Footnote: Special Tunings
Here are some of the tunings I suggest using for Middleearth Music. So far, all the ones I prefer are rational tunings, meaning that they consist of frequency ratios; and octaverepeating, meaning that each octave is divided into the same set of intervals. All are listed in 12 toneperoctave, +/ 99 cents format since most digital synthesizer tuning tables at least allow some kind of implementation of that, to some degree of resolution.
 [What do I do with this information?] 
Septochromatic Gothic #2 

Chromatic Scale Degree 
Ratio 
Cents 
1  1/1  0.000 
2  21/20  84.467 
3  448/405  174.692 
4  32/27  294.135 
5  56/45  378.602 
6  4/3  498.045 
7  7/5  582.512 
8  3/2  701.955 
9  63/40  786.422 
10  224/135  876.647 
11  16/9  996.090 
12  28/15  1080.557 

Comments
Diatonic scales are intended. This tuning is closely related to Pythagorean; in fact, some modes are purely so. The unique feature is that each whole tone (9:8) interval is divided into the pair 21:20 and 15:14. This yeilds a large number of unique modes from only three generating intervals (the other of which is 256:243).
According to Gothic music theory student Margo Schulter, this tuning follows a principle of Gothic music but takes it even further: the leading tones are intervalically smaller, which is more extreme. Here, the classic Gothic tuning system ("Pythagorean"), which used only multiples of the prime number 3, is colored by the introduction of semitone intervals using primes 5 and 7; thus "septochromatic."
Septochromatic Gothic #1, incidentally, divides each 9:8 first by 15:14 (ascending), leaving 21:20 remaining, whereas #2 divides 9:8 first by 21:20, leaving 15:14 remaining. #2 seemed to me to provide more modes with Middleearthish colors (totally a subjective judgement, of course). 
31base Otonal #3 

Chromatic Scale Degree 
Ratio 
Cents 
1  1/1*  0.000 
2  32/31  54.964 
3  35/31  210.104 
4  37/31  306.309 
5  39/31  397.447 
6  41/31  484.027 
7  43/31  566.482 
8  47/31  720.471 
9  49/31  792.616 
10  51/31  861.875 
11  55/31  992.596 
12  59/31  1114.136 
*Note that 1/1 = 31/31 
Comments
This is a highly evocative tuning, good with harp when the strings are allowed to ring and resonate with each other. It is highly consonant due to the completely overtonal nature of the scale member relationships, yet nontonal in that it doesn't provide diatonic scale relationships, nor the lowprime, triadic harmonic movement upon which most Western music is based (such as the familiar IIVV chords). Melodyoverdrone is a good technique with this one. The 2nd degree of the tuning (32/31) makes a nice drone.
Listen to "Forochel," a musical example of this tuning:
(MIDI w/ pitch bends)
Copyright 1999 by David J. Finnamore, all rights reserved 
3base Otonal 

Chromatic Scale Degree 
Ratio 
Cents 
1  1/1  0.000 
2  13/12  138.573 
3  9/8  203.910 
4  7/6  266.871 
5  5/4  386.314 
6  4/3  498.045 
7  17/12  603.000 
8  3/2  701.955 
9  19/12  795.558 
10  5/3  884.359 
11  7/4  968.826 
12  11/6  1049.363 

Comments
Tuned to harmonic overtones 12 through 22, & 27. There are lots of evocative, fantasticalmedieval sounding modes, and some very sour ones that might be good for orc music or something! For some reason, several of the Phrygian modes jumped out at me in this tuning. (I use the mode names in accordance with the modern interpretation of ecclesiastical usage, in which Phrygian is the mode on the third degree of the diatonic major scale.) 
What do I do with this information?
Most synthesizers and sample playback units have a way to set the tuning of each physical key on the keyboard, or of each of the 12 keys per octave, in terms of cents (There are 100 cents per semitone, 1200 cents per octave). Sometimes it's +/ cents from 12tone per octave equal temperament; sometimes it's absolute cents, or both. Please consult your users manual.
Either way, with a little interpolation, the data from this page can be entered fairly easily into almost any modern, digital synth's tuning table and you're ready to learn a whole new musical vocabulary! If you're lucky enough to have a real folk harp or lyre, you can use a synth as a tuning reference to put the strings in some subset of one of these tunings.
To find out more about inventing and using alternate tunings, visit John Starret's Microtonal Music Page or join me on The Alternate Tuning List, a large internet mailing list devoted to detailed discussion of all matters related to musical tunings both historical and modern (see Starrett's page for instructions on how to join).
If you don't see a colorful navigation bar on the left side of this page, please go to the first page of Music for Middleearth.
Written by David J. Finnamore
Orlando, FL, USA
Page last updated October 17, 1999
