5L 4s: Difference between revisions

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{{MOS intro}}
{{MOS intro}}
5L 4s tunings can be divided into two major ranges:
# [[hard]]-of-[[basic]] 5L 4s, generated by semifourths flatter than 3\14 (257.14¢). This implies a diatonic fifth.
#: The generator could be viewed as a 15/13, and the resulting "ultramajor" chords and "inframinor" triads could be viewed as approximating 10:13:15 and 26:30:39. See [[Arto and Tendo Theory]].
# [[soft]]-of-basic 5L 4s, generated by semifourths sharper than 3\14 (257.14¢). This implies a "[[mavila]]" or [[superdiatonic]] fifth.


It is also equal to a degenerate form of [[diasem]].
It is also equal to a degenerate form of [[diasem]].
Line 12: Line 8:
The [[TAMNAMS]] convention, used by this article, uses '''semiquartal''' (derived from 'half a fourth') for the 5L 4s pattern. Another attested name is '''hemifourths'''.
The [[TAMNAMS]] convention, used by this article, uses '''semiquartal''' (derived from 'half a fourth') for the 5L 4s pattern. Another attested name is '''hemifourths'''.


== Notation ==
== Scale properties ==
This article uses the convention JKLMNOPQR = LsLsLsLsL. The accidentals & and @ are used for raising and lowering by the chroma = L − s, respectively.
{{TAMNAMS use}}


== Temperaments ==
=== Intervals ===
The familiar harmonic entropy minimum with this MOS pattern is [[godzilla]], in which a generator is [[8/7]] or [[7/6]] (tempered to be the same interval) so two of them make a [[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.  
{{MOS intervals}}
 
=== Modes ===
{{MOS mode degrees}}
====Proposed Names====
Inthar and cellularAutomaton have named 5L 4s modes after scientific names of various corvids.
{| class="wikitable"
|-
! style="text-align:center;" |Mode
! style="text-align:center;" |[[Modal UDP Notation|UDP]]
! style="text-align:center;" |[[User:Inthar|Inthar]]'s names as of 5/2/23
! style="text-align:center;" |Origin
|-
| |LLsLsLsLs
| style="text-align:center;" |<nowiki>8|0</nowiki>|| Cristatan || Bluejay (''Cyanocitta cristata'')
|-
| |LsLLsLsLs
| style="text-align:center;" |<nowiki>7|1</nowiki>|| Pican || Magpie (''Pica pica'')
|-
| |LsLsLLsLs
| style="text-align:center;" |<nowiki>6|2</nowiki>|| Stellerian || Steller's jay (''Cyanocitta stelleri'')
|-
| |LsLsLsLLs
| style="text-align:center;" |<nowiki>5|3</nowiki>|| Podocian || Ground jay (genus ''Podoces'')
|-
| |LsLsLsLsL
| style="text-align:center;" |<nowiki>4|4</nowiki>|| Nucifragan || Nutcracker (genus ''Nucifraga'')
|-
| |sLLsLsLsL
| style="text-align:center;" |<nowiki>3|5</nowiki>|| Coracian || Common raven (''Corvus corax'')
|-
| |sLsLLsLsL
| style="text-align:center;" |<nowiki>2|6</nowiki>|| Frugilegian || Rook (''Corvus frugilegus'')
|-
| |sLsLsLLsL
| style="text-align:center;" |<nowiki>1|7</nowiki>|| Temnurian || Ratchet-tailed treepie (genus ''Temnurus'')
|-
| |sLsLsLsLL
| style="text-align:center;" |<nowiki>0|8</nowiki>|| Pyrrhian || Chough (genus ''Pyrrhocorax'')
|}
Note that the darkest two modes have no diatonic or [[armotonic]] fifth on the root in nonextreme semiquartal tunings.
 
== 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.  


== Tuning ranges ==
== Tuning ranges ==
=== Hard-of-basic ===
=== Hard-of-basic ===
These tunings satisfy the property that two [[semifourth]] generators make a ''diatonic'' ([[5L 2s]]) fourth, i.e. any tuning where the semifourth is between 1\5 (240¢) and 3\14 (257.14¢).
Hard-of-basic tunings have [[Semifourth|semifourths]] as generators, between 1\5 (240¢) and 3\14 (257.14¢), where two of them create a diatonic 4th. The generator could be viewed as a 15/13, and the resulting "ultramajor" chords and "inframinor" triads could be viewed as approximating 10:13:15 and 26:30:39. 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 (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 (2/1 ≤ L/s ≤ 3/1) tunings.
Line 87: Line 127:


=== Soft-of-basic ===
=== Soft-of-basic ===
These are tunings where two [[semifourth]] generators make a ''superdiatonic'' ([[7L 2s]]) fourth (i.e. 514.29¢ to 533.33¢), i.e. any tuning where the semifourth is between 3\14 (257.14¢) and 2\9 (266.67¢). [[23edo]]'s 5\23 (260.87¢) is an example of this generator.
Soft-of-basic tunings have semifourths that are between 3\14 (257.14¢) and 2\9 (266.67¢), creating a "[[mavila]]" or "[[superdiatonic]]" 4th. [[23edo]]'s 5\23 (260.87¢) 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.
Line 125: Line 165:
[[File:Diasem Lydian Example 33edo semiquartal.mp3]] [[33edo]], [[semihard]] semiquartal
[[File:Diasem Lydian Example 33edo semiquartal.mp3]] [[33edo]], [[semihard]] semiquartal


== Intervals ==
== Scale tree ==
Note: In TAMNAMS, a k-step interval class in semiquartal may be called a "k-step", "k-mosstep", or "k-thonstep". TAMNAMS discourages 1-indexed terms such as "mos(k+1)th" for non-diatonic mosses.
{{Scale tree|Comments=5/4: Septimin;
4/3: Beep;
3/2: Bug;
13/8: Golden bug;
13/5: Golden semiquartal (unnamed temperament interpretation);
3/1: Godzilla;
11/3: Semaphore}}
[[Category:9-tone scales]]
[[Category:Semiquartal| ]]


== Modes ==
== Gallery ==
{{MOS mode degrees}}
[[File:Hemifourths.png|thumb|An alternative diagram with branch depth = 5|alt=|none|507x507px]]
===Proposed Names===
Inthar and cellularAutomaton have named 5L 4s modes after scientific names of various corvids.
{| class="wikitable"
|-
! style="text-align:center;" |Mode
! style="text-align:center;" |[[Modal UDP Notation|UDP]]
! style="text-align:center;" |[[User:Inthar|Inthar]]'s names as of 5/2/23
! style="text-align:center;" |Origin
|-
| |LLsLsLsLs
| style="text-align:center;" |<nowiki>8|0</nowiki> || Cristatan || Bluejay (''Cyanocitta cristata'')
|-
| |LsLLsLsLs
| style="text-align:center;" |<nowiki>7|1</nowiki> || Pican || Magpie (''Pica pica'')
|-
| |LsLsLLsLs
| style="text-align:center;" |<nowiki>6|2</nowiki> || Stellerian || Steller's jay (''Cyanocitta stelleri'')
|-
| |LsLsLsLLs
| style="text-align:center;" |<nowiki>5|3</nowiki> || Podocian || Ground jay (genus ''Podoces'')
|-
| |LsLsLsLsL
| style="text-align:center;" |<nowiki>4|4</nowiki> || Nucifragan || Nutcracker (genus ''Nucifraga'')
|-
| |sLLsLsLsL
| style="text-align:center;" |<nowiki>3|5</nowiki> || Coracian || Common raven (''Corvus corax'')
|-
| |sLsLLsLsL
| style="text-align:center;" |<nowiki>2|6</nowiki> || Frugilegian || Rook (''Corvus frugilegus'')
|-
| |sLsLsLLsL
| style="text-align:center;" |<nowiki>1|7</nowiki> || Temnurian || Ratchet-tailed treepie (genus ''Temnurus'')
|-
| |sLsLsLsLL
| style="text-align:center;" |<nowiki>0|8</nowiki> || Pyrrhian || Chough (genus ''Pyrrhocorax'')
|}
Note that the darkest two modes have no diatonic or [[armotonic]] fifth on the root in nonextreme semiquartal tunings.


== Music ==
== Music ==
* [https://soundcloud.com/starshine99/rins-ufo-ride ''Rin's UFO Ride''] by Starshine, in [[19edo]]
*[https://soundcloud.com/starshine99/rins-ufo-ride ''Rin's UFO Ride''] by Starshine, in [[19edo]]
* [[:File:Dream EP 14edo Sketch.mp3|''Dream EP 14edo Sketch'']] by [[Inthar]], a short swing ditty in [[14edo]], in the 212121221 mode
*[[:File:Dream EP 14edo Sketch.mp3|''Dream EP 14edo Sketch'']] by [[Inthar]], a short swing ditty in [[14edo]], in the 212121221 mode
* [[:File:19edo Semaphore Fugue.mp3|''19edo Semaphore Fugue'']] by [[Inthar]], an unfinished fugue in [[19edo]], in the 212121221 mode
*[[:File:19edo Semaphore Fugue.mp3|''19edo Semaphore Fugue'']] by [[Inthar]], an unfinished fugue in [[19edo]], in the 212121221 mode
* [[:File:qt_mode_chord_prog.mp3|qt mode chord prog.mp3]]
*[[:File:qt_mode_chord_prog.mp3|qt mode chord prog.mp3]]
* [http://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}}<!-- main article -->
 
== Scale tree ==
[[File:Hemifourths.png|thumb|An alternative diagram with branch depth = 5]]
 
{| class="wikitable center-all"
! colspan="6" rowspan="2" | Generator
! colspan="2" | Cents
! rowspan="2" | L
! rowspan="2" | s
! rowspan="2" | L/s
! rowspan="2" | Comments
|-
! Chroma-positive
! Chroma-negative
|-
| 7\9 || || || || || || 933.333 || 266.667 || 1 || 1 || 1.000 ||
|-
| || || || || || 39\50 || 936.000 || 264.000 || 6 || 5 || 1.200 ||
|-
| || || || || 32\41 || || 936.585 || 263.415 || 5 || 4 || 1.250 || Septimin
|-
| || || || || || 57\73 || 936.986 || 263.014 || 9 || 7 || 1.286 ||
|-
| || || || 25\32 || || || 937.500 || 262.500 || 4 || 3 || 1.333 || Beep
|-
| || || || || || 68\87 || 937.931 || 262.069 || 11 || 8 || 1.375 ||
|-
| || || || || 43\55 || || 938.182 || 261.818 || 7 || 5 || 1.400 ||
|-
| || || || || || 61\78 || 938.462 || 261.538 || 10 || 7 || 1.428 ||
|-
| || || 18\23 || || || || 939.130 || 260.870 || 3 || 2 || 1.500 || L/s = 3/2, bug
|-
| || || || || || 65\83 || 939.759 || 260.241 || 11 || 7 || 1.571 ||
|-
| || || || || 47\60 || || 940.000 || 260.000 || 8 || 5 || 1.600 ||
|-
| || || || || || 76\97 || 940.206 || 259.794 || 13 || 8 || 1.625 || Golden bug
|-
| || || || 29\37 || || || 940.541 || 259.459 || 5 || 3 || 1.667 ||
|-
| || || || || || 69\88 || 940.909 || 259.091 || 12 || 7 || 1.714 ||
|-
| || || || || 40\51 || || 941.176 || 258.824 || 7 || 4 || 1.750 ||
|-
| || || || || || 51\65 || 941.538 || 258.462 || 9 || 5 || 1.800 ||
|-
| || 11\14 || || || || || 942.857 || 257.143 || 2 || 1 || 2.000 || Basic semiquartal<br>(Generators smaller than this are proper)
|-
| || || || || || 48\61 || 944.262 || 255.738 || 9 || 4 || 2.250 ||
|-
| || || || || 37\47 || || 944.681 || 255.319 || 7 || 3 || 2.333 ||
|-
| || || || || || 63\80 || 945.000 || 255.000 || 12 || 5 || 2.400 ||
|-
| || || || 26\33 || || || 945.455 || 254.545 || 5 || 2 || 2.500 ||
|-
| || || || || || 67\85 || 945.882 || 254.118 || 13 || 5 || 2.600 || Unnamed golden tuning
|-
| || || || || 41\52 || || 946.154 || 253.846 || 8 || 3 || 2.667 ||
|-
| || || || || || 56\71 || 946.479 || 253.521 || 11 || 4 || 2.750 ||
|-
| || || 15\19 || || || || 947.368 || 252.632 || 3 || 1 || 3.000 || L/s = 3/1, godzilla
|-
| || || || || || 49\62 || 948.387 || 251.613 || 10 || 3 || 3.333 ||
|-
| || || || || 34\43 || || 948.837 || 251.163 || 7 || 2 || 3.500 ||
|-
| || || || || || 53\67 || 949.254 || 250.746 || 11 || 3 || 3.667 || Semaphore
|-
| || || || 19\24 || || || 950.000 || 250.000 || 4 || 1 || 4.000 ||
|-
| || || || || || 42\53 || 950.943 || 249.057 || 9 || 2 || 4.500 ||
|-
| || || || || 23\29 || || 951.724 || 248.276 || 5 || 1 || 5.000 ||
|-
| || || || || || 27\34 || 952.941 || 247.059 || 6 || 1 || 6.000 ||
|-
| 4\5 || || || || || || 960.000 || 240.000 || 1 || 0 || → inf ||
|}
 
[[Category:9-tone scales]]
[[Category:Semiquartal| ]] <!-- main article -->

Revision as of 11:12, 29 July 2024

↖ 4L 3s ↑ 5L 3s 6L 3s ↗
← 4L 4s 5L 4s 6L 4s →
↙ 4L 5s ↓ 5L 5s 6L 5s ↘ 
┌╥╥┬╥┬╥┬╥┬┐
│║║│║│║│║││
│││││││││││
└┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLsLsLsLs
sLsLsLsLL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 7\9 to 4\5 (933.3 ¢ to 960.0 ¢)
Dark 1\5 to 2\9 (240.0 ¢ to 266.7 ¢)
TAMNAMS information
Name semiquartal
Prefix cthon-
Abbrev. ct
Related MOS scales
Parent 4L 1s
Sister 4L 5s
Daughters 9L 5s, 5L 9s
Neutralized 1L 8s
2-Flought 14L 4s, 5L 13s
Equal tunings
Equalized (L:s = 1:1) 7\9 (933.3 ¢)
Supersoft (L:s = 4:3) 25\32 (937.5 ¢)
Soft (L:s = 3:2) 18\23 (939.1 ¢)
Semisoft (L:s = 5:3) 29\37 (940.5 ¢)
Basic (L:s = 2:1) 11\14 (942.9 ¢)
Semihard (L:s = 5:2) 26\33 (945.5 ¢)
Hard (L:s = 3:1) 15\19 (947.4 ¢)
Superhard (L:s = 4:1) 19\24 (950.0 ¢)
Collapsed (L:s = 1:0) 4\5 (960.0 ¢)

5L 4s, named semiquartal in TAMNAMS, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 5 large steps and 4 small steps, repeating every octave. Generators that produce this scale range from 933.3 ¢ to 960 ¢, or from 240 ¢ to 266.7 ¢.

It is also equal to a degenerate form of diasem.

Names

The TAMNAMS convention, used by this article, uses semiquartal (derived from 'half a fourth') for the 5L 4s pattern. Another attested name is hemifourths.

Scale properties

This article uses TAMNAMS conventions for the names of this scale's intervals and scale degrees. The use of 1-indexed ordinal names is reserved for interval regions.

Intervals

Intervals of 5L 4s
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-cthonstep Perfect 0-cthonstep P0cts 0 0.0 ¢
1-cthonstep Minor 1-cthonstep m1cts s 0.0 ¢ to 133.3 ¢
Major 1-cthonstep M1cts L 133.3 ¢ to 240.0 ¢
2-cthonstep Perfect 2-cthonstep P2cts L + s 240.0 ¢ to 266.7 ¢
Augmented 2-cthonstep A2cts 2L 266.7 ¢ to 480.0 ¢
3-cthonstep Minor 3-cthonstep m3cts L + 2s 240.0 ¢ to 400.0 ¢
Major 3-cthonstep M3cts 2L + s 400.0 ¢ to 480.0 ¢
4-cthonstep Minor 4-cthonstep m4cts 2L + 2s 480.0 ¢ to 533.3 ¢
Major 4-cthonstep M4cts 3L + s 533.3 ¢ to 720.0 ¢
5-cthonstep Minor 5-cthonstep m5cts 2L + 3s 480.0 ¢ to 666.7 ¢
Major 5-cthonstep M5cts 3L + 2s 666.7 ¢ to 720.0 ¢
6-cthonstep Minor 6-cthonstep m6cts 3L + 3s 720.0 ¢ to 800.0 ¢
Major 6-cthonstep M6cts 4L + 2s 800.0 ¢ to 960.0 ¢
7-cthonstep Diminished 7-cthonstep d7cts 3L + 4s 720.0 ¢ to 933.3 ¢
Perfect 7-cthonstep P7cts 4L + 3s 933.3 ¢ to 960.0 ¢
8-cthonstep Minor 8-cthonstep m8cts 4L + 4s 960.0 ¢ to 1066.7 ¢
Major 8-cthonstep M8cts 5L + 3s 1066.7 ¢ to 1200.0 ¢
9-cthonstep Perfect 9-cthonstep P9cts 5L + 4s 1200.0 ¢

