5edo: Difference between revisions

Revision as of 10:27, 11 October 2018

5-edo divides the 1200-cent octave into 5 equal parts, making its smallest interval exactly 240 cents, or the fifth root of two.

5 Equal Divisions of the Octave: Theory

5-edo is the 3rd prime edo, after 2edo and 3edo. Most importantly, 5-edo is the smallest edo containing xenharmonic intervals! (1edo 2edo 3edo 4edo are all subsets of 12edo.)

There is a lot of near-equipentatonic world music, just google "gyil" or "amadinda" or "slendro".

Listen to the sound of the 5-edo scale

For any musician, there is no substitute for the experience of a particular xenharmonic sound. The user going by the name Hyacinth on Wikipedia and Wikimedia Commons has many xenharmonic MIDI's and has graciously copylefted them! This is his 5-edo scale MIDI:

http://commons.wikimedia.org/wiki/File:5-tet_scale_on_C.mid

Intervals in 5-edo

degrees	size in cents	Closest diatonic interval name	The "neighborhood" of just intervals
0	0	unison / prime	exactly 1/1
1	240	second, third	+8.826¢ from septimal second 8/7 -4.969¢ from diminished third 144/125 -13.076¢ from augmented second 125/108 -26.871¢ from septimal minor third 7/6
2	480	fourth	+9.219¢ from narrow fourth 21/16 -0.686¢ from smaller fourth 33/25 -18.045¢ from just fourth 4/3
3	720	fifth	+18.045¢ from just fifth 3/2 +0.686¢ from bigger fifth 50/33 -9.219¢ from wide fifth 32/21
4	960	sixth, seventh	26.871¢ from septimal major sixth 12/7 13.076¢ from diminished seventh 216/125 4.969¢ from augmented sixth 125/72 -8.826¢ from septimal seventh 7/4
5	1200	octave / eighth	exactly 2/1

5ed2-001.svg

Related scales

By its cardinality, 5-edo is related to other pentatonic scales, and it is especially close in sound to many Indonesian slendros.
Due to the interest around the "fifth" interval size, there are many nonoctave "stretch sisters" to 5-edo: square root of 4/3, cube root of 3/2, 8th root of 3, etc.
For the same reason there are many "circle sisters":
- Make a chain of five "bigger fifths" (50/33), which makes three octaves 3.227¢ flat. (50/33)^5=7.985099.

As a temperament

If 5-edo is regarded as a temperament, which is to say as 5-et, then the most salient fact is that 16/15 is tempered out. This means in 5-et the major third and the fourth, and the minor sixth and the fifth, are not distinguished; this is 5-limit father temperament.

Also tempered out is 27/25, if we temper this out in preference to 16/15 we obtain bug temperament, which equates 10/9 with 6/5: it is a little more perverse even than father. Because these intervals are so large, this sort of analysis is less significant with 5 than it becomes with larger and more accurate divisions, but it still plays a role. For example, I-IV-V-I is the same as I-III-V-I and involves triads with common intervals because of fourth-thirds equivalence.

Despite its lack of accuracy, 5EDO is the second zeta integral edo, after 2EDO. It also is the smallest equal division representing the 9-limit consistently, giving a distinct value modulo five to 2, 3, 5, 7 and 9. Hence in a way similar to how 4edo can be used, and which is discussed in that article, it can be used to represent 7-limit intervals in terms of their position in a pentad, by giving a triple of integers representing a pentad in the lattice of tetrads/pentads together with the number of scale steps in 5EDO. However, while 2edo represents the 3-limit consistently, 3edo the 5-limit, 4edo the 7-limit and 5edo the 9-limit, to represent the 11-limit consistently with a patent val requires going all the way to 22edo.

