Template:Harmonics in equal/doc

This template generates a table for prime approximations in equal-step tunings.

Usage

Simple

For divisions of the octave (edo), you can use one unnamed argument:

{{primes in equal|<EDO number>}}

For other divisions, you can use two or three unnamed arguments:

{{primes in equal|<steps>|<numerator>|<denominator>}}

By default, the titles for divisions of 2/1, 3/1 and 3/2 will be displayed as 'edo', 'edt' and 'edf' respectively. When the denominator is 1, it will not be displayed.

Advanced

The template takes up to 7 arguments:

{{primes in equal
| steps = <number of steps>
| num = <numerator>
| denom = <denominator>
| columns = <column count>
| start = <start column>
| prec = <decimals of abs error>
| title = <your title>
}}

steps

Number of steps. This parameter can also be given without the parameter name.

num

Numerator of the interval that is divided equally. Can be used without parameter name. Default: 2.

denom

Denominator of the interval that is divided equally. Can be used without parameter name. Default: 1.

columns

number of primes to include, the default (8) means 2, 3, 5, 7, 11, 13, 17, 19

start

Default is 1 (which means the prime 2), set to 2 to skip the octave.

prec

Precision of absolute error (digits after the decimal point), default is estimated according to the step size.

title

Default is: "Approximations of prime intervals in name". By default, the names for divisions of 2/1, 3/1 and 3/2 will be displayed as 'edo', 'edt' and 'edf' respectively. When the denominator is 1, it will not be displayed.

Examples

Basic

For edos it is sufficient to only input the number of steps:

{{primes in equal|31}}

For tritave or other prime divisions, two arguments is enough:

{{primes in equal|13|3}}

In the most general case, we can input the number of steps, numerator and denominator.

{{primes in equal|15|7|3}}

Advanced

Sometimes you want to see more or skip some lower columns and have to adjust the title:

{{primes in equal|13|3|columns=11|start=2|title=Primes in [[13edt]]}}

For large divisions (313edo in this example) the absolute error gets very small. The default precision gets calculated automatically, but if we want to increase it even further, we can set prec to a higher value. This is not recommended generally.

{{primes in equal|313|columns=9|start=2}}
{{primes in equal|313|columns=9|start=2|prec=5|title=Same with prec=5}}