User:Fastaro/Generalized Pythagorean tuning: Difference between revisions

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# For x=0, n=0, the ratio p^x/q^n is: 1.0000000000000000 For x=0, n=0, the ratio q^(n+1)/p^x is: 2.0000000000000000 For x=1, n=1, the ratio p^x/q^n is: 1.5000000000000000 For x=1, n=1, the ratio q^(n+1)/p^x is: 1.3333333333333333 For x=2, n=3, the ratio p^x/q^n is: 1.1250000000000000 For x=2, n=3, the ratio q^(n+1)/p^x is: 1.7777777777777777 For x=3, n=4, the ratio p^x/q^n is: 1.6875000000000000 For x=3, n=4, the ratio q^(n+1)/p^x is: 1.1851851851851851 For x=4, n=6, the ratio p^x/q^n is: 1.2656250000000000 For x=4, n=6, the ratio q^(n+1)/p^x is: 1.5802469135802468 For x=5, n=7, the ratio p^x/q^n is: 1.8984375000000000 For x=5, n=7, the ratio q^(n+1)/p^x is: 1.0534979423868314 For x=6, n=9, the ratio p^x/q^n is: 1.4238281250000000 For x=6, n=9, the ratio q^(n+1)/p^x is: 1.4046639231824416 For x=7, n=11, the ratio p^x/q^n is: 1.0678710937500000 For x=7, n=11, the ratio q^(n+1)/p^x is: 1.8728852309099222 For x=8, n=12, the ratio p^x/q^n is: 1.6018066406250000 For x=8, n=12, the ratio q^(n+1)/p^x is: 1.2485901539399482 For x=9, n=14, the ratio p^x/q^n is: 1.2013549804687500 For x=9, n=14, the ratio q^(n+1)/p^x is: 1.6647868719199308 For x=10, n=15, the ratio p^x/q^n is: 1.8020324707031250 For x=10, n=15, the ratio q^(n+1)/p^x is: 1.1098579146132872 For x=11, n=17, the ratio p^x/q^n is: 1.3515243530273438 For x=11, n=17, the ratio q^(n+1)/p^x is: 1.4798105528177163

# For x=0, n=0, the ratio p^x/q^n is: 1.0000000000000000# For x=0, n=0, the ratio q^(n+1)/p^x is: 2.0000000000000000 # For x=1, n=1, the ratio p^x/q^n is: 1.5000000000000000 # For x=1, n=1, the ratio q^(n+1)/p^x is: 1.3333333333333333# For x=2, n=3, the ratio p^x/q^n is: 1.1250000000000000 # For x=2, n=3, the ratio q^(n+1)/p^x is: 1.7777777777777777# For x=3, n=4, the ratio p^x/q^n is: 1.6875000000000000# For x=3, n=4, the ratio q^(n+1)/p^x is: 1.1851851851851851# For x=4, n=6, the ratio p^x/q^n is: 1.2656250000000000# For x=4, n=6, the ratio q^(n+1)/p^x is: 1.5802469135802468# For x=5, n=7, the ratio p^x/q^n is: 1.8984375000000000# For x=5, n=7, the ratio q^(n+1)/p^x is: 1.0534979423868314# For x=6, n=9, the ratio p^x/q^n is: 1.4238281250000000# For x=6, n=9, the ratio q^(n+1)/p^x is: 1.4046639231824416# For x=7, n=11, the ratio p^x/q^n is: 1.0678710937500000# For x=7, n=11, the ratio q^(n+1)/p^x is: 1.8728852309099222# For x=8, n=12, the ratio p^x/q^n is: 1.6018066406250000# For x=8, n=12, the ratio q^(n+1)/p^x is: 1.2485901539399482# For x=9, n=14, the ratio p^x/q^n is: 1.2013549804687500# For x=9, n=14, the ratio q^(n+1)/p^x is: 1.6647868719199308# For x=10, n=15, the ratio p^x/q^n is: 1.8020324707031250# For x=10, n=15, the ratio q^(n+1)/p^x is: 1.1098579146132872# For x=11, n=17, the ratio p^x/q^n is: 1.3515243530273438# For x=11, n=17, the ratio q^(n+1)/p^x is: 1.4798105528177163

== Implications and Applications ==

The generalized Pythagorean tuning provides a more versatile framework for musical tuning, allowing composers and musicians to explore scales and harmonies beyond the traditional limits. This approach can lead to new musical expressions and better alignment with various musical traditions and instruments.

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-# For x=0, n=0, the ratio p^x/q^n is: 1.0000000000000000  For x=0, n=0, the ratio q^(n+1)/p^x is: 2.0000000000000000  For x=1, n=1, the ratio p^x/q^n is: 1.5000000000000000  For x=1, n=1, the ratio q^(n+1)/p^x is: 1.3333333333333333  For x=2, n=3, the ratio p^x/q^n is: 1.1250000000000000  For x=2, n=3, the ratio q^(n+1)/p^x is: 1.7777777777777777  For x=3, n=4, the ratio p^x/q^n is: 1.6875000000000000  For x=3, n=4, the ratio q^(n+1)/p^x is: 1.1851851851851851  For x=4, n=6, the ratio p^x/q^n is: 1.2656250000000000  For x=4, n=6, the ratio q^(n+1)/p^x is: 1.5802469135802468  For x=5, n=7, the ratio p^x/q^n is: 1.8984375000000000  For x=5, n=7, the ratio q^(n+1)/p^x is: 1.0534979423868314  For x=6, n=9, the ratio p^x/q^n is: 1.4238281250000000  For x=6, n=9, the ratio q^(n+1)/p^x is: 1.4046639231824416  For x=7, n=11, the ratio p^x/q^n is: 1.0678710937500000  For x=7, n=11, the ratio q^(n+1)/p^x is: 1.8728852309099222  For x=8, n=12, the ratio p^x/q^n is: 1.6018066406250000  For x=8, n=12, the ratio q^(n+1)/p^x is: 1.2485901539399482  For x=9, n=14, the ratio p^x/q^n is: 1.2013549804687500  For x=9, n=14, the ratio q^(n+1)/p^x is: 1.6647868719199308  For x=10, n=15, the ratio p^x/q^n is: 1.8020324707031250  For x=10, n=15, the ratio q^(n+1)/p^x is: 1.1098579146132872  For x=11, n=17, the ratio p^x/q^n is: 1.3515243530273438  For x=11, n=17, the ratio q^(n+1)/p^x is: 1.4798105528177163
+# For x=0, n=0, the ratio p^x/q^n is: 1.0000000000000000# For x=0, n=0, the ratio q^(n+1)/p^x is: 2.0000000000000000 # For x=1, n=1, the ratio p^x/q^n is: 1.5000000000000000 # For x=1, n=1, the ratio q^(n+1)/p^x is: 1.3333333333333333# For x=2, n=3, the ratio p^x/q^n is: 1.1250000000000000 # For x=2, n=3, the ratio q^(n+1)/p^x is: 1.7777777777777777# For x=3, n=4, the ratio p^x/q^n is: 1.6875000000000000# For x=3, n=4, the ratio q^(n+1)/p^x is: 1.1851851851851851# For x=4, n=6, the ratio p^x/q^n is: 1.2656250000000000# For x=4, n=6, the ratio q^(n+1)/p^x is: 1.5802469135802468# For x=5, n=7, the ratio p^x/q^n is: 1.8984375000000000# For x=5, n=7, the ratio q^(n+1)/p^x is: 1.0534979423868314# For x=6, n=9, the ratio p^x/q^n is: 1.4238281250000000# For x=6, n=9, the ratio q^(n+1)/p^x is: 1.4046639231824416# For x=7, n=11, the ratio p^x/q^n is: 1.0678710937500000# For x=7, n=11, the ratio q^(n+1)/p^x is: 1.8728852309099222# For x=8, n=12, the ratio p^x/q^n is: 1.6018066406250000# For x=8, n=12, the ratio q^(n+1)/p^x is: 1.2485901539399482# For x=9, n=14, the ratio p^x/q^n is: 1.2013549804687500# For x=9, n=14, the ratio q^(n+1)/p^x is: 1.6647868719199308# For x=10, n=15, the ratio p^x/q^n is: 1.8020324707031250# For x=10, n=15, the ratio q^(n+1)/p^x is: 1.1098579146132872# For x=11, n=17, the ratio p^x/q^n is: 1.3515243530273438# For x=11, n=17, the ratio q^(n+1)/p^x is: 1.4798105528177163
 == Implications and Applications ==
 The generalized Pythagorean tuning provides a more versatile framework for musical tuning, allowing composers and musicians to explore scales and harmonies beyond the traditional limits. This approach can lead to new musical expressions and better alignment with various musical traditions and instruments.