5L 12s: Difference between revisions

Line 1:

{{Infobox MOS

| Periods = 1

| nLargeSteps = 5

| nSmallSteps = 12

| Equalized = 7

| Paucitonic = 2

| Pattern = sssLssLsssLssLssL

| Name = Superpyth mega-chromatic

}}

'''5L 12s''' is the MOS pattern of the [[superpyth]] mega-chromatic scale. In contrast to the [[12L 5s|schismic mega-chromatic scale]], in which mega-chromatic semitones (negative diminished seconds) are smaller than chromatic semitones, here the reverse is true: mega-chromatic semitones are larger than chromatic semitones, so the [[5L 7s|diatonic scale]] subset is actually [[Rothenberg propriety|improper]].

The supra/quasisuper version is proper, but the superpyth/ultrapyth version is improper (it doesn't become proper until you add 5 more notes to form the schismic 22-note scale).

== Modes ==

* 16|0 LssLssLsssLssLsss

* 15|1 LssLsssLssLssLsss

* 14|2 LssLsssLssLsssLss

* 13|3 LsssLssLssLsssLss

* 12|4 LsssLssLsssLssLss

* 11|5 sLssLssLsssLssLss

* 10|6 sLssLsssLssLssLss

* 9|7 sLssLsssLssLsssLs

* 8|8 sLsssLssLssLsssLs

* 7|9 sLsssLssLsssLssLs

* 6|10 ssLssLssLsssLssLs

* 5|11 ssLssLsssLssLssLs

* 4|12 ssLssLsssLssLsssL

* 3|13 ssLsssLssLssLsssL

* 2|14 ssLsssLssLsssLssL

* 1|15 sssLssLssLsssLssL

* 0|16 sssLssLsssLssLssL

== Scale tree ==

{| class="wikitable center-all"

! colspan="6" | Generator

! ~~Cents~~

! Fifth <br>(cents)

! L

! s

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| || || || || || 76\129 || 706.977 || 9 || 7 || 1.286 ||

|-

| || || || 33\56 || || || 707.143 || 4 || 3 || 1.333 || Supra

| || || || 33\56 || || || 707.143 || 4 || 3 || 1.333 || [[Supra]]

|-

| || || || || || 89\151 || 707.285 || 11 || 8 || 1.375 ||

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| || || || || || 79\134 || 707.463 || 10 || 7 || 1.428 ||

|-

| || || 23\39 || || || || 707.692 || 3 || 2 || 1.500 || ~~L/s = 3/2~~

| || || 23\39 || || || || 707.692 || 3 || 2 || 1.500 ||

|-

| || || || || || 82\139 || 707.914 || 11 || 7 || 1.571 ||

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| || || || || 59\100 || || 708.000 || 8 || 5 || 1.600 ||

|-

| || || || || || 95\161 || 708.075 || 13 || 8 || 1.625 || Golden supra

| || || || || || 95\161 || 708.075 || 13 || 8 || 1.625 || Golden supra (Fifth = 708.0539 cents)

|-

| || || || 36\61 || || || 708.197 || 5 || 3 || 1.667 || Quasisuper, quasisupra

| || || || 36\61 || || || 708.197 || 5 || 3 || 1.667 || [[Quasisuper]] / [[quasisupra]]

|-

| || || || || || 85\144 || 708.333 || 12 || 7 || 1.714 ||

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| || || || || || 62\105 || 708.571 || 9 || 5 || 1.800 ||

|-

| || 13\22 || || || || || 709.091 || 2 || 1 || 2.000 || Basic 5L 12s<br>(~~Generators~~ smaller than this are proper)

| || 13\22 || || || || || 709.091 || 2 || 1 || 2.000 || Basic 5L 12s <br>(Fifths smaller than this are proper)

|-

| || || || || || 55\93 || 709.677 || 9 || 4 || 2.250 ||

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| || || || || || 71\120 || 710.000 || 12 || 5 || 2.400 ||

