Heptadecatonic Drops: More Information

Excerpt from the preface of 17 Tones, a collection of pieces in 17-tone equal temperament published by Thürmchen Verlag:

Microtonal music played an important role in Johannes Fritsch’s seminar at the Cologne Hochschule für Musik. His preoccupation with universal harmony was supported by Clarence Barlow’s theory of quantized harmony. Departing from his treatise I started to develop my own theory of harmonic energy which predicts the amount of stability for a given tuning1. According to this, temperaments with 17, 19, and 22 steps per octave are marked by low system energies (i.e. high stability) for a musical context that allows a clear pitch percept, in addition to 12-tone temperament, of course. Despite their prevalence in older theories and compositions, tunings derived through equal subdivision of a tempered whole tone (into three, four, five, etc. steps) seem to have less importance due to relatively low stability.
The following graph shows the relevance of tempered tunings as a function of the number of steps per octave. (Relevance is an arbitrary measure for the stability of a tuning in a given acoustical and musical context [values from 0-10]. A clear pitch percept was assumed in the present case.)

For two reasons, we decided upon 17-tone temperament for our project (instead of the more favorable 19-tone tuning which, according to Joseph Yasser, will eventually replace the standard tuning). First, the 17 tones of the heptadecatonic tuning form an enharmonic system with two alternative pitches for each black piano key, as the naming of the pitches would suggest (c# <=> db). Thus, the traditional diatonic structure is maintained after the assignment of the 17 pitch classes onto two piano keyboards. Second, its 11th step (705.9 ct) deviates only by 4 cts from the just fifth (3:2), an almost unnoticeable difference. The circle of fifths closes after 17 fifths, e# and gb being enharmonically equivalent.
Easley Blackwood explored all tunings with 13 to 24 steps and wrote a collection of etudes for them. He describes the characteristics of the 17-tone temperament as follows (note Blackwood’s usage of note instead of tone):

This tuning has much in common with 12-note tuning, in that each contains diatonic scales of five equal major seconds and two equal minor seconds. In 17-note tuning, each major second spans three chromatic degrees (rather than two, as in the case of 12-note tuning), and each minor second spans one chromatic degree. But the 17-note triads are very discordant due to their large major thirds, and so the fundamental consonant harmony of the tuning is a major triad with an added minor seventh. The scale is very good due to the relatively small minor second, and the minor seventh chord may serve as tonics in the Dorian, Phrygian, and Aeolian modes.

The aim of our project was to encourage composers to create pieces that were suitable for two pianos (occasionally with some additional instruments). After overcoming some bureaucratic obstacles, the Cologne Hochschule für Musik provided the pianos for a semester in 1988, giving us the opportunity to experiment with this tuning.

The 17 pitches were assigned to both pianos as follows:

 

Step	Cents	Piano I	Piano II
1	0	x	x
2	71		x
3	141	x
4	212	x	x
5	282		x
6	353	x
7	424	x	x
8	494	x	x
9	565		x
10	635	x
11	706	x	x
12	776		x
13	847	x
14	918	x	x
15	988		x
16	1059	x
17	1129	x	x
18	1200	x	x