5L 4s: Difference between revisions

Line 40:

== Theory ==

The ~~familiar~~ harmonic entropy minimum with this MOS pattern is [[godzilla]], in which the generator [[8/7]] or [[7/6]] ~~(tempered~~ to be the same interval), and two generators is [[4/3]]. However, in addition to godzilla (tempering out 81/80) and the 2.3.7 temperament [[semaphore]], there is also a weird scale called "[[pseudo-semaphore]]", in which two different flavors of [[3/2]] exist in the same scale: an octave minus two generators makes a sharp 3/2, and two octaves minus seven generators makes a flat 3/2. The 2.3.13/5 [[barbados]] temperament is another possible interpretation.

The harmonic entropy minimum with this MOS pattern is [[godzilla]], in which the generator tempers [[8/7]] or [[7/6]] to be the same interval, and two generators is [[4/3]]. However, in addition to godzilla (tempering out 81/80) and the 2.3.7 temperament [[semaphore]], there is also a weird scale called "[[pseudo-semaphore]]", in which two different flavors of [[3/2]] exist in the same scale: an octave minus two generators makes a sharp 3/2, and two octaves minus seven generators makes a flat 3/2. The 2.3.13/5 [[barbados]] temperament is another possible interpretation.

== Tuning ranges ==

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==== Hypohard ====

The sizes of the generator, large step and small step of 5L 4s are as follows in various hypohard (2/1 ≤ L/s ≤ 3/1) tunings.

The sizes of the generator, large step and small step of 5L 4s are as follows in various hypohard ({{nowrap|2/1 ≤ L/s ≤ 3/1}}) tunings.

{| class="wikitable right-2 right-3 right-4 right-5 right-6"

!

! [[14edo]] (L/s = 2/1)

! [[14edo]] ({{nowrap|L/s {{=}} 2/1}})

! [[47edo]] (L/s = 7/3)

! [[47edo]] ({{nowrap|L/s {{=}} 7/3}})

! [[33edo]] (L/s = 5/2)

! [[33edo]] ({{nowrap|L/s {{=}} 5/2}})

! [[52edo]] (L/s = 8/3)

! [[52edo]] ({{nowrap|L/s {{=}} 8/3}})

! [[19edo]] (L/s = 3/1)

! [[19edo]] ({{nowrap|L/s {{=}} 3/1}})

|-

| generator (g)

Line 63:

| 4\19, 252.63

|-

| L (octave - 4g)

| L ({{nowrap|octave − 4g}})

| 171.43

| 178.72

Line 70:

| 189.47

|-

| s (5g - octave)

| s ({{nowrap|5g − octave}})

| 85.71

| 76.60

Line 77:

| 63.16

|}

This range is notable for having many simple tunings that are close to being "eigentunings" (tunings that tune a certain JI interval exactly):

* 33edo semiquartal has close 7/5 (error -0.69¢), 9/5 (error -0.59¢) and 9/7 (error +1.28¢), thus can be used for the close 5:7:9 in the two Locrian-like modes 1|7 and 0|8

* 33edo semiquartal has close 7/5 (error −0.69¢), 9/5 (error −0.59¢) and 9/7 (error +1.28¢), thus can be used for the close 5:7:9 in the two Locrian-like modes 1{{pipe}}7 and 0{{pipe}}8

* 52edo semiquartal has close 22/19 (error +0.04¢)

* 19edo semiquartal has close 6/5 (error +0.15¢) and 28/27 (error +0.20¢)

Line 99:

Line 100:

| 6\29, 248.28

|-

| L (octave - 4g)

| L ({{nowrap|octave − 4g}})

| 189.47

| 200.00

| 206.90

|-

| s (5g - octave)

| s ({{nowrap|5g − octave}})

| 63.16

| 50.00

Line 126:

Line 127:

| 8\37, 259.46

|-

| L (octave - 4g)

| L ({{nowrap|octave − 4g}})

| 156.52

| 150.00

| 162.16

|-

| s (5g - octave)

| s ({{nowrap|5g − octave}})

| 104.35

| 112.50

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== Music ==

* [https://www.soundclick.com/bands/songInfo.cfm?bandID=376205&songID=5327098 ''Entropy, the Grandfather of Wind''] (broken link. 2011-03-04) in [[14edo]]{{dead link}}

* [https://www.soundclick.com/bands/songInfo.cfm?bandID=376205&songID=5327098 ''Entropy, the Grandfather of Wind''] (broken link. 2011-03-04) In [[14edo]]{{dead link}}

; [[Frédéric Gagné]]

* ''Whalectric'' (2022) – [https://youtu.be/_E6qvbJWYY8 YouTube] | [https://musescore.com/fredg999/whalectric score] ~~– in~~ [[51edo]], 4|4 mode

* ''Whalectric'' (2022) – [https://youtu.be/_E6qvbJWYY8 YouTube] | [https://musescore.com/fredg999/whalectric score] – In [[51edo]], 4{{pipe}}4 mode

; [[Inthar]]

* [[:File:Dream EP 14edo Sketch.mp3|''Dream EP 14edo Sketch'']] (2021) ~~– a~~ short swing ditty in [[14edo]], in the 212121221 mode

* [[:File:Dream EP 14edo Sketch.mp3|''Dream EP 14edo Sketch'']] (2021) – A short swing ditty in [[14edo]], in the 212121221 mode

* [[:File:19edo Semaphore Fugue.mp3|''19edo Semaphore Fugue'']] (2021) ~~– an~~ unfinished fugue in [[19edo]], in the 212121221 mode

* [[:File:19edo Semaphore Fugue.mp3|''19edo Semaphore Fugue'']] (2021) – An unfinished fugue in [[19edo]], in the 212121221 mode

; [[Starshine]]

* [https://soundcloud.com/starshine99/rins-ufo-ride ''Rin's UFO Ride''] (2020) – Semaphore[9] in [[19edo]]

; [[Sevish]]

* [http://www.youtube.com/watch?v=Gcgawrr2xao | ''Desert Island Rain;''] – Semaphore[9] in [[313edo]] using 65\313 as the generator

[[Category:Semiquartal| ]]

@@ Line 40: / Line 40: @@
 == Theory ==
-The familiar harmonic entropy minimum with this MOS pattern is [[godzilla]], in which the generator [[8/7]] or [[7/6]] (tempered to be the same interval), and two generators is [[4/3]]. However, in addition to godzilla (tempering out 81/80) and the 2.3.7 temperament [[semaphore]], there is also a weird scale called "[[pseudo-semaphore]]", in which two different flavors of [[3/2]] exist in the same scale: an octave minus two generators makes a sharp 3/2, and two octaves minus seven generators makes a flat 3/2. The 2.3.13/5 [[barbados]] temperament is another possible interpretation.
+The harmonic entropy minimum with this MOS pattern is [[godzilla]], in which the generator tempers [[8/7]] or [[7/6]] to be the same interval, and two generators is [[4/3]]. However, in addition to godzilla (tempering out 81/80) and the 2.3.7 temperament [[semaphore]], there is also a weird scale called "[[pseudo-semaphore]]", in which two different flavors of [[3/2]] exist in the same scale: an octave minus two generators makes a sharp 3/2, and two octaves minus seven generators makes a flat 3/2. The 2.3.13/5 [[barbados]] temperament is another possible interpretation.
 == Tuning ranges ==
@@ Line 47: / Line 47: @@
 ==== Hypohard ====
-The sizes of the generator, large step and small step of 5L 4s are as follows in various hypohard (2/1 ≤ L/s ≤ 3/1) tunings.
+The sizes of the generator, large step and small step of 5L 4s are as follows in various hypohard ({{nowrap|2/1 &le; L/s &le; 3/1}}) tunings.
 {| class="wikitable right-2 right-3 right-4 right-5 right-6"
-!
+! &nbsp;
-! [[14edo]] (L/s = 2/1)
+! [[14edo]] ({{nowrap|L/s {{=}} 2/1}})
-! [[47edo]] (L/s = 7/3)
+! [[47edo]] ({{nowrap|L/s {{=}} 7/3}})
-! [[33edo]] (L/s = 5/2)
+! [[33edo]] ({{nowrap|L/s {{=}} 5/2}})
-! [[52edo]] (L/s = 8/3)
+! [[52edo]] ({{nowrap|L/s {{=}} 8/3}})
-! [[19edo]] (L/s = 3/1)
+! [[19edo]] ({{nowrap|L/s {{=}} 3/1}})
 |-
 | generator (g)
@@ Line 63: / Line 63: @@
 | 4\19, 252.63
 |-
-| L (octave - 4g)
+| L ({{nowrap|octave &minus; 4g}})
 | 171.43
 | 178.72
@@ Line 70: / Line 70: @@
 | 189.47
 |-
-| s (5g - octave)
+| s ({{nowrap|5g &minus; octave}})
 | 85.71
 | 76.60
@@ Line 77: / Line 77: @@
 | 63.16
 |}
 This range is notable for having many simple tunings that are close to being "eigentunings" (tunings that tune a certain JI interval exactly):
-* 33edo semiquartal has close 7/5 (error -0.69¢), 9/5 (error -0.59¢) and 9/7 (error +1.28¢), thus can be used for the close 5:7:9 in the two Locrian-like modes 1|7 and 0|8
+* 33edo semiquartal has close 7/5 (error &minus;0.69¢), 9/5 (error &minus;0.59¢) and 9/7 (error +1.28¢), thus can be used for the close 5:7:9 in the two Locrian-like modes 1{{pipe}}7 and 0{{pipe}}8
 * 52edo semiquartal has close 22/19 (error +0.04¢)
 * 19edo semiquartal has close 6/5 (error +0.15¢) and 28/27 (error +0.20¢)
@@ Line 99: / Line 100: @@
 | 6\29, 248.28
 |-
-| L (octave - 4g)
+| L ({{nowrap|octave &minus; 4g}})
 | 189.47
 | 200.00
 | 206.90
 |-
-| s (5g - octave)
+| s ({{nowrap|5g &minus; octave}})
 | 63.16
 | 50.00
@@ Line 126: / Line 127: @@
 | 8\37, 259.46
 |-
-| L (octave - 4g)
+| L ({{nowrap|octave &minus; 4g}})
 | 156.52
 | 150.00
 | 162.16
 |-
-| s (5g - octave)
+| s ({{nowrap|5g &minus; octave}})
 | 104.35
 | 112.50
@@ Line 166: / Line 167: @@
 == Music ==
-* [https://www.soundclick.com/bands/songInfo.cfm?bandID=376205&songID=5327098 ''Entropy, the Grandfather of Wind''] (broken link. 2011-03-04) in [[14edo]]{{dead link}}
+* [https://www.soundclick.com/bands/songInfo.cfm?bandID=376205&songID=5327098 ''Entropy, the Grandfather of Wind''] (broken link. 2011-03-04) In [[14edo]]{{dead link}}
 ; [[Frédéric Gagné]]
-* ''Whalectric'' (2022) – [https://youtu.be/_E6qvbJWYY8 YouTube] | [https://musescore.com/fredg999/whalectric score] – in [[51edo]], 4|4 mode
+* ''Whalectric'' (2022) &ndash; [https://youtu.be/_E6qvbJWYY8 YouTube] | [https://musescore.com/fredg999/whalectric score] &ndash; In [[51edo]], 4{{pipe}}4 mode
 ; [[Inthar]]
-* [[:File:Dream EP 14edo Sketch.mp3|''Dream EP 14edo Sketch'']] (2021) – a short swing ditty in [[14edo]], in the 212121221 mode
+* [[:File:Dream EP 14edo Sketch.mp3|''Dream EP 14edo Sketch'']] (2021) &ndash; A short swing ditty in [[14edo]], in the 212121221 mode
-* [[:File:19edo Semaphore Fugue.mp3|''19edo Semaphore Fugue'']] (2021) – an unfinished fugue in [[19edo]], in the 212121221 mode
+* [[:File:19edo Semaphore Fugue.mp3|''19edo Semaphore Fugue'']] (2021) &ndash; An unfinished fugue in [[19edo]], in the 212121221 mode
 ; [[Starshine]]
-* [https://soundcloud.com/starshine99/rins-ufo-ride ''Rin's UFO Ride''] (2020) – Semaphore[9] in [[19edo]]
+* [https://soundcloud.com/starshine99/rins-ufo-ride ''Rin's UFO Ride''] (2020) &ndash; Semaphore[9] in [[19edo]]
+; [[Sevish]]
+* [http://www.youtube.com/watch?v=Gcgawrr2xao | ''Desert Island Rain;''] &ndash; Semaphore[9] in [[313edo]] using 65\313 as the generator
 [[Category:Semiquartal| ]] <!-- main article -->