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

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''Assume hemipyth[10] nominal names and intervals (and zero-indexing) unless otherwise stated. This article is meant to apply MMTM's theory on this scale, but it is attempted to be explained better here.''

~~The [[User:2^67-~~1~~/7L 11s (√12-equivalent)|7L 11s (√12-equivalent)]] scale~~, also '''pochhammeroid''' (see below), '''colianexoid''', '''greater f-enhar electric''' or '''greater f-enhar smitonic''' is a MOS scale. The notation "<~~√12~~>" means the period of the MOS is ~~√12~~, disambiguating it from octave-repeating [[~~7L 11s~~]]. The name of ~~this~~ period interval is called the '''oktokaidekatave'''. It is also equivalent to '''~~14L 22s~~ <~~12/1~~>''' ~~and is the notation used in the [[User:2^67-1/7L 11s (√12-equivalent)#Scale tree|scale tree]] and the MOS infobox on the right~~. Its basic tuning is ~~25ed√12 or~~ [[50ed12]]. 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''', '''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.

The generator range is 597 to 615 cents (5\18<√12> to 2\7<√12>). The dark generator is ~~obviously~~ 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.

The equave/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'''.

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==Standing assumptions==

The [[TAMNAMS]] system is used in this article to name ~~7L 11s~~ <~~√12~~> intervals ~~and~~ step size ratios and step ratio ranges.

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 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)".

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)".

==Modes==

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 ''Assume hemipyth[10] nominal names and intervals (and zero-indexing) unless otherwise stated. This article is meant to apply MMTM's theory on this scale, but it is attempted to be explained better here.''
-{{Infobox MOS|Tuning=14L 22s<12/1>}}
+{{Infobox MOS|Tuning = 14L 22s <12/1>}}
-The [[User:2^67-1/7L 11s (√12-equivalent)|7L 11s (√12-equivalent)]] scale, also '''pochhammeroid''' (see below), '''colianexoid''', '''greater f-enhar electric''' or '''greater f-enhar smitonic''' is a MOS scale. The notation "<√12>" means the period of the MOS is √12, disambiguating it from octave-repeating [[7L 11s]]. The name of this period interval is called the '''oktokaidekatave'''. It is also equivalent to '''14L 22s <12/1>''' and is the notation used in the [[User:2^67-1/7L 11s (√12-equivalent)#Scale tree|scale tree]] and the MOS infobox on the right. Its basic tuning is 25ed√12 or [[50ed12]]. 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''', '''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.
-The generator range is 597 to 615 cents (5\18<√12> to 2\7<√12>). The dark generator is obviously 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.
 The equave/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'''.
@@ Line 13: / Line 13: @@
 ==Standing assumptions==
-The [[TAMNAMS]] system is used in this article to name 7L 11s <√12> intervals and step size ratios and step ratio ranges.
+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 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)".
+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)".
 ==Modes==