5L 4s: Difference between revisions
ArrowHead294 (talk | contribs) mNo edit summary |
ArrowHead294 (talk | contribs) mNo edit summary |
||
| (15 intermediate revisions by 4 users not shown) | |||
| Line 10: | Line 10: | ||
=== Intervals === | === Intervals === | ||
{{MOS intervals}} | {{MOS intervals}} | ||
=== Generator chain === | |||
{{MOS genchain}} | |||
=== Modes === | === Modes === | ||
{{MOS mode degrees}} | {{MOS mode degrees}} | ||
Note that the darkest two modes have no diatonic or [[armotonic]] fifth on the root in nonextreme semiquartal tunings. | Note that the darkest two modes have no diatonic or [[armotonic]] fifth on the root in nonextreme semiquartal tunings. | ||
| Line 40: | Line 24: | ||
== Tuning ranges == | == Tuning ranges == | ||
=== Hard-of-basic === | === Hard-of-basic === | ||
Hard-of-basic tunings have [[ | Hard-of-basic tunings have [[semifourth]]s as generators, between 1\5 (240{{c}}) and 3\14 (257.14{{c}}), where two of them create a diatonic 4th. The generator could be viewed as a 15/13, and the resulting "inframinor" and "ultramajor" chords and triads could be viewed as approximating, respectively, 26:30:39 and 10:13:15 (see [[Arto and tendo theory]]). | ||
==== Hypohard ==== | ==== Hypohard ==== | ||
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. | 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" | {| class="wikitable right-2 right-3 right-4 right-5 right-6" | ||
|- | |- | ||
| Line 61: | Line 44: | ||
| 4\19, 252.63 | | 4\19, 252.63 | ||
|- | |- | ||
| L ({{nowrap|octave | | L ({{nowrap|octave − 4g}}) | ||
| 171.43 | | 171.43 | ||
| 178.72 | | 178.72 | ||
| Line 68: | Line 51: | ||
| 189.47 | | 189.47 | ||
|- | |- | ||
| s ({{nowrap|5g | | s ({{nowrap|5g − octave}}) | ||
| 85.71 | | 85.71 | ||
| 76.60 | | 76.60 | ||
| Line 77: | Line 60: | ||
This range is notable for having many simple tunings that are close to being "eigentunings" (tunings that tune a certain JI interval exactly): | 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 | * 33edo semiquartal has close 7/5 (error −0.69{{c}}), 9/5 (error −0.59{{c}}) and 9/7 (error +1.28{{c}}), thus can be used for the close 5:7:9 in the two Locrian-like modes 1|7 and 0|8 | ||
* 52edo semiquartal has close 22/19 (error +0. | * 52edo semiquartal has close 22/19 (error +0.04{{c}}) | ||
* 19edo semiquartal has close 6/5 (error +0. | * 19edo semiquartal has close 6/5 (error +0.15{{c}}) and 28/27 (error +0.20{{c}}) | ||
However, for the more complex intervals such as 22/19 and 28/27, you might want to use the exact eigentuning for the full effect, unless you specifically need an edo for modulatory purposes. | However, for the more complex intervals such as 22/19 and 28/27, you might want to use the exact eigentuning for the full effect, unless you specifically need an edo for modulatory purposes. | ||
| Line 85: | Line 68: | ||
One important sub-range is given by stipulating that two semifourth generators must make a ''meantone'' fourth; i.e. that four fifths should approximate a [[5/4]] major third. This can be considered the [[19edo]] (4\19)-to-[[24edo]] (5\24) range, i.e. parahard semiquartal, which also contains [[43edo]] (9\43) and [[62edo]] (13\62). Parahard semiquartal can be given an RTT interpretation known as [[godzilla]]. | One important sub-range is given by stipulating that two semifourth generators must make a ''meantone'' fourth; i.e. that four fifths should approximate a [[5/4]] major third. This can be considered the [[19edo]] (4\19)-to-[[24edo]] (5\24) range, i.e. parahard semiquartal, which also contains [[43edo]] (9\43) and [[62edo]] (13\62). Parahard semiquartal can be given an RTT interpretation known as [[godzilla]]. | ||
