7L 1s - Revision history

ArrowHead294: substitute deprecated template

2025-05-05T14:00:58Z

substitute deprecated template

← Older revision		Revision as of 14:00, 5 May 2025
Line 5:		Line 5:

	== Scale properties ==		== Scale properties ==
	{{MOS ~~scale properties~~}}
			=== Intervals ===
			{{MOS intervals}}

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

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

	=== Proposed names ===		=== Proposed names ===

ArrowHead294 at 13:55, 3 March 2025

2025-03-03T13:55:51Z

← Older revision		Revision as of 13:55, 3 March 2025
Line 7:		Line 7:
	{{MOS scale properties}}		{{MOS scale properties}}

	==== Proposed names ====		=== Proposed names ===
	Mode names are from [[Porcupine Temperament Modal Harmony\|Porcupine temperament modal harmony]]. Descriptive mode names are based on using 1-4-7, i.e. 3+3 triads as a basis for harmony.		Mode names are from [[Porcupine Temperament Modal Harmony\|Porcupine temperament modal harmony]]. Descriptive mode names are based on using {{dash\|1, 4, 7}}, i.e. 3+3 triads as a basis for harmony.
	{\| ~~class~~=~~"wikitable"~~		{{MOS modes
	~~!Mode~~		\| Mode names =
	~~!UDP~~		octopus $
	~~!Mode name~~		mantis $
	~~!Descriptive mode name~~		dolphin $
	\|-		crab $
	~~\|LLLLLLLs~~		tuna $
	\|~~<nowiki>7\|0</nowiki>~~		salmon $
	\|~~octopus~~		starfish $
	\|Bright quartal		whale $
	\|-		\| Table Headers=Name Origin
	~~\|LLLLLLsL~~		\| Table Entries=
	~~\|<nowiki>6\|1</nowiki>~~		Bright quartal $
	~~\|mantis~~		Dark quartal $
	\|Dark quartal		Bright major $
	\|-		Middle major $
	~~\|LLLLLsLL~~		Dark major $
	~~\|<nowiki>5\|2</nowiki>~~		Bright minor $
	~~\|dolphin~~		Middle minor $
	\|Bright major		Dark minor $
	\|-		}}
	~~\|LLLLsLLL~~
	~~\|<nowiki>4\|3</nowiki>~~
	~~\|crab~~
	\|Middle major
	\|-
	~~\|LLLsLLLL~~
	~~\|<nowiki>3\|4</nowiki>~~
	~~\|tuna~~
	\|Dark major
	\|-
	~~\|LLsLLLLL~~
	~~\|<nowiki>2\|5</nowiki>~~
	~~\|salmon~~
	\|Bright minor
	\|-
	~~\|LsLLLLLL~~
	~~\|<nowiki>1\|6</nowiki>~~
	~~\|starfish~~
	\|Middle minor
	\|-
	~~\|sLLLLLLL~~
	~~\|<nowiki>0\|7</nowiki>~~
	~~\|whale~~
	\|Dark minor
	\|}

	== Theory ==		== Theory ==
	=== Low harmonic entropy scales ===		=== Low harmonic entropy scales ===
	There are three notable [[harmonic entropy]] minima with this [[mos]] pattern. The lowest accuracy one is [[porcupine]], in which two generators make a [[6/5]] and three make a [[4/3]]. The range of porcupine tunings is about 2\15 to 3\22. Less well-known and more accurate is [[greeley]], in which two generators are still 6/5 but three fall quite short of a 4/3, but the scale happens to closely approximate a lot of higher-complexity intervals like [[10/7]], [[11/7]], etc. Thirdly and finally, [[tempering out]] [[4000/3993\|S10/S11]] so that ([[4/3]])/([[11/10]])<sup>3</sup> is tempered out results in an unusually high accuracy and efficient rank-2 temperament in the 2.3.11/5 subgroup for which interpretation as a rank-3 temperament in 2.3.5.11 (the no-7's [[11-limit]]) is natural, making [[10/9]] and [[12/11]] [[square superparticular\|equidistant from 11/10]] and offering many fruitful tempering opportunities. Note therefore that [[porkypine]] can be seen as a trivial tuning of [[4000/3993\|pine]] tempering out [[100/99]] = S10 and [[121/120]] = S11.		There are three notable [[harmonic entropy]] minima with this [[mos]] pattern.

