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14L 22s (12/1-equivalent): Difference between revisions

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{{Infobox MOS|Tuning = 14L 22s <12/1>}}
{{Infobox MOS|Tuning = 14L 22s <12/1>}}


'''14L 22s <12/1>''', also '''pochhammeroid''' (see below), '''colianexoid''', '''greater f-enhar electric''' or '''greater f-enhar smitonic''' is a MOS scale. The notation "<12/1>" means the period of the MOS is 12/1, disambiguating it from octave-repeating [[14L 22s]]. The name of the period interval of this scale is called the '''oktokaidekatave''', and the . It is also equivalent to '''7L 11s <√12>'''. Its basic tuning is [[50ed12]] or 25ed√12. However, the √12-based form will be used for most of this article as it is far more practical and is the original form of the scale when it was discovered.
'''14L 22s <12/1>''', also '''pochhammeroid''' (see below), '''colianexoid''', '''hemipythic octadecatonic''', '''greater f-enhar electric''' or '''greater f-enhar smitonic''' is a MOS scale. The notation "<12/1>" means the period of the MOS is 12/1, disambiguating it from octave-repeating [[14L 22s]]. The name of the period interval of this scale is called the '''oktokaidekatave'''. It is also equivalent to '''7L 11s <√12>'''. Its basic tuning is [[50ed12]] or 25ed√12. However, the √12-based form will be used for most of this article as it is far more practical and is the original form of the scale when it was discovered.


The generator range is 597 to 615 cents (5\18<√12> to 2\7<√12>, or 5\36<12/1> to 1\7<12/1>) . The dark generator is its √12-complement. Because this is a perfect eighteenth-repeating scale, each tone has an √12 perfect eighteenth above it.
The generator range is 597 to 615 cents (5\18<√12> to 2\7<√12>, or 5\36<12/1> to 1\7<12/1>) . The dark generator is its √12-complement. Because this is a perfect eighteenth-repeating scale, each tone has an √12 perfect eighteenth above it.
Line 11: Line 11:
The period can range from [[24/7]] to [[7/2]], including the pure-hemipyth √12 and 1/QPochhammer[1/2]. It is because of the latter constant that [[User:2^67-1|Cole]] proposes naming this scale '''pochhammeroid'''.
The period can range from [[24/7]] to [[7/2]], including the pure-hemipyth √12 and 1/QPochhammer[1/2]. It is because of the latter constant that [[User:2^67-1|Cole]] proposes naming this scale '''pochhammeroid'''.


==Standing assumptions==
== Standing assumptions ==
The notation used in this article is ''0'' Pacific-Hemipyth = 0123456789ABCDEFGH (see the section on modes below), unless specified otherwise. (Alternatively, one can use any octodecimal or niftimal/triacontaheximal digit set as the numbers, as long as it is clear which set one is using.) Octodecimal digitsets will be used for naming notes as it more practical. We denote raising and lowering by a chroma (L − s, about √(256/243) using the hemipyth interpretation) by # and ♭.


The [[TAMNAMS]] system is used in this article to name 14L 22s <12/1> intervals, step size ratios and step ratio ranges. However, the equave is taken to be the period of the scale, √12, as it is more practical.
The notation used in this article is ''0'' Pacific-Hemipyth = 0123456789ABCDEFGH (see the section on modes below), unless specified otherwise. (Alternatively, one can use any octodecimal or niftimal/triacontaheximal digit set as the numbers, as long as it is clear which set one is using.) We denote raising and lowering by a chroma (L − s, about √(256/243) using the hemipyth interpretation) by # and ♭ "flat (F molle)".
==Scale properties==
==Scale properties==
''Assume 36-nominal notation for this section.''
''Assume 36-nominal notation for this section.''
{{TAMNAMS use}}
{{TAMNAMS use}}
{{MOS data}}


==Modes==
=== Intervals ===
{{MOS intervals}}
 
=== Generator chain ===
{{MOS genchain}}
 
=== Modes ===
{{MOS mode degrees}}
 
===Modes===


For clarity, each scale, which is taken to have 18 notes, is split up into three pentachords and a trichord. There are three modes which defy the classification of three 2L 3s pentachords and a 1L 2s trichord, having pentachords with one large step and four small steps. However, they are still included for completeness. An ambiguous mode is named after the first two pentachords.
[[User:2^67-1|Cole]] proposes naming the modes this way: Each period is split up into three pentachords and a trichord. There are three modes which defy the classification of three 2L 3s pentachords and a 1L 2s trichord, having pentachords with one large step and four small steps. However, they are still included for completeness. An ambiguous mode is named after the first two pentachords. Pacific-Hemipyth is regarded as mode 0 or 18.


