205edo: Difference between revisions

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 {{Infobox ET}}
-The '''205 equal divisions of the octave''' ('''205edo'''), or the '''205(-tone) equal temperament''' ('''205tet''', '''205et''') when viewed from a [[regular temperament]] perspective, divides the [[octave]] into 205 parts of 5.854 [[cent]]s each.
+{{EDO intro|205}}
 == Theory ==
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 The 119\205 meantone fifth is extremely close to the 1/4-comma fifth, being only 0.007 cents sharp of it. Moreover the steps are half a cent flat of 1/4 of a syntonic comma. This makes the Tonal Plexus keyboard potentially of use in implementing [[Wikipedia: Nicola Vicentino|Nicola Vicentino]]'s [http://www.tonalsoft.com/monzo/vicentino/vicentino.aspx adaptive-JI scheme of 1555]. It also means that authentic 1/4-comma meantone tuning is, for practical purposes, available in 205 and allows for historically authentic performances of 1/4-comma music on the historically newfangled Tonal Plexus.
-=== Miscellaneous properties ===
+=== Divisors ===
 factors into primes as 5 × 41, a fact some advocates of the division make use of; it is also [[2460edo|2460/12]], so that a single step is precisely 12 [[mina]]s.
 == Regular temperament properties ==
 {| class="wikitable center-4 center-5 center-6"
-! rowspan="2" | Subgroup
+! rowspan="2" | [[Subgroup]]
 ! rowspan="2" | [[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 52: / Line 52: @@
 {| class="wikitable center-all left-5"
 |+Table of rank-2 temperaments by generator
-! Periods<br>per octave
+! Periods<br>per 8ve
-! Generator<br>(reduced)
+! Generator<br>(Reduced)
-! Cents<br>(reduced)
+! Cents<br>(Reduced)
-! Associated<br>ratio
+! Associated<br>Ratio
 ! Temperaments
 |-
@@ Line 92: / Line 92: @@
 | 386.341<br>(5.85)
 | 5/4<br>(32805/32768)
-| [[Counterpyth]]
+| [[Countercomp]]
 |}
 == Scales ==
-=== Quanic (24\205) MOS ===
+=== Quanic (24\205) mos ===
-==== 17 note ====
+; 17-note
-13 11 13 11 13 11 13 11 13 11 13 11 13 11 13 13
+: 11 13 11 13 11 13 11 13 11 13 11 13 11 13 11 13 13
+; 26-note
+: 11 11 2 11 11 2 11 11 2 11 11 2 11 11 2 11 11 2 11 11 2 11 11 2 11 2
-==== 26 note ====
+=== Amity (58\205) mos ===
-11 2 11 11 2 11 11 2 11 11 2 11 11 2 11 11 2 11 11 2 11 11 2 11 2
+; 11-note
+: 27 27 4 27 27 4 27 27 4 27 4
+; 18-note
+: 23 4 23 4 4 23 4 23 4 4 23 4 23 4 4 23 4 4
+; 25-note
+: 19 4 4 19 4 4 4 19 4 4 19 4 4 4 19 4 4 19 4 4 4 19 4 4 4
-=== Amity (58\205) MOS ===
