ED5: Difference between revisions

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=Division of the fifth harmonic into n equal parts=

The fifth harmonic is particularly wide as far as equivalences go. There are (at absolute most) ~4.8 pentaves within the human hearing range; imagine if that were the case with octaves. If one does indeed deal with pentave equivalence, this ~~fact shapes one's musical approach dramatically~~. ~~Following this, the~~ quintessential example of a pentave based tuning is hyperpyth (see [[17ed5]]). However, perhaps the more common reason to use these scales is in approximation with lower harmonic factors than 5. This approach is highlighted by Hieronymus ([[20ed5]]) which itself is a zeta peak tuning (not "no-fives", full on zeta). Other reasons for taking the nth root of 5 include finding temperaments like orwell, meantone, and thuja. This approach can of course be used indiscriminately.

The fifth harmonic is particularly wide as far as equivalences go. There are (at absolute most) ~4.8 pentaves within the human hearing range; imagine if that were the case with octaves. If one does indeed deal with pentave equivalence, this range restriction is a crucial consideration. Pentave equivalence itself may have a basis in Western music seeing as minor chords have an octave of 5 in their root (i.e. 10:12:15).

The quintessential example of a pentave based tuning is hyperpyth (see [[17ed5]]). However, perhaps the more common reason to use these scales is in approximation with lower harmonic factors than 5. This approach is highlighted by Hieronymus ([[20ed5]]) which itself is a zeta peak tuning (not "no-fives", full on zeta). Other reasons for taking the nth root of 5 include finding temperaments like orwell, meantone, and thuja. This approach can of course be used indiscriminately.

Below is a large list of ED5s; additionally, some equal divisions of the pentave are known by alternate names or have special interest:

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* [[Pentave Reduced Harmonics]]

* [[Pentave Reduced Subharmonics]]

*http://www.nonoctave.com/tuning/fifth_harmonic.html

*http://www.nonoctave.com/tuning/fifth_harmonic.html [[Category:Equal-step tuning]] [[Category:Ed5| ]]

[[Category:Equal-step tuning]]

[[Category:Ed5| ]]

[[Category:todo:add_sound_examples]]

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 =Division of the fifth harmonic into n equal parts=
-The fifth harmonic is particularly wide as far as equivalences go. There are (at absolute most) ~4.8 pentaves within the human hearing range; imagine if that were the case with octaves. If one does indeed deal with pentave equivalence, this fact shapes one's musical approach dramatically. Following this, the quintessential example of a pentave based tuning is hyperpyth (see [[17ed5]]). However, perhaps the more common reason to use these scales is in approximation with lower harmonic factors than 5. This approach is highlighted by Hieronymus ([[20ed5]]) which itself is a zeta peak tuning (not "no-fives", full on zeta). Other reasons for taking the nth root of 5 include finding temperaments like orwell, meantone, and thuja. This approach can of course be used indiscriminately.
+The fifth harmonic is particularly wide as far as equivalences go. There are (at absolute most) ~4.8 pentaves within the human hearing range; imagine if that were the case with octaves. If one does indeed deal with pentave equivalence, this range restriction is a crucial consideration. Pentave equivalence itself may have a basis in Western music seeing as minor chords have an octave of 5 in their root (i.e. 10:12:15).
+The quintessential example of a pentave based tuning is hyperpyth (see [[17ed5]]). However, perhaps the more common reason to use these scales is in approximation with lower harmonic factors than 5. This approach is highlighted by Hieronymus ([[20ed5]]) which itself is a zeta peak tuning (not "no-fives", full on zeta). Other reasons for taking the nth root of 5 include finding temperaments like orwell, meantone, and thuja. This approach can of course be used indiscriminately.
 Below is a large list of ED5s; additionally, some equal divisions of the pentave are known by alternate names or have special interest:
@@ Line 1,381: / Line 1,383: @@
 * [[Pentave Reduced Harmonics]]
 * [[Pentave Reduced Subharmonics]]
-*http://www.nonoctave.com/tuning/fifth_harmonic.html
+*http://www.nonoctave.com/tuning/fifth_harmonic.html  [[Category:Equal-step tuning]] [[Category:Ed5| ]] <!-- main article -->
-[[Category:Equal-step tuning]]
-[[Category:Ed5| ]] <!-- main article -->
 [[Category:todo:add_sound_examples]]

ED5: Difference between revisions

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