|MusicNovatory/Introduction/Reference/Comments and Questions/Harmony/Preface/Just Intonation|
At the beginning of the chapter on Just Intonation, you say "Within the broad conglomeration of tuning systems (in Just Intonation) we will concentrate on elaborating what we call Functional Tuning, limited to the ratios 2/1 (the octave), 3/2 (the perfect fifth), and 5/4 (the major third), which will seem the most natural and satisfying to the ear, and which will apply to music of all styles and periods." Do you mean by this that the music of all styles and periods will be tuned in the same fashion?
Not at all. What we meant was that this system of Functional Tuning is capable of tuning music of all styles and periods, each in its own fashion. Thanks for bringing this to our attention. A correction will be made shortly.
Thanks for answering my previous email. In the Just Intonation section you also say: "Functional Tuning is music itself, and cannot be studied without constantly referring to the structure of Melody and especially Harmony (for they are not tuned the same way)." By this do you mean that Just Intonation is more than a tuning procedure and that it plays a role in the very structure of music?
Yes, by all means. This is where music theory should start. The simplest mathematical proportions (ratios) are what give the octave, the fifth and the major third their preferential status in the structure of music (both Melody and Harmony). Harmony, in particular, is traditionally described as either (a) superimposed thirds on the different degrees of the scale, or (b) coming directly from the Natural Harmonics. We claim that neither of these theories will produce reliable results, and that the series of fifths is the beginning of music with the thirds of chords (which we call the medians) placed within the "frame" of each fifth. Once this musical generation is set in motion, it is of secondary importance that it be tuned according to its original generation or tuned according to equal temperament, which all agree is out of tune but which is very useful for fixed tuning (like keyboards). I hope that this answers your question. Do not hesitate to write back.
I've recently been getting into the functional tuning section on the website, and I have a couple of questions on this very interesting subject. First of all, are there any fixed-pitch melody instruments out there with Pythagorean/Trunk tuning? Also, are all the clips from the website in functional tuning? If so, how is this done with instruments such as the piano?
In answer to the first question, there are instruments that could be tuned Pythagorean, such as piano, various types
of harps, fretted instruments with moveable frets (guitars, lutes, etc.). These aren't strictly "melody instruments" since
they are capable of playing chords, but they could be used as melody instruments. String players (violin, etc.) usually tune
their open strings in perfect fifths, which is Pythagorean - but of course these are not "fixed-pitch." There may be others
that we are not aware of at this time. Perhaps that would be an interesting research project. Let us know if you find any
more info !
As a cello player I wonder about the convenience of tuning my instrument in temperated fifths (instead of perfect fifths) specially when I play with a piano in order to fit its tuning. Aternatively it could be interesting to tune the piano with the "Cordier" temperament (that preserves perfect fifths thus stretching octaves). The standard practice (cello in perfect fifths and piano in temperated fifths) doesn't seem to be the ideal. Playing alone (or in a string ensemble) perfect fifths seem better but what a mess if I should change to temperated fifths when I play with a piano. Or not? Thanks for your advice. PS: incredibly interesting your MusicNovatory. I feel there are some coincidences with Mathieu's book Harmonic Experience in the explanation of Just Intonation. Are there?
1. We certainly would not recommend that you tune your cello in tempered fifths unless very exposed use of open strings clashed
with the piano. It seems far preferable to keep the cello in tune with itself. However, tuning with the A of the piano might
not be the best solution. The difference between the perfect fifth and the tempered fifth is almost 2 cents (1.955 to be more
precise). Tuning with the A of the piano makes your low C almost 6 cents flat to the piano. However, tuning with the D of
the piano would make your A 2 cents sharp but the C only 4 cents flat, already an improvement. We are very flattered by the
fact that you ask us for advice but would it not seem more appropriate to consult other cellists? How do they tune when they
play with piano? We are not very familiar with the "Cordier temperament" but stretching the octave seems very difficult to
accept. Along with the additionnal stretch on the thirds, it seems like a high price to pay for the fifths. You can probably
find out more on Cordier tuning from some of its proponents and users, including this reference from the Nydana Notation web site FAQ answer to question #6 (see paragraph 6)
Is temperament inherent to atonal or post-tonal music? Is atonal or post-tonal music an epiphenomenon of temperament? Should we strictly avoid just intonation in atonal or post-tonal music? Thanks.
There may not be simple and definitive answers to these questions, but they may nonetheless be worth exploring. Before
proceeding, it will be necessary to lay some groundwork so that we have a common understanding of what is meant by certain
In the new major 7 tuning section it says that the chromatic line C, B, Bb, A from tonic to counter is unadvisable. However, this goes against what has been common practice. This line is a staple in love songs and sounds great. Some of the many examples include Something, You Are So Beautiful, and Can't Take My Eyes Off of You. They all have a progression that goes I,Imaj7,I7,IV in the beginning.
You have no idea how precious these comments are to us ! We will be examining these 3 songs carefully and get back to the drawing board.
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