Miracle: Difference between revisions

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[[~~de:Miracle~~]]

{{Interwiki

| en = Miracle

| de = Miracle

}}

{{Infobox regtemp

| Title = Miracle

| Subgroups = 2.3.5.7, 2.3.5.7.11

| Comma basis = [[225/224]], [[1029/1024]] (7-limit); [[225/224]], [[243/242]], [[385/384]] (11-limit)

| Edo join 1 = 31 | Edo join 2 = 41

| Generators = 15/14 | Generators tuning = 116.7 | Optimization method = CTE

| MOS scales = …, [[1L 9s]], [[10L 1s]], [[10L 11s]], [[10L 21s]]

| Mapping = 1; 6 -7 -2 15

| Pergen = (P8, P5/6)

| Odd limit 1 = 9 | Mistuning 1 = 3.32 | Complexity 1 = 21

| Odd limit 2 = 11-limit 21 | Mistuning 2 = 4.86 | Complexity 2 = 31

}}

'''Miracle''' is a [[regular temperament]] discovered by [[George Secor]] in 1974 which splits a tempered [[3/2]] into six [[generator]]s, called ''[[secor]]s'' (after George), that serve as both [[15/14]] and [[16/15]] semitones. A stack of two generators represents [[8/7]], and a stack of seven generators represents [[8/5]]. It is a member of both the [[marvel temperaments]], by [[tempering out]] [[225/224]], and the [[gamelismic clan]], by tempering out [[1029/1024]]. It ~~extends~~ naturally ~~to the~~ [[11-limit]] by treating the neutral third from three generators as [[11/9]], tempering out [[243/242]], [[385/384]], [[441/440]], and [[540/539]].

'''Miracle''' is a [[regular temperament]] discovered by [[George Secor]] in 1974 which splits a tempered [[3/2]] into six [[generator]]s, called ''[[secor]]s'' (after George), that serve as both [[15/14]] and [[16/15]] semitones. A stack of two generators represents [[8/7]], and a stack of seven generators represents [[8/5]]. It is a member of both the [[marvel temperaments]], by [[tempering out]] [[225/224]], and the [[gamelismic clan]], by tempering out [[1029/1024]]. It is naturally a full [[11-limit]] temperament, treating the neutral third from three generators as [[11/9]], tempering out [[243/242]], [[385/384]], [[441/440]], and [[540/539]]. It is supported by the highly notable [[EDO|edos]] [[31edo|31]], [[41edo|41]], and [[72edo|72]], with 72edo being an especially good tuning. (There is an alternative mapping for 11 known as [[revelation]], but there is little reason to use it unless you are using [[31edo]], in which case it is identical to miracle anyway.)

Miracle is an exceptionally efficient linear temperament. It is quite accurate, with [[TOP]] error only 0.63 [[cent]]s/[[octave]], meaning intervals of the [[11-odd-limit]] [[tonality diamond]] are represented with only one or two cents of error. Yet it is also very low-complexity (efficient), as evidenced by the high density of 11-odd-limit ratios in the [[#Interval chain]]. At least one inversion of every interval in the 11-odd-limit tonality diamond is represented within 22 secors of the starting value.

Some temperaments have 11/9 as a neutral third, meaning it is exactly half of a 3/2 (tempering out 243/242), and other temperaments have 8/7 as exactly a third of 3/2. Miracle is distinguished by doing both of these things at the same time, so 3/2 is divided into six equal parts.

[[Rastmic clan|Some temperaments]] have 11/9 as a neutral third, meaning it is exactly half of a 3/2 (tempering out 243/242), and [[Gamelismic clan|other temperaments]] have 8/7 as exactly a third of 3/2. Miracle is distinguished by doing both of these things at the same time, so 3/2 is divided into six equal parts.

Miracle can also be thought of as a [[cluster temperament]] with 10 clusters of notes in an octave. The small chroma interval between adjacent notes in each cluster is very versatile, representing [[45/44]] ~ [[49/48]] ~ [[50/49]] ~ [[55/54]] ~ [[56/55]] ~ [[64/63]] all [[tempered]] together.

