Rodan - Revision history

FloraC: Text replacement - "Category:Hemifamity temperaments" to "Category:Aberschismic temperaments"

2026-06-06T12:39:41Z

Text replacement - "Category:Hemifamity temperaments" to "Category:Aberschismic temperaments"

← Older revision		Revision as of 12:39, 6 June 2026
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	[[Category:Gamelismic clan]]		[[Category:Gamelismic clan]]
	[[Category:Sensamagic clan]]		[[Category:Sensamagic clan]]
	[[Category:~~Hemifamity~~ temperaments]]		[[Category:Aberschismic temperaments]]

FloraC: Update the complexity values in the infobox

2026-03-26T12:20:16Z

Update the complexity values in the infobox

← Older revision		Revision as of 12:20, 26 March 2026
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	\| MOS scales = [[1L 4s]], [[5L 1s]], [[5L 6s]], …, [[5L 36s]], [[41L 5s]]		\| MOS scales = [[1L 4s]], [[5L 1s]], [[5L 6s]], …, [[5L 36s]], [[41L 5s]]
	\| Pergen = (P8, P5/3)		\| Pergen = (P8, P5/3)
	\| Odd limit 1 = 9 \| Mistuning 1 = 5.05 \| Complexity 1 = 41		\| Odd limit 1 = 9 \| Mistuning 1 = 5.05 \| Complexity 1 = 21
	\| Odd limit 2 = 11-limit 21 \| Mistuning 2 = 5.34 \| Complexity 2 = 87		\| Odd limit 2 = 11-limit 21 \| Mistuning 2 = 5.34 \| Complexity 2 = 36
	}}		}}
	'''Rodan''' is one of the notable [[extension]]s of the [[slendric]] [[regular temperament\|temperament]], which divides the perfect fifth, [[3/2]], into three equal intervals representing [[8/7]] ([[tempering out]] the gamelisma, [[1029/1024]]), reaching the full [[7-limit]] such that 17 of these [[generators]] [[stacking\|stack]] to reach the interval class of the [[5/1\|5th harmonic]]. It tempers out [[245/243]], making it a [[sensamagic clan\|sensamagic temperament]], so that [[5/3]] is divided into two intervals of [[9/7]]; and it tempers out [[5120/5103]], making it also a [[hemifamity temperaments\|hemifamity temperament]], so that [[9/8]] stacks thrice into [[10/7]].		'''Rodan''' is one of the notable [[extension]]s of the [[slendric]] [[regular temperament\|temperament]], which divides the perfect fifth, [[3/2]], into three equal intervals representing [[8/7]] ([[tempering out]] the gamelisma, [[1029/1024]]), reaching the full [[7-limit]] such that 17 of these [[generators]] [[stacking\|stack]] to reach the interval class of the [[5/1\|5th harmonic]]. It tempers out [[245/243]], making it a [[sensamagic clan\|sensamagic temperament]], so that [[5/3]] is divided into two intervals of [[9/7]]; and it tempers out [[5120/5103]], making it also a [[hemifamity temperaments\|hemifamity temperament]], so that [[9/8]] stacks thrice into [[10/7]].

FloraC at 10:19, 9 February 2026

2026-02-09T10:19:55Z

← Older revision		Revision as of 10:19, 9 February 2026
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	{{Infobox ~~Regtemp~~		{{Infobox regtemp
	\| Title = Rodan		\| Title = Rodan
	\| Subgroups = 2.3.5.7, 2.3.5.7.11		\| Subgroups = 2.3.5.7, 2.3.5.7.11