|-

| || || || 29\49 || || || 710.204 || 5 || 2 || 2.500 || Superpyth

| || || || 29\49 || || || 710.204 || 5 || 2 || 2.500 || [[Superpyth]]

|-

| || || || || || 74\125 || 710.400 || 13 || 5 || 2.600 || ~~Unnamed golden tuning~~

| || || || || || 74\125 || 710.400 || 13 || 5 || 2.600 || Golden superpyth (Fifth = 710.4345 cents)

|-

| || || || || 45\76 || || 710.526 || 8 || 3 || 2.667 ||

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| || || || || || 61\103 || 710.680 || 11 || 4 || 2.750 ||

|-

| || || 16\27 || || || || 711.111 || 3 || 1 || 3.000 || ~~L/s = 3/1~~

| || || 16\27 || || || || 711.111 || 3 || 1 || 3.000 ||

|-

| || || || || || 51\86 || 711.628 || 10 || 3 || 3.333 ||

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| || || || || || 41\69 || 713.043 || 9 || 2 || 4.500 ||

|-

| || || || || 22\37 || || 713.514 || 5 || 1 || 5.000 ||

| || || || || 22\37 || || 713.514 || 5 || 1 || 5.000 || [[Oceanfront]] / [[Ultrapyth]]

|-

| || || || || || 25\42 || 714.286 || 6 || 1 || 6.000 || ~~Hemiseven↓~~

| || || || || || 25\42 || 714.286 || 6 || 1 || 6.000 || [[Hemiseven]]↓

|-

| 3\5 || || || || || || 720.000 || 1 || 0 || → inf ||

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[[Category:Abstract MOS patterns]]

[[Category:17-tone scales]]

[[Category:Mega chromatic scale]]

~~{{todo| intro }}~~

@@ Line 1: / Line 1: @@
+{{Infobox MOS
+| Periods = 1
+| nLargeSteps = 5
+| nSmallSteps = 12
+| Equalized = 7
+| Paucitonic = 2
+| Pattern = sssLssLsssLssLssL
+| Name = Superpyth mega-chromatic
+}}
+'''5L 12s''' is the MOS pattern of the [[superpyth]] mega-chromatic scale. In contrast to the [[12L 5s|schismic mega-chromatic scale]], in which mega-chromatic semitones (negative diminished seconds) are smaller than chromatic semitones, here the reverse is true: mega-chromatic semitones are larger than chromatic semitones, so the [[5L 7s|diatonic scale]] subset is actually [[Rothenberg propriety|improper]].
+The supra/quasisuper version is proper, but the superpyth/ultrapyth version is improper (it doesn't become proper until you add 5 more notes to form the schismic 22-note scale).
+== Modes ==
+* 16|0 LssLssLsssLssLsss
+* 15|1 LssLsssLssLssLsss
+* 14|2 LssLsssLssLsssLss
+* 13|3 LsssLssLssLsssLss
+* 12|4 LsssLssLsssLssLss
+* 11|5 sLssLssLsssLssLss
+* 10|6 sLssLsssLssLssLss
+* 9|7 sLssLsssLssLsssLs
+* 8|8 sLsssLssLssLsssLs
+* 7|9 sLsssLssLsssLssLs
+* 6|10 ssLssLssLsssLssLs
+* 5|11 ssLssLsssLssLssLs
+* 4|12 ssLssLsssLssLsssL
+* 3|13 ssLsssLssLssLsssL
+* 2|14 ssLsssLssLsssLssL
+* 1|15 sssLssLssLsssLssL
+* 0|16 sssLssLsssLssLssL
 == Scale tree ==
 {| class="wikitable center-all"
 ! colspan="6" | Generator
-! Cents
+! Fifth <br>(cents)
 ! L
 ! s
@@ Line 16: / Line 49: @@
 | || || || || || 76\129 || 706.977 || 9 || 7 || 1.286 ||
 |-
-| || || || 33\56 || || || 707.143 || 4 || 3 || 1.333 || Supra
+| || || || 33\56 || || || 707.143 || 4 || 3 || 1.333 || [[Supra]]
 |-
 | || || || || || 89\151 || 707.285 || 11 || 8 || 1.375 ||
@@ Line 24: / Line 57: @@
 | || || || || || 79\134 || 707.463 || 10 || 7 || 1.428 ||
 |-
-| || || 23\39 || || || || 707.692 || 3 || 2 || 1.500 || L/s = 3/2
+| || || 23\39 || || || || 707.692 || 3 || 2 || 1.500 ||
 |-
 | || || || || || 82\139 || 707.914 || 11 || 7 || 1.571 ||
@@ Line 30: / Line 63: @@
 | || || || || 59\100 || || 708.000 || 8 || 5 || 1.600 ||
 |-
-| || || || || || 95\161 || 708.075 || 13 || 8 || 1.625 || Golden supra
+| || || || || || 95\161 || 708.075 || 13 || 8 || 1.625 || Golden supra (Fifth = 708.0539 cents)
 |-
-| || || || 36\61 || || || 708.197 || 5 || 3 || 1.667 || Quasisuper, quasisupra
+| || || || 36\61 || || || 708.197 || 5 || 3 || 1.667 || [[Quasisuper]] / [[quasisupra]]
 |-
 | || || || || || 85\144 || 708.333 || 12 || 7 || 1.714 ||
@@ Line 40: / Line 73: @@
 | || || || || || 62\105 || 708.571 || 9 || 5 || 1.800 ||
 |-
-| || 13\22 || || || || || 709.091 || 2 || 1 || 2.000 || Basic 5L 12s<br>(Generators smaller than this are proper)
+| || 13\22 || || || || || 709.091 || 2 || 1 || 2.000 || Basic 5L 12s <br>(Fifths smaller than this are proper)
 |-
 | || || || || || 55\93 || 709.677 || 9 || 4 || 2.250 ||
@@ Line 48: / Line 81: @@
 | || || || || || 71\120 || 710.000 || 12 || 5 || 2.400 ||
 |-
-| || || || 29\49 || || || 710.204 || 5 || 2 || 2.500 || Superpyth
+| || || || 29\49 || || || 710.204 || 5 || 2 || 2.500 || [[Superpyth]]
 |-
-| || || || || || 74\125 || 710.400 || 13 || 5 || 2.600 || Unnamed golden tuning
+| || || || || || 74\125 || 710.400 || 13 || 5 || 2.600 || Golden superpyth (Fifth = 710.4345 cents)
 |-
 | || || || || 45\76 || || 710.526 || 8 || 3 || 2.667 ||
@@ Line 56: / Line 89: @@
 | || || || || || 61\103 || 710.680 || 11 || 4 || 2.750 ||
 |-
-| || || 16\27 || || || || 711.111 || 3 || 1 || 3.000 || L/s = 3/1
+| || || 16\27 || || || || 711.111 || 3 || 1 || 3.000 ||
 |-
 | || || || || || 51\86 || 711.628 || 10 || 3 || 3.333 ||
@@ Line 68: / Line 101: @@
 | || || || || || 41\69 || 713.043 || 9 || 2 || 4.500 ||
 |-
-| || || || || 22\37 || || 713.514 || 5 || 1 || 5.000 ||
+| || || || || 22\37 || || 713.514 || 5 || 1 || 5.000 || [[Oceanfront]] / [[Ultrapyth]]
 |-
-| || || || || || 25\42 || 714.286 || 6 || 1 || 6.000 || Hemiseven↓
+| || || || || || 25\42 || 714.286 || 6 || 1 || 6.000 || [[Hemiseven]]↓
 |-
 | 3\5 || || || || || || 720.000 || 1 || 0 || → inf ||
@@ Line 78: / Line 111: @@
 [[Category:Abstract MOS patterns]]
 [[Category:17-tone scales]]
+[[Category:Mega chromatic scale]]
-{{todo| intro }}