Cycles, Divisions

5 is a prime number so 5-edo contains no sub-edos. Only simple cycles:

Cycle of seconds: 0-1-2-3-4-0
Cycle of fourths: 0-2-4-1-3-0
Cycle of fifths: 0-3-1-4-2-0
Cycle of sevenths: 0-4-3-2-1-0

5-edo in Musicmaking

Compositions, Improvisations

Herman Miller: Daybreak on Slendro Mountain (2000)
Aaron K. Johnson: 5tet funk (2004)
Andrew Heathwaite: //Pinta Penta// (2004) play (rendered in 6 alternative pentatonics as well)
Hans Straub: Asîmchômsaia play
Brian Wong: Slendronica#1b play
Brian McLaren: various and sundry
Paul Rubenstein: various, with electric guitars in 10- and 15-edo
X.J.Scott: Sleeping Through It All (2004)
Bill Sethares: 5-tet funk (2004), Pentacle (2004)
"Cenobyte" Ukulele http://www.youtube.com/watch?v=UKUCRnEJKKU
"True Island" (album) by Small Scale Revolution (2011)
Ralph Jarzombek: Micro12

There is a lot of 5edo world music, search for "gyil" or "amadinda" or "slendro".

Ear Training

5edo ear-training exercises by Alex Ness available here.

Notation

via Reinhard's cents notation
naturals on a five-line staff, with enharmonics (used interchangably) E=F and B=C
a four-line hybrid treble/bass staff.

Harmony

5edo does not have any strong consonance nor dissonance. The 240 cent interval can serve as either a major second or minor third, and the 960 cent interval as either a major sixth or minor seventh. The fourth is about 18 cents flat of a just fourth, making it rather "dirty" but recognizable. The fifth is likewise about 18 cents sharp of a just fifth, dissonant but still easily recognizable.

In contrast to other EDOs, all of the notes can be used at once in order to get a functioning scale. (As in Blackwood in 10-EDO).

Important chords:

0+1+3
0+2+3
0+1+3+4
0+2+3+4

Melody

Smallest EDO that can be used for melodies in a "standard" way. The relatively large step of 240 cents can be used as major second for the melody construction. The scale has whole-tone as well as pentatonic character.

Chord or scale?

Either way, it is hard to wander very far from where you start. However, it has the scale-like feature that there are (barely) enough notes to create melody, in the form of an equal version of pentatonic.

Commas Tempered

5-EDO tempers out the following commas. (Note: This assumes the val < 5 8 12 14 17 19 |.)

Comma	Value (cents)	Name	Second Name	Third Name	Monzo
256/243	90.225	Limma	Pythagorean Minor 2nd		[8 -5⟩
81/80	21.506	Syntonic Comma	Didymos Comma	Meantone Comma	[-4 4 -1⟩
2889416/2882415	4.200	Vulture			[24 -21 4⟩
36/35	48.770	Septimal Quarter Tone			[2 2 -1 -1⟩
49/48	35.697	Slendro Diesis			[-4 -1 0 2⟩
64/63	27.264	Septimal Comma	Archytas' Comma	Leipziger Komma	[6 -2 0 -1⟩
245/243	14.191	Sensamagic			[0 -5 1 2⟩
1728/1715	13.074	Orwellisma	Orwell Comma		[6 3 -1 -3⟩
1029/1024	8.433	Gamelisma			[-10 1 0 3⟩
19683/19600	7.316	Cataharry			[-4 9 -2 -2⟩
5120/5103	5.758	Hemifamity			[10 -6 1 -1⟩
1065875/1063543	3.792	Wadisma			[-26 -1 1 9⟩
420175/419904	1.117	Wizma			[-6 -8 2 5⟩
99/98	17.576	Mothwellsma			[-1 2 0 -2 1⟩
896/891	9.688	Pentacircle			[7 -4 0 1 -1⟩
385/384	4.503	Keenanisma			[-7 -1 1 1 1⟩
441/440	3.930	Werckisma			[-3 2 -1 2 -1⟩
3025/3024	0.572	Lehmerisma			[-4 -3 2 -1 2⟩
91/90	19.130	Superleap			[-1 -2 -1 1 0 1⟩
676/675	2.563	Parizeksma			[2 -3 -2 0 0 2⟩
16/15	111.731	Diatonic semitone			[4 -1 -1⟩
14/13	128.298				[1 0 0 1 0 -1⟩
27/25	133.238	Large diatonic semit.			[0 3 -2⟩
11/10	165.004	Large neutral second			[-1 0 -1 0 1⟩

5edo: Difference between revisions

Revision as of 10:27, 11 October 2018

Contents

5 Equal Divisions of the Octave: Theory

Listen to the sound of the 5-edo scale

Intervals in 5-edo

Related scales

As a temperament

Cycles, Divisions

5-edo in Musicmaking

Compositions, Improvisations

Ear Training

Notation

Harmony

Melody

Chord or scale?