			* The lowest accuracy one is [[porcupine]], in which two generators make a [[6/5]] and three make a [[4/3]]. The range of porcupine tunings is about 2\15 to 3\22.
			* Less well-known and more accurate is [[greeley]], in which two generators are still 6/5 but three fall quite short of a 4/3, but the scale happens to closely approximate a lot of higher-complexity intervals like [[10/7]], [[11/7]], etc.
			* Thirdly and finally, [[tempering out]] [[4000/3993\|S10/S11]] so that ([[4/3]])/([[11/10]])<sup>3</sup> is tempered out results in an unusually high accuracy and efficient rank-2 temperament in the 2.3.11/5 subgroup for which interpretation as a rank-3 temperament in 2.3.5.11 (the no-7's [[11-limit]]) is natural, making [[10/9]] and [[12/11]] [[square superparticular\|equidistant from 11/10]] and offering many fruitful tempering opportunities. Note therefore that [[porkypine]] can be seen as a trivial tuning of [[4000/3993\|pine]] tempering out {{nowrap\|[[100/99]] {{=}} S10}} and {{nowrap\|[[121/120]] {{=}} S11}}.

			== Scale tree ==
			{{MOS tuning spectrum
			\| 5/2 = General range of porcupine
			\| 2/1 = Optimum rank range for porcupine
			\| 13/8 = Golden porcupine/hemikleismic
			\| 10/7 = General range of greeley
			}}

	~~==Scale tree==~~
	~~{{Scale tree\|Comments=5/2: General range of porcupine;~~
	~~2/1: Optimum rank range for porcupine;~~
	~~13/8: Golden porcupine/hemikleismic~~
	~~10/7: General range of greeley}}~~
	[[Category:8-tone scales]]		[[Category:8-tone scales]]

FloraC: /* Theory */ cleanup

2024-10-15T13:16:07Z

Theory: cleanup

← Older revision		Revision as of 13:16, 15 October 2024
Line 58:		Line 58:
	== Theory ==		== Theory ==
	=== Low harmonic entropy scales ===		=== Low harmonic entropy scales ===
	There are three notable [[~~Harmonic_Entropy\|~~harmonic entropy]] minima with this [[~~MOSScales\|MOS~~]] pattern. The lowest accuracy one is [[~~Porcupine_family\|~~porcupine]], in which two generators make a 6/5 and three make a 4/3. The range of porcupine tunings is about 2\15 to 3\22. Less well-known and more accurate is [[~~Chromatic_pairs#Greeley\|~~greeley]], in which two generators are still 6/5 but three fall quite short of a 4/3, but the scale happens to closely approximate a lot of higher-complexity intervals like 10/7, 11/7, etc. Thirdly and finally, tempering [[4000/3993\|S10/S11]] so that ([[4/3]])/([[11/10]])<sup>3</sup> is tempered results in an unusually high accuracy & efficient rank 2 temperament in the 2.3.11/10 subgroup for which interpretation as a rank 3 temperament in 2.3.5.11 (the no-7's [[11-limit]]) is natural, making [[10/9]] and [[12/11]] [[~~Square~~ superparticular\|equidistant from 11/10]] and offering many fruitful tempering opportunities. (Note therefore that [[~~Porcupine family#2.3.5.11 subgroup .28porkypine.29\|~~porkypine]] can be seen as a trivial tuning of [[4000/3993\|pine]] tempering [[100/99]] = S10 and [[121/120]] = S11.)		There are three notable [[harmonic entropy]] minima with this [[mos]] pattern. The lowest accuracy one is [[porcupine]], in which two generators make a [[6/5]] and three make a [[4/3]]. The range of porcupine tunings is about 2\15 to 3\22. Less well-known and more accurate is [[greeley]], in which two generators are still 6/5 but three fall quite short of a 4/3, but the scale happens to closely approximate a lot of higher-complexity intervals like [[10/7]], [[11/7]], etc. Thirdly and finally, [[tempering out]] [[4000/3993\|S10/S11]] so that ([[4/3]])/([[11/10]])<sup>3</sup> is tempered out results in an unusually high accuracy and efficient rank-2 temperament in the 2.3.11/5 subgroup for which interpretation as a rank-3 temperament in 2.3.5.11 (the no-7's [[11-limit]]) is natural, making [[10/9]] and [[12/11]] [[square superparticular\|equidistant from 11/10]] and offering many fruitful tempering opportunities. Note therefore that [[porkypine]] can be seen as a trivial tuning of [[4000/3993\|pine]] tempering out [[100/99]] = S10 and [[121/120]] = S11.

