ED5: Difference between revisions

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'''Ed5''' means '''Division of the Fifth Harmonic (5/1) into n equal parts'''.

~~<span style~~=~~"font-size: 150%;">~~Division of the fifth harmonic into n equal parts~~</span>~~

=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.

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

*[[3ed5]]: [[orwell]] generator (with octaves)

*[[4ed5]]: [[meantone]] generator (with octaves)

*[[5ed5]]: [[2L_7s|thuja]] generator (with octaves)

*[[6ed5]]: [[Trienstonic_clan#Uncle|uncle]] generator (with octaves)

*[[Hyperpyth|Hyperpyth tuning]] (e.g. [[17ed5]])

*[[20ed5|Hieronymus Tuning]]

*[[25ed5]] (Stockhausen, McLaren)

== Individual pages for ED5s ==

@@ Line 1: / Line 1: @@
 '''Ed5''' means '''Division of the Fifth Harmonic (5/1) into n equal parts'''.
-<span style="font-size: 150%;">Division of the fifth harmonic into n equal parts</span>
+=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.
+Below is a large list of ED5s; additionally, some equal divisions of the pentave are known by alternate names or have special interest:
+*[[3ed5]]: [[orwell]] generator (with octaves)
+*[[4ed5]]: [[meantone]] generator (with octaves)
+*[[5ed5]]: [[2L_7s|thuja]] generator (with octaves)
+*[[6ed5]]: [[Trienstonic_clan#Uncle|uncle]] generator (with octaves)
+*[[Hyperpyth|Hyperpyth tuning]] (e.g. [[17ed5]])
+*[[20ed5|Hieronymus Tuning]]
+*[[25ed5]] (Stockhausen, McLaren)
 == Individual pages for ED5s ==