77edo: Difference between revisions

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~~The '''~~77 equal divisions of the octave''' ('''77edo'''), or the '''77(-tone) equal temperament''' ('''77et''', '''77tet''') when viewed from a [[regular temperament]] perspective, divides the [[octave]] into 77 steps of size about 15.6 [[cent]]s each.

== Theory ==

With ~~fifths~~ less than a cent flat, ~~major thirds~~ a bit over three cents sharp and [[7/4]]'s less flat than that, 77edo represents an excellent tuning choice for both [[valentine]], the 31&46 temperament, and [[starling]], the [[126/125]] [[planar temperament]], giving the [[optimal patent val]] for [[11-limit]] valentine and its [[13-limit]] extensions dwynwen and valentino, as well as 11-limit starling and [[oxpecker]] temperaments. It also gives the optimal patent val for [[grackle]] and various members of the [[unicorn family]], with a [[generator]] of 4\77 instead of the 5\77 (which gives valentine). These are 7-limit [[Unicorn family #Alicorn|alicorn]] and 11- and 13-limit [[Unicorn family #Camahueto|camahueto]].

With [[3/1|harmonic 3]] less than a cent flat, [[5/1|harmonic 5]] a bit over three cents sharp and [[7/1|7]]'s less flat than that, 77edo represents an excellent tuning choice for both [[valentine]], the 31 & 46 temperament, and [[starling]], the [[126/125]] [[planar temperament]], giving the [[optimal patent val]] for [[11-limit]] valentine and its [[13-limit]] extensions dwynwen and valentino, as well as 11-limit starling and [[oxpecker]] temperaments. It also gives the optimal patent val for [[grackle]] and various members of the [[unicorn family]], with a [[generator]] of 4\77 instead of the 5\77 (which gives valentine). These are 7-limit [[Unicorn family #Alicorn|alicorn]] and 11- and 13-limit [[Unicorn family #Camahueto|camahueto]].

77et tempers out [[32805/32768]] in the [[5-limit]], [[126/125]], [[1029/1024]] and [[6144/6125]] in the 7-limit, [[121/120]], [[176/175]], [[385/384]] and [[441/440]] in the 11-limit, and [[196/195]], [[351/350]], [[352/351]], [[676/675]] and [[729/728]] in the 13-limit.

77edo is an excellent ~~EDO~~ for [[Carlos Alpha]] ~~scale~~, since the difference between 5 steps of 77edo and 1 step of Carlos Alpha is only -0.042912 cents.

77edo is an excellent edo for [[Carlos Alpha]], since the difference between 5 steps of 77edo and 1 step of Carlos Alpha is only -0.042912 cents.

=== Prime harmonics ===

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== Regular temperament properties ==

{| class="wikitable center-4 center-5 center-6"

! rowspan="2" | Subgroup

! rowspan="2" | [[Subgroup]]

! rowspan="2" | [[Comma list]]

! rowspan="2" | [[Comma list|Comma List]]

! rowspan="2" | [[Mapping]]

! rowspan="2" | Optimal<br>8ve ~~stretch~~ (¢)

! rowspan="2" | Optimal<br>8ve Stretch (¢)

! colspan="2" | Tuning ~~error~~

! colspan="2" | Tuning Error

|-

! [[TE error|Absolute]] (¢)

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== Music ==

~~'''~~[[Jake Freivald]]~~'''~~

; [[Jake Freivald]]

* [http://soonlabel.com/xenharmonic/wp-content/uploads/2013/10/Freivald-J.-A-Seed-Planted-2nd-Version-77edo.mp3 A Seed Planted], in an [http://soonlabel.com/xenharmonic/archives/1391 organ version] of Claudi Meneghin.

* [http://soonlabel.com/xenharmonic/wp-content/uploads/2013/10/Freivald-J.-A-Seed-Planted-2nd-Version-77edo.mp3 ''A Seed Planted''], in an [http://soonlabel.com/xenharmonic/archives/1391 organ version] of [[Claudi Meneghin]].

~~'''~~[[Joel Grant Taylor]]~~'''~~

* [http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/star_1-GrimaldiA+Bmod.mp3 Star 1-GrimaldiA+Bmod]

; [[Joel Grant Taylor]]

~~'''~~[[Chris Vaisvil]]~~'''~~

* [http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/star_1-GrimaldiA+Bmod.mp3 ''Star 1-GrimaldiA+Bmod'']

* [http://micro.soonlabel.com/star/20120830-77et-star.mp3 77et Star]

; [[Chris Vaisvil]]

* [http://micro.soonlabel.com/star/20120830-77et-star.mp3 ''77et Star'']

~~[[Category:Equal divisions of the octave|##]] ~~

[[Category:Listen]]

[[Category:Star]]

[[Category:Starling]]

[[Category:Valentine]]

