Description
An N-limit tonaility diamond, as used by Harry Partch.
With a 9-limit diamond in base 2, one row looks like:
It also is able to generate and navigate a 2 dimentinal table:
It is possible to do chord changes by 'walking' though the table.
Class Methods
.new
Create a new instance
Arguments:
| identities |
An array of numbers to use for numerators in otonality. Defaults to [2, 5, 3, 7, 9, 11, 13, 15, 17, 19, 21, 23] |
| base |
This is 2 for Octave-based systems. |
Discussion:
.limit
Create a new instance
Arguments:
| limit |
the limit for the tuning. So 5 for 5-limit, 7-for 7-limit, etc. |
| base |
This is 2 for Octave-based systems. |
Discussion:
.adjustOctave
Adjusts the octave of a tuning ratio so that it is between 1/1 and 2/1
Arguments:
| ratio |
the ratio to adjust |
| base |
The base of the tuning system. This is 2 for octave-based systems. The adjusted ratio will be between 1 and the base. |
Returns:
The adjusted ratio
Instance Methods
.niad
Rfor a given numerator and denominator, return a chord of n ratios
Arguments:
| numerator |
The numerator for the first item in the triad. The triad will wrap around if three spaces past the integer goes beyond the limit. |
| denominator |
The denominator for the first item in the triad. The triad will wrap around if three spaces past the integer goes beyond the limit. |
| orientation |
Use true for utonality or false for otonailty. |
|
the number of conitguious ratios for the N-iad; |
Returns:
An array of ratios
Discussion:
.walk
Find a pivot based on a start point, describe by numerator/denominator. Finding the new pivot point means picking one of the fractions in a n-iad Finding the new start means figuring out whether the new pivot is the top, middle, or bottom member of the triad and computing a new start index based on that computation
Arguments:
| numerator |
The starting numerator of the n-iad which we will launch from |
| denominator |
The starting denominator of the n-iad in which we will launch from |
| orientation |
If true, the overtones will change in the pivot for the first step. If false, the undertones will change in the pivot for the first step. This will alternate for every step. |
| niad |
The number of contigious ratios to return in the chord. This defaults to 3 for a triad |
Returns:
An Routine which yields a stream of arrays of ratios
Discussion:
The Routine takes an inval that is either an integer which indicates the number of ratios to return (ie 3 for a triad) or an Event. If it is an Event, it looks for an item index by \niad and uses that to determine the number of ratios to return. In the case that the number of ratios is not specified with an inval, it will use the last number specified.
.getInterval
For a given x and y index, return a ratio
Arguments:
| x |
The index in the diamond row for o[x]/o[y] This wraps if need be. |
| y |
The index in the diamond column for o[x]/o[y] This wraps if need be. |
Returns:
a ratio
.makeIntervals
For a given x and y index, return a n-iad of ratios
Arguments:
| x |
The index in the diamond row for o[x]/o[y] This wraps if need be. |
| y |
The index in the diamond column for o[x]/o[y] This wraps if need be. |
| orientation |
Use true for utonality such that the returned triads will change in the numerator, but not the demonimator. To change the denominator, use false. |
| niad |
The number of contigious ratios to return in the chord. This defaults to 3 for a triad |
Returns:
an Array of niad ratios
Discussion:
.d1Interval
Returns the fraction at the index
Arguments:
| index |
The index of the overtone or undertone |
| orientation |
true for otonality, false for utonality |
Returns:
a ratio
Discussion:
.d1Pivot
Find a pivot based on a start point. Finding the new pivot point means picking one of the fractions in a n-iad. Finding the new start means figuring out wether the new pivot is the top, middle, or bottom member of the n-iad and computing a new start index based on that computation
Arguments:
| start |
The starting index of the n-iad, in which we wish to pivot |
| niad |
The number of contigious ratios to return in the chord. This defaults to 3 for a triad |
Returns:
An array containing the index of the new start and the index of the pivot
.d1Intervals
For a given index, return a n-iad of ratios
Arguments:
| start |
he index in the lattice row in which to start. This wraps if need be. |
| orientation |
Use true for utonality or false for otonailty. |
| niad |
The number of contigious ratios to return in the chord. This defaults to 3 for a triad |
Returns:
An array of niad ratios
Discussion:
The n-iad is computed in regards to the base. ex:
.d2Pivot
Find a pivot based on a start point, describe by o[x]/o[y]. Finding the new pivot point means picking one of the fractions in a n-iad Finding the new start means figuring out whether the new pivot is the top, middle, or bottom member of the triad and computing a new start index based on that computation
Arguments:
| x |
The starting index of the numerator of the n-iad in which we wish to pivot |
| y |
The starting index of the denominator of the n-iad in which we wish to pivot |
| orientation |
If true, the overtones will change in the pivot. If false, the undertones will change in the pivot. |
| niad |
The number of contigious ratios to return in the chord. This defaults to 3 for a triad |
Returns:
An array containing the x of the first interval in the n-iad, the y of the first interval, the x of the pivot, and the y of the pivot
.d2WalkXY
Find a pivot based on a start point, describe by o[x]/o[y]. Finding the new pivot point means picking one of the fractions in a n-iad Finding the new start means figuring out whether the new pivot is the top, middle, or bottom member of the triad and computing a new start index based on that computation
Arguments:
| x |
The starting index of the numerator of the n-iad which we will launch from |
| y |
The starting index of the denominator of the n-iad in which we will launch from |
| orientation |
If true, the overtones will change in the pivot for the first step. If false, the undertones will change in the pivot for the first step. This will alternate for every step. |
| niad |
The number of contigious ratios to return in the chord. This defaults to 3 for a triad |
Returns:
An Routine which yields a stream of arrays of ratios
.postln
Prints out the tonality diamond
Discussion:
Examples
Using a Diamond with a Pbind: