Magic: Difference between revisions

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Because the generator is so close to 1\3 of an octave, and the interval left over is accordingly so small, all small magic MOSes consist of three large intervals alternating with three groups of this small interval. Specifically, there are the following MOSes, where s always represents the characteristic small interval, which simultaneously represents [[128/125]], [[36/35]], [[28/27]], and [[25/24]].

* [[3L 4s]]: LsLsLss where L represents 6/5

* [[3L 4s]]: LsLsLss, where L represents 6/5

* [[3L 7s]]: LssLssLsss where L represents 7/6

* [[3L 7s]]: LssLssLsss, where L represents 7/6

* [[3L 10s]]: LsssLsssLssss where L represents 9/8

* [[3L 10s]]: LsssLsssLssss, where L represents 9/8

* [[3L 13s]]: LssssLssssLsssss where L is a neutral second, which can be taken to represent 12/11 (in magic temperament) or 11/10 (in the related [[Magic family #Telepathy|telepathy]] temperament). In 22edo they are identical.

* [[3L 13s]]: LssssLssssLsssss, where L is a neutral second, which can be taken to represent 12/11 (in magic temperament) or 11/10 (in the related [[Magic family #Telepathy|telepathy]] temperament). In 22edo they are identical.

== Interval chain ==

{| class="wikitable center-all"

|-

! Cents*

! Cents{{asterisk}}

| 0

| 380.352

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| (12/11)

|}

<nowiki>*~~</nowiki> in~~ 7-limit [[POTE tuning]]

<nowiki />* In 7-limit [[POTE tuning]]

The generator chain val for 13-limit magic is {{val| 0 5 1 12 -8 18 }}, so that five generators give an approximate 3, twelve 14, minus eight 11/64, and eighteen 52.

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== Scales ==

; MOS scales

* [[Magic7]] ~~- improper~~ [[3L 4s]]

* [[Magic7]] – Improper [[3L 4s]]

* [[Magic10]] ~~- improper~~ [[3L 7s]]

* [[Magic10]] – Improper [[3L 7s]]

* [[Magic13]] ~~- improper~~ [[3L 10s]]

* [[Magic13]] – Improper [[3L 10s]]

* [[Magic16]] ~~- improper~~ [[3L 13s]]. The boundary of propriety is 19edo.

* [[Magic16]] – Improper [[3L 13s]]. The boundary of propriety is 19edo.

* [[Magic19]] ~~- proper~~ [[3L 16s]]. The boundary of propriety is 22edo.

* [[Magic19]] – Proper [[3L 16s]]. The boundary of propriety is 22edo.

* [[Magic22]] - [[19L 3s]] scale. The boundary of propriety is 41edo.

* [[Magic22]] – [[19L 3s]] scale. The boundary of propriety is 41edo.

; Transversal scales

* [[Magic19trans37]]

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* [[Magic22trans37]]

* [[Magic22trans37ex]]

; Others

* [[Paulsmagic]]

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{| class="wikitable center-all left-4"

|-

! ET generator

! ET generator

! [[eigenmonzo|~~eigenmonzo~~ (unchanged-interval)]]

! [[eigenmonzo|Eigenmonzo (unchanged-interval)]]

! ~~generator~~ (¢)

! Generator (¢)

! comments

|-

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{| class="wikitable center-all left-4"

|-

! ET generator

! ET generator

! [[eigenmonzo|~~eigenmonzo~~ (unchanged-interval)]]

! [[eigenmonzo|Eigenmonzo (unchanged-interval)]]

! generator (¢)

! generator (¢)

! comments

|-

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{| class="wikitable center-all left-4"

|-

! ET generator

! ET generator

! [[eigenmonzo|~~eigenmonzo~~ (unchanged-interval)]]

! [[eigenmonzo|Eigenmonzo (unchanged-interval)]]

! generator (¢)

! generator (¢)

