Bug and beep - Revision history

FloraC: Update

2026-05-17T05:33:32Z

Update

← Older revision		Revision as of 05:33, 17 May 2026
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	\| Odd limit 2 = 9 \| Mistuning 2 = 72.6 \| Complexity 2 = 5		\| Odd limit 2 = 9 \| Mistuning 2 = 72.6 \| Complexity 2 = 5
	}}		}}
	'''Bug''' is a remarkable [[complexity\|low-complexity]], though [[badness\|high-badness]] [[exotemperament]]. It [[tempering out\|tempers out]] [[27/25]] and is part of the [[bug family]]; as such, [[5/3]] and [[9/5]] are represented by the same interval which, in fact, is the [[generator]]. With the [[7-limit]] [[extension]] called '''beep~~''', a.k.a. '''titanium~~'''<ref group="note">~~Alias given~~ by [[Mason Green]]. </ref>, it tempers out the [[21/20\|septimal minor semitone (21/20)]], making it a [[septisemi temperaments\|septisemi temperament]], and the [[49/48\|slendro diesis (49/48)]], making it part of the [[semaphoresmic clan]]. As such, the generator also represents [[7/4]] and [[12/7]]. Two of these generators make a very flat [[3/2\|fifth]] which is also a very sharp [[10/7]]. Two fifths make a second that is neutral in [[interval quality\|quality]], so a good tuning typically has a ''negative'' [[syntonic comma]]. Since three fifths make a sixth that sounds minor, and four make a third that sounds minor, it is also similar to the [[mavila]] temperament ([[superpelog]] in particular). Finally it can be also considered a sort of messed-up variant of [[orwell]] temperament as well, since the generator falls into the same range of sizes.		'''Bug''' is a remarkable [[complexity\|low-complexity]], though [[badness\|high-badness]] [[exotemperament]]. It [[tempering out\|tempers out]] [[27/25]] and is part of the [[bug family]]; as such, [[5/3]] and [[9/5]] are represented by the same interval which, in fact, is the [[generator]]. With the [[7-limit]] [[extension]] called '''beep'''<ref group="note">Aliased ''titanium'' by [[Mason Green]]. </ref>, it tempers out the [[21/20\|septimal minor semitone (21/20)]], making it a [[septisemi temperaments\|septisemi temperament]], and the [[49/48\|slendro diesis (49/48)]], making it part of the [[semaphoresmic clan]]. As such, the generator also represents [[7/4]] and [[12/7]]. Two of these generators make a very flat [[3/2\|fifth]] which is also a very sharp [[10/7]]. Two fifths make a second that is neutral in [[interval quality\|quality]], so a good tuning typically has a ''negative'' [[syntonic comma]]. Since three fifths make a sixth that sounds minor, and four make a third that sounds minor, it is also similar to the [[mavila]] temperament ([[superpelog]] in particular). Finally it can be also considered a sort of messed-up variant of [[orwell]] temperament as well, since the generator falls into the same range of sizes.

	The edos whose [[patent val]]s support beep are [[4edo]], [[5edo]], [[9edo]], and [[14edo]]. Many other edos can be used as non-patent vals, such as 13.		The edos whose [[patent val]]s support beep are [[4edo]], [[5edo]], [[9edo]], and [[14edo]]. Many other edos can be used as non-patent vals, such as 13.
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	As a scale archetype, bug represents [[4L 1s]] and [[5L 4s]], and more generally [[Ploidacot/Alpha-dicot\|alpha-dicot]].		As a scale archetype, bug represents [[4L 1s]] and [[5L 4s]], and more generally [[Ploidacot/Alpha-dicot\|alpha-dicot]].

	The name ''beep'' was ~~given by [[Herman Miller]] in~~ 2004.<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/~~topicId_52458~~.html Yahoo! Tuning Group \| ''~~Beep as a temperament?~~'']</ref>		The name ''beep'' was attested as early as at least January, 2004<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_8809.html Yahoo! Tuning Group \| ''114 7-limit temperaments'']</ref>, and is likely a reference to the smallest step of the [[Bohlen–Pierce]] scale.

	See [[Bug family #Bug]] and [[Bug family #Beep\|#Beep]] for technical data.		See [[Bug family #Bug]] and [[Bug family #Beep\|#Beep]] for technical data.

FloraC: + source of the name beep

2026-04-26T12:50:29Z

+ source of the name *beep*

← Older revision		Revision as of 12:50, 26 April 2026
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	As a scale archetype, bug represents [[4L 1s]] and [[5L 4s]], and more generally [[Ploidacot/Alpha-dicot\|alpha-dicot]].		As a scale archetype, bug represents [[4L 1s]] and [[5L 4s]], and more generally [[Ploidacot/Alpha-dicot\|alpha-dicot]].

