Sagittal notation: Difference between revisions
added a prime approximation table, among other things and fixed some errors |
m tables too thicc |
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=== Promethean === | === Promethean === | ||
It adds 20 more symbols to Athenian symbol set, allowing for a maximum resolution of 47EDA. When used for JI, it defines the ''Standard High Precision JI'' capable of writing in the 23-limit, however, this JI notation is not recommended. It instead can be used to write in EDOs such as the [[Zeta peak edo|zeta edos]] [[270edo|270]] and [[311edo|311]], the latter to write music in the [[41-limit]]. | It adds 20 more symbols to Athenian symbol set, allowing for a maximum resolution of 47EDA. When used for JI, it defines the ''Standard High Precision JI'' capable of writing in the 23-limit or 41-limit, however, this JI notation is not recommended. It instead can be used to write in EDOs such as the [[Zeta peak edo|zeta edos]] [[270edo|270]] and [[311edo|311]], the latter to write music in the [[41-limit]]. | ||
=== Herculean === | === Herculean === | ||
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== Prime approximations == | == Prime approximations == | ||
Here are some approximations to octave reduced primes from D, using the several precision sets available in JI. Values in parentheses are | Here are some approximations to octave reduced primes from D, using the several precision sets available in JI. Values in parentheses are absolute error in cents from just; if exact, none is displayed. | ||
{| class="wikitable" | {| class="wikitable" | ||
| | | | ||
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|C {{sagittal|@2}}{{sagittal|(| }} (0.039) | |C {{sagittal|@2}}{{sagittal|(| }} (0.039) | ||
|} | |} | ||
Tempered systems might yield better or worse approximations to each just interval. Used for JI, only intervals some in the 23-limit will ever be exact. The error gets increasingly small however, down to hundredths of a cent in Magrathean. | |||
== Gallery == | == Gallery == | ||
=== Spartan single-shaft === | === Spartan single-shaft === | ||
| Line 375: | Line 377: | ||
!{{sagittal|`}} | !{{sagittal|`}} | ||
!{{sagittal|,}} | !{{sagittal|,}} | ||
|- | |||
|qui | |||
|quo | |||
|quiqui | |||
|quoquo | |||
|mi | |||
|mo | |||
|- | |||
|10241/10240 up | |||
|10241/10240 up | |||
|5832/5831 up | |||
|5832/5831 down | |||
|[https://en.xen.wiki/w/4096/4095 35/13sx] up | |||
|35/13sx down | |||
|} | |||
{| class="wikitable" | |||
!{{sagittal|@4}} | !{{sagittal|@4}} | ||
!{{sagittal|l4}} | !{{sagittal|l4}} | ||
| Line 381: | Line 399: | ||
!{{sagittal|``}} | !{{sagittal|``}} | ||
!{{sagittal|,,}} | !{{sagittal|,,}} | ||
|- | |||
|quimi | |||
|quomo | |||
|quiquimi | |||
|quoquomo | |||
|mimi | |||
|momo | |||
|- | |||
|3025/3024 up | |||
|3025/3024 up | |||
|2401/2400 up | |||
|2401/2400 down | |||
|[https://en.xen.wiki/w/2080/2079 77/65sx] up | |||
|77/65sx down | |||
|} | |||
{| class="wikitable" | |||
!{{sagittal|@7}} | !{{sagittal|@7}} | ||
!{{sagittal|l7}} | !{{sagittal|l7}} | ||
!{{sagittal|@8}} | !{{sagittal|@8}} | ||
!{{sagittal|l8}} | !{{sagittal|l8}} | ||
!{{sagittal|@9}} | !{{sagittal|@9}} | ||
!{{sagittal|l9}} | !{{sagittal|l9}} | ||
|- | |- | ||
|quimimi | |quimimi | ||
|quomomo | |quomomo | ||
|quiquimimi | |quiquimimi | ||
|quoquomomo | |quoquomomo | ||
|mimimi | |mimimi | ||
|momomo | |momomo | ||
|- | |- | ||
|1701/1700 up | |1701/1700 up | ||
|1701/1700 down | |1701/1700 down | ||
|382976/382725 up | |382976/382725 up | ||
|382976/382725 down | |382976/382725 down | ||
|131072/130977 up | |131072/130977 up | ||
|131072/130977 down | |131072/130977 down | ||
|} | |||
{| class="wikitable" | |||
!{{sagittal|@.}} | |||
!{{sagittal|l.}} | |||
|- | |||
|i | |||
|o | |||
|- | |||
|1515591/1515520 up | |1515591/1515520 up | ||
|1515591/1515520 down | |1515591/1515520 down | ||