FloraC: Cleanup on infobox

2026-02-09T09:37:24Z

Cleanup on infobox

← Older revision		Revision as of 09:37, 9 February 2026
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	\| Comma basis = [[245/243]], [[1029/1024]] (7-limit); <br> [[245/243]], [[385/384]], [[441/440]] (11-limit)		\| Comma basis = [[245/243]], [[1029/1024]] (7-limit); <br> [[245/243]], [[385/384]], [[441/440]] (11-limit)
	\| Edo join 1 = 41 \| Edo join 2 = 46		\| Edo join 1 = 41 \| Edo join 2 = 46
	\| ~~Generator~~ = 8/7 \| ~~Generator~~ tuning = 234.4 \| Optimization method = CWE		\| Mapping = 1; 3 17 -1 -13
			\| Generators = 8/7 \| Generators tuning = 234.4 \| Optimization method = CWE
	\| MOS scales = [[1L 4s]], [[5L 1s]], [[5L 6s]], …, [[5L 36s]], [[41L 5s]]		\| MOS scales = [[1L 4s]], [[5L 1s]], [[5L 6s]], …, [[5L 36s]], [[41L 5s]]
	~~\| Mapping = 1; 3 17 -1 -13~~
	\| Pergen = (P8, P5/3)		\| Pergen = (P8, P5/3)
	\| Odd limit 1 = 9 \| Mistuning 1 = 5.05 \| Complexity 1 = 41		\| Odd limit 1 = 9 \| Mistuning 1 = 5.05 \| Complexity 1 = 41
	\| Odd limit 2 = ~~(2.3.5.7.~~11) 21 \| Mistuning 2 = 5.34 \| Complexity 2 = 87		\| Odd limit 2 = 11-limit 21 \| Mistuning 2 = 5.34 \| Complexity 2 = 87
	}}		}}
	'''Rodan''' is one of the notable [[extension]]s of the [[slendric]] [[regular temperament\|temperament]], which divides the perfect fifth, [[3/2]], into three equal intervals representing [[8/7]] ([[tempering out]] the gamelisma, [[1029/1024]]), reaching the full [[7-limit]] such that 17 of these [[generators]] [[stacking\|stack]] to reach the interval class of the [[5/1\|5th harmonic]]. It tempers out [[245/243]], making it a [[sensamagic clan\|sensamagic temperament]], so that [[5/3]] is divided into two intervals of [[9/7]]; and it tempers out [[5120/5103]], making it also a [[hemifamity temperaments\|hemifamity temperament]], so that [[9/8]] stacks thrice into [[10/7]].		'''Rodan''' is one of the notable [[extension]]s of the [[slendric]] [[regular temperament\|temperament]], which divides the perfect fifth, [[3/2]], into three equal intervals representing [[8/7]] ([[tempering out]] the gamelisma, [[1029/1024]]), reaching the full [[7-limit]] such that 17 of these [[generators]] [[stacking\|stack]] to reach the interval class of the [[5/1\|5th harmonic]]. It tempers out [[245/243]], making it a [[sensamagic clan\|sensamagic temperament]], so that [[5/3]] is divided into two intervals of [[9/7]]; and it tempers out [[5120/5103]], making it also a [[hemifamity temperaments\|hemifamity temperament]], so that [[9/8]] stacks thrice into [[10/7]].

FloraC: /* Tunings */ + basic norm-based tunings

2025-11-16T12:37:18Z

Tunings: + basic norm-based tunings

@@ Line 312: / Line 312: @@
 == Tunings ==
 === Tuning spectrum ===
-{{see also|Slendric #Tuning spectrum}}
+{{See also| Slendric #Tuning spectrum }}
 {| class="wikitable center-all left-4 left-5"
 |-
-! EDO<br>generator
+! Edo<br>generator
 ! [[Eigenmonzo|Unchanged interval<br>(eigenmonzo)]]
 ! Generator (¢)

FloraC: bold lemma (radon)

2025-11-15T14:29:41Z

bold lemma (radon)

← Older revision		Revision as of 14:29, 15 November 2025
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	\| Odd limit 2 = (2.3.5.7.11) 21 \| Mistuning 2 = 5.34 \| Complexity 2 = 87		\| Odd limit 2 = (2.3.5.7.11) 21 \| Mistuning 2 = 5.34 \| Complexity 2 = 87
	}}		}}

