60edo: Difference between revisions

Line 578:

; 207ed11, 168ed7

The tunings [[207ed11]] and [[168ed7]] are almost identical. Each is [[60edo]] but with slightly ''~~[[Octave stretch|~~stretched]]'' octaves.

The tunings [[207ed11]] and [[168ed7]] are almost identical. Each is 60edo but with slightly ''stretched'' octaves.

Each ~~causes~~ relatively large improvement to [[5/1]], [[7/1]] and [[11/1]] at the cost of ~~moderate~~ worsening of [[2/1]] and [[3/1]].

Each induces relatively large improvement to [[5/1]], [[7/1]] and [[11/1]] at the cost of worsening of [[2/1]] and [[3/1]]. Each also causes the [[patent val]] to flip for [[11/1]] and [[13/1]].

Each also causes the [[val]]s to flip for [[11/1]] and [[13/1]].

{{Harmonics in equal|207|11|1|intervals=prime|columns=11|collapsed=1}}

{{Harmonics in equal|168|7|1|intervals=prime|columns=11|collapsed=1}}

Line 588:

Line 586:

; 139ed5

The tuning [[139ed5]] is [[60edo]] but with slightly ''~~[[Octave stretch|~~stretched]]'' octaves.

The tuning [[139ed5]] is 60edo but with slightly ''stretched'' octaves.

~~It causes relatively large improvement to [[5/1]], [[7/1]] and [[11/1]] at the cost of relatively small worsening of [[2/1]] and relatively large worsening of [[13/1]]~~.

It also causes the [[val]] for [[11/1]] to flip from 208 steps to 207 steps.

It induces relatively large improvement to 5/1, 7/1 and 11/1 at the cost of worsening of 2/1 and 13/1. It also causes the patent val for 11/1 to flip from 208 steps to 207 steps.

{{Harmonics in equal|139|5|1|intervals=prime|columns=11|collapsed=1}}

; 301zpi

The tuning [[301zpi]], the 301st [[zeta peak index]], is [[60edo]] but with slightly ''~~[[Octave stretch|~~stretched]]'' octaves.

The tuning [[301zpi]], the 301st [[zeta peak index]], is 60edo but with slightly ''stretched'' octaves.

~~It causes relatively large improvement to [[3/1]], [[5/1]], [[7/1]], [[11/1]] and [[17/1]] at the cost of relatively small worsening of [[2/1]] and relatively large worsening of [[13/1]]~~.

It also causes the [[val]] for [[11/1]] to flip from 208 steps to 207 steps.

It induces relatively large improvement to 3/1, 5/1, 7/1, 11/1 and 17/1 at the cost of worsening of 2/1 and 13/1. It also causes the patent val for 11/1 to flip from 208 steps to 207 steps.

301zpi is ~~both [[consistent]] and [[~~distinctly consistent]] up to the 10-[[integer-limit]]~~, which is unusually high for a two digit edo or three digit zpi~~.

Like 60edo, 301zpi is distinctly consistent up to the [[integer limit|10-integer-limit]].

{{Harmonics in equal|1|38083|37645|intervals=prime|columns=11|title= Approximation of prime harmonics in 301zpi|collapsed=1}}

{{Harmonics in equal|1|38083|37645|intervals=prime|columns=11|title=Approximation of prime harmonics in 301zpi|collapsed=1}}

; 60edo

Line 611:

Line 605:

; 255ed19

The tuning [[255ed19]] is [[60edo]] but with slightly ''~~[[Octave shrinking|~~compressed]]'' octaves.

The tuning [[255ed19]] is 60edo but with slightly ''compressed'' octaves.

It ~~causes~~ a relatively large improvement to [[11/1]], at the cost of ~~relatively small~~ worsening of every smaller prime.

It induces a relatively large improvement to 11/1, at the cost of worsening of every smaller prime. It also causes the patent val for 7/1 to flip from 168 steps to 169.

It also causes the [[val]] for [[7/1]] to flip from 168 steps to 169.

{{Harmonics in equal|255|19|1|intervals=prime|columns=11|collapsed=1}}

; 208ed11

The tuning [[208ed11]] is [[60edo]] but with slightly ''~~[[Octave shrinking|~~compressed]]'' octaves.

The tuning [[208ed11]] is 60edo but with slightly ''compressed'' octaves.

It ~~causes~~ a relatively large improvement to [[7/1]] and [[11/1]], at the cost of ~~moderate~~ worsening of [[2/1]], [[3/1]] and [[5/1]].

It induces a relatively large improvement to 7/1 and 11/1, at the cost of worsening of 2/1, 3/1 and 5/1. It also causes the patent val to flip for 5/1, 7/1 and 17/1.

It also causes the [[val~~]]s~~ to flip for [[5/1]], [[7/1]] and [[17/1]].

{{Harmonics in equal|208|11|1|intervals=prime|columns=11|collapsed=1}}

; 272ed23

The tuning [[272ed23]] is [[60edo]] but with slightly ''~~[[Octave shrinking|~~compressed]]'' octaves.

The tuning [[272ed23]] is 60edo but with slightly ''compressed'' octaves.

~~It causes a relatively large improvement to [[7/1]] and [[11/1]], at the cost of moderate worsening of [[2/1]], [[3/1]] and [[5/1]].~~

~~It also causes the [[val]]s to flip for [[5/1]], [[7/1]], [[13/1]] and [[17/1]]~~.

~~These characteristics~~, ~~particularly~~ the ~~flipped 5~~/1 and 13/1~~, are preferred over pure-octaves 60edo for [[catnip]] temperament specifically~~. ~~They change catnip’s [[wart]]s from 60cf~~ to ~~272dg (later letters in the alphabet are better)~~.

It induces a relatively large improvement to 7/1 and 11/1, at the cost of worsening of 2/1, 3/1 and 5/1. It also causes the patent val to flip for 5/1, 7/1, 13/1 and 17/1.

Given this, 272ed23 can be thought of as a 60edo clone tailor-made for catnip.

These characteristics, particularly the flipped 5/1 and 13/1, are preferred over pure-octaves 60edo for [[catnip]] temperament specifically. They change catnip's [[wart]]s from 60cf to i272dg (later letters in the alphabet are better). Given this, 272ed23 can be thought of as a 60edo clone tailor-made for catnip.

{{Harmonics in equal|272|23|1|intervals=prime|columns=11|collapsed=1}}

@@ Line 578: / Line 578: @@
 ; 207ed11, 168ed7
-The tunings [[207ed11]] and [[168ed7]] are almost identical. Each is [[60edo]] but with slightly ''[[Octave stretch|stretched]]'' octaves.
+The tunings [[207ed11]] and [[168ed7]] are almost identical. Each is 60edo but with slightly ''stretched'' octaves.
-Each causes relatively large improvement to [[5/1]], [[7/1]] and [[11/1]] at the cost of moderate worsening of [[2/1]] and [[3/1]].
+Each induces relatively large improvement to [[5/1]], [[7/1]] and [[11/1]] at the cost of worsening of [[2/1]] and [[3/1]]. Each also causes the [[patent val]] to flip for [[11/1]] and [[13/1]].
-Each also causes the [[val]]s to flip for [[11/1]] and [[13/1]].
 {{Harmonics in equal|207|11|1|intervals=prime|columns=11|collapsed=1}}
 {{Harmonics in equal|168|7|1|intervals=prime|columns=11|collapsed=1}}
@@ Line 588: / Line 586: @@
 ; 139ed5
-The tuning [[139ed5]] is [[60edo]] but with slightly ''[[Octave stretch|stretched]]'' octaves.
+The tuning [[139ed5]] is 60edo but with slightly ''stretched'' octaves.
-It causes relatively large improvement to [[5/1]], [[7/1]] and [[11/1]] at the cost of relatively small worsening of [[2/1]] and relatively large worsening of [[13/1]].
-It also causes the [[val]] for [[11/1]] to flip from 208 steps to 207 steps.
+It induces relatively large improvement to 5/1, 7/1 and 11/1 at the cost of worsening of 2/1 and 13/1. It also causes the patent val for 11/1 to flip from 208 steps to 207 steps.
 {{Harmonics in equal|139|5|1|intervals=prime|columns=11|collapsed=1}}
 ; 301zpi
-The tuning [[301zpi]], the 301st [[zeta peak index]], is [[60edo]] but with slightly ''[[Octave stretch|stretched]]'' octaves.
+The tuning [[301zpi]], the 301st [[zeta peak index]], is 60edo but with slightly ''stretched'' octaves.
-It causes relatively large improvement to [[3/1]], [[5/1]], [[7/1]], [[11/1]] and [[17/1]] at the cost of relatively small worsening of [[2/1]] and relatively large worsening of [[13/1]].
-It also causes the [[val]] for [[11/1]] to flip from 208 steps to 207 steps.
+It induces relatively large improvement to 3/1, 5/1, 7/1, 11/1 and 17/1 at the cost of worsening of 2/1 and 13/1. It also causes the patent val for 11/1 to flip from 208 steps to 207 steps.
-zpi is both [[consistent]] and [[distinctly consistent]] up to the 10-[[integer-limit]], which is unusually high for a two digit edo or three digit zpi.
+Like 60edo, 301zpi is distinctly consistent up to the [[integer limit|10-integer-limit]].
-{{Harmonics in equal|1|38083|37645|intervals=prime|columns=11|title= Approximation of prime harmonics in 301zpi|collapsed=1}}
+{{Harmonics in equal|1|38083|37645|intervals=prime|columns=11|title=Approximation of prime harmonics in 301zpi|collapsed=1}}
 ; 60edo
@@ Line 611: / Line 605: @@
 ; 255ed19
-The tuning [[255ed19]] is [[60edo]] but with slightly ''[[Octave shrinking|compressed]]'' octaves.
+The tuning [[255ed19]] is 60edo but with slightly ''compressed'' octaves.
-It causes a relatively large improvement to [[11/1]], at the cost of relatively small worsening of every smaller prime.
+It induces a relatively large improvement to 11/1, at the cost of worsening of every smaller prime. It also causes the patent val for 7/1 to flip from 168 steps to 169.
-It also causes the [[val]] for [[7/1]] to flip from 168 steps to 169.
 {{Harmonics in equal|255|19|1|intervals=prime|columns=11|collapsed=1}}
 ; 208ed11
-The tuning [[208ed11]] is [[60edo]] but with slightly ''[[Octave shrinking|compressed]]'' octaves.
+The tuning [[208ed11]] is 60edo but with slightly ''compressed'' octaves.
-It causes a relatively large improvement to [[7/1]] and [[11/1]], at the cost of moderate worsening of [[2/1]], [[3/1]] and [[5/1]].
+It induces a relatively large improvement to 7/1 and 11/1, at the cost of worsening of 2/1, 3/1 and 5/1. It also causes the patent val to flip for 5/1, 7/1 and 17/1.
-It also causes the [[val]]s to flip for [[5/1]], [[7/1]] and [[17/1]].
 {{Harmonics in equal|208|11|1|intervals=prime|columns=11|collapsed=1}}
 ; 272ed23
-The tuning [[272ed23]] is [[60edo]] but with slightly ''[[Octave shrinking|compressed]]'' octaves.
+The tuning [[272ed23]] is 60edo but with slightly ''compressed'' octaves.
-It causes a relatively large improvement to [[7/1]] and [[11/1]], at the cost of moderate worsening of [[2/1]], [[3/1]] and [[5/1]].
-It also causes the [[val]]s to flip for [[5/1]], [[7/1]], [[13/1]] and [[17/1]].
-These characteristics, particularly the flipped 5/1 and 13/1, are preferred over pure-octaves 60edo for [[catnip]] temperament specifically. They change catnip’s [[wart]]s from 60cf to 272dg (later letters in the alphabet are better).
+It induces a relatively large improvement to 7/1 and 11/1, at the cost of worsening of 2/1, 3/1 and 5/1. It also causes the patent val to flip for 5/1, 7/1, 13/1 and 17/1.
-Given this, 272ed23 can be thought of as a 60edo clone tailor-made for catnip.
+These characteristics, particularly the flipped 5/1 and 13/1, are preferred over pure-octaves 60edo for [[catnip]] temperament specifically. They change catnip's [[wart]]s from 60cf to i272dg (later letters in the alphabet are better). Given this, 272ed23 can be thought of as a 60edo clone tailor-made for catnip.
 {{Harmonics in equal|272|23|1|intervals=prime|columns=11|collapsed=1}}