! comments

|-

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{| class="wikitable center-all left-4"

|-

! ET generator

! ET generator

! [[eigenmonzo|~~eigenmonzo~~ (unchanged-interval)]]

! [[eigenmonzo|Eigenmonzo (unchanged-interval)]]

! generator (¢)

! generator (¢)

! comments

|-

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{| class="wikitable center-all left-4"

|-

! ET generator

! ET generator

! [[eigenmonzo|~~eigenmonzo~~ (unchanged-interval)]]

! [[eigenmonzo|Eigenmonzo (unchanged-interval)]]

! generator (¢)

! generator (¢)

! comments

|-

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{| class="wikitable center-all left-4"

|-

! ET generator

! ET generator

! [[eigenmonzo|~~eigenmonzo~~ (unchanged-interval)]]

! [[eigenmonzo|Eigenmonzo (unchanged-interval)]]

! generator (¢)

! generator (¢)

! comments

|-

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== Music ==

; [[Andrew Milne]]

* [https://soundcloud.com/andrew-j-milne/magic-traveller ''Magic Traveller''] (2008) ~~– magic~~[10] with 379.8-cent generator

* [https://soundcloud.com/andrew-j-milne/magic-traveller ''Magic Traveller''] (2008) – Magic[10] with 379.8-cent generator

; [[Cameron Bobro]]

* [https://web.archive.org/web/20201127015243/http://micro.soonlabel.com/gene_ward_smith/Others/Bobro/Magical_Daydream_CBobro.mp3 ''Magical Daydream''] ''A brief demonstration of the near-Just musical temperament which flattens the pure major third of 5:4 by a few cents, such that 5 major thirds does not exceed 3:1 (a pure fifth + 1 octave), but meets it precisely. In a purely tuned system, the thirds would exceed 3:1 by what is known as the small diesis, (a ratio 3125/3072, about thirty cents). This temperament, then, brings (almost) pure thirds and pure fifths together.''

* [https://web.archive.org/web/20201127015243/http://micro.soonlabel.com/gene_ward_smith/Others/Bobro/Magical_Daydream_CBobro.mp3 ''Magical Daydream''] – ''A brief demonstration of the near-Just musical temperament which flattens the pure major third of 5:4 by a few cents, such that 5 major thirds does not exceed 3:1 (a pure fifth + 1 octave), but meets it precisely. In a purely tuned system, the thirds would exceed 3:1 by what is known as the small diesis, (a ratio 3125/3072, about thirty cents). This temperament, then, brings (almost) pure thirds and pure fifths together.''

* [https://web.archive.org/web/20201127014810/http://micro.soonlabel.com/gene_ward_smith/Others/Bobro/EveningHorizon_CBobro.mp3 ''Evening Horizon''] ''The earliest implementation (by happy accident, it seems) of this temperament was, to my knowledge, by Paul von Janko over a century ago. More recently, an online tuning community has elaborated many precise variations, calling the temperament "magic". This piece is a demonstration of the array of pitches created by using 22 generators (the slightly tempered 5:4) within the octave, an approach which creates a "moment of symmetry", with all pitches separated by the same two intervals. This has many curious repercussions, creating some musical possibilities and restricting others.''

* [https://web.archive.org/web/20201127014810/http://micro.soonlabel.com/gene_ward_smith/Others/Bobro/EveningHorizon_CBobro.mp3 ''Evening Horizon''] – ''The earliest implementation (by happy accident, it seems) of this temperament was, to my knowledge, by Paul von Janko over a century ago. More recently, an online tuning community has elaborated many precise variations, calling the temperament "magic". This piece is a demonstration of the array of pitches created by using 22 generators (the slightly tempered 5:4) within the octave, an approach which creates a "moment of symmetry", with all pitches separated by the same two intervals. This has many curious repercussions, creating some musical possibilities and restricting others.''

; [[Chris Vaisvil]] ([http://www.chrisvaisvil.com/ site])

* [http://micro.soonlabel.com/magic/daily20120113-piano-magic16-.mp3 ''Chromatic piece in magic 16''] (2012) ~~– magic~~[16] in 145edo tuning (→ [[magic16]])

* [http://micro.soonlabel.com/magic/daily20120113-piano-magic16-.mp3 ''Chromatic piece in magic 16''] (2012) – Magic[16] in 145edo tuning (→ [[magic16]])

* [http://micro.soonlabel.com/22-ET/daily20120128-pauls-magic.mp3 ''A Piece in Paulsmagic''] (2012) ~~– in~~ [[paulsmagic]]

* [http://micro.soonlabel.com/22-ET/daily20120128-pauls-magic.mp3 ''A Piece in Paulsmagic''] (2012) – In [[paulsmagic]]

* [http://micro.soonlabel.com/41edo/20130910_magic%5b19%5dor_41_the_magic_of_belief.mp3 ''The Magic of Belief''] (2013) ~~– magic~~[19] in 41edo tuning

* [http://micro.soonlabel.com/41edo/20130910_magic%5b19%5dor_41_the_magic_of_belief.mp3 ''The Magic of Belief''] (2013) – Magic[19] in 41edo tuning

; [[Graham Breed]]

* [http://x31eq.com/music/dingsheng.mp3 ''Golden Age''] ~~– disco~~ involving magic comma pumps.

* [http://x31eq.com/music/dingsheng.mp3 ''Golden Age''] – Disco involving magic comma pumps.

* [http://x31eq.com/music/dingshi.mp3 ''Extravagant Food''] ~~– a~~ single magic comma pump in under 60 seconds in 60edo.

* [http://x31eq.com/music/dingshi.mp3 ''Extravagant Food''] – A single magic comma pump in under 60 seconds in 60edo.

* [http://x31eq.com/music/jitter.ogg ''Gene's Jitterbug''] – 9-odd-limit harmony, may not require magic.

; [[Jake Freivald]]

* ''Little Magical Object'' (2013) – [https://web.archive.org/web/20201127014655/http://micro.soonlabel.com/gene_ward_smith/Others/Freivald/little-magical-object.mp3 play] | [https://soundcloud.com/jdfreivald/little-magical-object SoundCloud] – ~~magic~~[19] in 41edo tuning

* ''Little Magical Object'' (2013) – [https://web.archive.org/web/20201127014655/http://micro.soonlabel.com/gene_ward_smith/Others/Freivald/little-magical-object.mp3 play] | [https://soundcloud.com/jdfreivald/little-magical-object SoundCloud] – Magic[19] in 41edo tuning

; [[User:Xenllium|Xenllium]]

* [https://youtube.com/watch?v=5iBXKRWE-_U ''Magical life''] (2023) ~~– in~~ 19-tone pure-fifth magic scale

* [https://youtube.com/watch?v=5iBXKRWE-_U ''Magical life''] (2023) – In 19-tone pure-fifth magic scale

== See also ==

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== External links ==

* [http://x31eq.com/magic/ Magic Temperament] – Graham Breed's documents

[[Category:Temperaments]]

[[Category:Magic| ]]

[[Category:Magic| ]]

[[Category:Magic family]]

[[Category:Marvel temperaments]]

[[Category:Sensamagic clan]]

[[Category:Keemic temperaments]]