	'''Rodan''' is one of the notable [[extension]]s of the [[slendric]] [[regular temperament\|temperament]], which divides the perfect fifth, [[3/2]], into three equal intervals representing [[8/7]] ([[tempering out]] the gamelisma, [[1029/1024]]), reaching the full [[7-limit]] such that 17 of these [[generators]] [[stacking\|stack]] to reach the interval class of the [[5/1\|5th harmonic]]. It tempers out [[245/243]], making it a [[sensamagic clan\|sensamagic temperament]], so that [[5/3]] is divided into two intervals of [[9/7]]; and it tempers out [[5120/5103]], making it also a [[hemifamity temperaments\|hemifamity temperament]], so that [[9/8]] stacks thrice into [[10/7]].		'''Rodan''' is one of the notable [[extension]]s of the [[slendric]] [[regular temperament\|temperament]], which divides the perfect fifth, [[3/2]], into three equal intervals representing [[8/7]] ([[tempering out]] the gamelisma, [[1029/1024]]), reaching the full [[7-limit]] such that 17 of these [[generators]] [[stacking\|stack]] to reach the interval class of the [[5/1\|5th harmonic]]. It tempers out [[245/243]], making it a [[sensamagic clan\|sensamagic temperament]], so that [[5/3]] is divided into two intervals of [[9/7]]; and it tempers out [[5120/5103]], making it also a [[hemifamity temperaments\|hemifamity temperament]], so that [[9/8]] stacks thrice into [[10/7]].

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	As can be elucidated by [[S-expression]]s, rodan is very much an "opposed counterpart" to mothra: the basic equivalence of slendric tempers S7 (49/48) = S8 (64/63), and mothra proceeds to equate it to S6 ([[36/35]]) as well; meanwhile, rodan extends the equivalence in the opposite direction to add S9 (81/80) to it, making it one of the five [[rank-2 temperament]]s definable by equating three adjacent square superparticulars.		As can be elucidated by [[S-expression]]s, rodan is very much an "opposed counterpart" to mothra: the basic equivalence of slendric tempers S7 (49/48) = S8 (64/63), and mothra proceeds to equate it to S6 ([[36/35]]) as well; meanwhile, rodan extends the equivalence in the opposite direction to add S9 (81/80) to it, making it one of the five [[rank-2 temperament]]s definable by equating three adjacent square superparticulars.

	As for further extensions, slendric temperaments often find [[55/32]] at 4 generator steps (tempering out [[385/384]] and [[441/440]]), giving new interpretations to the quark as [[55/54]] and [[56/55]]; 55/32 is particularly accurate in the tuning subrange appropriate for rodan, and so [[11/1\|harmonic 11]] can easily be found at -13 generator steps. It is also worth mentioning that this equates the diatonic major third to [[14/11]], tempering out [[896/891]]. A [[2.3.7.11 subgroup]] version of rodan, known as ''radon'', uses exclusively this mapping and forgoes interpreting the 5th harmonic.		As for further extensions, slendric temperaments often find [[55/32]] at 4 generator steps (tempering out [[385/384]] and [[441/440]]), giving new interpretations to the quark as [[55/54]] and [[56/55]]; 55/32 is particularly accurate in the tuning subrange appropriate for rodan, and so [[11/1\|harmonic 11]] can easily be found at -13 generator steps. It is also worth mentioning that this equates the diatonic major third to [[14/11]], tempering out [[896/891]]. A [[2.3.7.11 subgroup]] version of rodan, known as '''radon''', uses exclusively this mapping and forgoes interpreting the 5th harmonic.

	Toward the [[13-limit]], the diatonic minor third ([[32/27]]) in hemifamity temperaments represents the square root of [[7/5]], for which [[13/11]] is a good interpretation (tempering out [[352/351]] and [[847/845]]), which turns out to place [[13/1\|harmonic 13]] at -22 generator steps. Finally, [[17/13]] is a good interpretation of the slendric subfourth comprising two generators, otherwise equated to [[21/16]] (tempering out [[273/272]] and [[833/832]]), and this places [[17/1\|harmonic 17]] at -20 generator steps. Thus proceeds the canonical extension of rodan out to the [[17-limit]].		Toward the [[13-limit]], the diatonic minor third ([[32/27]]) in hemifamity temperaments represents the square root of [[7/5]], for which [[13/11]] is a good interpretation (tempering out [[352/351]] and [[847/845]]), which turns out to place [[13/1\|harmonic 13]] at -22 generator steps. Finally, [[17/13]] is a good interpretation of the slendric subfourth comprising two generators, otherwise equated to [[21/16]] (tempering out [[273/272]] and [[833/832]]), and this places [[17/1\|harmonic 17]] at -20 generator steps. Thus proceeds the canonical extension of rodan out to the [[17-limit]].