{| class="wikitable"
{| class="wikitable"
Line 29: Line 35:
|'''Mode'''
|'''Mode'''
|[[Modal UDP Notation|'''UDP''']]
|[[Modal UDP Notation|'''UDP''']]
|'''Cyclic order'''
|'''Name'''
|'''Name'''
|'''Name origin'''
|'''Name origin'''
|-
|-
| |LsLss LsLss LsLss Lss
| |LsLss LsLss LsLss Lss LsLss LsLss LsLss Lss
|<nowiki>17|0</nowiki>
|<nowiki>34|0(2)</nowiki>
| 1
| |Atlantic-QFind
| |Atlantic-QFind
| The canonically first 'core' of the Colian Nexus, [https://conwaylife.com/forums/viewtopic.php?f=9&t=2902&p=44615#p44615 qfind].
| The canonically first 'core' of the Colian Nexus, [https://conwaylife.com/forums/viewtopic.php?f=9&t=2902&p=44615#p44615 qfind].
|-
|-
| |LsLss LsLss LssLs Lss
| |LsLss LsLss LssLs Lss LsLss LsLss LssLs Lss
|<nowiki>16|1</nowiki>
|<nowiki>32|2(2)</nowiki>
| 6
| |Atlantic-Planet
| |Atlantic-Planet
| Named after PlanetN9ne.
| Named after PlanetN9ne.
|-
|-
| |LsLss LssLs LssLs Lss
| |LsLss LssLs LssLs Lss LsLss LssLs LssLs Lss
|<nowiki>15|2</nowiki>
|<nowiki>30|4(2)</nowiki>
| 11
| |Atlantic-Lumian
| |Atlantic-Lumian
| This mode's first dekatave has an Atlantic pentachord and a Lumian pentachord.
| This mode's first dekatave has an Atlantic pentachord and a Lumian pentachord.
|-
|-
| |LssLs LssLs LssLs Lss
| |LssLs LssLs LssLs Lss LssLs LssLs LssLs Lss
|<nowiki>14|3</nowiki>
|<nowiki>28|6(2)</nowiki>
| 16
| |Lumian-Q-Series
| |Lumian-Q-Series
| The canonically second 'core' of the Colian Nexus, 2-analogue-related functions. Named after the Q-series.
| The canonically second 'core' of the Colian Nexus, 2-analogue-related functions. Named after the Q-series.
|-
|-
| |LssLs LssLs LssLs sLs
| |LssLs LssLs LssLs sLs LssLs LssLs LssLs sLs
|<nowiki>13|4</nowiki>
|<nowiki>26|8(2)</nowiki>
| 3
| Lumian-Moosey
| Lumian-Moosey
| Named after Moosey.
| Named after Moosey.
|-
|-
| |LssLs LssLs sLsLs sLs
| |LssLs LssLs sLsLs sLs LssLs LssLs sLsLs sLs
|<nowiki>12|5</nowiki>
|<nowiki>24|10(2)</nowiki>
| 8
| |Lumian-Drone
| |Lumian-Drone
| Named after DroneBetter.
| Named after DroneBetter.
|-
|-
| |LssLs sLsLs sLsLs sLs
| |LssLs sLsLs sLsLs sLs LssLs sLsLs sLsLs sLs
|<nowiki>11|6</nowiki>
|<nowiki>22|12(2)</nowiki>
| 13
| |Lumian-Pacific
| |Lumian-Pacific
| This mode's first dekatave has a Lumian pentachord and a Pacific pentachord.
| This mode's first dekatave has a Lumian pentachord and a Pacific pentachord.
|-
|-
| |sLsLs sLsLs sLsLs sLs
| |sLsLs sLsLs sLsLs sLs sLsLs sLsLs sLsLs sLs
|<nowiki>10|7</nowiki>
|<nowiki>20|14(2)</nowiki>
| 18 or 0
| |Pacific-Hemipyth
| |Pacific-Hemipyth
| The canonically third 'core' of the Colian Nexus, [[hemipyth]].
| The canonically third 'core' of the Colian Nexus, [[hemipyth]].
|-
|-
| |sLsLs sLsLs sLssL sLs
| |sLsLs sLsLs sLssL sLs sLsLs sLsLs sLssL sLs
|<nowiki>9|8</nowiki>
|<nowiki>18|16(2)</nowiki>
| 5
| |Pacific-NimbleRogue
| |Pacific-NimbleRogue
| Named after NimbleRogue.
| Named after NimbleRogue.
|-
|-
| |sLsLs sLssL sLssL sLs
| |sLsLs sLssL sLssL sLs sLsLs sLssL sLssL sLs
|<nowiki>8|9</nowiki>
|<nowiki>16|18(2)</nowiki>
| 10
| |Pacific-Taliesin
| |Pacific-Taliesin
| This mode's first dekatave has a Pacific pentachord and a Taliesin pentachord.
