TAMNAMS: Difference between revisions

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By default, all ranges include their endpoints. For example, a hard tuning is considered a quasihard tuning. To exclude endpoints, the modifier ''strict'' can be used, for example ''strict hyposoft''.

Note that mosses with soft-of-basic step ratios always exhibit [[Rothenberg propriety]], or are ''proper'', whereas mosses with hard-of-basic step ratios do not, or are ''not proper'', with one exception: mosses with only one small step per period are always proper, regardless of the step ratio. It has been argued, however, that this is not a particularly important property, ~~especially as~~ larger moses tend to sound more distinct when L/s > 1, which is in some sense the more vast/varied side of the tuning spectrum, because as L/s becomes larger, the scale becomes increasingly close to the [[equalized]] tuning, which is usually radically different from most "proper" tunings while softer tunings don't have much room to be different compared to the basic tuning. (This is explained in more detail in [[TAMNAMS/Appendix#Extending the spectrum's edges]].)

Note that mosses with soft-of-basic step ratios always exhibit [[Rothenberg propriety]], or are ''proper'', whereas mosses with hard-of-basic step ratios do not, or are ''not proper'', with one exception: mosses with only one small step per period are always proper, regardless of the step ratio. It has been argued, however, that this is not a particularly important property, both because "improper" MOSSes still admit an ordering if you allow "off-by-one" errors and because larger moses tend to sound more distinct when L/s > 1, which is in some sense the more vast/varied side of the tuning spectrum, because as L/s becomes larger, the scale becomes increasingly close to the [[equalized]] tuning, which is usually radically different from most "proper" tunings while softer tunings don't have much room to be different compared to the basic tuning. (This is explained in more detail in [[TAMNAMS/Appendix#Extending the spectrum's edges]].)

{| class="wikitable"

|+Intermediate ranges

@@ Line 73: / Line 73: @@
 By default, all ranges include their endpoints. For example, a hard tuning is considered a quasihard tuning. To exclude endpoints, the modifier ''strict'' can be used, for example ''strict hyposoft''.
-Note that mosses with soft-of-basic step ratios always exhibit [[Rothenberg propriety]], or are ''proper'', whereas mosses with hard-of-basic step ratios do not, or are ''not proper'', with one exception: mosses with only one small step per period are always proper, regardless of the step ratio. It has been argued, however, that this is not a particularly important property, especially as larger moses tend to sound more distinct when L/s > 1, which is in some sense the more vast/varied side of the tuning spectrum, because as L/s becomes larger, the scale becomes increasingly close to the [[equalized]] tuning, which is usually radically different from most "proper" tunings while softer tunings don't have much room to be different compared to the basic tuning. (This is explained in more detail in [[TAMNAMS/Appendix#Extending the spectrum's edges]].)
+Note that mosses with soft-of-basic step ratios always exhibit [[Rothenberg propriety]], or are ''proper'', whereas mosses with hard-of-basic step ratios do not, or are ''not proper'', with one exception: mosses with only one small step per period are always proper, regardless of the step ratio. It has been argued, however, that this is not a particularly important property, both because "improper" MOSSes still admit an ordering if you allow "off-by-one" errors and because larger moses tend to sound more distinct when L/s > 1, which is in some sense the more vast/varied side of the tuning spectrum, because as L/s becomes larger, the scale becomes increasingly close to the [[equalized]] tuning, which is usually radically different from most "proper" tunings while softer tunings don't have much room to be different compared to the basic tuning. (This is explained in more detail in [[TAMNAMS/Appendix#Extending the spectrum's edges]].)
 {| class="wikitable"
 |+Intermediate ranges