			The name ''beep'' was given by [[Herman Miller]] in 2004.<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_52458.html Yahoo! Tuning Group \| ''Beep as a temperament?'']</ref>

	See [[Bug family #Bug]] and [[Bug family #Beep\|#Beep]] for technical data.		See [[Bug family #Bug]] and [[Bug family #Beep\|#Beep]] for technical data.
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	== Notes ==		== Notes ==
	<references group="note"/>		<references group="note"/>

			== References ==

	[[Category:Bug\| ]] <!-- main article -->		[[Category:Bug\| ]] <!-- main article -->

FloraC: Integer cent is enough in the infobox for an exotemp like this

2026-02-26T11:31:40Z

Integer cent is enough in the infobox for an exotemp like this

← Older revision		Revision as of 11:31, 26 February 2026
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	\| Mapping = 1; 2 3 1		\| Mapping = 1; 2 3 1
	\| Generators = 5/3		\| Generators = 5/3
	\| Generators tuning = 938~~.111~~		\| Generators tuning = 938
	\| Optimization method = CWE		\| Optimization method = CWE
	\| MOS scales = [[1L 3s]], [[4L 1s]], [[5L 4s]]		\| MOS scales = [[1L 3s]], [[4L 1s]], [[5L 4s]]

Xenllium at 09:01, 26 February 2026

2026-02-26T09:01:25Z

← Older revision		Revision as of 09:01, 26 February 2026
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			{{Infobox regtemp
			\| Title = Bug / Beep
			\| Subgroups = 2.3.5, 2.3.5.7
			\| Comma basis = [[27/25]] (2.3.5); <br>[[21/20]], [[27/25]] (2.3.5.7)
			\| Edo join 1 = 4 \| Edo join 2 = 5
			\| Mapping = 1; 2 3 1
			\| Generators = 5/3
			\| Generators tuning = 938.111
			\| Optimization method = CWE
			\| MOS scales = [[1L 3s]], [[4L 1s]], [[5L 4s]]
			\| Pergen = (P8, P4/2)
			\| Color name = Guguti
			\| Odd limit 1 = 7 \| Mistuning 1 = 44.4 \| Complexity 1 = 4
			\| Odd limit 2 = 9 \| Mistuning 2 = 72.6 \| Complexity 2 = 5
			}}
	'''Bug''' is a remarkable [[complexity\|low-complexity]], though [[badness\|high-badness]] [[exotemperament]]. It [[tempering out\|tempers out]] [[27/25]] and is part of the [[bug family]]; as such, [[5/3]] and [[9/5]] are represented by the same interval which, in fact, is the [[generator]]. With the [[7-limit]] [[extension]] called '''beep''', a.k.a. '''titanium'''<ref group="note">Alias given by [[Mason Green]]. </ref>, it tempers out the [[21/20\|septimal minor semitone (21/20)]], making it a [[septisemi temperaments\|septisemi temperament]], and the [[49/48\|slendro diesis (49/48)]], making it part of the [[semaphoresmic clan]]. As such, the generator also represents [[7/4]] and [[12/7]]. Two of these generators make a very flat [[3/2\|fifth]] which is also a very sharp [[10/7]]. Two fifths make a second that is neutral in [[interval quality\|quality]], so a good tuning typically has a ''negative'' [[syntonic comma]]. Since three fifths make a sixth that sounds minor, and four make a third that sounds minor, it is also similar to the [[mavila]] temperament ([[superpelog]] in particular). Finally it can be also considered a sort of messed-up variant of [[orwell]] temperament as well, since the generator falls into the same range of sizes.		'''Bug''' is a remarkable [[complexity\|low-complexity]], though [[badness\|high-badness]] [[exotemperament]]. It [[tempering out\|tempers out]] [[27/25]] and is part of the [[bug family]]; as such, [[5/3]] and [[9/5]] are represented by the same interval which, in fact, is the [[generator]]. With the [[7-limit]] [[extension]] called '''beep''', a.k.a. '''titanium'''<ref group="note">Alias given by [[Mason Green]]. </ref>, it tempers out the [[21/20\|septimal minor semitone (21/20)]], making it a [[septisemi temperaments\|septisemi temperament]], and the [[49/48\|slendro diesis (49/48)]], making it part of the [[semaphoresmic clan]]. As such, the generator also represents [[7/4]] and [[12/7]]. Two of these generators make a very flat [[3/2\|fifth]] which is also a very sharp [[10/7]]. Two fifths make a second that is neutral in [[interval quality\|quality]], so a good tuning typically has a ''negative'' [[syntonic comma]]. Since three fifths make a sixth that sounds minor, and four make a third that sounds minor, it is also similar to the [[mavila]] temperament ([[superpelog]] in particular). Finally it can be also considered a sort of messed-up variant of [[orwell]] temperament as well, since the generator falls into the same range of sizes.