	==Scale tree==		==Scale tree==
	{{Scale tree\|Comments=5/2: General range of porcupine;		{{Scale tree\|Comments=5/2: General range of porcupine;

Fitzgerald Lee: /* Proposed names */How did no one notice this

2024-10-15T10:21:18Z

Proposed names: How did no one notice this

← Older revision		Revision as of 10:21, 15 October 2024
Line 53:		Line 53:
	\|<nowiki>0\|7</nowiki>		\|<nowiki>0\|7</nowiki>
	\|whale		\|whale
	\|Dark ~~major~~		\|Dark minor
	\|}		\|}

Ganaram inukshuk: Adopt templates

2024-08-08T23:46:56Z

Adopt templates

← Older revision		Revision as of 23:46, 8 August 2024
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	{{MOS intro}}		{{MOS intro}}
	== Name ==		== Name ==
	[[TAMNAMS~~]] suggests the temperament-agnostic~~ name ~~'''pine''', in reference to porcupine temperament.~~		{{TAMNAMS name}}

	== ~~Theory~~ ==		== Scale properties ==
			{{MOS scale properties}}
	~~=== Low harmonic entropy scales ===~~
	~~There are three notable [[Harmonic_Entropy\|harmonic entropy]] minima with this [[MOSScales\|~~MOS]] pattern. The lowest accuracy one is [[Porcupine_family\|porcupine]], in which two generators make a 6/5 and three make a 4/3. The range of porcupine tunings is about 2\15 to 3\22. Less well-known and more accurate is [[Chromatic_pairs#Greeley\|greeley]], in which two generators are still 6/5 but three fall quite short of a 4/3, but the scale happens to closely approximate a lot of higher-complexity intervals like 10/7, 11/7, etc. Thirdly and finally, tempering [[4000/3993\|S10/S11]] so that ([[4/3]])/([[11/10]])<sup>3</sup> is tempered results in an unusually high accuracy & efficient rank 2 temperament in the 2.3.11/10 subgroup for which interpretation as a rank 3 temperament in 2.3.5.11 (the no-7's [[11-limit]]) is natural, making [[10/9]] and [[12/11]] [[Square superparticular\|equidistant from 11/10]] and offering many fruitful tempering opportunities. (Note therefore that [[Porcupine family#2.3.5.11 subgroup .28porkypine.29\|porkypine]] can be seen as a trivial tuning of [[4000/3993\|pine]] tempering [[100/99]] = S10 and [[121/120]] = S11.)

	== ~~Modes ==~~		==== Proposed names ====
	~~{{MOS mode degrees}}~~
	===~~Proposed Names~~===
	Mode names are from [[Porcupine Temperament Modal Harmony\|Porcupine temperament modal harmony]]. Descriptive mode names are based on using 1-4-7, i.e. 3+3 triads as a basis for harmony.		Mode names are from [[Porcupine Temperament Modal Harmony\|Porcupine temperament modal harmony]]. Descriptive mode names are based on using 1-4-7, i.e. 3+3 triads as a basis for harmony.
	{\| class="wikitable"		{\| class="wikitable"
Line 60:		Line 56:
	\|}		\|}

	== Scale tree ==		== Theory ==
			=== Low harmonic entropy scales ===
			There are three notable [[Harmonic_Entropy\|harmonic entropy]] minima with this [[MOSScales\|MOS]] pattern. The lowest accuracy one is [[Porcupine_family\|porcupine]], in which two generators make a 6/5 and three make a 4/3. The range of porcupine tunings is about 2\15 to 3\22. Less well-known and more accurate is [[Chromatic_pairs#Greeley\|greeley]], in which two generators are still 6/5 but three fall quite short of a 4/3, but the scale happens to closely approximate a lot of higher-complexity intervals like 10/7, 11/7, etc. Thirdly and finally, tempering [[4000/3993\|S10/S11]] so that ([[4/3]])/([[11/10]])<sup>3</sup> is tempered results in an unusually high accuracy & efficient rank 2 temperament in the 2.3.11/10 subgroup for which interpretation as a rank 3 temperament in 2.3.5.11 (the no-7's [[11-limit]]) is natural, making [[10/9]] and [[12/11]] [[Square superparticular\|equidistant from 11/10]] and offering many fruitful tempering opportunities. (Note therefore that [[Porcupine family#2.3.5.11 subgroup .28porkypine.29\|porkypine]] can be seen as a trivial tuning of [[4000/3993\|pine]] tempering [[100/99]] = S10 and [[121/120]] = S11.)
			==Scale tree==
	{{Scale tree\|Comments=5/2: General range of porcupine;		{{Scale tree\|Comments=5/2: General range of porcupine;
	2/1: Optimum rank range for porcupine;		2/1: Optimum rank range for porcupine;

