41edo: Difference between revisions

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41et forms the foundation of the [http://www.h-pi.com/theory/huntsystem1.html H-System], which uses the scale degrees of 41et as the basic [[13-limit]] intervals requiring fine tuning +/- 1 [http://www.h-pi.com/theory/huntsystem2.html average JND] from the 41et circle in [[205edo]]. 41et is also used by the [[Kite Guitar]], see below in [[#Instruments]].

~~41edo is the 13th [[prime edo]], following [[37edo]] and coming before [[43edo]].~~

=== Prime harmonics ===

~~<references/>~~

=== Divisors ===

41edo is the 13th [[prime edo]], following [[37edo]] and coming before [[43edo]].

== Intervals ==

{| class="wikitable center-1 right-2 center-5 center-6 center-7 center-8 center-9"

! #

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| 29th-partial chroma

|}

~~<references/>~~

=== Rank-2 temperaments ===

* [[List of edo-distinct 41et rank two temperaments]]

* [[Schismic-~~counterpyth~~ equivalence continuum]]

* [[Schismic-countercommatic equivalence continuum]]

{| class="wikitable right-1 right-2"

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! Temperament(s)

! [[Pergen]]

! ~~Some~~ MOS Scales ~~Available~~

! MOS Scales

|-

| 1

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* [[Bohpier33]]

A list of [[41edo modes]] (~~MOS~~ and others). See also [[The Kite Guitar Scales|Kite Guitar Scales]] and [[Kite Giedraitis's Categorizations of 41edo Scales]].

A list of [[41edo modes]] (mos and others). See also [[The Kite Guitar Scales|Kite Guitar Scales]] and [[Kite Giedraitis's Categorizations of 41edo Scales]].

=== Harmonic scale ===

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Taking every third degree of 41edo produces a scale extremely close to [[88cET]] or 88-cent equal temperament (or the 8th root of 3:2). Likewise, taking every fifth degree produces a scale very close to the equal-tempered <span style="">[[BP|Bohlen-Pierce]]</span>[[BP| Scale]] (or the 13th root of 3). See [[Relationship between Bohlen-Pierce and octave-ful temperaments]], and see this chart:

{| class="wikitable center-all right-3 right-4 right-5"

{| class="wikitable center-all right-3 right-4 right-5 mw-collapsible mw-collapsed"

! colspan="3" | 3 degrees of 41edo near 88cET

! overlap

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While the [[Hemif|Hemif[7]]] scale itself and ~~MODMOSes~~ related to it give the middle eastern sound well, 41 has other interesting properties that make it an ideal system for Arabic and Turkish music. It is considered a "Level 2 EDO" due to the fact that it has neutral seconds and thirds as well as submajor and supraminor ones added to a Pythagorean skeleton, with small semitones as minor seconds and major whole tones as major seconds. The submajor third is great for Turkish Rast, around [[Ozan Yarman]]’s ideal size, and is sharp enough to sound close to a [[5/4]], while the neutral third exists as half of a [[3/2]] and works well for Arabic Rast and some Persian scales. Additionally, a large [[apotome]] exists for the Hijaz maqam.

While the [[Hemif|Hemif[7]]] scale itself and modmosses related to it give the middle eastern sound well, 41 has other interesting properties that make it an ideal system for Arabic and Turkish music. It is considered a "Level 2 EDO" due to the fact that it has neutral seconds and thirds as well as submajor and supraminor ones added to a Pythagorean skeleton, with small semitones as minor seconds and major whole tones as major seconds. The submajor third is great for Turkish Rast, around [[Ozan Yarman]]’s ideal size, and is sharp enough to sound close to a [[5/4]], while the neutral third exists as half of a [[3/2]] and works well for Arabic Rast and some Persian scales. Additionally, a large [[apotome]] exists for the Hijaz maqam.

=== Indonesian ===

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=== Blues ===

Due to its pure sounding major thirds and approximations of standard western harmony, 41 naturally is good for jazz and blues music, though a great strength of this system as opposed to many others is its excellent harmonic seventh, alongside ~~MOS~~ scales that supply them, [[Miracle]] in particular.

Due to its pure sounding major thirds and approximations of standard western harmony, 41 naturally is good for jazz and blues music, though a great strength of this system as opposed to many others is its excellent harmonic seventh, alongside mos scales that supply them, [[Miracle]] in particular.

Coltrane changes can be represented with two Pythagorean major thirds and a pental one, or ~~an MOS~~ like ~~Magic~~, whose circles of major thirds give options for rotating major and minor triads within one scale.

Coltrane changes can be represented with two Pythagorean major thirds and a pental one, or a mos like magic, whose circles of major thirds give options for rotating major and minor triads within one scale.

Blue notes, rather than being considered inflections, can be notated as accidentals instead, such as the "blue third" which is represented by a neutral third, or any number of septimal intervals that sound great in a blues context.

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* [http://www.ronsword.com ''Tetracontamonophonic Scales for Guitar''] by [[Ron Sword]]

* [https://drive.google.com/open?id=0B3wIGTmjY_VZYllwcHI0d3hEc3M ''Intervals, Scales and Chords in 41EDO''] by [[Cam Taylor]] – a work in progress using just intonation concepts and simplified Sagittal notation.

