Mode numbers, March 5, 2000, reformated Oct 10, 2002: With enough 'accidentals' any tune can be scored in any of the 7 7-note 'Greek' modes. These different representations can all be taken care of for the normal 7, 6, and 5 note modes and a few others where there are assigned names for modes that are unambiguous, e.g., lydian, or ionian or mixolydian all with the 4th, 6th and 7th missing are pentatonic pi1 (Bronson's notation). There are also names for a few other modes, e.g., harmonic minor, but not enough names for most other tune scales (and there are a lot of them) to give an umambiguous basis for identifing the scale of a tune from a mode name. In yet other cases there are a bewildering variety of names for a given mode. What to do?-Mode number. For the tune mode, not necessarily the scoring mode we do the following. Consider a tune in C (or D) major/ionian and use 1 for note in and 0 for note out. Then we have: (D D#/Eb E F F#/Gb G G3/Ab A A#/Bb B C C#/Db) C C#/Db D D#/Eb E F F#/Gb G G#/Ab A A#/Bb B (1 1#/2b 2 2#/3b 3 4 4#/5b 5 5#/6b 6 6#/7b 7) 1 0 1 0 1 1 0 1 0 1 0 1 [Semitn sq 2 2 1 2 2 2 1] The string of 1's and 0's in the bottom row can be taken as a unique binary number representation of the ionian mode which doesn't depend on keynote or even the scoring mode. It just depends on the key and the notes in the tune. The first 1 on the left is always there, so we can ignore it (unless someone knows of a tune that doesn't contain the keynote). I've now chosen to use a mode identifier which is the decimal equivalant of taking of the binary number consisting of the rightmost 11 bits in reverse order, so the 1#/2b is the least significant bit and th 7th the most significant. This order is reverse in a mathematical sense, but forward for the scale so the farther from the keynote is the biggest number. See note below on computer coding for 'reverse order'. We can do this for the scale of any tune that can be represented by a 12 semitone scale. Now no matter what the scoring mode is for any tune we have a unique identifier for the scale or 'mode' of the tune, and from fairly simple math we can recover the complete scale from the mode number identifier. Reverse order is actually forward order for a DO/FOR loop in a computer to generate the mode #. Let M(I,j) be the binary code of the mode of tune # i, and j run from 1 to 12 over the notes of the scale with bits 1 or 0 in each of the 12 positions, with the bit for the keynote at j = 1. FOR/DO i = ifirst to ilast let Mode# = 0 FOR/DO j = 2 to 12 mode# = mode# + M(i,j)*2^(j-2) next J nmod(i)= mode# next i For forward order we would have ..... FOR/DO j= 2 to 12 mode#=mode# + M(i,j)*2^(12-j) next j ... All modes I've observed, 181 of them, are listed with mode number in file MODETABL.TXT