41edo: Difference between revisions

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41-ET can be seen as a tuning of the [[~~Schismatic_family~~#Garibaldi|~~Garibaldi~~ temperament]] [~~[#cite_note-1|[1]]~~] , [[~~#cite_note-2|[2~~]]] , [[~~#cite_note-3|[3]~~]] the [[~~Magic_family~~|Magic temperament]] [[~~#cite_note-4|[4]~~]] and the [[Superkleismic|superkleismic (41~~&26~~) temperament]]. It is the second smallest equal temperament (after [[29edo]]) whose perfect fifth is closer to just intonation than that of [[12edo|12-ET]], and is the seventh [[~~The_Riemann_Zeta_Function_and_Tuning~~#Zeta EDO lists|zeta integral edo]] after 31; it is not, however, a [[~~The_Riemann_Zeta_Function_and_Tuning~~#Zeta EDO lists|zeta gap edo]]. This has to do with the fact that it can deal with the [[11-limit]] fairly well, and the [[13-limit]] perhaps close enough for government work, though its [[13/10]] is 14 cents sharp. Various 13-limit [[magic extensions]] are supported by 41: 13-limit magic, and less successfully necromancy and witchcraft, all merge into one in 41edo tuning. The 41f val provides a superb tuning for sorcery, giving a less-complex version of the 13-limit, and the 41ef val likewise works well for telepathy; telepathy and sorcery merging into one however not in 41edo but in 22edo.

41-ET can be seen as a tuning of the [[Schismatic family #Garibaldi|garibaldi temperament]]<ref>[http://x31eq.com/schismic.htm Schismic Temperaments] at x31eq.com, the website of [[Graham Breed]]</ref><ref>[http://x31eq.com/decimal_lattice.htm Lattices with Decimal Notation] at x31eq.com</ref><ref>[[Wikipedia: Schismatic temperament]]</ref>, the [[Magic family #Magic|Magic temperament]]<ref>[[Wikipedia: Magic temperament]]</ref> and the [[Superkleismic|superkleismic (26&41) temperament]]. It is the second smallest equal temperament (after [[29edo]]) whose perfect fifth is closer to just intonation than that of [[12edo|12-ET]], and is the seventh [[The Riemann Zeta Function and Tuning #Zeta EDO lists|zeta integral edo]] after 31; it is not, however, a [[The Riemann Zeta Function and Tuning #Zeta EDO lists|zeta gap edo]]. This has to do with the fact that it can deal with the [[11-limit]] fairly well, and the [[13-limit]] perhaps close enough for government work, though its [[13/10]] is 14 cents sharp. Various 13-limit [[magic extensions]] are supported by 41: 13-limit magic, and less successfully necromancy and witchcraft, all merge into one in 41edo tuning. The 41f val provides a superb tuning for sorcery, giving a less-complex version of the 13-limit, and the 41ef val likewise works well for telepathy; telepathy and sorcery merging into one however not in 41edo but in 22edo.

41edo is consistent in the 15 odd limit. In fact, ''all'' of its intervals between 100 and 1100 cents in size are 15-odd-limit consonances, although 16\41 as 13/10 is debatable. (In comparison, [[31edo]] is only consistent up to the 11-limit, and the intervals 12/31 and 19/31 have no 11-limit approximations). Treated as a no-seventeens tuning, it is consistent all the way up to 21-odd-limit.

41edo is consistent in the [[15-odd-limit]]. In fact, ''all'' of its intervals between 100 and 1100 cents in size are 15-odd-limit consonances, although 16\41 as 13/10 is debatable. (In comparison, [[31edo]] is only consistent up to the 11-limit, and the intervals 12\31 and 19\31 have no 11-odd-limit approximations). Treated as a no-seventeens tuning, it is consistent all the way up to 21-odd-limit.

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

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

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

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

== Intervals ==

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== Links ==

* [[Wikipedia: 41 equal temperament]]

* [[Wikipedia:~~41_equal_temperament|~~41 ~~Equal Temperament - Wikipedia~~]]

* [[Magic22 as srutis]] describes a possible use of 41edo for [[indian]] music.

* [[~~Magic22_as_srutis#magic22assrutis|~~Magic22 as srutis]] describes a possible use of 41edo for [[indian]] music.

* [[Magic family]]

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

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

~~-----~~

* [[#cite_ref-1|^]] [http://x31eq.com/schismic.htm "Schismic Temperaments"] at x31eq.com, the website of [[Graham Breed]]

* [[#cite_ref-2|^]] [http://x31eq.com/decimal_lattice.htm "Lattices with Decimal Notation"] at x31eq.com

* [[#cite_ref-3|^]] [[Wikipedia:Schismatic_temperament|Schismatic temperament - Wikipedia]]

* [[#cite_ref-4|^]] [[Wikipedia:Magic_temperament|Magic temperament - Wikipedia]]

[[Category:Equal divisions of the octave]]