@@ Line 26: / Line 26: @@
 Because the generator is so close to 1\3 of an octave, and the interval left over is accordingly so small, all small magic MOSes consist of three large intervals alternating with three groups of this small interval. Specifically, there are the following MOSes, where s always represents the characteristic small interval, which simultaneously represents [[128/125]], [[36/35]], [[28/27]], and [[25/24]].
-* [[3L 4s]]: LsLsLss where L represents 6/5
+* [[3L 4s]]: LsLsLss, where L represents 6/5
-* [[3L 7s]]: LssLssLsss where L represents 7/6
+* [[3L 7s]]: LssLssLsss, where L represents 7/6
-* [[3L 10s]]: LsssLsssLssss where L represents 9/8
+* [[3L 10s]]: LsssLsssLssss, where L represents 9/8
-* [[3L 13s]]: LssssLssssLsssss where L is a neutral second, which can be taken to represent 12/11 (in magic temperament) or 11/10 (in the related [[Magic family #Telepathy|telepathy]] temperament). In 22edo they are identical.
+* [[3L 13s]]: LssssLssssLsssss, where L is a neutral second, which can be taken to represent 12/11 (in magic temperament) or 11/10 (in the related [[Magic family #Telepathy|telepathy]] temperament). In 22edo they are identical.
 == Interval chain ==
 {| class="wikitable center-all"
 |-
-! Cents*
+! Cents{{asterisk}}
 | 0
 | 380.352
@@ Line 66: / Line 67: @@
 | (12/11)
 |}
-<nowiki>*</nowiki> in 7-limit [[POTE tuning]]
+<nowiki />* In 7-limit [[POTE tuning]]
 The generator chain val for 13-limit magic is {{val| 0 5 1 12 -8 18 }}, so that five generators give an approximate 3, twelve 14, minus eight 11/64, and eighteen 52.
@@ Line 86: / Line 87: @@
 == Scales ==
 ; MOS scales
-* [[Magic7]] - improper [[3L 4s]]
+* [[Magic7]] &ndash; Improper [[3L 4s]]
-* [[Magic10]] - improper [[3L 7s]]
+* [[Magic10]] &ndash; Improper [[3L 7s]]
-* [[Magic13]] - improper [[3L 10s]]
+* [[Magic13]] &ndash; Improper [[3L 10s]]
-* [[Magic16]] - improper [[3L 13s]]. The boundary of propriety is 19edo.
+* [[Magic16]] &ndash; Improper [[3L 13s]]. The boundary of propriety is 19edo.
-* [[Magic19]] - proper [[3L 16s]]. The boundary of propriety is 22edo.
+* [[Magic19]] &ndash; Proper [[3L 16s]]. The boundary of propriety is 22edo.
-* [[Magic22]] - [[19L 3s]] scale. The boundary of propriety is 41edo.
+* [[Magic22]] &ndash; [[19L 3s]] scale. The boundary of propriety is 41edo.
 ; Transversal scales
 * [[Magic19trans37]]
@@ Line 97: / Line 99: @@
 * [[Magic22trans37]]
 * [[Magic22trans37ex]]
 ; Others
 * [[Paulsmagic]]
@@ Line 108: / Line 111: @@
 {| class="wikitable center-all left-4"
 |-
-! ET<br>generator
+! ET<br />generator
-! [[eigenmonzo|eigenmonzo<br>(unchanged-interval)]]
+! [[eigenmonzo|Eigenmonzo<br />(unchanged-interval)]]
-! generator<br>(¢)
+! Generator<br />(&#162;)
 ! comments
 |-
@@ Line 301: / Line 304: @@
 {| class="wikitable center-all left-4"
 |-
-! ET<br>generator
+! ET<br />generator
-! [[eigenmonzo|eigenmonzo<br>(unchanged-interval)]]
+! [[eigenmonzo|Eigenmonzo<br />(unchanged-interval)]]
-! generator<br>(¢)
+! generator<br />(&#162;)
 ! comments
 |-
@@ Line 494: / Line 497: @@
 {| class="wikitable center-all left-4"
 |-
-! ET<br>generator
+! ET<br />generator
-! [[eigenmonzo|eigenmonzo<br>(unchanged-interval)]]
+! [[eigenmonzo|Eigenmonzo<br />(unchanged-interval)]]
-! generator<br>(¢)
+! generator<br />(&#162;)
 ! comments
 |-
@@ Line 687: / Line 690: @@
