source file: mills2.txt Date: Fri, 21 Mar 1997 02:09:56 -0800 Subject: sorry...NDD 36 again .. From: Andrzej Gawel Dear Friends, Thank You for Your answers. J don't know what was happened with my previous mail. Our supervisor works days and nights to make us suprise. May be, he changes something in attachments today. Ok. J send to You text from Tom (Tomasz Liese) in pure ASCII. You can send Your comments to my e-mail. Regards, Andrew. (gawel@sejm.gov.pl) PS. My WWW page is closed (sorry!) -------------- His text starts here ---------------- The NPD 36 system, wich I presented at the Warsaw Academy of Music and Polish Radio Program 3 in Warsaw, is continuation of the diatonic major-minor system and extension of the principles of functional harmony. The system is based on the rules of physic and does not depend on common octave division. It can be achieved by the application of approximations wich result from dividing an octave into 29, 36,41,54,72 and more.For notation, melodies and harmony the system includes the logarytmic octave divisjon into 36 section and for the construction of music noises the division into 1152 and 768.Many new terms are of similai nature to traditional ones , which considerably facilitates the understanding of the NPD 36 system. THE NPD 36 The organisation of music sound system By Tomasz Liese, tel/fax: (+48)(22) 676 97 60, Warsaw, POLAND. 1. Measures octave 1200 cents 1152 stripes band 3.125 cents 3 stripes semiton 32 bands 96 stripes microton 33.33 cents 32 stripes sharp + 1 microton flat - 1 microton 2 The Microdiatonic System Number of sharps of major keys in order 0 to 17 : C, T.Q, G, Z, N, D, U, K, A, R, O, E, V, L, B, S, Win. Order of sharps :Fin, Win, Min, Cin, Tin, ... etc. Number of flat of major keys in order 1 to 18 : M, W, F, P, Len, Ven, En, Oen, Ren, Aen, Ken, Uen, Den, Nen, Zen, Gen, Qen, Ten. Order of flat : Ben, Len, Ven, En, ... etc. For exemple : For Qmajor-0 key are sharps : Fin, Win. For F major-0 key are flat : Ben, len, Ven. Replacement mark : Y , Xn , P¾n , Sn , Jn. 3.Modes Number of flat : 0 - A minor-0 key or C major-0 1 - M major-0 key or C major-1 2 - W major-0 key or C major-2 3 - F major-0 key or C major-3 4 - P major-0 key or C major-4 5 - Len major-0 key or C minor-4 6 - X major-0 key or C minor-3 7 - Y major-0 key or C minor-2 8 - Oen major key or C minor-1 9 - Ren major Key or C minor-0 4. The C major-0 key : C, Q, Z, D, K, R, E, L, F, M, T, G, N, U, A, O, V, B, W, c. The tierce round :C, E, G, B, D, M, A, Q, E, N, B, K, M, O, Q, L, N, W, K, T, O, Z, L, U, W, R, T, V, Z, F, U, C, R, G, V, D, F, A, C. 5. The Spectral Harmony For spectral harmony and for the construction of music noises the system includes 26 natural intervals the mark : h1 to h26. Size of interval expresed proportion frequency - H(n) B/A Size of interval expresed of stripes : h(n) 1162 log ( B/A ) when A n( n+2 ) , B A+1 For exemple : H3 x H4 x ... x H8 6/5 or h3 + h4 + ... + h8 303 [ stripes ]. 6. Subsystems The systems contains an open list of sub-systems concerning methods of using it. Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Fri, 21 Mar 1997 15:22 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA07888; Fri, 21 Mar 1997 15:22:28 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA07889 Received: from by ella.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) id GAA22679; Fri, 21 Mar 1997 06:19:22 -0800 Date: Fri, 21 Mar 1997 06:19:22 -0800 Message-Id: Errors-To: madole@mills.edu Reply-To: tuning@ella.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@ella.mills.edu