Rodan: Difference between revisions

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'''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 [[5/4|5th harmonic (5/4)]]. 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 [[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 [[5/4|5th harmonic (5/4)]]. 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; 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.

Revision as of 00:06, 14 June 2025 view source Lériendil (talk \| contribs) autopatrolled, Interface administrators, Sysops 7,596 edits m added 87edo info ← Older edit		Revision as of 00:07, 14 June 2025 view source Lériendil (talk \| contribs) autopatrolled, Interface administrators, Sysops 7,596 edits mNo edit summary Newer edit →
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	'''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 [[5/4\|5th harmonic (5/4)]]. 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 [[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 [[5/4\|5th harmonic (5/4)]]. 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; 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 [[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; 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.