Miracle can also be thought of as a [[cluster temperament]] with 10 clusters of notes in an octave. The small chroma interval between adjacent notes in each cluster is very versatile, representing [[45/44]]~[[49/48]]~[[50/49]]~[[55/54]]~[[56/55]]~[[64/63]] all [[tempered]] together.

See [[Miracle extensions]] for [[13-limit]] extensions. See [[Gamelismic clan #Miracle]] for technical data.

See [[Miracle extensions]] for [[13-limit]] and [[17-limit]] extensions. See [[Gamelismic clan #Miracle]] for technical data.

== Interval chain ==

Line 179:

Line 194:

Displayed on the right is a chart of the tuning spectrum of miracle by how the odd harmonics up to 11 are tuned, showing the minimax generator, i.e. the secor.

=== ~~Prime~~-~~optimized~~ tunings ===

=== Norm-based tunings ===

{| class="wikitable mw-collapsible mw-collapsed"

|+ style="font-size: 105%; white-space: nowrap;" | 7-limit ~~Prime~~-~~Optimized Tunings~~

|+ style="font-size: 105%; white-space: nowrap;" | 7-limit norm-based tunings

|-

! rowspan="2" |

! colspan="2" | Euclidean

! colspan="3" | Euclidean

|-

! ~~Unskewed~~

! Constrained

! ~~Skewed~~

! Constrained & skewed

! Destretched

|-

! Equilateral

| CEE: ~15/14 = 116.~~516¢~~

| CEE: ~15/14 = 116.5155{{c}}

| CSEE: ~15/14 = 116.~~561¢~~

| CSEE: ~15/14 = 116.5612{{c}}

| POEE: ~15/14 = 116.6465{{c}}

|-

! Tenney

| CTE: ~15/14 = 116.~~677¢~~

| CTE: ~15/14 = 116.6772{{c}}

| CWE: ~15/14 = 116.~~676¢~~

| CWE: ~15/14 = 116.6756{{c}}

| POTE: ~15/14 = 116.6752{{c}}

|-

! Benedetti, Wilson

| CBE: ~15/14 = 116.~~730¢~~

| CBE: ~15/14 = 116.7297{{c}}

| CSBE: ~15/14 = 116.~~714¢~~

| CSBE: ~15/14 = 116.7136{{c}}

| POBE: ~15/14 = 116.6903{{c}}

|}

{| class="wikitable mw-collapsible mw-collapsed"

|+ style="font-size: 105%; white-space: nowrap;" | 11-limit ~~Prime~~-~~Optimized Tunings~~

|+ style="font-size: 105%; white-space: nowrap;" | 11-limit norm-based tunings

|-

! rowspan="2" |

! colspan="2" | Euclidean

! colspan="3" | Euclidean

|-

! ~~Unskewed~~

! Constrained

! ~~Skewed~~

! Constrained & skewed

! Destretched

|-

! Equilateral

| CEE: ~15/14 = 116.~~687¢~~

| CEE: ~15/14 = 116.6868{{c}}

| CSEE: ~15/14 = 116.~~630¢~~

| CSEE: ~15/14 = 116.6304{{c}}

| POEE: ~15/14 = 116.5817{{c}}

|-

! Tenney

| CTE: ~15/14 = 116.~~711¢~~

| CTE: ~15/14 = 116.7112{{c}}

| CWE: ~15/14 = 116.~~647¢~~

| CWE: ~15/14 = 116.6469{{c}}

| POTE: ~15/14 = 116.6327{{c}}

|-

! Benedetti, Wilson

| CBE: ~15/14 = 116.~~736¢~~

| CBE: ~15/14 = 116.7355{{c}}

| CSBE: ~15/14 = 116.~~677¢~~

| CSBE: ~15/14 = 116.6768{{c}}

| POBE: ~15/14 = 116.6643{{c}}

|}

=== Target tunings ===

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

{| class="wikitable center-all left-5 mw-collapsible mw-collapsed"

|+ style="white-space: nowrap;" | ~~Minimax~~ tunings

|+ style="white-space: nowrap;" | Target tunings

|-

! Target

! rowspan="2" | Target

! colspan="2" | Minimax

! colspan="2" | Least squares

|-

! Generator

! Eigenmonzo*

! Generator

! Eigenmonzo*

Line 235:

Line 263:

| ~16/15 = 116.588{{c}}

| 5/3

| ~16/15 = 116.578{{c}}

| {{Monzo| 0 -19 20 }}

|-

| 7-odd-limit

| ~15/14 = 116.588{{c}}

| 5/3

| ~15/14 = 116.573{{c}}

| {{Monzo| 0 -27 25 5 }}

|-

| 9-odd-limit

| ~15/14 = 116.716{{c}}

| 9/5

| ~15/14 = 116.721{{c}}

| {{Monzo| 0 117 -44 -19 }}

|-

| 11-odd-limit

| ~15/14 = 116.716{{c}}

| 9/5

|}

~~{| class="wikitable center-all left-3 mw-collapsible mw-collapsed"~~

~~|+ style="white-space: nowrap;" | Least squares tunings~~

|-

~~! Target~~

~~! Generator~~

! Eigenmonzo*

|-

~~| 5-odd-limit~~

~~| ~16/15 = 116.578{{c}}~~

~~| {{Monzo| 0 -19 20 }}~~

|-

~~| 7-odd-limit~~

~~| ~15/14 = 116.573{{c}}~~

~~| {{Monzo| 0 -27 25 5 }}~~

|-

~~| 9-odd-limit~~

~~| ~15/14 = 116.721{{c}}~~

~~| {{Monzo| 0 117 -44 -19 }}~~

|-

~~| 11-odd-limit~~

| ~15/14 = 116.672{{c}}

| {{Monzo| 0 17 -11 -6 11 }}

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|-

! Edo generator

! [[Eigenmonzo|~~Eigenmonzo~~ (~~unchanged-interval~~)]]*

! [[Eigenmonzo|Unchanged interval (eigenmonzo)]]*

! Generator (¢)

! Comments

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Line 346:

| 5/3

| 116.588

| 5- and 7-odd-limit minimax

| 5- and 7-odd-limit, 11-limit 15- and 21-odd-limit minimax

|-

|

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Line 427:

== Music ==

; [[Herman Miller]]

* [https://soundcloud.com/morphosyntax-1/realm-of-possibility ''Realm of Possibility''] (2021) – Miracle[31] with a 116.72-cent generator and 1200.53-cent octave

* [https://soundcloud.com/morphosyntax-1/realm-of-possibility ''Realm of Possibility''] (2021) – in Miracle[31] with a 116.72-cent generator and 1200.53-cent octave

; [[Joseph Pehrson]]

* ''Blackjack'' (2001) – [https://web.archive.org/web/20201127013023/http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Pehrson/josephpehrson+blackjack.mp3 play] | [https://soundclick.com/share.cfm?id=706344 SoundClick] – [[Blackjack|Blackjack (Miracle{{lbrack}}21{{rbrack}})]]

* ''Blackjack'' (2001) – [https://web.archive.org/web/20201127013023/http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Pehrson/josephpehrson+blackjack.mp3 play] | [https://soundclick.com/share.cfm?id=706344 SoundClick] – in [[Blackjack|Blackjack (Miracle{{lbrack}}21{{rbrack}})]]

* ''Blacklight'' (2002) – [https://web.archive.org/web/20201127015033/http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Pehrson/josephpehrson+blacklight.mp3 play] | [https://soundclick.com/share.cfm?id=710783 SoundClick] – Blackjack (Miracle[21])

* ''Blacklight'' (2002) – [https://web.archive.org/web/20201127015033/http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Pehrson/josephpehrson+blacklight.mp3 play] | [https://soundclick.com/share.cfm?id=710783 SoundClick] – in Blackjack (Miracle[21])

* ''Black and Jill'' (2003) – Blackjack (Miracle[21])

* ''Black and Jill'' (2003) – in Blackjack (Miracle[21])

** Soprano version – [https://web.archive.org/web/20201127012730/http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Pehrson/blackandjill.mp3 play] | [https://soundclick.com/share.cfm?id=2373400 SoundClick]

