Submajor and supraminor: Difference between revisions

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Submajor and supraminor intervals are hard to find as just intervals (partially due to the range of supraminor sixths corresponding to [[acoustic phi]]), and do not correspond cleanly to any subgroup of JI. However, here are some examples of just submajor and supraminor intervals:

* [[14/13]] (128c), supraminor second

* [[11/10]] (165c), submajor second

* [[17/14]] (336c), supraminor third

* [[21~~/17~~]] (~~366c~~), submajor third

* [[26/21]] (370c), submajor third

* [[34/21]] (~~834c~~), supraminor sixth

* [[21/13]] (830c), supraminor sixth

* [[28/17]] (864c), submajor sixth

* [[20/11]] (1035c), supraminor seventh

* [[13/7]] (1072c), submajor seventh

Submajor and supraminor intervals are found in flatly tuned diatonic scales, such as where the fifth is tuned to around 691 cents. For a given neutral interval k in cents, submajor ranges from roughly k+10 to k+24 cents, and supraminor ranges from roughly k-24 to k-10 cents. For example, submajor seconds are found between about 157 to 171 cents, containing the lower range of the "equable heptatonic" region defined by Margo Schulter.

Submajor and supraminor intervals are found in flatly tuned [[5L 2s|diatonic scales]], such as where the fifth is tuned to around 691 cents. For a given [[neutral]] interval ''k'' in cents, submajor ranges from roughly ''k''+10 to ''k''+24 cents, and supraminor ranges from roughly ''k''-24 to ''k''-10 cents. For example, submajor seconds are found between about 157 to 171 cents, containing the lower range of the "[[equable heptatonic]]" region defined by [[Margo Schulter]].

== Terminology ==

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 Submajor and supraminor intervals are hard to find as just intervals (partially due to the range of supraminor sixths corresponding to [[acoustic phi]]), and do not correspond cleanly to any subgroup of JI. However, here are some examples of just submajor and supraminor intervals:
+* [[14/13]] (128c), supraminor second
 * [[11/10]] (165c), submajor second
 * [[17/14]] (336c), supraminor third
-* [[21/17]] (366c), submajor third
+* [[26/21]] (370c), submajor third
-* [[34/21]] (834c), supraminor sixth
+* [[21/13]] (830c), supraminor sixth
 * [[28/17]] (864c), submajor sixth
 * [[20/11]] (1035c), supraminor seventh
+* [[13/7]] (1072c), submajor seventh
-Submajor and supraminor intervals are found in flatly tuned diatonic scales, such as where the fifth is tuned to around 691 cents. For a given neutral interval k in cents, submajor ranges from roughly k+10 to k+24 cents, and supraminor ranges from roughly k-24 to k-10 cents. For example, submajor seconds are found between about 157 to 171 cents, containing the lower range of the "equable heptatonic" region defined by Margo Schulter.
+Submajor and supraminor intervals are found in flatly tuned [[5L 2s|diatonic scales]], such as where the fifth is tuned to around 691 cents. For a given [[neutral]] interval ''k'' in cents, submajor ranges from roughly ''k''+10 to ''k''+24 cents, and supraminor ranges from roughly ''k''-24 to ''k''-10 cents. For example, submajor seconds are found between about 157 to 171 cents, containing the lower range of the "[[equable heptatonic]]" region defined by [[Margo Schulter]].
 == Terminology ==