Nick Vuci: /* Modes */ added MOS mode degrees template, added "proposed names" subheading

2024-07-24T23:36:02Z

Modes: added MOS mode degrees template, added "proposed names" subheading

← Older revision		Revision as of 23:36, 24 July 2024
Line 10:		Line 10:

	== Modes ==		== Modes ==
			{{MOS mode degrees}}
			===Proposed Names===
	Mode names are from [[Porcupine Temperament Modal Harmony\|Porcupine temperament modal harmony]]. Descriptive mode names are based on using 1-4-7, i.e. 3+3 triads as a basis for harmony.		Mode names are from [[Porcupine Temperament Modal Harmony\|Porcupine temperament modal harmony]]. Descriptive mode names are based on using 1-4-7, i.e. 3+3 triads as a basis for harmony.
	{\| class="wikitable"		{\| class="wikitable"

Ganaram inukshuk: a space

2024-02-03T11:49:48Z

a space

← Older revision		Revision as of 11:49, 3 February 2024
Line 1:		Line 1:
	{{Infobox MOS}}		{{Infobox MOS}}
	{{MOS intro}}		{{MOS intro}}

	== Name ==		== Name ==
	[[TAMNAMS]] suggests the temperament-agnostic name '''pine''', in reference to porcupine temperament.		[[TAMNAMS]] suggests the temperament-agnostic name '''pine''', in reference to porcupine temperament.

Ganaram inukshuk: Updated rothenprop

2024-02-03T07:52:36Z

Updated rothenprop

@@ Line 1: / Line 1: @@
-{{Infobox MOS
+{{Infobox MOS}}
 {{MOS intro}}
 == Name ==

Ganaram inukshuk: Added section for name, modes; added scale tree template

2023-10-07T18:06:56Z

Added section for name, modes; added scale tree template

Show changes

Godtone: highly significant harmonic entropy minima not discussed

2023-06-13T15:34:17Z

highly significant harmonic entropy minima not discussed

← Older revision		Revision as of 15:34, 13 June 2023
Line 10:		Line 10:

	{{MOS intro}}		{{MOS intro}}
	There are ~~two~~ notable [[Harmonic_Entropy\|harmonic entropy]] minima with this [[MOSScales\|MOS]] pattern. The ~~first~~ is [[Porcupine_family\|porcupine]], in which two generators make a 6/5 and three make a 4/3. The range of porcupine tunings is about 2\15 to 3\22. Less well-known is [[Chromatic_pairs#Greeley\|greeley]], in which two generators are still 6/5 but three fall quite short of a 4/3, but the scale happens to closely approximate a lot of higher-complexity intervals like 10/7, 11/7, etc.		There are three notable [[Harmonic_Entropy\|harmonic entropy]] minima with this [[MOSScales\|MOS]] pattern. The lowest accuracy one is [[Porcupine_family\|porcupine]], in which two generators make a 6/5 and three make a 4/3. The range of porcupine tunings is about 2\15 to 3\22. Less well-known and more accurate is [[Chromatic_pairs#Greeley\|greeley]], in which two generators are still 6/5 but three fall quite short of a 4/3, but the scale happens to closely approximate a lot of higher-complexity intervals like 10/7, 11/7, etc. Thirdly and finally, tempering [[4000/3993\|S10/S11]] so that ([[4/3]])/([[11/10]])<sup>3</sup> is tempered results in an unusually high accuracy & efficient rank 2 temperament in the 2.3.11/10 subgroup for which interpretation as a rank 3 temperament in 2.3.5.11 (the no-7's [[11-limit]]) is natural, making [[10/9]] and [[12/11]] [[Square superparticular\|equidistant from 11/10]] and offering many fruitful tempering opportunities. (Note therefore that [[Porcupine family#2.3.5.11 subgroup .28porkypine.29\|porkypine]] can be seen as a trivial tuning of [[4000/3993\|pine]] tempering [[100/99]] = S10 and [[121/120]] = S11.)

	== Modes ==		== Modes ==
Line 99:		Line 99:
	\|166.67		\|166.67
	\| style="text-align:center;" \|5 5 5 5 5 5 5 1		\| style="text-align:center;" \|5 5 5 5 5 5 5 1
			\| style="text-align:center;" \|pine is around here
	\|		\|
	\|-		\|-