** [https://soundclick.com/share.cfm?id=9583778 Udderbot version]

* [https://soundclick.com/share.cfm?id=2623155 ''Inner Voices''] (2005) – Blackjack (Miracle[21])

* [https://soundclick.com/share.cfm?id=2623155 ''Inner Voices''] (2005) – in Blackjack (Miracle[21])

* [https://soundclick.com/share.cfm?id=6593353 ''Transpian''] (2006) – Blackjack (Miracle[21])

* [https://soundclick.com/share.cfm?id=6593353 ''Transpian''] (2006) – in Blackjack (Miracle[21])

* [https://soundclick.com/share.cfm?id=5049231 ''microproj''] (2007) – Blackjack (Miracle[21])

* [https://soundclick.com/share.cfm?id=5049231 ''microproj''] (2007) – in Blackjack (Miracle[21])

; [[Gene Ward Smith]]

* ''Rachmaninoff Plays Blackjack'' (archived 2010) – [http://www.archive.org/details/RachmaninoffPlaysBlackjack detail] | [http://www.archive.org/download/RachmaninoffPlaysBlackjack/rachman.mp3 play] – Blackjack (Miracle[21] in 175edo tuning

* ''Rachmaninoff Plays Blackjack'' (archived 2010) – [http://www.archive.org/details/RachmaninoffPlaysBlackjack detail] | [http://www.archive.org/download/RachmaninoffPlaysBlackjack/rachman.mp3 play] – in Blackjack (Miracle[21]), 175edo tuning

== External links ==

* [https://x31eq.com/decimal_lattice.htm ''Lattices with Decimal Notation''] by [[Graham Breed]]

~~[[Category:Temperaments]]~~

[[Category:Miracle| ]]

[[Category:Rank-2 temperaments]]

[[Category:Marvel temperaments]]

[[Category:Gamelismic clan]]

@@ Line 1: / Line 1: @@
-[[de:Miracle]]
+{{Interwiki
+| en = Miracle
+| de = Miracle
+}}
+{{Infobox regtemp
+| Title = Miracle
+| Subgroups = 2.3.5.7, 2.3.5.7.11
+| Comma basis = [[225/224]], [[1029/1024]] (7-limit); <br>[[225/224]], [[243/242]], [[385/384]] (11-limit)
+| Edo join 1 = 31 | Edo join 2 = 41
+| Generators = 15/14 | Generators tuning = 116.7 | Optimization method = CTE
+| MOS scales = …, [[1L 9s]], [[10L 1s]], [[10L 11s]], [[10L 21s]]
+| Mapping = 1; 6 -7 -2 15
+| Pergen = (P8, P5/6)
+| Odd limit 1 = 9 | Mistuning 1 = 3.32 | Complexity 1 = 21
+| Odd limit 2 = 11-limit 21 | Mistuning 2 = 4.86 | Complexity 2 = 31
+}}
 {{Wikipedia|Miracle temperament}}
-'''Miracle''' is a [[regular temperament]] discovered by [[George Secor]] in 1974 which splits a tempered [[3/2]] into six [[generator]]s, called ''[[secor]]s'' (after George), that serve as both [[15/14]] and [[16/15]] semitones. A stack of two generators represents [[8/7]], and a stack of seven generators represents [[8/5]]. It is a member of both the [[marvel temperaments]], by [[tempering out]] [[225/224]], and the [[gamelismic clan]], by tempering out [[1029/1024]]. It extends naturally to the [[11-limit]] by treating the neutral third from three generators as [[11/9]], tempering out [[243/242]], [[385/384]], [[441/440]], and [[540/539]].
+'''Miracle''' is a [[regular temperament]] discovered by [[George Secor]] in 1974 which splits a tempered [[3/2]] into six [[generator]]s, called ''[[secor]]s'' (after George), that serve as both [[15/14]] and [[16/15]] semitones. A stack of two generators represents [[8/7]], and a stack of seven generators represents [[8/5]]. It is a member of both the [[marvel temperaments]], by [[tempering out]] [[225/224]], and the [[gamelismic clan]], by tempering out [[1029/1024]]. It is naturally a full [[11-limit]] temperament, treating the neutral third from three generators as [[11/9]], tempering out [[243/242]], [[385/384]], [[441/440]], and [[540/539]]. It is supported by the highly notable [[EDO|edos]] [[31edo|31]], [[41edo|41]], and [[72edo|72]], with 72edo being an especially good tuning. (There is an alternative mapping for 11 known as [[revelation]], but there is little reason to use it unless you are using [[31edo]], in which case it is identical to miracle anyway.)
 Miracle is an exceptionally efficient linear temperament. It is quite accurate, with [[TOP]] error only 0.63 [[cent]]s/[[octave]], meaning intervals of the [[11-odd-limit]] [[tonality diamond]] are represented with only one or two cents of error. Yet it is also very low-complexity (efficient), as evidenced by the high density of 11-odd-limit ratios in the [[#Interval chain]]. At least one inversion of every interval in the 11-odd-limit tonality diamond is represented within 22 secors of the starting value.
-Some temperaments have 11/9 as a neutral third, meaning it is exactly half of a 3/2 (tempering out 243/242), and other temperaments have 8/7 as exactly a third of 3/2. Miracle is distinguished by doing both of these things at the same time, so 3/2 is divided into six equal parts.
+[[Rastmic clan|Some temperaments]] have 11/9 as a neutral third, meaning it is exactly half of a 3/2 (tempering out 243/242), and [[Gamelismic clan|other temperaments]] have 8/7 as exactly a third of 3/2. Miracle is distinguished by doing both of these things at the same time, so 3/2 is divided into six equal parts.
-Miracle can also be thought of as a [[cluster temperament]] with 10 clusters of notes in an octave. The small chroma interval between adjacent notes in each cluster is very versatile, representing [[45/44]] ~ [[49/48]] ~ [[50/49]] ~ [[55/54]] ~ [[56/55]] ~ [[64/63]] all [[tempered]] together.
