5th-octave temperaments: Difference between revisions

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Thunderclysmic is a weak extension of slendroschismic (above), [[rainy]] and [[cata]], with a generator of a slightly sharp ~6/5 (befitting of any [[kleismic]] temperament), three of which making [[26/15]]~[[19/11]]. More interesting though is that the period is [[5edo|1\5]]; slendroschismic gives this a very accurate interpretation of [[147/128]] = ([[3/2]])/([[8/7]])<sup>2</sup> = [[8/7]] * [[1029/1024|S7/S8]] which is a significant interval as it is the "harmonic 5edostep" (in that it's a [[rooted]] (/2^n) interval in the 2.3.7 subgroup that approximates 1\5 very well). Thunderclysmic gives a wealth of interpretations to [[5edo]] intervals, which are available everywhere due to 1\5 = 240{{cent}} being the period of Thunderclysmic. In fact, Thunderclysmic combines many convergents and semiconvergents to intervals of [[5edo]] into a single, high-limit temperament:

1\5 = [[23/20]] = [[31/27]] = [[85/74]] = [[54/47]] (which Thunderclysmic also equates with [[63/50]]), and 2\5 = [[33/25]] = [[95/72]] = [[29/22]] = [[62/47]] = [[128/97]] (which Thunderclysmic also equates with [[37/28]] and [[120/91]]).

1\5 = [[23/20]] = [[31/27]] = [[85/74]] = [[54/47]] (which Thunderclysmic also equates with [[63/55]]), and 2\5 = [[33/25]] = [[95/72]] = [[29/22]] = [[62/47]] = [[128/97]] (which Thunderclysmic also equates with [[37/28]] and [[120/91]]).

Thunderclysmic can be thought of as the [[125edo|125f]] & [[140edo|140]] temperament in the [[37-limit]] add-47 add-97, with both tunings notable in all corresponding limits.

Thunderclysmic can be thought of as the [[125edo|125f]] & [[140edo|140]] temperament in the [[37-limit]] add-47 add-97, with both tunings notable in all corresponding limits. It was conceived as observing that both of these tunings are great general-purpose tunings in of themselves. It is especially notable in the [[29-limit]], and in general, any higher-limit mapping (of which there are many) is to make useful MOS scales of sizes 5 times 13, 16, 19 and 22, that is, 65, 80, 95 and 110-note mosses, in any preferred tuning; for this reason, choosing an edo tuning that combines multiple higher-limit extensions and learning to use the harmony within is recommendable, hence underlining its conception as 125f & 140.

It is a complex temperament, however note that it is especially strong and elegant in the no-13's no-17's no-31's [[37-limit]] add-97, on which its mapping is especially efficient, so that the gen range is -3 to 7 for a(n inclusive) span of 11 notes per 1\5 period, so that a 5*11=55 note-per-octave (multiperiod) [[MOS]] may be used.

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 Thunderclysmic is a weak extension of slendroschismic (above), [[rainy]] and [[cata]], with a generator of a slightly sharp ~6/5 (befitting of any [[kleismic]] temperament), three of which making [[26/15]]~[[19/11]]. More interesting though is that the period is [[5edo|1\5]]; slendroschismic gives this a very accurate interpretation of [[147/128]] = ([[3/2]])/([[8/7]])<sup>2</sup> = [[8/7]] * [[1029/1024|S7/S8]] which is a significant interval as it is the "harmonic 5edostep" (in that it's a [[rooted]] (/2^n) interval in the 2.3.7 subgroup that approximates 1\5 very well). Thunderclysmic gives a wealth of interpretations to [[5edo]] intervals, which are available everywhere due to 1\5 = 240{{cent}} being the period of Thunderclysmic. In fact, Thunderclysmic combines many convergents and semiconvergents to intervals of [[5edo]] into a single, high-limit temperament:
-\5 = [[23/20]] = [[31/27]] = [[85/74]] = [[54/47]] (which Thunderclysmic also equates with [[63/50]]), and 2\5 = [[33/25]] = [[95/72]] = [[29/22]] = [[62/47]] = [[128/97]] (which Thunderclysmic also equates with [[37/28]] and [[120/91]]).
+\5 = [[23/20]] = [[31/27]] = [[85/74]] = [[54/47]] (which Thunderclysmic also equates with [[63/55]]), and 2\5 = [[33/25]] = [[95/72]] = [[29/22]] = [[62/47]] = [[128/97]] (which Thunderclysmic also equates with [[37/28]] and [[120/91]]).
-Thunderclysmic can be thought of as the [[125edo|125f]] & [[140edo|140]] temperament in the [[37-limit]] add-47 add-97, with both tunings notable in all corresponding limits.
+Thunderclysmic can be thought of as the [[125edo|125f]] & [[140edo|140]] temperament in the [[37-limit]] add-47 add-97, with both tunings notable in all corresponding limits. It was conceived as observing that both of these tunings are great general-purpose tunings in of themselves. It is especially notable in the [[29-limit]], and in general, any higher-limit mapping (of which there are many) is to make useful MOS scales of sizes 5 times 13, 16, 19 and 22, that is, 65, 80, 95 and 110-note mosses, in any preferred tuning; for this reason, choosing an edo tuning that combines multiple higher-limit extensions and learning to use the harmony within is recommendable, hence underlining its conception as 125f & 140.
 It is a complex temperament, however note that it is especially strong and elegant in the no-13's no-17's no-31's [[37-limit]] add-97, on which its mapping is especially efficient, so that the gen range is -3 to 7 for a(n inclusive) span of 11 notes per 1\5 period, so that a 5*11=55 note-per-octave (multiperiod) [[MOS]] may be used.

5th-octave temperaments: Difference between revisions

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