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-The '''77 equal divisions of the octave''' ('''77edo'''), or the '''77(-tone) equal temperament''' ('''77et''', '''77tet''') when viewed from a [[regular temperament]] perspective, divides the [[octave]] into 77 steps of size about 15.6 [[cent]]s each.
+{{EDO intro|77}}
 == Theory ==
-With fifths less than a cent flat, major thirds a bit over three cents sharp and [[7/4]]'s less flat than that, 77edo represents an excellent tuning choice for both [[valentine]], the 31&amp;46 temperament, and [[starling]], the [[126/125]] [[planar temperament]], giving the [[optimal patent val]] for [[11-limit]] valentine and its [[13-limit]] extensions dwynwen and valentino, as well as 11-limit starling and [[oxpecker]] temperaments. It also gives the optimal patent val for [[grackle]] and various members of the [[unicorn family]], with a [[generator]] of 4\77 instead of the 5\77 (which gives valentine). These are 7-limit [[Unicorn family #Alicorn|alicorn]] and 11- and 13-limit [[Unicorn family #Camahueto|camahueto]].
+With [[3/1|harmonic 3]] less than a cent flat, [[5/1|harmonic 5]] a bit over three cents sharp and [[7/1|7]]'s less flat than that, 77edo represents an excellent tuning choice for both [[valentine]], the 31 &amp; 46 temperament, and [[starling]], the [[126/125]] [[planar temperament]], giving the [[optimal patent val]] for [[11-limit]] valentine and its [[13-limit]] extensions dwynwen and valentino, as well as 11-limit starling and [[oxpecker]] temperaments. It also gives the optimal patent val for [[grackle]] and various members of the [[unicorn family]], with a [[generator]] of 4\77 instead of the 5\77 (which gives valentine). These are 7-limit [[Unicorn family #Alicorn|alicorn]] and 11- and 13-limit [[Unicorn family #Camahueto|camahueto]].
 et tempers out [[32805/32768]] in the [[5-limit]], [[126/125]], [[1029/1024]] and [[6144/6125]] in the 7-limit, [[121/120]], [[176/175]], [[385/384]] and [[441/440]] in the 11-limit, and [[196/195]], [[351/350]], [[352/351]], [[676/675]] and [[729/728]] in the 13-limit.
-edo is an excellent EDO for [[Carlos Alpha]] scale, since the difference between 5 steps of 77edo and 1 step of Carlos Alpha is only -0.042912 cents.
+edo is an excellent edo for [[Carlos Alpha]], since the difference between 5 steps of 77edo and 1 step of Carlos Alpha is only -0.042912 cents.
 === Prime harmonics ===
@@ Line 335: / Line 335: @@
 == Regular temperament properties ==
 {| class="wikitable center-4 center-5 center-6"
-! rowspan="2" | Subgroup
+! rowspan="2" | [[Subgroup]]
-! rowspan="2" | [[Comma list]]
+! rowspan="2" | [[Comma list|Comma List]]
 ! rowspan="2" | [[Mapping]]
-! rowspan="2" | Optimal<br>8ve stretch (¢)
+! rowspan="2" | Optimal<br>8ve Stretch (¢)
-! colspan="2" | Tuning error
+! colspan="2" | Tuning Error
 |-
 ! [[TE error|Absolute]] (¢)
@@ Line 541: / Line 541: @@
 == Music ==
-'''[[Jake Freivald]]'''
+; [[Jake Freivald]]
-* [http://soonlabel.com/xenharmonic/wp-content/uploads/2013/10/Freivald-J.-A-Seed-Planted-2nd-Version-77edo.mp3 A Seed Planted], in an [http://soonlabel.com/xenharmonic/archives/1391 organ version] of Claudi Meneghin.
+* [http://soonlabel.com/xenharmonic/wp-content/uploads/2013/10/Freivald-J.-A-Seed-Planted-2nd-Version-77edo.mp3 ''A Seed Planted''], in an [http://soonlabel.com/xenharmonic/archives/1391 organ version] of [[Claudi Meneghin]].
-'''[[Joel Grant Taylor]]'''
-* [http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/star_1-GrimaldiA+Bmod.mp3 Star 1-GrimaldiA+Bmod]
+; [[Joel Grant Taylor]]
-'''[[Chris Vaisvil]]'''
+* [http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/star_1-GrimaldiA+Bmod.mp3 ''Star 1-GrimaldiA+Bmod'']
-* [http://micro.soonlabel.com/star/20120830-77et-star.mp3 77et Star]
+; [[Chris Vaisvil]]
+* [http://micro.soonlabel.com/star/20120830-77et-star.mp3 ''77et Star'']
-[[Category:Equal divisions of the octave|##]] <!-- 2-digit number -->
 [[Category:Listen]]
 [[Category:Star]]
 [[Category:Starling]]
 [[Category:Valentine]]