| This mode's first dekatave has a Pacific pentachord and a Taliesin pentachord.
|-
|-
| |sLssL sLssL sLssL sLs
| |sLssL sLssL sLssL sLs sLssL sLssL sLssL sLs
|<nowiki>7|10</nowiki>
|<nowiki>14|20(2)</nowiki>
| 15
| |Taliesin-Riemannic
| |Taliesin-Riemannic
| The canonically fourth 'core' of the Colian Nexus, Riemannic, a conlang created by [[User:2^67-1|Cole]].
| The canonically fourth 'core' of the Colian Nexus, Riemannic, a conlang created by [[User:2^67-1|Cole]].
|-
|-
| |sLssL sLssL sLssL ssL
| |sLssL sLssL sLssL ssL sLssL sLssL sLssL ssL
|<nowiki>6|11</nowiki>
|<nowiki>12|22(2)</nowiki>
| 2
| |Taliesin-Wwei
| |Taliesin-Wwei
| Named after wwei47.
| Named after wwei47.
|-
|-
| |sLssL sLssL ssLsL ssL
| |sLssL sLssL ssLsL ssL sLssL sLssL ssLsL ssL
|<nowiki>5|12</nowiki>
|<nowiki>10|24(2)</nowiki>
| 7
| |Taliesin-LaundryPizza
| |Taliesin-LaundryPizza
| Named after LaundryPizza03.
| Named after LaundryPizza03.
|-
|-
| |sLssL ssLsL ssLsL ssL
| |sLssL ssLsL ssLsL ssL sLssL ssLsL ssLsL ssL
|<nowiki>4|13</nowiki>
|<nowiki>8|26(2)</nowiki>
| 12
| |Taliesin-Dresden
| |Taliesin-Dresden
| This mode's first dekatave has a Taliesin pentachord and a Dresden pentachord.
| This mode's first dekatave has a Taliesin pentachord and a Dresden pentachord.
|-
|-
| |ssLsL ssLsL ssLsL ssL
| |ssLsL ssLsL ssLsL ssL ssLsL ssLsL ssLsL ssL
|<nowiki>3|14</nowiki>
|<nowiki>6|28(2)</nowiki>
| 17
| |Dresden-Heav
| |Dresden-Heav
| Named after Heav.
| Named after Heav.
|-
|-
| |ssLsL ssLsL ssLss LsL
| |ssLsL ssLsL ssLss LsL ssLsL ssLsL ssLss LsL
|<nowiki>2|15</nowiki>
|<nowiki>4|30(2)</nowiki>
| 4
| |Subdresden-Nimrgod
| |Subdresden-Nimrgod
| Named after the canonically first of three tuppers created by [[User:2^67-1]], Nimrgod.
| Named after the canonically first of three tuppers created by [[User:2^67-1]], Nimrgod.
|-
|-
| |ssLsL ssLss LsLss LsL
| |ssLsL ssLss LsLss LsL ssLsL ssLss LsLss LsL
|<nowiki>1|16</nowiki>
|<nowiki>2|32(2)</nowiki>
| 9
| |Subdresden-Boris
| |Subdresden-Boris
| Named after the canonically second of three tuppers created by [[User:2^67-1]], Boris Grothendieck.
| Named after the canonically second of three tuppers created by [[User:2^67-1]], Boris Grothendieck.
|-
|-
| |ssLss LsLss LsLss LsL
| |ssLss LsLss LsLss LsL ssLss LsLss LsLss LsL
|<nowiki>0|17</nowiki>
|<nowiki>0|34(2)</nowiki>
| 14
| |Subdresden-Pergele
| |Subdresden-Pergele
| Named after the canonically third of three tuppers created by [[User:2^67-1]], Pergele (originator of this idea is [[User:Frostburn|Frostburn]] in a meme post).
| Named after the canonically third of three tuppers created by [[User:2^67-1]], Pergele (originator of this idea is [[User:Frostburn|Frostburn]] in a meme post).
|}
|}


==Genchain==
==Intervals on 0==


The genchain for this scale is as follows:
Here are some intervals on the note 0.


{| class="wikitable center-all"
{| class="wikitable center-all"
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| A1 || A6 || A11 || A16 || A3 || A8 || AA13 ||  
| A1 || A6 || A11 || A16 || A3 || A8 || AA13 ||  
|}
|}
==Simple tunings==
{{MOS tunings}}


==Scale tree==
==Scale tree==
Retrieved from "https://en.xen.wiki/w/14L_22s_(12/1-equivalent)"