5edo: Difference between revisions

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| en = 5edo  

| ja = 5平均律

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== Theory ==

== Intervals ==

! degrees

! The "neighborhood" of just intervals

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== Notation ==

* via Reinhard's cents notation

* naturals on a five-line staff, with enharmonics (used interchangably) E=F and B=C

=== Related scales ===

* 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.

=== Cycles, Divisions ===

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

=== 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.

=== 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 ==

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

! [[Monzo]]

! [[cent]]s

! Name

! Second Name

| {{Monzo| 8 -5 }}

| style="text-align:right;" | 90.225

| Limma

| Pythagorean Minor 2nd

| {{Monzo| 0 3 -2 }}

| style="text-align:right;" | 133.238

| Large diatonic semit.

|  

| {{Monzo| 4 -1 -1 }}

| style="text-align:right;" | 111.731

| Diatonic semitone

|  

| {{Monzo| -4 4 -1 }}

| style="text-align:right;" | 21.506

| Syntonic Comma

| Didymos Comma

| {{Monzo| 24 -21 4 }}

| style="text-align:right;" | 4.200

| Vulture

|  

| {{Monzo| 2 2 -1 -1 }}

| style="text-align:right;" | 48.770

| Septimal Quarter Tone

|  

| {{Monzo| -4 -1 0 2 }}

| style="text-align:right;" | 35.697

| Slendro Diesis

|  

| {{Monzo| 6 -2 0 -1 }}

| style="text-align:right;" | 27.264

| Septimal Comma

| Archytas' Comma

| {{Monzo| 0 -5 1 2 }}

| style="text-align:right;" | 14.191

| Sensamagic

|  

| {{Monzo| 6 3 -1 -3 }}

| style="text-align:right;" | 13.074

| Orwellisma

| Orwell Comma

| {{Monzo| -10 1 0 3 }}

| style="text-align:right;" | 8.433

| Gamelisma

|  

| {{Monzo| -4 9 -2 -2 }}

| style="text-align:right;" | 7.316

| Cataharry

|  

| {{Monzo| 10 -6 1 -1 }}

| style="text-align:right;" | 5.758

| Hemifamity

|  

| {{Monzo| -26 -1 1 9 }}

| style="text-align:right;" | 3.792

| Wadisma

|  

| {{Monzo| -6 -8 2 5 }}

| style="text-align:right;" | 1.117

| Wizma

|  

| {{Monzo| -1 0 -1 0 1 }}

| style="text-align:right;" | 165.004

| Large neutral second

|  

| {{Monzo| -1 2 0 -2 1 }}

| style="text-align:right;" | 17.576

| Mothwellsma

|  

| {{Monzo| 7 -4 0 1 -1 }}

| style="text-align:right;" | 9.688

| Pentacircle

|  

| {{Monzo| -7 -1 1 1 1 }}

| style="text-align:right;" | 4.503

| Keenanisma

|  

| {{Monzo| -3 2 -1 2 -1 }}

| style="text-align:right;" | 3.930

| Werckisma

|  

| {{Monzo| -4 -3 2 -1 2 }}

| style="text-align:right;" | 0.572

| Lehmerisma

|  

| {{Monzo| 1 0 0 1 0 -1 }}

| style="text-align:right;" | 128.298

|  

|  

| {{Monzo| -1 -2 -1 1 0 1 }}

| style="text-align:right;" | 19.130

| Superleap

|  

| {{Monzo| 2 -3 -2 0 0 2 }}

| style="text-align:right;" | 2.563

| Parizeksma

|  

== Ear Training ==

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:

== Music ==

* [http://www.io.com/%7Ehmiller/ Herman Miller]: ''[http://micro.soonlabel.com/herman_miller/Daybreak.mp3 Daybreak on Slendro Mountain]'' (2000)

* [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)

* "Cenobyte" Ukulele 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)

There is much 5-edo (or nearly so) world music, just search for "gyil" or "amadinda" or "slendro".