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. | 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" | {| class="wikitable right-2 right-3 right-4 right-5" | ||
|- | |- | ||
| Line 98: | Line 81: | ||
| 6\29, 248.28 | | 6\29, 248.28 | ||
|- | |- | ||
| L ({{nowrap|octave | | L ({{nowrap|octave − 4g}}) | ||
| 189.47 | | 189.47 | ||
| 200.00 | | 200.00 | ||
| 206.90 | | 206.90 | ||
|- | |- | ||
| s ({{nowrap|5g | | s ({{nowrap|5g − octave}}) | ||
| 63.16 | | 63.16 | ||
| 50.00 | | 50.00 | ||
| Line 110: | Line 93: | ||
=== Soft-of-basic === | === Soft-of-basic === | ||
Soft-of-basic tunings have semifourths that are between 3\14 | Soft-of-basic tunings have semifourths that are between 3\14 (257.14{{c}}) and 2\9 (266.67{{c}}), creating a "[[mavila]]" or "[[superdiatonic]]" 4th. [[23edo]]'s 5\23 (260.87{{c}}) is an example of this generator. | ||
The sizes of the generator, large step and small step of 5L 4s are as follows in various soft-of-basic tunings. | The sizes of the generator, large step and small step of 5L 4s are as follows in various soft-of-basic tunings. | ||
{| class="wikitable right-2 right-3 right-4 right-5" | {| class="wikitable right-2 right-3 right-4 right-5" | ||
|- | |- | ||
| Line 125: | Line 108: | ||
| 8\37, 259.46 | | 8\37, 259.46 | ||
|- | |- | ||
| L ({{nowrap|octave | | L ({{nowrap|octave − 4g}}) | ||
| 156.52 | | 156.52 | ||
| 150.00 | | 150.00 | ||
| 162.16 | | 162.16 | ||
|- | |- | ||
| s ({{nowrap|5g | | s ({{nowrap|5g − octave}}) | ||
| 104.35 | | 104.35 | ||
| 112.50 | | 112.50 | ||
| 97.30 | | 97.30 | ||
|} | |} | ||
=== Tuning examples === | === Tuning examples === | ||
An example in the Diasem Lydian mode LSLSLMLSLM with M and S equated. ([[:File:Diasem Lydian Example Score.pdf|score]]) | An example in the Diasem Lydian mode LSLSLMLSLM with M and S equated. ([[:File:Diasem Lydian Example Score.pdf|score]]) | ||
| Line 149: | Line 133: | ||
== Scale tree == | == Scale tree == | ||
{{ | {{MOS tuning spectrum | ||
| | | 5/4 = Septimin | ||
| 4/3 = Beep | |||
4/3 | | 3/2 = Bug | ||
3/2 | | 13/8 = Golden bug | ||
13/8 | | 13/5 = Golden semaphore | ||
13/5 | | 3/1 = Godzilla | ||
3/1 | | 11/3 = Semaphore | ||
11/3 | }} | ||
== Gallery == | == Gallery == | ||
| Line 170: | Line 154: | ||
; [[Frédéric Gagné]] | ; [[Frédéric Gagné]] | ||
* ''Whalectric'' (2022) | * ''Whalectric'' (2022) – [https://youtu.be/_E6qvbJWYY8 YouTube] | [https://musescore.com/fredg999/whalectric score] – In [[51edo]], 4|4 mode | ||
; [[Inthar]] | ; [[Inthar]] | ||
* [[:File:Dream EP 14edo Sketch.mp3|''Dream EP 14edo Sketch'']] (2021) | * [[: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) | * [[:File:19edo Semaphore Fugue.mp3|''19edo Semaphore Fugue'']] (2021) – An unfinished fugue in [[19edo]], in the 212121221 mode | ||
; [[Starshine]] | ; [[Starshine]] | ||
* [https://soundcloud.com/starshine99/rins-ufo-ride ''Rin's UFO Ride''] (2020) | * [https://soundcloud.com/starshine99/rins-ufo-ride ''Rin's UFO Ride''] (2020) – Semaphore[9] in [[19edo]] | ||
; [[Sevish]] | ; [[Sevish]] | ||
* [http://www.youtube.com/watch?v=Gcgawrr2xao ''Desert Island Rain''] | * [http://www.youtube.com/watch?v=Gcgawrr2xao ''Desert Island Rain''] – Semaphore[9] in [[313edo]] using 65\313 as the generator | ||
[[Category:Semiquartal| ]] <!-- Main article --> | [[Category:Semiquartal| ]] <!-- Main article --> | ||