+Miracle can also be thought of as a [[cluster temperament]] with 10 clusters of notes in an octave. The small chroma interval between adjacent notes in each cluster is very versatile, representing [[45/44]]~[[49/48]]~[[50/49]]~[[55/54]]~[[56/55]]~[[64/63]] all [[tempered]] together.
-See [[Miracle extensions]] for [[13-limit]] extensions. See [[Gamelismic clan #Miracle]] for technical data.
+See [[Miracle extensions]] for [[13-limit]] and [[17-limit]] extensions. See [[Gamelismic clan #Miracle]] for technical data.
 == Interval chain ==
@@ Line 179: / Line 194: @@
 Displayed on the right is a chart of the tuning spectrum of miracle by how the odd harmonics up to 11 are tuned, showing the minimax generator, i.e. the secor.
-=== Prime-optimized tunings ===
+=== Norm-based tunings ===
 {| class="wikitable mw-collapsible mw-collapsed"
-|+ style="font-size: 105%; white-space: nowrap;" | 7-limit Prime-Optimized Tunings
+|+ style="font-size: 105%; white-space: nowrap;" | 7-limit norm-based tunings
 |-
 ! rowspan="2" |
-! colspan="2" | Euclidean
+! colspan="3" | Euclidean
 |-
-! Unskewed
+! Constrained
-! Skewed
+! Constrained & skewed
+! Destretched
 |-
 ! Equilateral
-| CEE: ~15/14 = 116.516¢
+| CEE: ~15/14 = 116.5155{{c}}
-| CSEE: ~15/14 = 116.561¢
+| CSEE: ~15/14 = 116.5612{{c}}
+| POEE: ~15/14 = 116.6465{{c}}
 |-
 ! Tenney
-| CTE: ~15/14 = 116.677¢
+| CTE: ~15/14 = 116.6772{{c}}
-| CWE: ~15/14 = 116.676¢
+| CWE: ~15/14 = 116.6756{{c}}
+| POTE: ~15/14 = 116.6752{{c}}
 |-
 ! Benedetti, <br>Wilson
-| CBE: ~15/14 = 116.730¢
+| CBE: ~15/14 = 116.7297{{c}}
-| CSBE: ~15/14 = 116.714¢
+| CSBE: ~15/14 = 116.7136{{c}}
+| POBE: ~15/14 = 116.6903{{c}}
 |}
 {| class="wikitable mw-collapsible mw-collapsed"
-|+ style="font-size: 105%; white-space: nowrap;" | 11-limit Prime-Optimized Tunings
+|+ style="font-size: 105%; white-space: nowrap;" | 11-limit norm-based tunings
 |-
 ! rowspan="2" |
-! colspan="2" | Euclidean
+! colspan="3" | Euclidean
 |-
-! Unskewed
+! Constrained
-! Skewed
+! Constrained & skewed
+! Destretched
 |-
 ! Equilateral
-| CEE: ~15/14 = 116.687¢
+| CEE: ~15/14 = 116.6868{{c}}
-| CSEE: ~15/14 = 116.630¢
+| CSEE: ~15/14 = 116.6304{{c}}
+| POEE: ~15/14 = 116.5817{{c}}
 |-
 ! Tenney
-| CTE: ~15/14 = 116.711¢
+| CTE: ~15/14 = 116.7112{{c}}
-| CWE: ~15/14 = 116.647¢
+| CWE: ~15/14 = 116.6469{{c}}
+| POTE: ~15/14 = 116.6327{{c}}
 |-
 ! Benedetti, <br>Wilson
-| CBE: ~15/14 = 116.736¢
+| CBE: ~15/14 = 116.7355{{c}}
-| CSBE: ~15/14 = 116.677¢
+| CSBE: ~15/14 = 116.6768{{c}}
+| POBE: ~15/14 = 116.6643{{c}}
 |}
 === Target tunings ===
-{| class="wikitable center-all mw-collapsible mw-collapsed"
+{| class="wikitable center-all left-5 mw-collapsible mw-collapsed"
-|+ style="white-space: nowrap;" | Minimax tunings
+|+ style="white-space: nowrap;" | Target tunings
 |-
-! Target
+! rowspan="2" | Target
+! colspan="2" | Minimax
+! colspan="2" | Least squares
+|-
+! Generator
+! Eigenmonzo*
 ! Generator
 ! Eigenmonzo*
@@ Line 235: / Line 263: @@
 | ~16/15 = 116.588{{c}}
 | 5/3
+| ~16/15 = 116.578{{c}}
+| {{Monzo| 0 -19 20 }}
 |-
 | 7-odd-limit
 | ~15/14 = 116.588{{c}}
 | 5/3
+| ~15/14 = 116.573{{c}}
+| {{Monzo| 0 -27 25 5 }}
 |-
 | 9-odd-limit
 | ~15/14 = 116.716{{c}}
 | 9/5
+| ~15/14 = 116.721{{c}}
+| {{Monzo| 0 117 -44 -19 }}
 |-
 | 11-odd-limit
 | ~15/14 = 116.716{{c}}
 | 9/5
-|}
-{| class="wikitable center-all left-3 mw-collapsible mw-collapsed"
-|+ style="white-space: nowrap;" | Least squares tunings
-|-
-! Target
-! Generator
-! Eigenmonzo*
-|-
-| 5-odd-limit
-| ~16/15 = 116.578{{c}}
-| {{Monzo| 0 -19 20 }}
-|-
-| 7-odd-limit
-| ~15/14 = 116.573{{c}}
-| {{Monzo| 0 -27 25 5 }}
-|-
-| 9-odd-limit
-| ~15/14 = 116.721{{c}}
-| {{Monzo| 0 117 -44 -19 }}