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--ET can be seen as a tuning of the [[Schismatic_family#Garibaldi|Garibaldi temperament]] [[#cite_note-1|[1]]] , [[#cite_note-2|[2]]] , [[#cite_note-3|[3]]] the [[Magic_family|Magic temperament]] [[#cite_note-4|[4]]] and the [[Superkleismic|superkleismic (41&amp;26) temperament]]. It is the second smallest equal temperament (after [[29edo]]) whose perfect fifth is closer to just intonation than that of [[12edo|12-ET]], and is the seventh [[The_Riemann_Zeta_Function_and_Tuning#Zeta EDO lists|zeta integral edo]] after 31; it is not, however, a [[The_Riemann_Zeta_Function_and_Tuning#Zeta EDO lists|zeta gap edo]]. This has to do with the fact that it can deal with the [[11-limit]] fairly well, and the [[13-limit]] perhaps close enough for government work, though its [[13/10]] is 14 cents sharp. Various 13-limit [[magic extensions]] are supported by 41: 13-limit magic, and less successfully necromancy and witchcraft, all merge into one in 41edo tuning. The 41f val provides a superb tuning for sorcery, giving a less-complex version of the 13-limit, and the 41ef val likewise works well for telepathy; telepathy and sorcery merging into one however not in 41edo but in 22edo.
+-ET can be seen as a tuning of the [[Schismatic family #Garibaldi|garibaldi temperament]]<ref>[http://x31eq.com/schismic.htm Schismic Temperaments] at x31eq.com, the website of [[Graham Breed]]</ref><ref>[http://x31eq.com/decimal_lattice.htm Lattices with Decimal Notation] at x31eq.com</ref><ref>[[Wikipedia: Schismatic temperament]]</ref>, the [[Magic family #Magic|Magic temperament]]<ref>[[Wikipedia: Magic temperament]]</ref> and the [[Superkleismic|superkleismic (26&41) temperament]]. It is the second smallest equal temperament (after [[29edo]]) whose perfect fifth is closer to just intonation than that of [[12edo|12-ET]], and is the seventh [[The Riemann Zeta Function and Tuning #Zeta EDO lists|zeta integral edo]] after 31; it is not, however, a [[The Riemann Zeta Function and Tuning #Zeta EDO lists|zeta gap edo]]. This has to do with the fact that it can deal with the [[11-limit]] fairly well, and the [[13-limit]] perhaps close enough for government work, though its [[13/10]] is 14 cents sharp. Various 13-limit [[magic extensions]] are supported by 41: 13-limit magic, and less successfully necromancy and witchcraft, all merge into one in 41edo tuning. The 41f val provides a superb tuning for sorcery, giving a less-complex version of the 13-limit, and the 41ef val likewise works well for telepathy; telepathy and sorcery merging into one however not in 41edo but in 22edo.
-edo is consistent in the 15 odd limit. In fact, ''all'' of its intervals between 100 and 1100 cents in size are 15-odd-limit consonances, although 16\41 as 13/10 is debatable. (In comparison, [[31edo]] is only consistent up to the 11-limit, and the intervals 12/31 and 19/31 have no 11-limit approximations). Treated as a no-seventeens tuning, it is consistent all the way up to 21-odd-limit.
+edo is consistent in the [[15-odd-limit]]. In fact, ''all'' of its intervals between 100 and 1100 cents in size are 15-odd-limit consonances, although 16\41 as 13/10 is debatable. (In comparison, [[31edo]] is only consistent up to the 11-limit, and the intervals 12\31 and 19\31 have no 11-odd-limit approximations). Treated as a no-seventeens tuning, it is consistent all the way up to 21-odd-limit.
--ET forms the foundation of the [http://www.h-pi.com/theory/huntsystem1.html H-System], which uses the scale degrees of 41-ET as the basic [[13-limit]] intervals requiring fine tuning +/- 1 [http://www.h-pi.com/theory/huntsystem2.html average JND] from the 41-ET circle in [[205edo]]. 41-ET is also used by the [[The Kite Guitar|Kite Guitar]], see below in "Instruments".
+-ET forms the foundation of the [http://www.h-pi.com/theory/huntsystem1.html H-System], which uses the scale degrees of 41-ET as the basic [[13-limit]] intervals requiring fine tuning +/- 1 [http://www.h-pi.com/theory/huntsystem2.html average JND] from the 41-ET circle in [[205edo]]. 41-ET is also used by the [[The Kite Guitar|Kite Guitar]], see below in [[#Instruments]].
-edo is the 13th [[prime_numbers|prime]] edo, following [[37edo]] and coming before [[43edo]]
+edo is the 13th [[prime numbers|prime]] edo, following [[37edo]] and coming before [[43edo]].
+<references/>
 == Intervals ==
@@ Line 1,891: / Line 1,893: @@
 == Links ==
+* [[Wikipedia: 41 equal temperament]]
-* [[Wikipedia:41_equal_temperament|41 Equal Temperament - Wikipedia]]
+* [[Magic22 as srutis]] describes a possible use of 41edo for [[indian]] music.
-* [[Magic22_as_srutis#magic22assrutis|Magic22 as srutis]] describes a possible use of 41edo for [[indian]] music.
 * [[Magic family]]
 * Sword, Ron. [http://www.ronsword.com "Tetracontamonophonic Scales for Guitar"]
 * Taylor, Cam. [https://drive.google.com/open?id=0B3wIGTmjY_VZYllwcHI0d3hEc3M Intervals, Scales and Chords in 41EDO], a work in progress using just intonation concepts and simplified Sagittal notation.
------
-* [[#cite_ref-1|^]] [http://x31eq.com/schismic.htm "Schismic Temperaments"] at x31eq.com, the website of [[Graham Breed]]
-* [[#cite_ref-2|^]] [http://x31eq.com/decimal_lattice.htm "Lattices with Decimal Notation"] at x31eq.com
-* [[#cite_ref-3|^]] [[Wikipedia:Schismatic_temperament|Schismatic temperament - Wikipedia]]
-* [[#cite_ref-4|^]] [[Wikipedia:Magic_temperament|Magic temperament - Wikipedia]]
 [[Category:Equal divisions of the octave]]