 {| class="wikitable center-all left-4"
 |-
-! ET<br>generator
+! ET<br />generator
-! [[eigenmonzo|eigenmonzo<br>(unchanged-interval)]]
+! [[eigenmonzo|Eigenmonzo<br />(unchanged-interval)]]
-! generator<br>(¢)
+! generator<br />(&#162;)
 ! comments
 |-
@@ Line 880: / Line 883: @@
 {| class="wikitable center-all left-4"
 |-
-! ET<br>generator
+! ET<br />generator
-! [[eigenmonzo|eigenmonzo<br>(unchanged-interval)]]
+! [[eigenmonzo|Eigenmonzo<br />(unchanged-interval)]]
-! generator<br>(¢)
+! generator<br />(&#162;)
 ! comments
 |-
@@ Line 1,073: / Line 1,076: @@
 {| class="wikitable center-all left-4"
 |-
-! ET<br>generator
+! ET<br />generator
-! [[eigenmonzo|eigenmonzo<br>(unchanged-interval)]]
+! [[eigenmonzo|Eigenmonzo<br />(unchanged-interval)]]
-! generator<br>(¢)
+! generator<br />(&#162;)
 ! comments
 |-
@@ Line 1,256: / Line 1,259: @@
 == Music ==
 ; [[Andrew Milne]]
-* [https://soundcloud.com/andrew-j-milne/magic-traveller ''Magic Traveller''] (2008) – magic[10] with 379.8-cent generator
+* [https://soundcloud.com/andrew-j-milne/magic-traveller ''Magic Traveller''] (2008) &ndash; Magic[10] with 379.8-cent generator
 ; [[Cameron Bobro]]
-* [https://web.archive.org/web/20201127015243/http://micro.soonlabel.com/gene_ward_smith/Others/Bobro/Magical_Daydream_CBobro.mp3 ''Magical Daydream''] ''A brief demonstration of the near-Just musical temperament which flattens the pure major third of 5:4 by a few cents, such that 5 major thirds does not exceed 3:1 (a pure fifth + 1 octave), but meets it precisely. In a purely tuned system, the thirds would exceed 3:1 by what is known as the small diesis, (a ratio 3125/3072, about thirty cents). This temperament, then, brings (almost) pure thirds and pure fifths together.''
+* [https://web.archive.org/web/20201127015243/http://micro.soonlabel.com/gene_ward_smith/Others/Bobro/Magical_Daydream_CBobro.mp3 ''Magical Daydream''] &ndash; ''A brief demonstration of the near-Just musical temperament which flattens the pure major third of 5:4 by a few cents, such that 5 major thirds does not exceed 3:1 (a pure fifth + 1 octave), but meets it precisely. In a purely tuned system, the thirds would exceed 3:1 by what is known as the small diesis, (a ratio 3125/3072, about thirty cents). This temperament, then, brings (almost) pure thirds and pure fifths together.''
-* [https://web.archive.org/web/20201127014810/http://micro.soonlabel.com/gene_ward_smith/Others/Bobro/EveningHorizon_CBobro.mp3 ''Evening Horizon''] ''The earliest implementation (by happy accident, it seems) of this temperament was, to my knowledge, by Paul von Janko over a century ago. More recently, an online tuning community has elaborated many precise variations, calling the temperament "magic". This piece is a demonstration of the array of pitches created by using 22 generators (the slightly tempered 5:4) within the octave, an approach which creates a "moment of symmetry", with all pitches separated by the same two intervals. This has many curious repercussions, creating some musical possibilities and restricting others.''
