source file: mills2.txt Date: Wed, 19 Mar 1997 04:50:26 -0800 Subject: On the tuning of augmented sixth chord (Paul E) From: Manuel.Op.de.Coul@ezh.nl (Manuel Op de Coul) From: PAULE No disrespect intended, but it is silly to try to calculate the "5-limit" ratios of common-practice chromatically altered harmonies. I believe the preponderance of this kind of numerology to hurt the case for alternative tuning systems among the musical community. a) The diatonic system is only a 5-limit system insofar as the consonant harmonies approximate ratios of odd numbers 5 or less. Even calculating the ratios of a purely diatonic progression such as I-IV-ii-V-I is a futile exercise; in any meantone temperament, including 12-equal, the musical reality obliterates all distinctions between varying quantifications of the above progression, and is more beautiful than any of them to boot. To claim (as many would) that the arithmetical construction is more valid than the musical reality is to cease to have any relevance for the realm of music and to engage in a meta-musical game reminiscent of the worst excesses of serialism. b) The fact is that certain chromatic alterations were chosen from a pool of many possibilities that would satisfy the rules of melodic/contrapuntal movement. The latter would dictate simply that two voices can be chromatically altered in opposite directions if both resolve by step in the direction of the alteration. But we don't have augmented thirds progressing to perfect fifths, and instances of augmented seconds and augmented fourths seem to be restricted to the case where at least one note is diatonic. The augmented sixth distinguished itself from other possibilities for acoustical reasons; namely, its proximity to a septimal ratio. If nothing else, septimal ratios define a set of "not-too-dissonant" intervals outside the 5-limit system, and need not be taken as a foreign musical language. I would suggest that people using the limit terminology review Partch's original definition since the "prime" definition seems to lead to a lot of confusion and unneeded complexity while the "odd" or Partch definition seems more suited to musical practice and acoustical theory. The "prime" definition is sometimes useful in describing a tuning system or the practice of tuning itself, but musical reality as concerns the listener is better understood in terms of the "odd" definition. -Paul E. Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Thu, 20 Mar 1997 01:30 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA06537; Thu, 20 Mar 1997 01:30:16 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA06538 Received: from by ella.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) id QAA22767; Wed, 19 Mar 1997 16:28:14 -0800 Date: Wed, 19 Mar 1997 16:28:14 -0800 Message-Id: <009B181E69F47816.705F@vbv40.ezh.nl> Errors-To: madole@mills.edu Reply-To: tuning@ella.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@ella.mills.edu