+=== Hemithirds (33\205) mos ===
+; 13-note
+: 26 7 26 7 26 7 26 7 26 7 26 7 7
+; 19-note
+: 19 7 7 19 7 7 19 7 7 19 7 7 19 7 7 19 7 7 7
+; 25-note
+: 12 7 7 7 12 7 7 7 12 7 7 7 12 7 7 7 12 7 7 7 12 7 7 7 7
+; 31-notes
+: 5 7 7 7 7 5 7 7 7 7 5 7 7 7 7 5 7 7 7 7 5 7 7 7 7 5 7 7 7 7 7
-==== 11 note ====
+=== Meantone (119\205) mos ===
-27 4 27 27 4 27 27 4 27 4
+; 12-note
+: 13 20 13 20 13 20 20 13 20 13 20 20
+; 19-note
+: 13 13 7 13 13 7 13 13 7 13 7 13 13 7 13 13 7 13 7
+; 31-note
+: 6 7 6 7 7 6 7 6 7 7 6 7 6 7 7 6 7 7 6 7 6 7 7 6 7 6 7 7 6 7 7
-==== 18 note ====
+=== Myna (53\205) mos ===
-4 23 4 4 23 4 23 4 4 23 4 23 4 4 23 4 4
+; 11-note
+: 7 7 39 7 7 39 7 7 39 7 39
+; 15-note
+: 7 7 7 32 7 7 7 32 7 7 7 32 7 7 32
+; 19-note
+: 7 7 7 7 25 7 7 7 7 25 7 7 7 7 25 7 7 7 25
+; 23-note
+: 7 7 7 7 7 18 7 7 7 7 7 18 7 7 7 7 7 18 7 7 7 7 18
+; 27-note
+: 7 7 7 7 7 7 11 7 7 7 7 7 7 11 7 7 7 7 7 7 11 7 7 7 7 7 11
+; 31-note
+: 7 7 7 7 7 7 7 4 7 7 7 7 7 7 7 4 7 7 7 7 7 7 7 4 7 7 7 7 7 7 4
-==== 25 note ====
+=== Porcupine (28\205) mos ===
-4 4 19 4 4 4 19 4 4 19 4 4 4 19 4 4 19 4 4 4 19 4 4 4
+; 15-note
+: 19 9 19 9 19 9 19 9 19 9 19 9 19 9 9
-=== Hemithirds (33\205) MOS ===
+; 22-note
-==== 13 note ====
+: 10 9 9 10 9 9 10 9 9 10 9 9 10 9 9 10 9 9 10 9 9 9
-7 26 7 26 7 26 7 26 7 26 7 7
+; 29-note
+: 1 9 9 9 1 9 9 9 1 9 9 9 1 9 9 9 1 9 9 9 1 9 9 9 1 9 9 9 9
-==== 19 note ====
-7 7 19 7 7 19 7 7 19 7 7 19 7 7 19 7 7 7
-==== 25 note ====
-7 7 7 12 7 7 7 12 7 7 7 12 7 7 7 12 7 7 7 12 7 7 7 7
-==== 31 notes ====
-7 7 7 7 5 7 7 7 7 5 7 7 7 7 5 7 7 7 7 5 7 7 7 7 5 7 7 7 7 7
-=== Meantone (119\205) MOS ===
-==== 12 note ====
-20 13 20 13 20 20 13 20 13 20 20
-==== 19 note ====
-13 7 13 13 7 13 13 7 13 7 13 13 7 13 13 7 13 7
-==== 31 notes ====
-7 6 7 7 6 7 6 7 7 6 7 6 7 7 6 7 7 6 7 6 7 7 6 7 6 7 7 6 7 7
-=== Myna (53\205) MOS ===
-==== 11 note ====
-7 39 7 7 39 7 7 39 7 39
-==== 15 note ====
-7 7 32 7 7 7 32 7 7 7 32 7 7 32
-==== 19 note ====
-7 7 7 25 7 7 7 7 25 7 7 7 7 25 7 7 7 25
-==== 23 note ====
-7 7 7 7 18 7 7 7 7 7 18 7 7 7 7 7 18 7 7 7 7 18
-==== 27 note ====
-7 7 7 7 7 11 7 7 7 7 7 7 11 7 7 7 7 7 7 11 7 7 7 7 7 11
-==== 31 notes ====
-7 7 7 7 7 7 4 7 7 7 7 7 7 7 4 7 7 7 7 7 7 7 4 7 7 7 7 7 7 4
-=== Porcupine (28\205) MOS ===
-==== 15 note ====
-9 19 9 19 9 19 9 19 9 19 9 19 9 9
-==== 22 note ====
-9 9 10 9 9 10 9 9 10 9 9 10 9 9 10 9 9 10 9 9 9
-==== 29 note ====
-9 9 9 1 9 9 9 1 9 9 9 1 9 9 9 1 9 9 9 1 9 9 9 1 9 9 9 9
 [[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->