Diamond monotone: Difference between revisions

(2 intermediate revisions by the same user not shown)

Line 6:

The "empirical" range is likely to fall somewhere between diamond monotone and diamond tradeoff. Though, when one is using tempered spectra to match the tuning, it is possible the empirical range can be made wider.

~~The page [[Monotonicity limits of small edos]] shows the largest odd limit that a given edo is monotonic in.~~

== Temperaments without diamond monotone tunings ==

While diamond tradeoff tunings are always guaranteed to occur, diamond monotone tunings are not.

While diamond tradeoff tunings are always guaranteed to occur, diamond monotone tunings are not (even though in most practical cases they do occur).

Let's look at an example: the rank-2 temperament with mapping {{mapping| 1 0 5 | 0 1 -2 }}, tempering out [[45/32]].

Line 27:

Line 25:

== See also ==

~~For~~ examples and other information~~, see~~ the ~~topic page~~ [[~~Tuning ranges of regular temperaments~~]].

* [[Tuning ranges of regular temperaments]] – for examples and other information

* [[Monotonicity limits of small edos]] – the largest odd limit each edo from 1 to 72 is monotonic in

* [[Minimum monotone vals]] – the earliest [[generalized patent val]] monotone in each odd limit from 1 to 127

== References ==

@@ Line 6: / Line 6: @@
 The "empirical" range is likely to fall somewhere between diamond monotone and diamond tradeoff. Though, when one is using tempered spectra to match the tuning, it is possible the empirical range can be made wider.
-The page [[Monotonicity limits of small edos]] shows the largest odd limit that a given edo is monotonic in.
 == Temperaments without diamond monotone tunings ==
-While diamond tradeoff tunings are always guaranteed to occur, diamond monotone tunings are not.
+While diamond tradeoff tunings are always guaranteed to occur, diamond monotone tunings are not (even though in most practical cases they do occur).
 Let's look at an example: the rank-2 temperament with mapping {{mapping| 1 0 5 | 0 1 -2 }}, tempering out [[45/32]].
@@ Line 27: / Line 25: @@
 == See also ==
-For examples and other information, see the topic page [[Tuning ranges of regular temperaments]].
+* [[Tuning ranges of regular temperaments]] – for examples and other information
+* [[Monotonicity limits of small edos]] – the largest odd limit each edo from 1 to 72 is monotonic in
+* [[Minimum monotone vals]] – the earliest [[generalized patent val]] monotone in each odd limit from 1 to 127
 == References ==