487: @@
 /32 = 1172.736... cents; 35 degrees of 36edo = 1166.666... cents.
+=== 15-odd-limit approximations ===
+{{Q-odd-limit intervals|36}}
+{{Q-odd-limit intervals|35.98|apx=val|header=none|tag=none|title=15-odd-limit intervals by 36e val mapping}}
 {{clear}}
-=== Zeta peak index ===
-{{ZPI
-| zpi = 155
-| steps = 35.9823877000425
-| step size = 33.3496490006021
-| tempered height = 6.027497
-| pure height = 5.885059
-| integral = 1.028887
-| gap = 14.706508
-| octave = 1200.58736402167
-| consistent = 8
-| distinct = 8
-}}
 == Regular temperament properties ==
@@ Line 582: / Line 571: @@
 === Uniform maps ===
-{{Uniform map|edo=36}}
+{{Uniform map|min=35.8|max=36.2}}
 === Commas ===
@@ Line 911: / Line 900: @@
 | Go comma
 |}
+<references group="note" />
 === Rank-2 temperaments ===
@@ Line 1,024: / Line 1,014: @@
 |}
 <nowiki/>* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
+== Octave stretch or compression ==
+What follows is a comparison of stretched- and compressed-octave 36edo tunings.
+; [[21edf]]
+* Step size: 33.426{{c}}, octave size: 1203.351{{c}}
+Stretching the octave of 36edo by a little over 3{{c}} results in improved primes 5, 11, and 13, but worse primes 2, 3, and 7. This approximates all harmonics up to 16 within 13.4{{c}}. The tuning 21edf does this.
+{{Harmonics in equal|21|3|2|columns=11|collapsed=true}}
+{{Harmonics in equal|21|3|2|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 21edf (continued)}}
+; [[57edt]]
+* Step size: 33.368{{c}}, octave size: 1201.235{{c}}
+If one intends to use both 36edo's vals for 5/1 at once, stretching the octave of 36edo by about 1{{c}} optimises 36edo for that dual-5 usage, while also making slight improvements to primes 3, 7, 11, and 13. This approximates all harmonics up to 16 within 16.6{{c}}. Several almost-identical tunings do this: 57edt, [[93ed6]], [[101ed7]], [[zpi|155zpi]], and the 2.3.7.13-subgroup [[TE]] and [[WE]] tunings of 36et.
+{{Harmonics in equal|57|3|1|columns=11|collapsed=true}}
+{{Harmonics in equal|57|3|1|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 57edt (continued)}}
+; 36edo
+* Step size: 33.333{{c}}, octave size: 1200.000{{c}}
+Pure-octaves 36edo approximates all harmonics up to 16 within 15.3{{c}}.
+{{Harmonics in equal|36|2|1|intervals=integer|columns=11|collapsed=true}}
+{{Harmonics in equal|36|2|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 36edo (continued)}}
+; [[TE|36et, 13-limit TE tuning]]
+* Step size: 33.304{{c}}, octave size: 1198.929{{c}}
+Compressing the octave of 36edo by about 2{{c}} results in much improved primes 5 and 11, but much worse primes 7 and 13. This approximates all harmonics up to 16 within 11.6{{c}}. The 11- and 13-limit TE tunings of 36et both do this, as do their respective WE tunings.
+{{Harmonics in cet|33.303596|columns=11|collapsed=true|title=Approximation of harmonics in 13-limit TE tuning of 36et}}
+{{Harmonics in cet|33.303596|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 13-limit TE tuning of 36et (continued)}}
+{| class="wikitable sortable center-all mw-collapsible mw-collapsed"
+|+ style="white-space: nowrap;" | Comparison of stretched and compressed tunings
+|-
+! rowspan="2" | Tuning !! rowspan="2" | Octave size<br>(cents) !! colspan="6" | Prime error (cents)
+! rowspan="2" | Mapping of primes 2–13 (steps)
+|-
+! 2 !! 3 !! 5 !! 7 !! 11 !! 13
+|-
+! 21edf
+| 1203.351
+| +3.3 || +3.3 || −12.0 || +7.2 || −6.5 || +5.1
+| 36, 57, 83, 101, 124, 133
+|-
+! 57edt
+| 1201.235
+| +1.2 || 0.0 || +16.6 || +1.3 || −13.7 || −2.6
+| 36, 57, 84, 101, 124, 133
+|-
+! 155zpi
+| 1200.587
+| +0.6 || −1.0 || +15.1 || −0.5 || −16.0|| −5.0
+| 36, 57, 83, 101, 124, 133
+|-
+! 36edo
+| '''1200.000'''
+| '''0.0''' || '''−2.0''' || '''+13.7''' || '''−2.2''' || '''+15.3''' || '''−7.2'''
+| '''36, 57, 84, 101, 125, 133'''
+|-
+! 13-limit TE
+| 1198.929
+| −1.1 || −3.7 || +11.2 || −5.2 || +11.6 || −11.1
+| 36, 57, 84, 101, 125, 133
+|-
+! 11-limit TE
+| 1198.330
+| −1.7 || −4.6 || +9.8 || −6.8 || +9.5 || −13.4
+| 36, 57, 84, 101, 125, 133
+|}
 == Scales ==
@@ Line 1,029: / Line 1,085: @@
 '''Catler'''
-* [[Lost spirit]] (approximated from [[Meantone]] in [[31edo]]): '''9 6 2 4 7 2 6'''
+* [[Lost spirit]]{{idio}} (approximated from [[Meantone]] in [[31edo]]): '''9 6 2 4 7 2 6'''
 '''Hedgehog'''
 * [[Hedgehog]][14] MOS: '''3 2 3 2 3 2 3 3 2 3 2 3 2 3'''
-* Palace (subset of Hedgehog[14]): '''5 5 5 6 5 5 5'''
+* Palace{{idio}} (subset of Hedgehog[14]): '''5 5 5 6 5 5 5'''
 [[833 Cent Golden Scale (Bohlen)]]: '''3 4 4 3 4 4 3'''
@@ Line 1,057: / Line 1,112: @@
 ; [[Ivan Bratt]]
 * [http://micro.soonlabel.com/gene_ward_smith/36edo/boomers.mp3 ''Boomers'']
+; [[Bryan Deister]]
+* [https://www.youtube.com/watch?v=psvrsa10-Wo ''36edo jam''] (2025)
 ; [[E8 Heterotic]]
@@ Line 1,078: / Line 1,136: @@
 ; [[NullPointerException Music]]
 * [https://www.youtube.com/watch?v=i5Pa5R7PKu4 ''Jungle Hillocks''] (2020)
+; [[Chris Orphal]]
+* [https://www.youtube.com/watch?v=qbOOzC4360M ''Vademecum - Vadetecum (36-EDO) - Perf. New Music New Mexico''] (2023) (Saxophone: Edwin Anthony; Horn: Samuel Lutz; Trumpet: Doug Falk; Guitar: Carlos Arellano; Guitar tuned -31¢: Chris Orphal; Piano: Axel Retif)
 ; {{W|Henri Pousseur}}
@@ Line 1,090: / Line 1,151: @@
 ; [[Stephen Weigel]]
 * [https://soundcloud.com/overtoneshock/exponentially-more-lost-and-forgetful-36-edo ''Exponentially More Lost and Forgetful''] (2017) played by flautists Orlando Cela and Wei Zhao
-== Notes ==
-<references group="note" />
 [[Category:Listen]]