Commas Tempered

Navigation menu

@@ Line 3: / Line 3: @@
 -----
-=5 Equal Divisions of the Octave: Theory=
+'''5-edo''' divides the 1200-[[cent]] octave into 5 equal parts, making its smallest interval exactly 240 [[cent|cents]], or the fifth root of two.
-==="Equal Pentatonic"===
+== 5 Equal Divisions of the Octave: Theory ==
--edo divides the 1200-[[cent|cent]] octave into 5 equal parts, making its smallest interval exactly 240 [[cent|cents]], or the fifth root of two. 5-edo is the 3rd [[prime_numbers|prime]] edo, after [[2edo|2edo]] and [[3edo|3edo]]. Most importantly, 5-edo is the smallest [[EDO|edo]] containing xenharmonic intervals! (1edo 2edo 3edo 4edo are all subsets of 12edo.)
+-edo is the 3rd [[prime numbers|prime]] edo, after [[2edo]] and [[3edo]]. Most importantly, 5-edo is the smallest [[EDO|edo]] containing xenharmonic intervals! (1edo 2edo 3edo 4edo are all subsets of 12edo.)
 There is a lot of near-equipentatonic world music, just google "gyil" or "amadinda" or "slendro".
-==Listen to the sound of the 5-edo scale==
+=== Listen to the sound of the 5-edo scale ===
 For any musician, there is no substitute for the experience of a particular xenharmonic sound. The user going by the name Hyacinth on Wikipedia and Wikimedia Commons has many xenharmonic MIDI's and has graciously copylefted them! This is his 5-edo scale MIDI:
-[http://commons.wikimedia.org/wiki/File:5-tet_scale_on_C.mid http://commons.wikimedia.org/wiki/File:5-tet_scale_on_C.mid]
+* [http://commons.wikimedia.org/wiki/File:5-tet_scale_on_C.mid http://commons.wikimedia.org/wiki/File:5-tet_scale_on_C.mid]
-==Intervals in 5-edo==
+=== Intervals in 5-edo ===
 {| class="wikitable"
 |-
-! | degrees
+! degrees
-! | size
+! size <br/> in [[cent|cents]]
+! Closest diatonic <br/> interval name
-in [[cent|cents]]
+! The "neighborhood" of just intervals
-! | Closest diatonic
-interval name
-! | The "neighborhood" of just intervals
 |-
 | style="text-align:center;" | 0
 | style="text-align:center;" | 0
 | style="text-align:center;" | unison / prime
-| | exactly 1/1
+| exactly 1/1
 |-
 | style="text-align:center;" | 1
 | style="text-align:center;" | 240
 | style="text-align:center;" | second, third
-| | +8.826¢ from septimal second [[8/7|8/7]]
+| +8.826¢ from septimal second [[8/7|8/7]]
 -4.969¢ from diminished third [[144/125|144/125]]
@@ Line 49: / Line 45: @@
 | style="text-align:center;" | 480
 | style="text-align:center;" | fourth
-| | +9.219¢ from narrow fourth [[21/16|21/16]]
+| +9.219¢ from narrow fourth [[21/16|21/16]]
 -0.686¢ from smaller fourth [[33/25|33/25]]
@@ Line 58: / Line 54: @@
 | style="text-align:center;" | 720
 | style="text-align:center;" | fifth
-| | +18.045¢ from just fifth [[3/2|3/2]]
+| +18.045¢ from just fifth [[3/2|3/2]]
 +0.686¢ from bigger fifth [[50/33|50/33]]
@@ Line 67: / Line 63: @@
 | style="text-align:center;" | 960
 | style="text-align:center;" | sixth, seventh
-| | 26.871¢ from septimal major sixth [[12/7|12/7]]
+| 26.871¢ from septimal major sixth [[12/7|12/7]]
 .076¢ from diminished seventh 216/125
@@ Line 78: / Line 74: @@
 | style="text-align:center;" | 1200