-|-
-| 11-odd-limit
 | ~15/14 = 116.672{{c}}
 | {{Monzo| 0 17 -11 -6 11 }}
@@ Line 277: / Line 289: @@
 |-
 ! Edo<br>generator
-! [[Eigenmonzo|Eigenmonzo<br>(unchanged-interval)]]*
+! [[Eigenmonzo|Unchanged interval<br>(eigenmonzo)]]*
 ! Generator (¢)
 ! Comments
@@ Line 334: / Line 346: @@
 | 5/3
 | 116.588
-| 5- and 7-odd-limit minimax
+| 5- and 7-odd-limit, 11-limit 15- and 21-odd-limit minimax
 |-
 |
@@ Line 415: / Line 427: @@
 == Music ==
 ; [[Herman Miller]]
-* [https://soundcloud.com/morphosyntax-1/realm-of-possibility ''Realm of Possibility''] (2021) – Miracle[31] with a 116.72-cent generator and 1200.53-cent octave
+* [https://soundcloud.com/morphosyntax-1/realm-of-possibility ''Realm of Possibility''] (2021) – in Miracle[31] with a 116.72-cent generator and 1200.53-cent octave
 ; [[Joseph Pehrson]]
-* ''Blackjack'' (2001) – [https://web.archive.org/web/20201127013023/http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Pehrson/josephpehrson+blackjack.mp3 play] | [https://soundclick.com/share.cfm?id=706344 SoundClick] – [[Blackjack|Blackjack (Miracle{{lbrack}}21{{rbrack}})]]
+* ''Blackjack'' (2001) – [https://web.archive.org/web/20201127013023/http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Pehrson/josephpehrson+blackjack.mp3 play] | [https://soundclick.com/share.cfm?id=706344 SoundClick] – in [[Blackjack|Blackjack (Miracle{{lbrack}}21{{rbrack}})]]
-* ''Blacklight'' (2002) – [https://web.archive.org/web/20201127015033/http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Pehrson/josephpehrson+blacklight.mp3 play] | [https://soundclick.com/share.cfm?id=710783 SoundClick] – Blackjack (Miracle[21])
+* ''Blacklight'' (2002) – [https://web.archive.org/web/20201127015033/http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Pehrson/josephpehrson+blacklight.mp3 play] | [https://soundclick.com/share.cfm?id=710783 SoundClick] – in Blackjack (Miracle[21])
-* ''Black and Jill'' (2003) – Blackjack (Miracle[21])
+* ''Black and Jill'' (2003) – in Blackjack (Miracle[21])
 ** Soprano version – [https://web.archive.org/web/20201127012730/http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Pehrson/blackandjill.mp3 play] | [https://soundclick.com/share.cfm?id=2373400 SoundClick]
 ** [https://soundclick.com/share.cfm?id=9583778 Udderbot version]
-* [https://soundclick.com/share.cfm?id=2623155 ''Inner Voices''] (2005) – Blackjack (Miracle[21])
+* [https://soundclick.com/share.cfm?id=2623155 ''Inner Voices''] (2005) – in Blackjack (Miracle[21])
-* [https://soundclick.com/share.cfm?id=6593353 ''Transpian''] (2006) – Blackjack (Miracle[21])
+* [https://soundclick.com/share.cfm?id=6593353 ''Transpian''] (2006) – in Blackjack (Miracle[21])
-* [https://soundclick.com/share.cfm?id=5049231 ''microproj''] (2007) – Blackjack (Miracle[21])
+* [https://soundclick.com/share.cfm?id=5049231 ''microproj''] (2007) – in Blackjack (Miracle[21])
 ; [[Gene Ward Smith]]
-* ''Rachmaninoff Plays Blackjack'' (archived 2010) – [http://www.archive.org/details/RachmaninoffPlaysBlackjack detail] | [http://www.archive.org/download/RachmaninoffPlaysBlackjack/rachman.mp3 play] – Blackjack (Miracle[21] in 175edo tuning
+* ''Rachmaninoff Plays Blackjack'' (archived 2010) – [http://www.archive.org/details/RachmaninoffPlaysBlackjack detail] | [http://www.archive.org/download/RachmaninoffPlaysBlackjack/rachman.mp3 play] – in Blackjack (Miracle[21]), 175edo tuning
+== External links ==
+* [https://x31eq.com/decimal_lattice.htm ''Lattices with Decimal Notation''] by [[Graham Breed]]
-[[Category:Temperaments]]
 [[Category:Miracle| ]] <!-- main article -->
+[[Category:Rank-2 temperaments]]
 [[Category:Marvel temperaments]]
 [[Category:Gamelismic clan]]