About the calculator
The original Helmholtz-Ellis 31-Limit Harmonic Space Calculator is a tool for composers and musicians discovering and working with the properties of intervals tuned in just intonation. The calculator has been modified to use the color notation developed by Kite Giedraitis. The calculator maps primes 11, 13, 23 and 31 to P4, M6, A4 and P8 respectively, however color notation allows for flexible mappings.
REFERENCE
The origin or reference of the notation and harmonic space can be defined by octave (default = 4, in scientific pitch notation), by diatonic note name (default = A), and by chromatic alteration of the diatonic pitch (default = natural). The reference
can be further refined by altering the frequency of the "tuning note"
A4 (default = 440 Hz) or by altering the frequency of 1/1 itself
(default = 440 Hz). The relationship between these notes is defined in
terms of 12 equal divisions of the octave.
INPUT
Input of pitches can follow one of two workflows - by notation or by ratio - selected prior to making calculations.
input by notation
The calculator's default workflow is to input pitches using the
notation palette by selecting octave (default = 4), diatonic note
name (default = A), and just intonation accidental (default = natural).
The first row represents the accidentals historically used to notate a
series of perfect fifths. Subsequent rows represent various prime
dimensions of harmonic space up to 31 arranged in ascending deviation
from left to right. The direction of otonal/utonal movement is indicated
by an arrow up (for otonal) and an arrow down (for utonal) in the
prime's row label on each side of the palette.
input by ratio
Pitches may also be entered by inputting any ratio, representing an interval above or below the reference. In addition, an offset ratio (default = 1/1) may be specified. The input is multiplied by the offset before being expressed in terms of the reference. The offset may be entered directly or the current output of the calculator may be saved by clicking "save current"; "reset" restores the offset to 1/1. By successively clicking "save current", it is possible to compound the input ratio.
OUTPUT
The output shows information about the input pitch in relation to the reference: its ratio, spelling in color notation, cent deviation from the nearest MIDI pitch class, total cents value,
frequency, and Tenney distance. The output reflects staff notation, with the letter representing the notehead. In text, the order would be changed, and y#C would be written yC#. No relative notation is shown.
MELODIC
The melodic distance function allows a user to compare pitches by determining the interval between them. The current output of the calculator may be saved by clicking "save current" or restored to 1/1 by clicking "reset"; the current value of the calculator may be checked against the saved interval by clicking "check current".