 | style="text-align:center;" | octave / eighth
-| | exactly 2/1
+| exactly 2/1
 |}
@@ Line 85: / Line 81: @@
 [[:File:5ed2-001.svg|5ed2-001.svg]]
-==Related scales==
+=== Related scales ===
-<ul><li>By its cardinality, 5-edo is related to other [[pentatonic|pentatonic]] scales, and it is especially close in sound to many Indonesian [[slendro|slendros]].</li><li>Due to the interest around the "fifth" interval size, there are many [[nonoctave|nonoctave]] "stretch sisters" to 5-edo: square root of 4/3, cube root of 3/2, 8th root of 3, etc.</li><li>For the same reason there are many "circle sisters":<ul><li>Make a chain of five "bigger fifths" (50/33), which makes three octaves 3.227¢ flat. (50/33)^5=7.985099.</li></ul></li></ul>
+* By its cardinality, 5-edo is related to other [[pentatonic]] scales, and it is especially close in sound to many Indonesian [[slendro|slendros]].
+* Due to the interest around the "fifth" interval size, there are many [[nonoctave|nonoctave]] "stretch sisters" to 5-edo: square root of 4/3, cube root of 3/2, 8th root of 3, etc.
+* For the same reason there are many "circle sisters":
+** Make a chain of five "bigger fifths" (50/33), which makes three octaves 3.227¢ flat. (50/33)^5=7.985099.
-==As a temperament==
-If 5-edo is regarded as a temperament, which is to say as 5-et, then the most salient fact is that 16/15 is tempered out. This means in 5-et the major third and the fourth, and the minor sixth and the fifth, are not distinguished; this is 5-limit [[Trienstonic_clan|father temperament]].
-Also tempered out is 27/25, if we temper this out in preference to 16/15 we obtain [[Bug_family|bug temperament]], which equates 10/9 with 6/5: it is a little more perverse even than father. Because these intervals are so large, this sort of analysis is less significant with 5 than it becomes with larger and more accurate divisions, but it still plays a role. For example, I-IV-V-I is the same as I-III-V-I and involves triads with common intervals because of fourth-thirds equivalence.
+=== As a temperament ===
+If 5-edo is regarded as a temperament, which is to say as 5-et, then the most salient fact is that 16/15 is tempered out. This means in 5-et the major third and the fourth, and the minor sixth and the fifth, are not distinguished; this is 5-limit [[Trienstonic clan|father temperament]].
-Despite its lack of accuracy, 5EDO is the second [[The_Riemann_Zeta_Function_and_Tuning#Zeta EDO lists|zeta integral edo]], after 2EDO. It also is the smallest equal division representing the [[9-limit|9-limit]] [[consistent|consistent]]ly, giving a distinct value modulo five to 2, 3, 5, 7 and 9. Hence in a way similar to how [[4edo|4edo]] can be used, and which is discussed in that article, it can be used to represent [[7-limit|7-limit]] intervals in terms of their position in a pentad, by giving a triple of integers representing a pentad in the [[The_Seven_Limit_Symmetrical_Lattices|lattice]] of tetrads/pentads together with the number of scale steps in 5EDO. However, while [[2edo|2edo]] represents the [[3-limit|3-limit]] consistently, [[3edo|3edo]] the [[5-limit|5-limit]], [[4edo|4edo]] the [[7-limit|7-limit]] and [[5edo|5edo]] the [[9-limit|9-limit]], to represent the [[11-limit|11-limit]] consistently with a [[Patent_val|patent val]] requires going all the way to [[22edo|22edo]].
+Also tempered out is 27/25, if we temper this out in preference to 16/15 we obtain [[Bug family|bug temperament]], which equates 10/9 with 6/5: it is a little more perverse even than father. Because these intervals are so large, this sort of analysis is less significant with 5 than it becomes with larger and more accurate divisions, but it still plays a role. For example, I-IV-V-I is the same as I-III-V-I and involves triads with common intervals because of fourth-thirds equivalence.
-==Cycles, Divisions==
+Despite its lack of accuracy, 5EDO is the second [[The Riemann Zeta Function and Tuning#Zeta EDO lists|zeta integral edo]], after 2EDO. It also is the smallest equal division representing the [[9-limit]] [[consistent|consistently]], giving a distinct value modulo five to 2, 3, 5, 7 and 9. Hence in a way similar to how [[4edo]] can be used, and which is discussed in that article, it can be used to represent [[7-limit]] intervals in terms of their position in a pentad, by giving a triple of integers representing a pentad in the [[The_Seven_Limit_Symmetrical_Lattices|lattice]] of tetrads/pentads together with the number of scale steps in 5EDO. However, while [[2edo]] represents the [[3-limit]] consistently, [[3edo]] the [[5-limit]], [[4edo]] the [[7-limit]] and 5edo the [[9-limit]], to represent the [[11-limit]] consistently with a [[patent val]] requires going all the way to [[22edo]].
+=== Cycles, Divisions ===
 is a prime number so 5-edo contains no sub-edos. Only simple cycles:
-Cycle of seconds: 0-1-2-3-4-0
+* Cycle of seconds: 0-1-2-3-4-0
+* Cycle of fourths: 0-2-4-1-3-0
+* Cycle of fifths: 0-3-1-4-2-0
+* Cycle of sevenths: 0-4-3-2-1-0
-Cycle of fourths: 0-2-4-1-3-0
+== 5-edo in Musicmaking ==
-Cycle of fifths: 0-3-1-4-2-0
+=== Compositions, Improvisations ===
+* [http://www.io.com/%7Ehmiller/ Herman Miller]: ''[http://micro.soonlabel.com/herman_miller/Daybreak.mp3 Daybreak on Slendro Mountain]'' (2000)
-Cycle of sevenths: 0-4-3-2-1-0
+* Aaron K. Johnson: ''[http://www.akjmusic.com/audio/5tet_funk.mp3 5tet funk]'' (2004)
+* [http://www.soundclick.com/bands/page_songInfo.cfm?bandID=122613&songID=1519939 Andrew Heathwaite: //Pinta Penta// (2004)] [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+pintapentain5tet.mp3 play] (rendered in 6 alternative pentatonics as well)
-=5-edo in Musicmaking=
+* [[Hans_Straub|Hans Straub]]: [http://home.datacomm.ch/straub/mamuth/5tet_e.html#asimchomsaia Asîmchômsaia] [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Straub/asimchomsaia.mp3 play]
+* [[Brian_Wong|Brian Wong]]: [http://bwong.ca/template1.php?sub=3 Slendronica#1b] [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Wong/Slendronica1b.ogg play]
-=='''Compositions''', improvisations==
+* Brian McLaren: various and sundry</li><li>Paul Rubenstein: various, with electric guitars in 10- and 15-edo</li><li>X.J.Scott: ''Sleeping Through It All'' (2004)
-<ul><ul><li>[http://www.io.com/%7Ehmiller/ Herman Miller]: ''[http://micro.soonlabel.com/herman_miller/Daybreak.mp3 Daybreak on Slendro Mountain]'' (2000)</li><li>Aaron K. Johnson: ''[http://www.akjmusic.com/audio/5tet_funk.mp3 5tet funk]'' (2004)</li><li>[http://www.soundclick.com/bands/page_songInfo.cfm?bandID=122613&songID=1519939 Andrew Heathwaite: //Pinta Penta// (2004)] [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+pintapentain5tet.mp3 play] (rendered in 6 alternative pentatonics as well)</li><li>[[Hans_Straub|Hans Straub]]: [http://home.datacomm.ch/straub/mamuth/5tet_e.html#asimchomsaia Asîmchômsaia] [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Straub/asimchomsaia.mp3 play]</li><li>[[Brian_Wong|Brian Wong]]: [http://bwong.ca/template1.php?sub=3 Slendronica#1b] [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Wong/Slendronica1b.ogg play]</li><li>Brian McLaren: various and sundry</li><li>Paul Rubenstein: various, with electric guitars in 10- and 15-edo</li><li>X.J.Scott: ''Sleeping Through It All'' (2004)</li><li>Bill Sethares: ''5-tet funk'' (2004), ''Pentacle'' (2004)</li><li>"Cenobyte" Ukulele [http://www.youtube.com/watch?v=UKUCRnEJKKU  http://www.youtube.com/watch?v=UKUCRnEJKKU]</li><li>"[http://www.jamendo.com/en/list/a104474/true-island-5-equal-divisions-of-the-octave-ukulele True Island]" (album) by Small Scale Revolution (2011)</li><li>Ralph Jarzombek: [http://webzoom.freewebs.com/ralphjarzombek/micro12.mp3 Micro12]</li></ul></ul>
+* Bill Sethares: ''5-tet funk'' (2004), ''Pentacle'' (2004)
+* "Cenobyte" Ukulele [http://www.youtube.com/watch?v=UKUCRnEJKKU  http://www.youtube.com/watch?v=UKUCRnEJKKU]
+* "[http://www.jamendo.com/en/list/a104474/true-island-5-equal-divisions-of-the-octave-ukulele True Island]" (album) by Small Scale Revolution (2011)
+* Ralph Jarzombek: [http://webzoom.freewebs.com/ralphjarzombek/micro12.mp3 Micro12]
 There is a lot of 5edo world music, search for "gyil" or "amadinda" or "slendro".
-==Ear Training==
+=== Ear Training ===
 edo ear-training exercises by Alex Ness available [https://drive.google.com/folderview?id=0BwsXD8q2VCYUT3VEZUVmeVZUcmc&usp=drive_web here].
-==Notation==
+=== Notation ===
-<ul><ul><li>via Reinhard's cents notation</li><li>naturals on a five-line staff, with enharmonics (used interchangably) E=F and B=C</li><li>a four-line hybrid treble/bass staff.</li></ul></ul>
+* via Reinhard's cents notation
+* naturals on a five-line staff, with enharmonics (used interchangably) E=F and B=C
+* a four-line hybrid treble/bass staff.
-==Harmony==
+=== Harmony ===
 edo does not have any strong consonance nor dissonance. The 240 cent interval can serve as either a major second or minor third, and the 960 cent interval as either a major sixth or minor seventh. The fourth is about 18 cents flat of a just fourth, making it rather "dirty" but recognizable. The fifth is likewise about 18 cents sharp of a just fifth, dissonant but still easily recognizable.
-In contrast to other EDOs, all of the notes can be used at once in order to get a functioning scale. (As in Blackwood in 10-EDO).
+In contrast to other EDOs, all of the notes can be used at once in order to get a functioning scale. (As in Blackwood in [[10edo|10-EDO]]).
 Important chords:
+* 0+1+3
+* 0+2+3
+* 0+1+3+4
+* 0+2+3+4
-<ul><li>0+1+3</li><li>0+2+3</li><li>0+1+3+4</li><li>0+2+3+4</li></ul>
+=== Melody ===
-==Melody==
 Smallest EDO that can be used for melodies in a "standard" way. The relatively large step of 240 cents can be used as major second for the melody construction. The scale has whole-tone as well as pentatonic character.
-==Chord or scale?==
+=== Chord or scale? ===
 Either way, it is hard to wander very far from where you start. However, it has the scale-like feature that there are (barely) enough notes to create melody, in the form of an equal version of pentatonic.
-==Commas Tempered==
+=== Commas Tempered ===
 -EDO tempers out the following commas. (Note: This assumes the val &lt; 5 8 12 14 17 19 |.)
 {| class="wikitable"
 |-
-! | Comma
+! [[Comma]]
-! | Value (cents)
+! Value ([[cent]]s)
-! | Name
+! Name
-! | Second Name
+! Second Name
-! | Third Name
+! Third Name
-! | Monzo
+! [[Monzo]]
 |-
 | style="text-align:center;" | 256/243
 | style="text-align:right;" | 90.225
-| | Limma
+| Limma
-| | Pythagorean Minor 2nd
+| Pythagorean Minor 2nd
-| |
+|
-| | | 8 -5 &gt;
+| {{Monzo| 8 -5 }}
 |-
 | style="text-align:center;" | 81/80
 | style="text-align:right;" | 21.506
-| | Syntonic Comma
+| Syntonic Comma
-| | Didymos Comma
+| Didymos Comma
-| | Meantone Comma
+| Meantone Comma
-| | | -4 4 -1 &gt;
+| {{Monzo| -4 4 -1 }}
 |-
 | style="text-align:center;" | 2889416/2882415
 | style="text-align:right;" | 4.200
-| | Vulture
+| Vulture
-| |
+|
-| |
+|
-| | | 24 -21 4 &gt;
+| {{Monzo| 24 -21 4 }}
 |-
 | style="text-align:center;" | 36/35
 | style="text-align:right;" | 48.770
-| | Septimal Quarter Tone
+| Septimal Quarter Tone
-| |
+|
-| |
+|
-| | | 2 2 -1 -1 &gt;
+| {{Monzo| 2 2 -1 -1 }}
 |-
 | style="text-align:center;" | 49/48
 | style="text-align:right;" | 35.697
-| | Slendro Diesis
+| Slendro Diesis
-| |
+|
-| |
+|
-| | | -4 -1 0 2 &gt;
+| {{Monzo| -4 -1 0 2 }}
 |-
 | style="text-align:center;" | 64/63
 | style="text-align:right;" | 27.264
-| | Septimal Comma
+| Septimal Comma
-| | Archytas' Comma
+| Archytas' Comma
-| | Leipziger Komma
+| Leipziger Komma
-| | | 6 -2 0 -1 &gt;
+| {{Monzo| 6 -2 0 -1 }}
 |-
 | style="text-align:center;" | 245/243
 | style="text-align:right;" | 14.191
-| | Sensamagic
+| Sensamagic
-| |
+|
-| |
+|
-| | | 0 -5 1 2 &gt;
+| {{Monzo| 0 -5 1 2 }}
 |-
 | style="text-align:center;" | 1728/1715
 | style="text-align:right;" | 13.074
-| | Orwellisma
+| Orwellisma
-| | Orwell Comma
+| Orwell Comma
-| |
+|
-| | | 6 3 -1 -3 &gt;
+| {{Monzo| 6 3 -1 -3 }}
 |-
 | style="text-align:center;" | 1029/1024
 | style="text-align:right;" | 8.433
-| | Gamelisma
+| Gamelisma
-| |
+|
-| |
+|
-| | | -10 1 0 3 &gt;
+| {{Monzo| -10 1 0 3 }}
 |-
 | style="text-align:center;" | 19683/19600
 | style="text-align:right;" | 7.316
-| | Cataharry
+| Cataharry
-| |
+|
-| |
+|
-| | | -4 9 -2 -2 &gt;