Lériendil at 08:15, 30 August 2025

2025-08-30T08:15:22Z

← Older revision		Revision as of 08:15, 30 August 2025
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	== Interval chain ==		== Interval chain ==
	When speaking of interval categories, as an extension of slendric it is possible to use a system [[Slendric#Interval categories\|designed for slendric]], where notes are inflected from the diatonic [[chain of fifths]] by means of the prefixes "super" and "sub", such that three of these inflections stack to a diatonic minor second. These "super" and "sub" prefixes are equivalent to "up" and "down" in [[#Notation\|the notation]] system, where lifts and drops would represent a single edostep in [[ups and downs notation]] in the context of larger rodan edos that map this comma to multiple edosteps.		When speaking of interval categories, as an extension of slendric it is possible to use a system [[Slendric#Interval categories\|designed for slendric]], where notes are inflected from the diatonic [[chain of fifths]] by means of the prefixes "super" and "sub", such that three of these inflections stack to a diatonic minor second. Such an inflection is equivalent to a quark, and due to the quark's versatile nature in rodan as a generalized comma, simple pental and septimal intervals tend to be represented by single-quark offsets from the diatonic spine. These "super" and "sub" prefixes are equivalent to "up" and "down" in [[#Notation\|the notation]] system, where lifts and drops would represent a single edostep in [[ups and downs notation]] in the context of larger rodan edos that map this comma to multiple edosteps.

	In the following table, odd harmonics and subharmonics 1–21 are in '''bold'''.		In the following table, odd harmonics and subharmonics 1–21 are in '''bold'''.

Lériendil at 08:12, 30 August 2025

2025-08-30T08:12:47Z

← Older revision		Revision as of 08:12, 30 August 2025
Line 12:		Line 12:
	}}		}}

	'''Rodan''' is one of the notable [[extension]]s of the [[slendric]] [[regular temperament\|temperament]], which divides [[3/2]] into three equal intervals representing [[8/7]] ([[tempering out]] the gamelisma, [[1029/1024]]), reaching the full [[7-limit]] such that 17 of these [[generators]] [[stacking\|stack]] to reach the interval class of the [[5/1\|5th harmonic]]. It tempers out [[245/243]], making it a [[sensamagic clan\|sensamagic temperament]], so that [[5/3]] is divided into two intervals of [[9/7]]; and it tempers out [[5120/5103]], making it also a [[hemifamity temperaments\|hemifamity temperament]], so that [[9/8]] stacks thrice into [[10/7]].		'''Rodan''' is one of the notable [[extension]]s of the [[slendric]] [[regular temperament\|temperament]], which divides the perfect fifth, [[3/2]], into three equal intervals representing [[8/7]] ([[tempering out]] the gamelisma, [[1029/1024]]), reaching the full [[7-limit]] such that 17 of these [[generators]] [[stacking\|stack]] to reach the interval class of the [[5/1\|5th harmonic]]. It tempers out [[245/243]], making it a [[sensamagic clan\|sensamagic temperament]], so that [[5/3]] is divided into two intervals of [[9/7]]; and it tempers out [[5120/5103]], making it also a [[hemifamity temperaments\|hemifamity temperament]], so that [[9/8]] stacks thrice into [[10/7]].

