14L 22s (12/1-equivalent) - Revision history

ArrowHead294 at 14:27, 5 May 2025

2025-05-05T14:27:29Z

← Older revision		Revision as of 14:27, 5 May 2025
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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'''.		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 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.''		''Assume 36-nominal notation for this section.''
	{{TAMNAMS use}}		{{TAMNAMS use}}
	{{MOS ~~data~~}}
			=== Intervals ===
			{{MOS intervals}}

			=== Generator chain ===
			{{MOS genchain}}

			=== Modes ===
			{{MOS mode degrees}}

	===Modes===		===Modes===

2^67-1 at 04:21, 5 May 2025

2025-05-05T04:21:22Z

← Older revision		Revision as of 04:21, 5 May 2025
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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'''. 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.

2^67-1 at 10:12, 7 April 2025

2025-04-07T10:12:41Z

← Older revision		Revision as of 10:12, 7 April 2025
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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''', '''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.

2^67-1 at 02:47, 4 March 2025

2025-03-04T02:47:39Z

← Older revision		Revision as of 02:47, 4 March 2025
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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==

2^67-1 at 14:19, 3 March 2025

2025-03-03T14:19:52Z

← Older revision		Revision as of 14:19, 3 March 2025
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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"		{\| class="wikitable center-all"

2^67-1 at 08:55, 3 March 2025

2025-03-03T08:55:13Z

← Older revision		Revision as of 08:55, 3 March 2025
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	==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 ♭.		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 ♭.

2^67-1: /* Modes */

2025-03-03T08:49:46Z

Modes

← Older revision		Revision as of 08:49, 3 March 2025
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	===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"		{\| class="wikitable"

2^67-1 at 08:49, 3 March 2025

2025-03-03T08:49:12Z

Show changes

2^67-1: /* Mode =name origins */

2025-03-03T08:47:13Z

Mode =name origins

← Older revision		Revision as of 08:47, 3 March 2025
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	==Mode =name origins==		==Mode name origins==

	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.		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.

2^67-1 at 08:45, 3 March 2025

2025-03-03T08:45:48Z

@@ Line 21: / Line 21: @@
 {{TAMNAMS use}}
 {{MOS data}}
-==Mode names and name origins==
 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.