Maqamat in maqamic temperament

From Xenharmonic Wiki
Jump to: navigation, search

Introduction

Maqamat (singular "maqam") are scale-like abstractions in Arabic, Turkish, and Persian music. This article, for the most part, treats maqamat simply as scales and disregards everything else about them (emotional connotation, melodic idioms, emphasized pitches...). Also note that in performance, depending on the instrument, a wide variety of subtle microtonal inflections may be used, rather than sticking rigidly to the pitches of a scale. This article deals with only the "central" or "canonical" pitches for each note of a maqam. See http://launch.groups.yahoo.com/group/tuning/message/101523 for an explanation of the level of abstraction being used here.

Other theorists have developed completely different and often very complicated regular temperament structures to accomodate maqamat. This article is based on a simple rank-2 temperament known variously as "2.3.5.11 maqamic", or "2.3.5.11 mohajira", or "mohaha". Whatever its name, it is the 2.3.5.11 temperament that tempers out 81/80, 121/120, and 243/242. This means that every other note in the generator chain is meantone, and the fifth generator is split into two equal "neutral thirds" that represent 11/9. An interval is 5-limit if and only if the number of generators needed to reach it is even. Therefore "quarter tones" (i.e. intervals outside meantone) and "intervals outside the 5 limit" are identified in this temperament. See Neutral third scales for more information.

Note that, because the fifth is divided into two equal parts, the chromatic semitone (aka apotome, the interval by which sharps and flats alter pitches) is also divided into two equal parts. Therefore, although "quarter tone" is a misnomer because 9/8 is not divided into four equal parts (except in the particular tuning of 24edo), "half flat" and "half sharp" are perfectly accurate. This is helpful in notating maqamic temperament because two new accidentals can be introduced (this article uses ^ and v) that obey the equations ^^ = # and vv = b.

Online sources

Scale fragments (tetrachords, ajnas)

Ajam/Çargah/Jiharkah

Ajam (Arabic): Bb C D Eb

Çargah (Turkish): C D E F

Jiharkah trichord (Arabic): F G A

This tetrachord can be identified with LLs from meantone[7]. Maqam World notes "...the 3rd note [is] tuned slightly lower. This makes it more mellow than a major scale.", which is perfectly consistent with meantone.

Maqam World also notes that the third note of Jiharkah is "even lower than in the Ajam trichord", but this subtle distinction is not preserved in maqamic temperament.

Bayati/Uşşak

Bayati (Arabic): D Ev F G

Uşşak (Turkish): A Bv C D

The Bayati or Uşşak tetrachord can be identified with ssL from maqamic[7]. Maqam World notes "The tuning of the 2nd note (Ev) is slightly lower and more mellow than the Ev used in the Rast and Sikah sets.". This subtle distinction is not preserved in maqamic temperament, in which Ev is simply Ev.

Busalik/Bûselik/Puselik/Nahawand/Nihawand

C D Eb F

A B C D

This tetrachord can be identified with LsL from meantone[7]. Maqam World notes "The tuning of the third note is played lower than in the Nahawand tetrachord. This difference in tuning is about 1/9th of a tone (also know as a koma in Turkish music).". The "1/9th of a tone" part implies 53edo (in which 9/8 is 9 steps) as some kind of theoretical basis, and perhaps it implies that Busalik should have a 32/27 whereas Nahawand should have a 6/5. This subtle distinction is not preserved in maqamic temperament, in which 81/80 is tempered out.

Hicaz/Hijaz

D Eb F# G

A Bb C# D

The Hijaz tetrachord can be identified with sAs from a meantone[7] MODMOS such as harmonic minor. Maqam World notes "The Eb is tuned slightly higher than usual, while the F# is tuned slightly lower, in order to narrow down the 1 1/2 tone difference and make it more mellow.". This is perfectly consistent with meantone in which the middle interval is an augmented second (~7/6) rather than a minor third (~6/5).

Huzam/Hüzzam

Bv C D Eb

Ev F G Ab

The Huzam tetrachord can be identified with sLd from a maqamic[7] MODMOS (neutral second, major second, minor second). Note the interesting outer interval of a half-diminished fourth (450 cents in 24edo and 465 cents in 31edo).

Iraq/Segâh

Bv C D Ev

Ev F G Av

The Iraq (Arabic) or Segâh (Turkish) tetrachord can be identified with sLs from maqamic[7].

Kurd/Kürdi

D Eb F G

A Bb C D

The Kurd tetrachord can be identified with sLL from meantone[7].

Mustaar

Rast

C D Ev F

G A Bv C

The Rast tetrachord can be identified with Lss from maqamic[7].

Saba

D Ev F Gb

A Bv C Db

The Saba tetrachord can be identified with ssd from a maqamic[7] MODMOS (that is, neutral second, neutral second, minor second). It is important that the fourth note is spelled as a diminished fourth from the lowest note rather than a major third. (Saba is not D Ev F F#.) Note that the online sources spell it correctly this way. Maqam World confirms this further by stating "notes 3 and 4 are usually used to start a Hijaz tetrachord", which begins with a diatonic semitone rather than a chromatic semitone.

(What Are Makams? appears to give A Bv C Dv, with the symbol for "lower pitch by 1/4 tone" on the D, but this is probably an error for the different symbol for "lower pitch by 3/8 tone", or perhaps a normal flat. The outer interval should definitely be a diminished fourth rather than a half-diminished fourth.)

Sikah

Ev F G A

The Sikah tetrachord can be identified with sLL from a maqamic[7] MODMOS. Note that the outer interval is the one that represents 11/8 in maqamic temperament; however, it is practically never used as a harmonic interval in traditional music.

Zamzama

D Eb F Gb

The Zamzama tetrachord can be identified with sLs from a meantone[7] MODMOS such as harmonic or melodic minor. It is important that the fourth note is spelled as a diminished fourth from the lowest note rather than a major third. Maqam World says "This is the Westernized version of Saba with the 2nd note changed from a quarter tone to a semitone.", which makes sense.

Maqamat

Ajam/Çargah

Bb C D Eb F G A Bb

Maqam Ajam and Makam Çargah can both be identified with the meantone major scale, meantone[7] 5|1.

Bayati/Uşşak

D Ev F G A Bb C D

Maqam Bayati and Makam Uşşak can both be identified with maqamic[7] 2|4 b3 b6 (ssLLdLL).

Potential for harmony beyond 5-limit

Ev is the only "quarter tone", so the only non-5-limit chords are those that include Ev.

  • Ev is the 12/11~11/10 of D, so on D there is a nice 10:11:12:15:18 chord (a minor chord where Ev is a neutral second)
  • Ev is the 11/6 of F, so on F there are interesting chords like 6:9:11 or 6:9:10:11.
  • Ev is the 13/8 of G (in mohoho temperament), so on G there is a 8:9:12:13 chord and also the chord G Bb D Ev (minor w/ neutral sixth)
  • Ev is the half-diminished fifth of A, so the chords on A are quite dissonant.
  • Ev is the 11/8 of Bb, so on Bb there is a complete 8:9:10:11:12(:15) otonality. Obviously this could be quite a powerful chord.
  • Ev is the 11/9 of C, so there are neutral chords on C (between major and minor).

Hijaz

D Eb F# G A Bv C D

D Eb F# G A Bb C D

Maqam Hijaz has two forms, one which can be identified with meantone[7] 1|5 #3 (meantone phrygian dominant), and another which differs by having a neutral sixth degree instead of a minor sixth.

Potential for harmony beyond 5-limit

Bv is the only "quarter tone", so the only non-5-limit chords are those that include Bv.

  • Bv is the 13/8 of D (in mohoho temperament), and there is a 8:10:12:13 chord on D.
  • Bv is the half-augmented fifth of Eb, so the chords on Eb are quite dissonant.
  • Bv is the half-diminished fourth of F#, which is fairly dissonant (it represents 13/10 in mohoho).
  • Bv is the 11/9 of G, so there are neutral chords on G.
  • Bv is the 12/11~11/10 of A, and there is a 10:11:12:18 chord on A (no fifth though).
  • Bv is the 11/6 of C, so there are 6:9:11 and 6:9:10:11 chords on C.