+| {{Monzo| -4 9 -2 -2 }}
 |-
 | style="text-align:center;" | 5120/5103
 | style="text-align:right;" | 5.758
-| | Hemifamity
+| Hemifamity
-| |
+|
-| |
+|
-| | | 10 -6 1 -1 &gt;
+| {{Monzo| 10 -6 1 -1 }}
 |-
 | style="text-align:center;" | 1065875/1063543
 | style="text-align:right;" | 3.792
-| | Wadisma
+| Wadisma
-| |
+|
-| |
+|
-| | | -26 -1 1 9 &gt;
+| {{Monzo| -26 -1 1 9 }}
 |-
 | style="text-align:center;" | 420175/419904
 | style="text-align:right;" | 1.117
-| | Wizma
+| Wizma
-| |
+|
-| |
+|
-| | | -6 -8 2 5 &gt;
+| {{Monzo| -6 -8 2 5 }}
 |-
 | style="text-align:center;" | 99/98
 | style="text-align:right;" | 17.576
-| | Mothwellsma
+| Mothwellsma
-| |
+|
-| |
+|
-| | | -1 2 0 -2 1 &gt;
+| {{Monzo| -1 2 0 -2 1 }}
 |-
 | style="text-align:center;" | 896/891
 | style="text-align:right;" | 9.688
-| | Pentacircle
+| Pentacircle
-| |
+|
-| |
+|
-| | | 7 -4 0 1 -1 &gt;
+| {{Monzo| 7 -4 0 1 -1 }}
 |-
 | style="text-align:center;" | 385/384
 | style="text-align:right;" | 4.503
-| | Keenanisma
+| Keenanisma
-| |
+|
-| |
+|
-| | | -7 -1 1 1 1 &gt;
+| {{Monzo| -7 -1 1 1 1 }}
 |-
 | style="text-align:center;" | 441/440
 | style="text-align:right;" | 3.930
-| | Werckisma
+| Werckisma
-| |
+|
-| |
+|
-| | | -3 2 -1 2 -1 &gt;
+| {{Monzo| -3 2 -1 2 -1 }}
 |-
 | style="text-align:center;" | 3025/3024
 | style="text-align:right;" | 0.572
-| | Lehmerisma
+| Lehmerisma
-| |
+|
-| |
+|
-| | | -4 -3 2 -1 2 &gt;
+| {{Monzo| -4 -3 2 -1 2 }}
 |-
 | style="text-align:center;" | 91/90
 | style="text-align:right;" | 19.130
-| | Superleap
+| Superleap
-| |
+|
-| |
+|
-| | | -1 -2 -1 1 0 1 &gt;
+| {{Monzo| -1 -2 -1 1 0 1 }}
 |-
 | style="text-align:center;" | 676/675
 | style="text-align:right;" | 2.563
-| | Parizeksma
+| Parizeksma
-| |
+|
-| |
+|
-| | | 2 -3 -2 0 0 2 &gt;
+| {{Monzo| 2 -3 -2 0 0 2 }}
 |-
 | style="text-align:center;" | 16/15
 | style="text-align:right;" | 111.731
-| | Diatonic semitone
+| Diatonic semitone
-| |
+|
-| |
+|
-| | | 4 -1 -1 &gt;
+| {{Monzo| 4 -1 -1 }}
 |-
 | style="text-align:center;" | 14/13
 | style="text-align:right;" | 128.298
-| |
+|
-| |
+|
-| |
+|
-| | | 1 0 0 1 0 -1 &gt;
+| {{Monzo| 1 0 0 1 0 -1 }}
 |-
 | style="text-align:center;" | 27/25
 | style="text-align:right;" | 133.238
-| | Large diatonic semit.
+| Large diatonic semit.
-| |
+|
-| |
+|
-| | | 0 3 -2 &gt;
+| {{Monzo| 0 3 -2 }}
 |-
 | style="text-align:center;" | 11/10
 | style="text-align:right;" | 165.004
-| | Large neutral second
+| Large neutral second
-| |
+|
-| |
+|
-| | | -1 0 -1 0 1 &gt;
+| {{Monzo| -1 0 -1 0 1 }}
 |}
 [[Category:5-tone]]
 [[Category:5edo]]
@@ Line 325: / Line 336: @@
 [[Category:todo:unify_precision]]
 [[Category:zeta]]
+<!-- interwiki -->
+[[es:5 EDO]]

5edo: Difference between revisions

Revision as of 10:27, 11 October 2018

5 Equal Divisions of the Octave: Theory

Listen to the sound of the 5-edo scale

Intervals in 5-edo

Related scales

As a temperament

Cycles, Divisions

5-edo in Musicmaking

Compositions, Improvisations

Ear Training

Notation

Harmony

Melody

Chord or scale?

Commas Tempered

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