source file: mills2.txt Date: Sun, 4 May 1997 07:45:40 -0700 Subject: Re: Request.Info just- and pythagorian tuning From: mr88cet@texas.net (Gary Morrison) >Would somebody help me in explaining the differences between playing in >Justatonic mode and Pythagorean mode? Sure. First of all, "Justonic" is a trade name of Justonic Tuning, Inc., in Canada. Their name comes from the idea of "Just Intonation", which is the general concept you're undoubtedly asking about. Just Intonation is not any single tuning really, but instead a general principle for choosing pitches, based upon making their sound-wave frequencies in simple whole-number relations to one another, like 2:1 for octaves, 3:2 for perfect fifths, 5:4 for major thirds, and many others. As with "equal temperament" and "meantone", "just intonation" also carries a historical meaning, which is a subset of the more recent, generalized meaning. The major-scale tuning for the historical subset meaning (example in C): C D E F G A B C 1:1 9:8 5:4 4:3 3:2 5:3 15:8 2:1 This tuning came later, in Western culture anyway, than the "pythagorean" tuning of: C D E F G A B C 1:1 9:8 81:64 4:3 3:2 27:16 243:128 2:1 So that is the distinction between "pythagorean" and "just", even though pythagorean is in fact just, since it's built upon whole-number ratios, although 243:128 would hardly qualify as a "simple" whole-number ratio, which is of course part of the reason why it evolved into 15:8 in most scenarios. >How can one learn to play in these modes without using electronic >equipment? >Is there any valid models used in learning how to use your ear to >recognise these different modes? It doesn't take a huge amount of effort for most competent and motivated musicians to learn to hear new whole-number pitch relationships, although it's deadly critical to bear in mind that how easy it is to hear them depends greatly on how they're used. Well, it depends on the same factors that playing in tune in any tuning depends upon: whether you're paying the notes melodically or harmonically, how fast the notes are going by, and such. Probably the best way to get used to hearing these new pitch relationships is a combination of mimicking pitch relationships from recordings or electronic aids of whatever sort, and then try them out for yourself, listening to beat rates in sustained chords. As you get a feel for those beat rates, you simultaneously will get an increasingly more secure feel for recognizing those intervals by their melodic pitch distance. Johnny Reinhard and his "AFFM" troopers routinely play a wide variety of tunings on traditional acoustic instruments, Johnny himself mostly on bassoon, using alternate fingerings. Also with regard to nonelectronic instruments, lots of people investigate new tunings by refretting guitars and other strings. That works really well for a lot of people, and for certain styles of music. Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Sun, 4 May 1997 16:54 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA04233; Sun, 4 May 1997 16:54:15 +0200 Received: from ella.mills.edu by ns (smtpxd); id XA04146 Received: from by ella.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) id HAA23230; Sun, 4 May 1997 07:52:28 -0700 Date: Sun, 4 May 1997 07:52:28 -0700 Message-Id: Errors-To: madole@mills.edu Reply-To: tuning@ella.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@ella.mills.edu