Modes

Scale degrees of the modes of 5L 4s
UDP Cyclic
order 		Step
pattern 		Scale degree (cthondegree)
0 1 2 3 4 5 6 7 8 9
8|0 1 LLsLsLsLs Perf. Maj. Aug. Maj. Maj. Maj. Maj. Perf. Maj. Perf.
7|1 8 LsLLsLsLs Perf. Maj. Perf. Maj. Maj. Maj. Maj. Perf. Maj. Perf.
6|2 6 LsLsLLsLs Perf. Maj. Perf. Maj. Min. Maj. Maj. Perf. Maj. Perf.
5|3 4 LsLsLsLLs Perf. Maj. Perf. Maj. Min. Maj. Min. Perf. Maj. Perf.
4|4 2 LsLsLsLsL Perf. Maj. Perf. Maj. Min. Maj. Min. Perf. Min. Perf.
3|5 9 sLLsLsLsL Perf. Min. Perf. Maj. Min. Maj. Min. Perf. Min. Perf.
2|6 7 sLsLLsLsL Perf. Min. Perf. Min. Min. Maj. Min. Perf. Min. Perf.
1|7 5 sLsLsLLsL Perf. Min. Perf. Min. Min. Min. Min. Perf. Min. Perf.
0|8 3 sLsLsLsLL Perf. Min. Perf. Min. Min. Min. Min. Dim. Min. Perf.

Proposed Names

Inthar and cellularAutomaton have named 5L 4s modes after scientific names of various corvids.

Mode UDP Inthar's names as of 5/2/23 Origin
LLsLsLsLs 8|0 Cristatan Bluejay (Cyanocitta cristata)
LsLLsLsLs 7|1 Pican Magpie (Pica pica)
LsLsLLsLs 6|2 Stellerian Steller's jay (Cyanocitta stelleri)
LsLsLsLLs 5|3 Podocian Ground jay (genus Podoces)
LsLsLsLsL 4|4 Nucifragan Nutcracker (genus Nucifraga)
sLLsLsLsL 3|5 Coracian Common raven (Corvus corax)
sLsLLsLsL 2|6 Frugilegian Rook (Corvus frugilegus)
sLsLsLLsL 1|7 Temnurian Ratchet-tailed treepie (genus Temnurus)
sLsLsLsLL 0|8 Pyrrhian Chough (genus Pyrrhocorax)

Note that the darkest two modes have no diatonic or armotonic fifth on the root in nonextreme semiquartal tunings.

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.

Tuning ranges

Hard-of-basic

Hard-of-basic tunings have semifourths as generators, between 1\5 (240¢) and 3\14 (257.14¢), where two of them create a diatonic 4th. The generator could be viewed as a 15/13, and the resulting "ultramajor" chords and "inframinor" triads could be viewed as approximating 10:13:15 and 26:30:39. See Arto and Tendo Theory.

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.

14edo (L/s = 2/1) 47edo (L/s = 7/3) 33edo (L/s = 5/2) 52edo (L/s = 8/3) 19edo (L/s = 3/1)
generator (g) 3\14, 257.14 10\47, 255.32 7\33, 254.54 11\52, 253.85 4\19, 252.63
L (octave - 4g) 171.43 178.72 181.81 184.62 189.47
s (5g - octave) 85.71 76.60 72.73 69.23 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
  • 52edo semiquartal has close 22/19 (error +0.04¢)
  • 19edo semiquartal has close 6/5 (error +0.15¢) and 28/27 (error +0.20¢)

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.

Parahard and ultrahard

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 (2/1 ≤ L/s ≤ 3/1) tunings.

19edo 24edo 29edo
generator (g) 4\19, 252.63 5\24, 250.00 6\29, 248.28
L (octave - 4g) 189.47 200.00 206.90
s (5g - octave) 63.16 50.00 41.38

Soft-of-basic

Soft-of-basic tunings have semifourths that are between 3\14 (257.14¢) and 2\9 (266.67¢), creating a "mavila" or "superdiatonic" 4th. 23edo's 5\23 (260.87¢) 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.

23edo 32edo 37edo
generator (g) 5\23, 260.87 7\32, 262.50 8\37, 259.46
L (octave - 4g) 156.52 150.00 162.16
s (5g - octave) 104.35 112.50 97.30

Tuning examples

An example in the Diasem Lydian mode LSLSLMLSLM with M and S equated. (score)

14edo, basic semiquartal

19edo, hard semiquartal

23edo, soft semiquartal

24edo, superhard semiquartal

33edo, semihard semiquartal

Scale tree

Template:Scale tree

Gallery

An alternative diagram with branch depth = 5

Music

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