Prime number: Difference between revisions

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''todo: improve definition rearrange contents of pages [[prime number]] and [[prime EDO]]''

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A prime edo is useful for avoiding intervals and patterns that are familiar-sounding due to their occurrence in 12edo. Since 12 is 2*2*3, it contains [[2edo|2EDO]], [[3edo|3EDO]], [[4edo|4EDO]] and [[6edo|6EDO]]. All edos with a 2, 3, 4, or 6 in their factorization will share at least one interval with 12edo, if not a whole chord or subset scale. Of course, if the goal is simply to avoid intervals of 12, then non-prime edos which don't have a 2, 3, 4, or 6 in their factorization, such as [[35edo|35EDO]], will work just as well for this purpose.

If you like a certain EDO for its intervals or other reasons, but do not like its primality or non-primality, choosing another equivalence interval, such as the [[~~edt~~|tritave (3/1)]] instead of the octave, can be an option. For example, [[27edt]] is a non-prime system very similar to [[17edo]], while [[~~19edt~~|19edt (Stopper tuning)]] is a prime system very similar to the ubiquitous [[12edo]]. (See [[~~edt~~#EDO~~-EDT~~ correspondence|EDO~~-EDT~~ correspondence]] for more of these.) Anyway, for every prime EDO system there is a non-prime [[~~ed4~~|ED4]] system with identical step sizes.

If you like a certain EDO for its intervals or other reasons, but do not like its primality or non-primality, choosing another equivalence interval, such as the [[Edt|tritave (3/1)]] instead of the octave, can be an option. For example, [[27edt]] is a non-prime system very similar to [[17edo]], while [[19ED3|19edt (Stopper tuning)]] is a prime system very similar to the ubiquitous [[12edo]]. (See [[Edt#EDT-EDO correspondence|EDT-EDO correspondence]] for more of these.) Anyway, for every prime EDO system there is a non-prime [[Ed4|ED4]] system with identical step sizes.

The larger ''n'' is, the less these points matter, since the difference between an ''absolutely'' uniform scale and an approximated, ''nearly'' uniform scale eventually become inaudible.

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-<span style="display: block; text-align: right;">[[素数|日本穂]]</span>
+<span style="display: block; text-align: right;">[[素数|日本語]]</span>
 ''todo: improve definition rearrange contents of pages [[prime number]] and [[prime EDO]]''
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 A prime edo is useful for avoiding intervals and patterns that are familiar-sounding due to their occurrence in 12edo. Since 12 is 2*2*3, it contains [[2edo|2EDO]], [[3edo|3EDO]], [[4edo|4EDO]] and [[6edo|6EDO]]. All edos with a 2, 3, 4, or 6 in their factorization will share at least one interval with 12edo, if not a whole chord or subset scale. Of course, if the goal is simply to avoid intervals of 12, then non-prime edos which don't have a 2, 3, 4, or 6 in their factorization, such as [[35edo|35EDO]], will work just as well for this purpose.
-If you like a certain EDO for its intervals or other reasons, but do not like its primality or non-primality, choosing another equivalence interval, such as the [[edt|tritave (3/1)]] instead of the octave, can be an option. For example, [[27edt]] is a non-prime system very similar to [[17edo]], while [[19edt|19edt (Stopper tuning)]] is a prime system very similar to the ubiquitous [[12edo]]. (See [[edt#EDO-EDT correspondence|EDO-EDT correspondence]] for more of these.) Anyway, for every prime EDO system there is a non-prime [[ed4|ED4]] system with identical step sizes.
+If you like a certain EDO for its intervals or other reasons, but do not like its primality or non-primality, choosing another equivalence interval, such as the [[Edt|tritave (3/1)]] instead of the octave, can be an option. For example, [[27edt]] is a non-prime system very similar to [[17edo]], while [[19ED3|19edt (Stopper tuning)]] is a prime system very similar to the ubiquitous [[12edo]]. (See [[Edt#EDT-EDO correspondence|EDT-EDO correspondence]] for more of these.) Anyway, for every prime EDO system there is a non-prime [[Ed4|ED4]] system with identical step sizes.
 The larger ''n'' is, the less these points matter, since the difference between an ''absolutely'' uniform scale and an approximated, ''nearly'' uniform scale eventually become inaudible.