4L 7s: Difference between revisions
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TAMNAMS formerly used the name ''kleistonic'' for the name of this scale (prefix ''klei-''). Other names include '''p-chro smitonic''' or '''smipechromic'''. | TAMNAMS formerly used the name ''kleistonic'' for the name of this scale (prefix ''klei-''). Other names include '''p-chro smitonic''' or '''smipechromic'''. | ||
== Intervals == | == Scale properties == | ||
{{TAMNAMS use}} | |||
=== Intervals === | |||
{{MOS intervals}} | {{MOS intervals}} | ||
== Tuning ranges == | === Generator chain === | ||
{{MOS genchain}} | |||
=== Modes === | |||
{{MOS mode degrees}} | |||
== Tuning ranges== | |||
=== Soft range === | === Soft range === | ||
The soft range for tunings of 4L 7s encompasses parasoft and hyposoft tunings. This implies step ratios smaller than 2/1, meaning a generator sharper than 4\15 = | The soft range for tunings of 4L 7s encompasses parasoft and hyposoft tunings. This implies step ratios smaller than 2/1, meaning a generator sharper than {{nowrap|4\15 {{=}} 320{{c}}}}. | ||
This is the range associated with extensions of [[Orgone|Orgone[7]]]. The small step is recognizable as a near diatonic semitone, while the large step is in the ambiguous area of neutral seconds. | This is the range associated with extensions of [[Orgone|Orgone[7]]]. The small step is recognizable as a near diatonic semitone, while the large step is in the ambiguous area of neutral seconds. | ||
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|- | |- | ||
! | ! | ||
![[15edo]] (basic) | ! [[15edo]] (basic) | ||
! [[26edo]] (soft) | ! [[26edo]] (soft) | ||
! Some JI approximations | ! Some JI approximations | ||
| Line 48: | Line 57: | ||
=== Hypohard === | === Hypohard === | ||
Hypohard tunings of 4L 7s have step ratios between 2/1 and 3/1, implying a generator sharper than 5\19 = 315. | Hypohard tunings of 4L 7s have step ratios between 2/1 and 3/1, implying a generator sharper than {{nowrap|5\19 {{=}} 315.79{{c}}}} and flatter than {{nowrap|4\15 {{=}} 320{{c}}}}. | ||
This range represents one of the harmonic entropy minimums, where 6 generators make a just diatonic fifth ([[3/2]]), an octave above. This is the range associated with the eponymous Kleismic (aka [[Hanson]]) temperament and its extensions. | This range represents one of the harmonic entropy minimums, where 6 generators make a just diatonic fifth ([[3/2]]), an octave above. This is the range associated with the eponymous Kleismic (aka [[Hanson]]) temperament and its extensions. | ||
Hypohard edos include [[15edo]], [[19edo]], and [[34edo]]. | Hypohard edos include [[15edo]], [[19edo]], and [[34edo]]. | ||
The sizes of the generator, large step and small step of 4L 7s are as follows in various hypohard tunings: | The sizes of the generator, large step and small step of 4L 7s are as follows in various hypohard tunings: | ||
{| class="wikitable right-2 right-3 right-4" | {| class="wikitable right-2 right-3 right-4" | ||
|- | |- | ||
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| 6/5 | | 6/5 | ||
|- | |- | ||
| L (octave | | L ({{nowrap|octave − 3g}}) | ||
| 2\15, 160.00 | | 2\15, 160.00 | ||
| 3\19, 189.47 | | 3\19, 189.47 | ||
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| 10/9, 11/10 (in 15edo) | | 10/9, 11/10 (in 15edo) | ||
|- | |- | ||
| s (4g | | s ({{nowrap|4g − octave}}) | ||
| 1\15, 80.00 | | 1\15, 80.00 | ||
| 1\19, 63.16 | | 1\19, 63.16 | ||
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|- | |- | ||
! | ! | ||
![[19edo]] (hard) | ! [[19edo]] (hard) | ||
![[23edo]] (superhard) | ! [[23edo]] (superhard) | ||
! [[42edo]] (parahard) | ! [[42edo]] (parahard) | ||
! Some JI approximations | ! Some JI approximations | ||
| Line 102: | Line 111: | ||
| 6/5 | | 6/5 | ||
|- | |- | ||
| L (octave | | L ({{nowrap|octave − 3g}}) | ||
| 3\19, 189.47 | | 3\19, 189.47 | ||
| 4\23, 208.70 | | 4\23, 208.70 | ||
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| 10/9, 9/8 | | 10/9, 9/8 | ||
|- | |- | ||
| s (4g | | s ({{nowrap|4g − octave}}) | ||
| 1\19, 63.16 | | 1\19, 63.16 | ||
| 1\23, 52.17 | | 1\23, 52.17 | ||
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|} | |} | ||
=== Hyperhard === | === Hyperhard=== | ||
Hyperhard tunings of 4L 7s have step ratios between 4/1 and 6/1, implying a generator sharper than 8\31 = 309.68¢ and flatter than 6\23 = 313.04¢. | Hyperhard tunings of 4L 7s have step ratios between 4/1 and 6/1, implying a generator sharper than 8\31 = 309.68¢ and flatter than 6\23 = 313.04¢. | ||
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| 6/5 | | 6/5 | ||
|- | |- | ||
| L (octave | | L ({{nowrap|octave − 3g}}) | ||
| 4\23, 208.70 | | 4\23, 208.70 | ||
| 6\31, 232.26 | | 6\31, 232.26 | ||
| Line 143: | Line 152: | ||
| 8/7, 9/8 | | 8/7, 9/8 | ||
|- | |- | ||
| s (4g | | s ({{nowrap|4g − octave}}) | ||
| 1\23, 52.17 | | 1\23, 52.17 | ||
| 1\31, 38.71 | | 1\31, 38.71 | ||
| Line 150: | Line 159: | ||
|} | |} | ||
== Temperaments == | == Temperaments == | ||
== Scales == | == Scales == | ||
* [[Oregon11]] | * [[Oregon11]] | ||
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== Scale tree == | == Scale tree == | ||
{{ | {{MOS tuning spectrum | ||
10/7 | | 6/5 = [[Oregon]] | ||
11/7 | | 10/7 = [[Orgone]] | ||
13/8 | | 11/7 = [[Magicaltet]] | ||
5/3 | | 13/8 = Golden superklesimic | ||
7/3 | | 5/3 = [[Superkleismic]] | ||
13/5 | | 7/3 = [[Catalan]] | ||
8/3 | | 13/5 = [[Countercata]] | ||
10/3 | | 8/3 = [[Hanson]]/[[cata]] | ||
9/2 | | 11/4 = [[Catakleismic]] | ||
5/1 | | 10/3 = [[Parakleismic]] | ||
6/1 | | 9/2 = [[Oolong]] | ||
| 5/1 = [[Starlingtet]] | |||
| 6/1 = [[Myna]] | |||
}} | |||
== Gallery == | |||
[[File:19EDO_Kleistonic_cheat_sheet.png|825x825px|thumb|Cheat sheet for 19EDO, a hard tuning for 4L 7s (or kleistonic).|alt=|left]] | |||
[[Category:11-tone scales]] | [[Category:11-tone scales]] | ||
[[Category:Kleistonic]] <!-- main article --> | [[Category:Kleistonic]] <!-- main article --> | ||