== Notes ==

[[Category:Magic]]

@@ Line 13: / Line 13: @@
 et forms the foundation of the [http://www.h-pi.com/theory/huntsystem1.html H-System], which uses the scale degrees of 41et as the basic [[13-limit]] intervals requiring fine tuning +/- 1 [http://www.h-pi.com/theory/huntsystem2.html average JND] from the 41et circle in [[205edo]]. 41et is also used by the [[Kite Guitar]], see below in [[#Instruments]].
-edo is the 13th [[prime edo]], following [[37edo]] and coming before [[43edo]].
 === Prime harmonics ===
 {{Harmonics in equal|41}}
-<references/>
+=== Divisors ===
+edo is the 13th [[prime edo]], following [[37edo]] and coming before [[43edo]].
 == Intervals ==
-{{See also|41edo solfege}}
+{{See also| 41edo solfege }}
 {| class="wikitable center-1 right-2 center-5 center-6 center-7 center-8 center-9"
 ! #
@@ Line 1,125: / Line 1,125: @@
 | 29th-partial chroma
 |}
-<references/>
 === Rank-2 temperaments ===
 * [[List of edo-distinct 41et rank two temperaments]]
-* [[Schismic-counterpyth equivalence continuum]]
+* [[Schismic-countercommatic equivalence continuum]]
 {| class="wikitable right-1 right-2"
@@ Line 1,138: / Line 1,137: @@
 ! Temperament(s)
 ! [[Pergen]]
-! Some MOS Scales Available
+! MOS Scales
 |-
 | 1
@@ Line 1,268: / Line 1,267: @@
 * [[Bohpier33]]
-A list of [[41edo modes]] (MOS and others). See also [[The Kite Guitar Scales|Kite Guitar Scales]] and [[Kite Giedraitis's Categorizations of 41edo Scales]].
+A list of [[41edo modes]] (mos and others). See also [[The Kite Guitar Scales|Kite Guitar Scales]] and [[Kite Giedraitis's Categorizations of 41edo Scales]].
 === Harmonic scale ===
@@ Line 1,344: / Line 1,343: @@
 Taking every third degree of 41edo produces a scale extremely close to [[88cET]] or 88-cent equal temperament (or the 8th root of 3:2). Likewise, taking every fifth degree produces a scale very close to the equal-tempered <span style="">[[BP|Bohlen-Pierce]]</span>[[BP| Scale]] (or the 13th root of 3). See [[Relationship between Bohlen-Pierce and octave-ful temperaments]], and see this chart:
-{| class="wikitable center-all right-3 right-4 right-5"
+{| class="wikitable center-all right-3 right-4 right-5 mw-collapsible mw-collapsed"
 ! colspan="3" | 3 degrees of 41edo near 88cET
 ! overlap
@@ Line 1,850: / Line 1,849: @@
 {{See also| Arabic, Turkish, Persian }}
-While the [[Hemif|Hemif[7]]] scale itself and MODMOSes related to it give the middle eastern sound well, 41 has other interesting properties that make it an ideal system for Arabic and Turkish music. It is considered a "Level 2 EDO" due to the fact that it has neutral seconds and thirds as well as submajor and supraminor ones added to a Pythagorean skeleton, with small semitones as minor seconds and major whole tones as major seconds. The submajor third is great for Turkish Rast, around [[Ozan Yarman]]’s ideal size, and is sharp enough to sound close to a [[5/4]], while the neutral third exists as half of a [[3/2]] and works well for Arabic Rast and some Persian scales. Additionally, a large [[apotome]] exists for the Hijaz maqam.
+While the [[Hemif|Hemif[7]]] scale itself and modmosses related to it give the middle eastern sound well, 41 has other interesting properties that make it an ideal system for Arabic and Turkish music. It is considered a "Level 2 EDO" due to the fact that it has neutral seconds and thirds as well as submajor and supraminor ones added to a Pythagorean skeleton, with small semitones as minor seconds and major whole tones as major seconds. The submajor third is great for Turkish Rast, around [[Ozan Yarman]]’s ideal size, and is sharp enough to sound close to a [[5/4]], while the neutral third exists as half of a [[3/2]] and works well for Arabic Rast and some Persian scales. Additionally, a large [[apotome]] exists for the Hijaz maqam.
 === Indonesian ===
@@ Line 1,866: / Line 1,865: @@
 === Blues ===
-Due to its pure sounding major thirds and approximations of standard western harmony, 41 naturally is good for jazz and blues music, though a great strength of this system as opposed to many others is its excellent harmonic seventh, alongside MOS scales that supply them, [[Miracle]] in particular.
+Due to its pure sounding major thirds and approximations of standard western harmony, 41 naturally is good for jazz and blues music, though a great strength of this system as opposed to many others is its excellent harmonic seventh, alongside mos scales that supply them, [[Miracle]] in particular.
-Coltrane changes can be represented with two Pythagorean major thirds and a pental one, or an MOS like Magic, whose circles of major thirds give options for rotating major and minor triads within one scale.
+Coltrane changes can be represented with two Pythagorean major thirds and a pental one, or a mos like magic, whose circles of major thirds give options for rotating major and minor triads within one scale.
 Blue notes, rather than being considered inflections, can be notated as accidentals instead, such as the "blue third" which is represented by a neutral third, or any number of septimal intervals that sound great in a blues context.
@@ Line 1,914: / Line 1,913: @@
 * [http://www.ronsword.com ''Tetracontamonophonic Scales for Guitar''] by [[Ron Sword]]
 * [https://drive.google.com/open?id=0B3wIGTmjY_VZYllwcHI0d3hEc3M ''Intervals, Scales and Chords in 41EDO''] by [[Cam Taylor]] – a work in progress using just intonation concepts and simplified Sagittal notation.
+== Notes ==
+<references/>
 [[Category:Magic]]