+* [https://web.archive.org/web/20201127014810/http://micro.soonlabel.com/gene_ward_smith/Others/Bobro/EveningHorizon_CBobro.mp3 ''Evening Horizon''] &ndash; ''The earliest implementation (by happy accident, it seems) of this temperament was, to my knowledge, by Paul von Janko over a century ago. More recently, an online tuning community has elaborated many precise variations, calling the temperament "magic". This piece is a demonstration of the array of pitches created by using 22 generators (the slightly tempered 5:4) within the octave, an approach which creates a "moment of symmetry", with all pitches separated by the same two intervals. This has many curious repercussions, creating some musical possibilities and restricting others.''
 ; [[Chris Vaisvil]] ([http://www.chrisvaisvil.com/ site])
-* [http://micro.soonlabel.com/magic/daily20120113-piano-magic16-.mp3 ''Chromatic piece in magic 16''] (2012) – magic[16] in 145edo tuning (→ [[magic16]])
+* [http://micro.soonlabel.com/magic/daily20120113-piano-magic16-.mp3 ''Chromatic piece in magic 16''] (2012) &ndash; Magic[16] in 145edo tuning (&rarr; [[magic16]])
-* [http://micro.soonlabel.com/22-ET/daily20120128-pauls-magic.mp3 ''A Piece in Paulsmagic''] (2012) – in [[paulsmagic]]
+* [http://micro.soonlabel.com/22-ET/daily20120128-pauls-magic.mp3 ''A Piece in Paulsmagic''] (2012) &ndash; In [[paulsmagic]]
-* [http://micro.soonlabel.com/41edo/20130910_magic%5b19%5dor_41_the_magic_of_belief.mp3 ''The Magic of Belief''] (2013) – magic[19] in 41edo tuning
+* [http://micro.soonlabel.com/41edo/20130910_magic%5b19%5dor_41_the_magic_of_belief.mp3 ''The Magic of Belief''] (2013) &ndash; Magic[19] in 41edo tuning
 ; [[Graham Breed]]
-* [http://x31eq.com/music/dingsheng.mp3 ''Golden Age''] – disco involving magic comma pumps.
+* [http://x31eq.com/music/dingsheng.mp3 ''Golden Age''] &ndash; Disco involving magic comma pumps.
-* [http://x31eq.com/music/dingshi.mp3 ''Extravagant Food''] – a single magic comma pump in under 60 seconds in 60edo.
+* [http://x31eq.com/music/dingshi.mp3 ''Extravagant Food''] &ndash; A single magic comma pump in under 60 seconds in 60edo.
-* [http://x31eq.com/music/jitter.ogg ''Gene's Jitterbug''] – 9-odd-limit harmony, may not require magic.
+* [http://x31eq.com/music/jitter.ogg ''Gene's Jitterbug''] &ndash; 9-odd-limit harmony, may not require magic.
 ; [[Jake Freivald]]
-* ''Little Magical Object'' (2013) – [https://web.archive.org/web/20201127014655/http://micro.soonlabel.com/gene_ward_smith/Others/Freivald/little-magical-object.mp3 play] | [https://soundcloud.com/jdfreivald/little-magical-object SoundCloud] – magic[19] in 41edo tuning
+* ''Little Magical Object'' (2013) &ndash; [https://web.archive.org/web/20201127014655/http://micro.soonlabel.com/gene_ward_smith/Others/Freivald/little-magical-object.mp3 play] | [https://soundcloud.com/jdfreivald/little-magical-object SoundCloud] – Magic[19] in 41edo tuning
 ; [[User:Xenllium|Xenllium]]
-* [https://youtube.com/watch?v=5iBXKRWE-_U ''Magical life''] (2023) – in 19-tone pure-fifth magic scale
+* [https://youtube.com/watch?v=5iBXKRWE-_U ''Magical life''] (2023) &ndash; In 19-tone pure-fifth magic scale
 == See also ==
@@ Line 1,284: / Line 1,287: @@
 == External links ==
-* [http://x31eq.com/magic/ Magic Temperament] – Graham Breed's documents
+* [http://x31eq.com/magic/ Magic Temperament] &ndash; Graham Breed's documents
 [[Category:Temperaments]]
-[[Category:Magic| ]] <!-- main article -->
+[[Category:Magic| ]] <!-- Main article -->
 [[Category:Magic family]]
 [[Category:Marvel temperaments]]
 [[Category:Sensamagic clan]]
 [[Category:Keemic temperaments]]