	The edos whose [[patent val]]s support beep are [[4edo]], [[5edo]], [[9edo]], and [[14edo]]. Many other edos can be used as non-patent vals, such as 13.		The edos whose [[patent val]]s support beep are [[4edo]], [[5edo]], [[9edo]], and [[14edo]]. Many other edos can be used as non-patent vals, such as 13.

	As a scale archetype, bug represents [[4L 1s]] and [[5L 4s]], and more generally [[Ploidacot/~~Omega~~-dicot\|~~omega~~-dicot]].		As a scale archetype, bug represents [[4L 1s]] and [[5L 4s]], and more generally [[Ploidacot/Alpha-dicot\|alpha-dicot]].

	See [[Bug family #Bug]] and [[Bug family #Beep\|#Beep]] for technical data.		See [[Bug family #Bug]] and [[Bug family #Beep\|#Beep]] for technical data.

VectorGraphics at 01:31, 22 November 2025

2025-11-22T01:31:08Z

← Older revision		Revision as of 01:31, 22 November 2025
Line 2:		Line 2:

	The edos whose [[patent val]]s support beep are [[4edo]], [[5edo]], [[9edo]], and [[14edo]]. Many other edos can be used as non-patent vals, such as 13.		The edos whose [[patent val]]s support beep are [[4edo]], [[5edo]], [[9edo]], and [[14edo]]. Many other edos can be used as non-patent vals, such as 13.

			As a scale archetype, bug represents [[4L 1s]] and [[5L 4s]], and more generally [[Ploidacot/Omega-dicot\|omega-dicot]].

	See [[Bug family #Bug]] and [[Bug family #Beep\|#Beep]] for technical data.		See [[Bug family #Bug]] and [[Bug family #Beep\|#Beep]] for technical data.

Yourmusic Productions: /* Chords and harmony */ fix link

2025-11-19T11:08:50Z

Chords and harmony: fix link

← Older revision		Revision as of 11:08, 19 November 2025
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	== Chords and harmony ==		== Chords and harmony ==
	In beep, the 7-limit tetrad has very low [[Graham complexity]] (only 3). The fact that [[7/5]] is also [[4/3]] allows a type of "tritone substitution" distinct from that which appears in [[jubilismic]] temperaments; namely, one in which the 4/3 of one chord becomes the 7/5 of the next or vice versa. This is equivalent to modulating upward or downward by a generator. The more usual type of modulation (upward or downward by fifths) is also easy since two generators make a fifth. These tetrads, despite being relatively inaccurate, are still easily recognizable and not necessarily unpleasant-sounding (though of course it depends on the timbre of the instrument they are played on). Another thing to watch out for is that due to tempering, the tetrads are of the form Lsss, which means they are their own inverses (i.e. the utonal and otonal tetrads are the same). The 4:5:6:7 and 5:6:7:9 tetrads are also the same. This gives them a chameleonic quality, akin to power chords; they can sound either major or minor, which strongly depends on the voicing used. The terms major and minor can still be used to refer to ''inversions'' of the basic tetrad (the major inversion being Lsss, and the minor inversion being sLss).		In beep, the 7-limit tetrad has very low [[Graham complexity]] (only 3). The fact that [[7/5]] is also [[4/3]] allows a type of "tritone substitution" distinct from that which appears in [[Jubilismic_clan\|jubilismic]] temperaments; namely, one in which the 4/3 of one chord becomes the 7/5 of the next or vice versa. This is equivalent to modulating upward or downward by a generator. The more usual type of modulation (upward or downward by fifths) is also easy since two generators make a fifth. These tetrads, despite being relatively inaccurate, are still easily recognizable and not necessarily unpleasant-sounding (though of course it depends on the timbre of the instrument they are played on). Another thing to watch out for is that due to tempering, the tetrads are of the form Lsss, which means they are their own inverses (i.e. the utonal and otonal tetrads are the same). The 4:5:6:7 and 5:6:7:9 tetrads are also the same. This gives them a chameleonic quality, akin to power chords; they can sound either major or minor, which strongly depends on the voicing used. The terms major and minor can still be used to refer to ''inversions'' of the basic tetrad (the major inversion being Lsss, and the minor inversion being sLss).

