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

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'''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.

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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 [[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.) 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 ♭.

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''Assume 36-nominal notation for this section.''

=== Intervals ===

=== Generator chain ===

=== Modes ===

===Modes===

[[User:2^67-1|Cole]] proposes naming the modes this way:

[[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.

~~''For clarity, 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.''

{| class="wikitable"

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|}

==~~Genchain~~==

==Intervals on 0==

~~The genchain for this scale is as follows:~~

Here are some intervals on the note 0.

{| class="wikitable center-all"

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| A1 || A6 || A11 || A16 || A3 || A8 || AA13 ||

|}

==Simple tunings==

==Scale tree==

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 {{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.
@@ 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'''.
-==Standing assumptions==
+== Standing assumptions ==
-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.) 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 ♭.
@@ Line 20: / Line 17: @@
 ''Assume 36-nominal notation for this section.''
 {{TAMNAMS use}}
-{{MOS data}}
+=== Intervals ===
+{{MOS intervals}}
+=== Generator chain ===
+{{MOS genchain}}
+=== Modes ===
+{{MOS mode degrees}}
 ===Modes===
-[[User:2^67-1|Cole]] proposes naming the modes this way:
+[[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.
-''For clarity, 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.''
 {| class="wikitable"
@@ Line 145: / Line 148: @@
 |}
-==Genchain==
+==Intervals on 0==
-The genchain for this scale is as follows:
+Here are some intervals on the note 0.
 {| class="wikitable center-all"
@@ Line 171: / Line 174: @@
 | A1 || A6 || A11 || A16 || A3 || A8 || AA13 ||
 |}
+==Simple tunings==
+{{MOS tunings}}
 ==Scale tree==