Partch Diamond

Prent: Harry usually rotated the Diamond on its side so that the
1/1 (2/1) column ascended, and he indicated when the tower of intervals
surpassed the 2/1, but your plot is basically correct.

Ratios such as 15/8, 16/15, 81/80, etc. are "secondary ratios,"
outside of the Diamond, but included in his gamut both to make
the scale more even (especially near 1/1 and 2/1) and to make more
Otonal and Utonal chords available. Otherwise, he would not have
been able to play progressions such as V7-I or IV-I in the same
O/Utonality.

--John


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Kami,

Here is the unformatted overview from the on-line help for Just.
There are a couple of versions 'out there'. The latest version
supports midi in, so you can play tunings from a midi keyboard. If
your version doesn't do that and you wish to, let me know. Also the
newer version is FAT so it will run on Intel-NeXTStep as well as NeXT
hardware.


If you need more help, let me know.

Bill Parod




Overview

This application provides a means of exploring arbitrary tuning
systems using standard representations (pitch, musical interval,
cents, frequency, and ratio), as well as exploiting theoretical
systems such as Just Intonation and N-tone equal temperament. The
application organizes these features into two main window styles and
a few auxiliary panels. The two window styles: Keyboard and Matrix,
contain Keys that may be tuned and played with the mouse or MIDI
keyboard. A Tuning Panel provides controls that are used to tune,
play, compare, or change the representation of selected keys.

The user may also play standard NeXT and MIDI score files. These
scores may be retuned from tuning information in Keyboard or Matrix
Windows.

Keyboard Windows

Keyboard windows contain an arbitrary number of marimba style keys.
Keys are sounded by clicking with the mouse. Multiple keys may be
selected at one time. This is useful for listening to chords, or
examining relationships within a subset of a tuning.


Keys are moved within or between Keyboards with the standard cut,
copy, and paste mechanisms. Each Key may be tuned and presented in a
variety of representation styles:


Pitch
Cents Relative to a Reference Key
Cents Relative to the Previous Key
Hertz
Ratio Relative to a Reference Key
Ratio Relative to the Previous Key
Interval from Reference Key
Interval from Previous Key
MIDI Key Number
User Label (arbitrary names, i.e Do, Re, Mi)

Matrix Windows


There are two types of Matrices available: Transpositional and
Extended Just. Each presents a palette of ratios to be used in the
formation of new Keyboards, although representation is not restricted
to ratios. Any of the above tuning representations may be used.


A Transposition matrix is formed by selecting two keyboards as axes,
and creating a matrix consisting of each keyboard transposed by each
step of the other.

An Extended Just Matrix also provides a system of ratios. Each axis
represents powers of a specified ratio, reduced and brought to within
an octave of the origin (1/1), which is centered in the matrix.


Tuning a Keyboard or Matrix

The Tuning Panel is the mechanism used to tune a key or change its
representation. Controls in the Tuning Panel are applied to the last
key played. The desired representation or tuning style for individual
Keys or an entire Keyboard/Matrix are chosen with the Tuning Panel.


Tuning a Score

Once a tuning is described, it may be used to affect the performance
of a score. Re-tuning a score is accomplished by installing a
Keyboard's tuning as the default tuning system for Musickit
performance. A score may be heard with a variety of tunings by
installing those from different Keyboards.



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