	Beep forms enneatonic scales which may be either of the form LLsLsLsLs or ssLsLsLsL; where both step sizes are equal this simply gives [[9edo]]. An enneatonic scale has six tetrads, and just like the diatonic scale it allows a variant of the familiar "I-IV-V" type of chord progression (which, using enneatonic notation, would be I-V-VI). Beep's enneatonic scales provide an alternative to the Erlich decatonic; they are lower in accuracy, but are also simpler and offer more freedom of modulation, and thus for some listeners they might actually be less xenharmonic.		Beep forms enneatonic scales which may be either of the form LLsLsLsLs or ssLsLsLsL; where both step sizes are equal this simply gives [[9edo]]. An enneatonic scale has six tetrads, and just like the diatonic scale it allows a variant of the familiar "I-IV-V" type of chord progression (which, using enneatonic notation, would be I-V-VI). Beep's enneatonic scales provide an alternative to the Erlich decatonic; they are lower in accuracy, but are also simpler and offer more freedom of modulation, and thus for some listeners they might actually be less xenharmonic.

FloraC: - unused category

2025-11-19T11:07:38Z

- unused category

← Older revision		Revision as of 11:07, 19 November 2025
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	[[Category:Bug\| ]] <!-- main article -->		[[Category:Bug\| ]] <!-- main article -->
	~~[[Category:Beep\| ]] <!-- main article -->~~
	[[Category:Rank-2 temperaments]]		[[Category:Rank-2 temperaments]]
	[[Category:Exotemperaments]]		[[Category:Exotemperaments]]

FloraC: FloraC moved page Beep to Bug and beep: Beep is the de facto canonical extension of bug

2025-11-19T11:05:22Z

FloraC moved page Beep to Bug and beep: Beep is the de facto canonical extension of bug

← Older revision	Revision as of 11:05, 19 November 2025
(No difference)

FloraC: Bug and beep both be here

2025-11-19T11:04:07Z

Bug and beep both be here

← Older revision		Revision as of 11:04, 19 November 2025
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	'''~~Beep~~''' is a remarkable low-complexity, though high-badness ~~[[7-limit]] [[temperament~~]]~~. It is also called '''titanium''' by~~ [[~~Mason Green~~]].		'''Bug''' is a remarkable [[complexity\|low-complexity]], though [[badness\|high-badness]] [[exotemperament]]. It [[tempering out\|tempers out]] [[27/25]] and is part of the [[bug family]]; as such, [[5/3]] and [[9/5]] are represented by the same interval which, in fact, is the [[generator]]. With the [[7-limit]] [[extension]] called '''beep''', a.k.a. '''titanium'''<ref group="note">Alias given by [[Mason Green]]. </ref>, it tempers out the [[21/20\|septimal minor semitone (21/20)]], making it a [[septisemi temperaments\|septisemi temperament]], and the [[49/48\|slendro diesis (49/48)]], making it part of the [[semaphoresmic clan]]. As such, the generator also represents [[7/4]] and [[12/7]]. Two of these generators make a very flat [[3/2\|fifth]] which is also a very sharp [[10/7]]. Two fifths make a second that is neutral in [[interval quality\|quality]], so a good tuning typically has a ''negative'' [[syntonic comma]]. Since three fifths make a sixth that sounds minor, and four make a third that sounds minor, it is also similar to the [[mavila]] temperament ([[superpelog]] in particular). Finally it can be also considered a sort of messed-up variant of [[orwell]] temperament as well, since the generator falls into the same range of sizes.

	It [[tempering out\|tempers out]] [[27/25]] and is part of the [[bug family]]; as such, [[6/5]] and [[10/9]] are represented by the same interval which, in fact, is the [[generator]]. ~~It also~~ tempers out the [[21/20\|septimal minor semitone (21/20)]], making it a [[septisemi temperaments\|septisemi temperament]], and the [[49/48\|slendro diesis (49/48)]], making it part of the [[~~slendro~~ clan]]. As such, the generator also represents [[7/6]] and [[8/7]]. Two of these generators make a very ~~sharp~~ [[4/3\|~~fourth~~]] which is also a very ~~flat~~ [[7/5]]. Two fifths make a second that is neutral in [[interval quality\|quality]], so a good tuning typically has a ''negative'' [[syntonic comma]]. Since three fifths make a sixth that sounds minor, and four make a third that sounds minor, it is also similar to the [[~~pelogic~~]] temperament ([[superpelog]] in particular). Finally it can be also considered a sort of messed-up variant of [[orwell]] temperament as well, since the generator falls into the same range of sizes.