Hijaz Kar

C Db E F G Ab B C

Maqam Hijaz Kar can be identified with meantone[7] 5|1 b2 b6 (equivalently meantone[7] 1|5 #3 #7). This is also known as the meantone "double harmonic scale" or simply "Arabic scale".

Kurd

D Eb F G A Bb C D

Maqam Kurd can be identified with the meantone Phrygian scale, meantone[7] 1|5.

Nahawand

C D Eb F G Ab B C

C D Eb F G Ab Bb C

Almost exactly like the meantone natural minor / harmonic minor scale pair, Maqam Nahawand has two forms, meantone aeolian (meantone[7] 4|2) and meantone harmonic minor (meantone[7] 4|2 #7). In other words Maqam Nahawand is the same as meantone natural minor with a major seventh as an alternate.

Rast

C D Ev F G A Bv C

C D Ev F G A Bb C

Maqam Rast has two forms, one that can be identified with maqamic[7] 2|4 #6 (equivalently maqamic[7] 0|6 b4), and another form with a minor seventh degree rather than a neutral seventh.

Potential for harmony beyond 5-limit

Ev and Bv are both "quarter tones" so non-5-limit chords could include either of them.

  • Ev is the 11/9 of C, so the tonic chord is neutral (neither major nor minor). There is also a neutral seventh chord, C Ev G Bv.
  • Ev is the 12/11~11/10 of D, so there is a nice 10:11:12:15:18 chord on D.
  • Ev is the 11/6 of F, so there are 6:9:11 and 6:9:10:11 chords on F.
  • Ev is the 13/8 of G (in mohoho temperament), and there is a 8:9:12:13 chord on G. There is also a neutral sixth chord, G Bv D Ev.
  • Ev is the half-diminished fifth of A, so chords on A are quite dissonant.
  • Ev is the 11/8 of Bb, and there is a complete 8:9:10:11:12(:15) otonality on Bb.
  • Chords with Ev and Bv as the root and fifth are very interesting because the root is on a "quarter tone". There is a neutral triad, and a nice 8:11:12:13 chord on Ev.
  • Bv is the 11/6 of C, and there are 6:9:11 and 6:9:10:11 chords on C as well as the neutral seventh chord.
  • Bv is the 13/8 of D (in mohoho temperament) and there is a 8:12:13 chord on D as well as D F A Bv which is a minor w/ neutral sixth.
  • Bv is the 11/8 of F, and there is a complete 8:9:10:11:12 otonality on F.
  • Bv is the 11/9 of G, so there are neutral chords on G.
  • Bv is the 12/11~11/10 of A, and there is a 10:11:12:18 chord on A (no fifth though).

Saba

D Ev F Gb A Bb C D

Maqam Saba can be identified with maqamic[7] 0|6 bb4 #5 b6, or equivalently maqamic[7] 2|4 b3 bb4 b6. This is a rather complex MODMOS (but it sounds awesome).

Weird form of Saba

D Ev F Gb A Bb C Db E F

This alternate form of Saba "doesn't include the octave of the tonic", and includes another non-octave as well (Ev-E). It could possibly be thought of as an octave-repeating scale with more than 7 notes, but it's unclear to what extent it's used this way in traditional music.

Potential for harmony beyond 5-limit

Sikah

Ev F G A Bv C D Ev

Ev F G A Bb C D Ev

Maqam Sikah has two forms, one which can be identified as maqamic[7] 5|1 b2 (equivalently maqamic[7] 3|3 #4), and another which has a half-diminished fifth degree instead of a perfect fifth (maqamic[7] 5|1 b2 b5).

Maqam Sikah has by far the largest number of neutral scale degrees relative to the tonic.

Potential for harmony beyond 5-limit

UNDER CONSTRUCTION

d (minor), s (neutral), L (major), ? (half-augmented), A (augmented)

ddA (not named)

Add (not named)

ds? d?s sd? s?d ?ds ?sd (not named, ? only appears in mustaar)

dAd hijaz

dLL kurd

LdL nahawand

LLd ajam

ssL bayati

sLs iraq

Lss rast