	Unlike [[mothra]], which flattens the fifth to a [[meantone]] fifth, the fifth of rodan is slightly sharp of just, ranging from that of [[41edo]] to that of [[46edo]] (with [[87edo]] being an essentially optimal tuning). As a result, the [[256/243\|diatonic minor second]] is compressed, and the interval known as the [[quark]], which represents [[49/48]], [[64/63]], and in rodan also [[81/80]], is even smaller than it is in tunings of slendric with a nearly just fifth. This entails that the [[mos scale]]s of rodan [[cluster MOS\|cluster]] even more strongly around [[5edo]], although this can be thought of as an advantage in that it simplifies the conceptualization of rodan's inventory of intervals (see [[#As a detemperament of 5et]]). Rather than directly using mos scales, which are either extremely imbalanced or overly large, an approach to rodan may involve picking and choosing which intervals from each [[pentatonic]] category to keep in the scale.		Unlike in [[mothra]], which flattens the fifth to a [[meantone]] fifth, the fifth of rodan is slightly sharp of just, ranging from that of [[41edo]] to that of [[46edo]] (with [[87edo]] being an essentially optimal tuning). As a result, the [[256/243\|diatonic minor second]] is compressed, and the interval known as the [[quark]], which represents [[49/48]], [[64/63]], and in rodan also [[81/80]], is even smaller than it is in tunings of slendric with a nearly just fifth. This entails that the [[mos scale]]s of rodan [[cluster MOS\|cluster]] even more strongly around [[5edo]], although this can be thought of as an advantage in that it simplifies the conceptualization of rodan's inventory of intervals (see [[#As a detemperament of 5et]]). Rather than directly using mos scales, which are either extremely imbalanced or overly large, an approach to rodan may involve picking and choosing which intervals from each [[pentatonic]] category to keep in the scale.

	As can be elucidated by [[S-expression]]s, rodan is very much an "opposed counterpart" to mothra: the basic equivalence of slendric tempers S7 (49/48) = S8 (64/63), and mothra proceeds to equate it to S6 ([[36/35]]) as well; meanwhile, rodan extends the equivalence in the opposite direction to add S9 (81/80) to it, making it one of the five [[rank-2 temperament]]s definable by equating three adjacent square superparticulars.		As can be elucidated by [[S-expression]]s, rodan is very much an "opposed counterpart" to mothra: the basic equivalence of slendric tempers S7 (49/48) = S8 (64/63), and mothra proceeds to equate it to S6 ([[36/35]]) as well; meanwhile, rodan extends the equivalence in the opposite direction to add S9 (81/80) to it, making it one of the five [[rank-2 temperament]]s definable by equating three adjacent square superparticulars.

Lériendil at 07:28, 30 August 2025

2025-08-30T07:28:16Z

← Older revision		Revision as of 07:28, 30 August 2025
Line 25:		Line 25:

	== Interval chain ==		== Interval chain ==
	When speaking of interval categories, as an extension of slendric it is possible to use a system [[Slendric#Interval categories\|designed for slendric]], where notes are inflected from the diatonic [[chain of fifths]] by means of the prefixes "super" and "sub", such that three of these inflections stack to a diatonic minor second. These "super" and "sub" prefixes are equivalent to "up" and "down" in [[#Notation\|the notation]] system, ~~but can disambiguate from "up"~~ and ~~"down" symbols from~~ [[ups and downs notation]] in the context of larger rodan edos that map this comma to multiple edosteps.		When speaking of interval categories, as an extension of slendric it is possible to use a system [[Slendric#Interval categories\|designed for slendric]], where notes are inflected from the diatonic [[chain of fifths]] by means of the prefixes "super" and "sub", such that three of these inflections stack to a diatonic minor second. These "super" and "sub" prefixes are equivalent to "up" and "down" in [[#Notation\|the notation]] system, where lifts and drops would represent a single edostep in [[ups and downs notation]] in the context of larger rodan edos that map this comma to multiple edosteps.

	In the following table, odd harmonics and subharmonics 1–21 are in '''bold'''.		In the following table, odd harmonics and subharmonics 1–21 are in '''bold'''.

Lériendil: added ups and downs

2025-08-30T07:26:46Z

added ups and downs

Show changes