205edo: Difference between revisions

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{{Infobox ET

| Prime factorization = 2 × 3<sup>2</sup> × 11

| Step size = 6.06061¢

| Fifth = 120\205 (702.44¢) (→ [[41edo|24\41]])

| Semitones = 20:15 (117.07¢ : 87.80¢)

| Consistency = 9

}}

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.

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205 factors into primes as 5 × 41, a fact some advocates of the division make use of; it is also 2460/12, so that a single step is precisely 12 [[mina]]s.

=== ~~Prime~~ harmonics ===

=== Odd harmonics ===

== Temperament generators and Tonal Plexus ==

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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.

== ~~205edo MOS~~ ==

== Scales ==

=== Quanic (24\205) MOS ===

@@ Line 1: / Line 1: @@
+{{Infobox ET
+| Prime factorization = 2 × 3<sup>2</sup> × 11
+| Step size = 6.06061¢
+| Fifth = 120\205 (702.44¢) (→ [[41edo|24\41]])
+| Semitones = 20:15 (117.07¢ : 87.80¢)
+| Consistency = 9
+}}
 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.
@@ Line 12: / Line 19: @@
 factors into primes as 5 × 41, a fact some advocates of the division make use of; it is also 2460/12, so that a single step is precisely 12 [[mina]]s.
-=== Prime harmonics ===
+=== Odd harmonics ===
-{{Primes in edo|205}}
+{{Harmonics in equal|205}}
 == Temperament generators and Tonal Plexus ==
@@ Line 20: / Line 27: @@
 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.
-== 205edo MOS ==
+== Scales ==
 === Quanic (24\205) MOS ===