Appendix 2

Modes of the first eight 7-note chord-mode classes

The first eight 7-note chord-mode classes have in common that the notes of their modes can be written as different chromatic alterations of the major mode diatonic scale. In fact, this could be done for the majority of 7-note chord-mode classes (forcing the enharmony to the extreme) but, except for some cases, only with the first eight chord-mode classes can this be done without adversely affecting the harmonic significance of the notes.

For example, the C-D-F-G-Ab-Bb-B scale (chord-mode class #19) could be written as a chromatism of the diatonic scale as follows: C-D-E#-Fx-G#-A#-B or C-Db-D -F-G-A-B (chord-mode class #11) could be as well written as C-Db-Ebb-F-G-A-B. But in both cases there could be an inaccuracy regarding the harmonic meaning of the notes because both scales contain the convergent structure (G:B:D:F) which is the one that establishes the tonic C. So, in the first case E# anf Fx should be F and G and in the second case Ebb has to be D. (Fig. 21)

The fact that the first eight chord-mode classes (and their modes and transpositions), could be written as major diatonic scale chromaticisms is very useful because there is no need to put notes to show the chord-mode classes modes, it is enough to indicate the key signature on the stave. This saves space and allows to express the harmonical relationships between all the modes of the eight chord-mode classes in a clear way.

The meaning of the modes table in this appendix is as follows:

Each column belongs to a chord-mode class and each row to a mode. Even if there are 13 rows, there is only 7 authentically different modes for each column (those marked with *), the rest are their chromatical transpositions (all those having C# or Cb Ėthe roman number shows the original modeĖ)

On the central row, belonging to I, there are the representatives of each chord-mode class as shown in page 59 of the tables. These are the most stable modes in the sense that they start with the most magnetized note. The left roman numbers show the mode degree in relation to their position in the representing scale. The right degrees show the transposition of the modes.

To know a mode, it is enough to form an heptatonic scale, starting by C and put the accidentals indicated on the key signature. For example, 7th. column, row 6 is the mode of the degree IV from chord-mode class #7 and has as a key signature F#, Eb and Ab. The scale C-D-Eb-F#-G-Ab-B will represent the structure of this mode (named gipsy or hungarian mode). The transpositions of this mode to another tone could be easily known looking at the degrees that appear on the right hand side of the table, bearing in mind that each row represents a 5th. interval. Like that, if one wants to transpose this mode a rising major 2nd. it will be sufficient to look two rows higher (or find the degree V+2aM=VI Ėon the rightĖ) and see the key signature of C#, G# and Bb. But now, instead of starting by C it is necessary to start obviously by D. So the scale D-E-F-G#-A-Bb-C# is the same mode applied to D (C+2aM) (See also Fig. 13 on page 43).

The division of the octave into seven sounds or intervals has been one of the most common in all musical cultures. Using only the modes of the first eight 7-note chord-mode classes we obtain a wide range of expressions and musical colours. The names of some of these modes are listed on p. 80 (assuming the needed tune adjustments in each case) according to the musical theories of different countries.1 Other known modes, particularly the indian, don't appear because they are in other chord-mode classes.



1-IV (a) Mode de Fa, Hipolidi grec, Tritus, Lidi (hipolidi), Mťshakaly‚ni, Kalyana, Gaur-Sŗrang, ichikotsucho (ryo), kung tiao

1-I (b) Mode major, Lidi grec, JÚnic (hipojÚnic), Dhira-shankar‚bharana, Bilaval, segah, chin tiao

1-V (c) Mode de Sol, Hipofrigi grec, Tetrardus, Mixolidi (hipomixolidi), Hari-k‚mbhoji, MatsarŪkrta, Khammaj(?), bayat-e tork (mahur?), rast, shang tiao

1-II (Á) Mode de Re, Frigi grec, Protus, DÚric (hipodÚric), Kharahara priya, Sudda Sadja, K‚fi(?), hyojo (ritsu), yŁ tiao

1-VI (d) Mode menor natural o descendent, HipodÚric grec, EÚlic (hipoeÚlic), Nata-bhairavi, As‚vari, Isfah‚n (afshari?), chŁeh tao

1-III (e) Mode de Mi, DÚric grec, Deuterus, Frigi (hipofrigi), Hanumat-todi, Bhairavi, shur (nava), zokuso, pien kung tiao

1-VII (f) Mode Mixolidi grec, Locri, Shahnaz (dashti?), pien chih tiao

2-IV (h) Mode dels harmÚnics II (Scriabin, Albrecht), V‚chaspati

2-I (i) Mode menor ascendent, Gauri-manohari

2-V (j) Ch‚ru-kťshi

2-II (k) N‚taka-priya

2-VII (m) Mode Super Locri

3-IV (Ů) Dharmavati

3-V (p) Chakrav‚ka

3-I (o) Mode major harmonic, Mode de Hauptmann, SaransŠngi

4-bVI (t) Kosala

4-bIII (u) Mode Misheberak

4-IV (v) Mode dÚric ukraniŗ, Haimavati, Homayun

4-I (w) Mode menor harmÚnic, Kirav‚ni, bayat-e esfahan

4-V (x) Mode Frigi espanyol, Gitano espanyol, Frigi-dominant, Freygish scale, Vakul‚bharana, Shad Araban

5-IV (A) Lat‚ngi

5-I (B) SŻrva-k‚nta

5-III (E) Sen‚pati

6-IV (H) Mode dels harmÚnics I, Rishabha-priya

6-I (I) Mode Napolitŗ major, Cercle tancat de quartes segons J.Darias, Kokila-priya

6-V (J) Mode locri major

6-bII (K) Escala de tons amb sensible

7-IV (—) Mode gitano, HongarŤs menor, Simhendra-madhyama

7-I (O) Mode doble harmÚnic, BizantŪ, M‚y‚-malava-gaula, Bhairav, Tchah‚rgah

7-V (P) Mode de Wollet, Oriental

7-bII (Q) R‚sika priya

8-bVI (T) ShŻlini

8-IV (V) Mode gitano hongarŤs, Shanmukha priya

8-I (W) Napolitŗ, Dhenuk‚, Todi (?)

8-bII (Y) Chitr‚mbari


Normal: modes occidentals

Cursiva: modes indis

Negreta: modes irano-ŗrabs

Negreta-cursiva: modes japonesos o xinesos

(1) Concerning to the ecclesiastical modes after the Oktoechos, it has been used the names appearing in Glaureanus'Dodecachordon (1547) grouped following the finalis=tonic (1st. degree) criterion. The same has been applied to the irano-arabian music for the 12 dastgah-ha. The indian modes have been drawn out from the 72 melakartas from the Carnatic (south) theory following Venkatamakhi and from the 10 thate of the Hindustani (north) theory following Bhatkhande. All this information mentioned comes from The New Grove Dictionary of Music (London), Encyclopťdie de la Musique (Paris), Danielou (1943) and wikipedia. There are some divergences between sources shown with a question mark.

LlorenÁ Balsach