	The edos whose [[patent val]]s support beep are [[4edo]], [[5edo]], [[9edo]], and [[14edo]]. Many other edos can be used as non-patent vals, such as 13.		The edos whose [[patent val]]s support beep are [[4edo]], [[5edo]], [[9edo]], and [[14edo]]. Many other edos can be used as non-patent vals, such as 13.
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	! #		! #
	! Cents*		! Cents*
	! Approximate ~~Ratios~~		! Approximate ratios
	\|-		\|-
	\| 0		\| 0
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	\| 15/8		\| 15/8
	\|}		\|}
	<nowiki />* ~~Octave reduced, in~~ 7-limit CTE tuning		<nowiki/>* In 7-limit CTE tuning, octave reduced

	== Chords and harmony ==		== Chords and harmony ==
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	\|-		\|-
	! Cents		! Cents
	! Generator ~~Steps~~		! Generator steps
	\|-		\|-
	\| 0		\| 0
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	{\| class="wikitable center-all left-4"		{\| class="wikitable center-all left-4"
	\|-		\|-
	! Edo<br>~~Generator~~ !! Eigenmonzo<br>(~~Unchanged~~-interval) !! Generator (¢) !! Comments		! Edo<br>generator !! Eigenmonzo<br>(unchanged-interval) !! Generator (¢) !! Comments
	\|-		\|-
	\| \|\| 5/3 \|\| 884.3 \|\|		\| \|\| 5/3 \|\| 884.3 \|\|
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	\|}		\|}

			== Notes ==
			<references group="note"/>

			[[Category:Bug\| ]] <!-- main article -->
	[[Category:Beep\| ]] <!-- main article -->		[[Category:Beep\| ]] <!-- main article -->
	[[Category:Rank-2 temperaments]]		[[Category:Rank-2 temperaments]]

FloraC: + link to technical data page

2025-11-19T10:52:38Z

+ link to technical data page

← Older revision		Revision as of 10:52, 19 November 2025
Line 3:		Line 3:
	It [[tempering out\|tempers out]] [[27/25]] and is part of the [[bug family]]; as such, [[6/5]] and [[10/9]] are represented by the same interval which, in fact, is the [[generator]]. It also tempers out the [[21/20\|septimal minor semitone (21/20)]], making it a [[septisemi temperaments\|septisemi temperament]], and the [[49/48\|slendro diesis (49/48)]], making it part of the [[slendro clan]]. As such, the generator also represents [[7/6]] and [[8/7]]. Two of these generators make a very sharp [[4/3\|fourth]] which is also a very flat [[7/5]]. Two fifths make a second that is neutral in [[interval quality\|quality]], so a good tuning typically has a ''negative'' [[syntonic comma]]. Since three fifths make a sixth that sounds minor, and four make a third that sounds minor, it is also similar to the [[pelogic]] temperament ([[superpelog]] in particular). Finally it can be also considered a sort of messed-up variant of [[orwell]] temperament as well, since the generator falls into the same range of sizes.		It [[tempering out\|tempers out]] [[27/25]] and is part of the [[bug family]]; as such, [[6/5]] and [[10/9]] are represented by the same interval which, in fact, is the [[generator]]. It also tempers out the [[21/20\|septimal minor semitone (21/20)]], making it a [[septisemi temperaments\|septisemi temperament]], and the [[49/48\|slendro diesis (49/48)]], making it part of the [[slendro clan]]. As such, the generator also represents [[7/6]] and [[8/7]]. Two of these generators make a very sharp [[4/3\|fourth]] which is also a very flat [[7/5]]. Two fifths make a second that is neutral in [[interval quality\|quality]], so a good tuning typically has a ''negative'' [[syntonic comma]]. Since three fifths make a sixth that sounds minor, and four make a third that sounds minor, it is also similar to the [[pelogic]] temperament ([[superpelog]] in particular). Finally it can be also considered a sort of messed-up variant of [[orwell]] temperament as well, since the generator falls into the same range of sizes.

	The edos whose [[patent val]]s support beep are [[4edo]], [[5edo]], [[9edo]], and [[14edo]]. Many other edos can be used as non-patent vals, such as 13.		The edos whose [[patent val]]s support beep are [[4edo]], [[5edo]], [[9edo]], and [[14edo]]. Many other edos can be used as non-patent vals, such as 13.

			See [[Bug family #Bug]] and [[Bug family #Beep\|#Beep]] for technical data.

	== Interval chain ==		== Interval chain ==