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=Division of the Fifth Harmonic (5/1) into n equal parts=
=Division of the Fifth Harmonic (5/1) into n equal parts=


The fifth harmonic is particularly wide as far as equivalences go.<span style=""> 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, </span>this fact shapes one's musical approach dramatically. Following this, the quintessential example of a pentave based tuning is hyperpyth (see [[17ed5|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|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.<span style=""> 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, </span>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.


[[2ed5]]
*[[3ed5]] : [[Orwell|orwell]] generator (with octaves)
 
*[[4ed5]] : [[Meantone|meantone]] generator (with octaves)
3ed5 [[Orwell|orwell]] generator (with octaves)
*[[5ed5]] : [[2L_7s|thuja]] generator (with octaves)
 
*[[6ed5]] : [[Trienstonic_clan#Uncle|uncle]] generator (with octaves)
4ed5 [[Meantone|meantone]] generator (with octaves)
*[[7ed5]] compare [[3edo]]
 
*[[8ed5]]
[[5ed5]] [[2L_7s|thuja]] generator (with octaves)
*[[9ed5]]
 
*[[10ed5]]
6ed5 [[Trienstonic_clan#Uncle|uncle]] generator (with octaves)
*[[11ed5]]
 
*[[12ed5]]
[[7ed5]] compare [[3edo]]
*[[13ed5]]
 
*[[14ed5]] compare [[6edo]]
[[8ed5]]
*[[15ed5]]
 
*[[16ed5]] compare [[7edo]]
[[9ed5]]
*[[17ed5]]
 
*[[18ed5]]
[[10ed5]]
*[[19ed5]] compare [[Bohlen-Pierce|Bohlen-Pierce]]
 
*[[20ed5]] (Hieronymus Tuning)
[[11ed5]]
*[[21ed5]] compare [[9edo]]
 
*[[22ed5]]
[[12ed5]]
*[[23ed5]] compare [[10edo]]
 
*[[24ed5]]
[[13ed5]]
*[[25ed5]] (Stockhausen, McLaren)
 
*[[26ed5]]
14ed5 compare [[6edo]]
*[[27ed5]]
 
*[[28ed5]] compare [[12edo]]
[[15ed5]]
*[[29ed5]]
 
*[[30ed5]] compare [[13edo]]
16ed5 compare [[7edo]]
*[[31ed5]]
 
*[[32ed5]] compare [[14edo]]
[[17ed5]]
*[[33ed5]]
 
*[[34ed5]]
[[18ed5]]
*[[35ed5]] compare [[15edo]]
 
*[[36ed5]]
[[19ed5]] compare [[Bohlen-Pierce|Bohlen-Pierce]]
*[[37ed5]] compare [[16edo]]
 
*[[38ed5]] compare [[26edt]]
[[20ed5]] (Hieronymus Tuning)
*[[39ed5]]
 
*[[40ed5]]
21ed5 compare [[9edo]]
*[[41ed5]]
 
*[[42ed5]]
[[22ed5]]
*[[43ed5]]
 
*[[44ed5]] compare [[19edo]]
23ed5 compare [[10edo]]
*[[45ed5]]
 
*[[46ed5]]
[[24ed5]]
*[[47ed5]]
 
*[[48ed5]]
[[25ed5]] (Stockhausen, McLaren)
*[[49ed5]]
 
*[[50ed5]]
[[26ed5]]
*[[51ed5]] compare [[22edo]]
 
*[[52ed5]]
[[27ed5]]
*[[53ed5]]
 
*[[54ed5]]
[[28ed5]] compare [[12edo]]
*[[55ed5]]
 
*[[56ed5]] compare [[24edo]]
[[29ed5]]
*[[57ed5]] compare [[39edt]]
 
*[[58ed5]] compare [[25edo]]
30ed5 compare [[13edo]]
*[[59ed5]]
 
*[[60ed5]]
[[31ed5]]
*[[61ed5]]
 
*[[62ed5]]
[[32ed5]] compare [[14edo]]
*[[63ed5]]
 
*[[64ed5]]
[[33ed5]]
*[[65ed5]]
 
*[[66ed5]]
[[34ed5]]
*[[67ed5]]
 
*[[68ed5]]
[[35ed5]] compare [[15edo]]
*[[69ed5]]
 
*[[70ed5]]
[[36ed5]]
*[[71ed5]]
 
*[[72ed5]]
37ed5 compare [[16edo]]
*[[73ed5]]
 
*[[74ed5]]
38ed5 compare [[26edt]]
*[[75ed5]]
 
*[[76ed5]]
[[39ed5]]
*[[77ed5]]
 
*[[78ed5]]
[[40ed5]]
*[[79ed5]]
 
*[[80ed5]]
[[41ed5]]
*[[81ed5]]
 
*[[82ed5]]
[[42ed5]]
*[[83ed5]]
 
*[[84ed5]]
[[43ed5]]
*[[85ed5]]
 
*[[86ed5]]
[[44ed5]] compare [[19edo]]
*[[87ed5]]
 
*[[88ed5]]
[[45ed5]]
*[[89ed5]]
 
*[[90ed5]]
[[46ed5]]
*[[91ed5]]
 
*[[92ed5]]
[[47ed5]]
*[[93ed5]]
 
*[[94ed5]]
[[48ed5]]
*[[95ed5]]
 
*[[96ed5]]
[[49ed5]]
*[[97ed5]]
 
*[[98ed5]]
[[50ed5]]
*[[99ed5]]
 
*[[100ed5]]
[[51ed5]] compare [[22edo]]
 
[[52ed5]]
 
[[53ed5]]
 
[[54ed5]]
 
[[55ed5]]
 
56ed5 compare [[24edo]]
 
[[57ed5]] compare [[39edt]]
 
[[58ed5]] compare [[25edo]]
 
[[59ed5]]
 
[[60ed5]]


==See also==
==See also==

Revision as of 09:45, 26 December 2018

Division of the Fifth Harmonic (5/1) 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.

See also

Pentave Reduced Harmonics

Pentave Reduced Subharmonics

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

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