source file: mills2.txt Date: Tue, 17 Jun 1997 09:07:17 +0200 Subject: ScaleCoding confusion (fwd) From: Charles Lucy ---------- Forwarded message ---------- Date: Wed, 21 May 1997 23:31:14 -1000 (HST) From: Charles Lucy To: Bill Alves Subject: ScaleCoding confusion Bill; I appreciated your interesting and thoughtful posting about your coding of modes and scales, yet I see the possibility of confusion arising between our two different systems. In about 1989, John Gibbon, Jonathan Glasier, and I, worked together to design a scalecoding system, and publicized it fairly widely amongst musicians and music academics. The paper follows. I feel confident that you will agree that the system covers all and every contingency for analysing synthesising and coding modes and scales from a chain of fifths perspective. The unfortunate similarity of our systems, is that your notation uses the same numerical pattern that we used. (3 sets of digits separated by '/') i.e. xx/yyy/z In our case the "x" is the number of steps in the chain "m" is the position(s) of the missing steps "T" is the "tonic" or "lowest note". In your case "x" is the number of pitches in the tuning system "y" is the number of pitches in the subset "z" is the number of commonly used auxiliary tones As we have both used the forward slash to separate the groups of digits, the unwary reader could be confused. May I suggest that one of us use a different separator to avoid this, or that we always attach our respective names to the coding to clarify the possible ambiguity. The difficulty that I have is that there are already in excess of 10,000 copies of the LucyTuning scalecoding document in circulation from printed pamphlets, internet fileservers, and downloads over the last seven or so years. It is also used and explained in the "LucyTuned Lullabies (from around the world)" booklet. BTW Bill; If you would be good enough to send me a snail address, I'll ship you a copy of the Lulls cassette plus booklet. File on scalecoding follows: SCALEMAKING - Analysis, Synthesis, and Coding by Charles E. H. Lucy copyright 1990 & 1994 This is an extract from "Pitch, Pi, and Other Musical Paradoxes, (A Practical Guide To Natural Microtonality)" - ISBN 0-9512879-0-7 You may think of scalemaking as some sort of esoteric musical alchemy. This is near the truth, for as with alchemy the intent may be to transmute something of little value into gold. This may be in the form of a valuable piece of music. The process, like chemistry, may be approached from two opposite directions: starting from an existing scale and by analysis breaking it down to its constituent parts to discover how it works, or by synthesis constructing a scale using some form of recipe. First a few definitions: A scale is a series of notes which are used in a piece of music. These may be identified by their musical names using the letters A through G. Each of these letters may also be followed by any number of sharp or flat symbols. For example the notes D-E-F-G-A-B-C-D make a scale of D minor Any scale may be transposed by changing the starting note which will change the other note names and the key signature. If we flatten all the notes of the scale of D minor by one Large interval from D to C, we create a scale of C minor C-D-Eb-F-G-A-Bb-C and the key signature now has two flats (Bb and Eb). Our two examples here have shown us two scales, D minor and C minor, which both use the same mode. This mode of L-s-L-L-L-s-L is known as the minor, Dorian or Kafi mode. The name is dependent upon whether you are using the English, Greek or Indian names for the mode. A Mode is a sequence of intervals, which may be defined by Large and small intervals. The sequence for the two minor scales used in the examples above are both L-s-L-L-L-s-L, which we described as the minor mode. This sequence of intervals added together gives a total of five Large and two small intervals, which gives us one octave. We can therefore consider this pattern as circular. That is it ends on the octave note above where it started. Using this same circular sequence we could start it at any point and each of the seven starting points gives us another mode. In this case we can make all the Greek modes using this sequence, which are the basis of Western music and harmony. These seven different notes are contiguous on the spiral of fourths and fifths, and arranged in pitch ascending order, give us a megamode. This is the circular pattern from which the seven Greek modes are derived. A Megamode is a circular sequence of intervals from which modes are derived. The megamode of seven contiguous positions on the spiral of fourths and fifths produce all the Greek modes. We could describe this as an expanse of six steps which contains seven notes. There is a comparable megamode of four steps which produces five contiguous notes and generates five pentatonic scales. 1. List all the different notes which are used in the piece regardless of octave. 2. Arrange the note names in order of fourths (flats) in one direction and fifths (sharps) in the other, leaving blank spaces where notes are missing. [Sequence ascending in fifths is: Bbb Fb Cb Gb Db Ab Eb Bb F C G D A E B F# C# G# D# A# E# B# F## C## etc.] The fifth may be considered as the dominant, and the fourth as the sub-dominant. 3. Count the total number of steps between the fourthmost (flat) and fifthmost (sharp) note. This is the extent of the string, or chain of fourths/fifths (x). 4. List the missing notes. Identify them by numbering the flatmost as 1 and the following as ascending numbers moving through fifths. Each of the missing notes may be defined as between 2 and x. 5. The megamode may now be defined by the number of steps and the position of the missing notes (m1, m2, etc.). Eg. x m1 m2 m3 and m4. Therefore there are four notes missing in the sequence. Therefore the extent is (x). So there are thirteen notes of which four (m1 to m4) are missing leaving 13-4 9 notes. In this case numbers 1, 3, 4, 6, 7, 8, 9, 10, and 12. 6. The mode is determined by which of the notes is chosen as the start of a sequence of ascending frequencies. This starting note may be identified by stating its position on the chain of fifths. For example, if the notes were six consecutive steps Eg. F C G D A E B. These pitches could be arranged in seven modes of different ascending pitch orders: (F) 1 (first note in chain) (Lydian) I,II,III,#IV,V,VI, and VII; (C) 2 (2nd in chain) (Major or Ionian) I,II,III,IV,V,VI,and VII; (G) 3 (Mixolydian) I,II,III,IV,V,VI,and bVII; (D) 4 (Dorian) I,II,bIII,IV,V,VI,and bVII; (A) 5 (Aeolian) I,II,bIII,IV,V,bVI,and bVII; (E) 6 (Phrygian) I,bII,bIII,IV,V,bVI,and bVII; (B) 7 (Locrian) I,bII,bIII,IV,bV,bVI, and bVII. 7. The key of the scale and scale is determined by the tonal center, which may defined as C,D,E,F,G,A, or B with the appropriate sharps or flats. The scale may then be listed in ascending frequency order by note name. 8. A scale or mode may therefore be defined as: Number of steps in chain (x)/position(s) of missing notes (counted from fourths towards fifths)/Position of tonic (counted from fourths towards fifths). Eg. The scale and mode described as 5/25/3 could give the notes F-G-D-E from the chain F-C-G-D-A-E. Using the third note of the chain (G) as the starting note giving a scale of G-D-E-F or the mode of I-V-VI-bVII. Charles Lucy lucy@hour.com http://www.wonderlandinorbit.com/projects/lullaby http://www.ilhawaii.net/~lucy http://ourworld.compuserve.com/homepages/lullaby Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Tue, 17 Jun 1997 09:24 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA00605; Tue, 17 Jun 1997 09:24:32 +0200 Date: Tue, 17 Jun 1997 09:24:32 +0200 Received: from ella.mills.edu by ns (smtpxd); id XA00603 Received: (qmail 21366 invoked from network); 16 Jun 1997 08:41:11 -0000 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 16 Jun 1997 08:41:11 -0000 Message-Id: <199706160750.PAA00692@csnt1.cs.ust.hk> Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu