User:BudjarnLambeth/116zpi: Difference between revisions
Created page with "{{Editable user page}} '''116zpi''', the 116th zeta peak index, is a stretched-octaves version of 29edo. It can be thought of as '''80ed1202.49c''' or as '''41.465cet'''. It has a step size of 41.465 cents, and the octave (2/1) is tuned slightly impurely to 80ed1202.49 cents. 29edo tunes almost all simple harmonics slightly flat by roughly the same amount, so 116zpi is one possible way of correcting for this. ==Prime har..." |
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{{Editable user page}} | {{Editable user page}} | ||
'''116zpi''', the 116th [[zeta peak index]], is a [[Octave stretching|stretched-octaves]] version of [[29edo]]. It can be thought of as ''' | '''116zpi''', the 116th [[zeta peak index]], is a [[Octave stretching|stretched-octaves]] version of [[29edo]]. It can be thought of as '''29ed1202.49c''' or as '''41.465cet'''. | ||
It has a step size of 41.465 [[cent]]s, and the [[octave]] ([[2/1]]) is tuned slightly impurely to | It has a step size of 41.465 [[cent]]s, and the [[octave]] ([[2/1]]) is tuned slightly impurely to 1202.49 cents. | ||
29edo tunes almost all simple [[harmonic]]s slightly flat by roughly the same amount, so 116zpi is one possible way of correcting for this. | 29edo tunes almost all simple [[harmonic]]s slightly flat by roughly the same amount, so 116zpi is one possible way of correcting for this. | ||
==Prime harmonics== | ==Prime harmonics== | ||
{{Harmonics in cet|41.465|columns= | {{Harmonics in cet|41.465|columns=10|intervals=prime|title=Approximation of prime harmonics in 116zpi}} | ||
For [[prime]]s up to 29: | For [[prime]]s up to 29: | ||
116zpi approximates these with less than 7 cents error (<17% relative error): | |||
* 2, 3, 11, 13, 19, 23 | * 2, 3, 11, 13, 19, 23 | ||
| Line 22: | Line 21: | ||
* 29 | * 29 | ||
This makes it usable as a full [[ | This makes it usable as a full [[23-limit]] tuning, or as a more accurate 2.3.5.11.13 [[subgroup]] tuning. | ||
==Scales== | ==Scales== | ||
| Line 30: | Line 29: | ||
All instruments listed under [[29edo#Instruments]] also work for 116zpi. | All instruments listed under [[29edo#Instruments]] also work for 116zpi. | ||
[[Category:Zeta peak indexes]] [[Category:29edo | [[Category:Zeta peak indexes]] [[Category:29edo]] | ||