This is a chapter of my new book "Oriental Jazz Improvisation: Microtonality and Harmony: Employing Turkish Makam, Arabic Maqam & Northern Indian Raga Scales and Modes," which is available online around the globe. Thanks for reading and maybe buying. Thomas Mikosch (the author) b. Northern Indian Rāgas and their Kinfolk The smoothest way to blend scales and modes, as we have already learned, is by employing scales that share at least certain interval sequences. Arabic maqamat begin on various tones, Turkish makamlar mainly on A or G, and Northern Indian rāgas (almost) exclusively on C. The Arabic maqamat in the following all have, except for Maqam Kurd, C inherently as the tonic and thus share the same intervallic structure with the respective raag family given, the thaat . The thaat is the motherscale that contains all intervals of the family. The respective Greek modes are given accordingly as well as, though not on C, the Turkish counterparts of the respective Arabic scales and modes. S Indian raag family Greek / Western mode Arabic / Turkish scale or mode Bilāval thaat = Ionian = Maqam ‘Ajam (asc.) / Çârgâh and Râst Makamı Kāfī thaat = Dorian = Maqam Nahāwand Kabīr (desc.) / Hüseynî Makamı Bhairavī thaat = Phrygian = Maqam Kurd / Kürdî Makamı Kalyān thaat = Lydian = Maqam Zaweel Mārvā thaat = Lydian ♭ 9 Khamāj thaat = Mixolydian = Maqam ‘Ajam (desc.) / Acem Makamı Āsāvari thaat = Aeolian = Maqam Nahāwand / Bûselik Makamı Bhairav thaat = Double harmonic major = Maqam Hijāzkar / Zîrgûle'li Hicâz Makamı Tōḍi thaat = Maqam Athar Kurd As already stated, just because two scales look quite the same in notation does not mean that they are really the same and equivalent to their counterpart. Therefore, we are going to have a closer look at the scales from the table above. We will begin with the Western equal-tempered Dorian scale and compare it to its Indian, Turkish, and Arabic counterparts, respectively. Please note that the cent values of these scales and modes are according to the A-E-U/Pythagorean and the Didymean tuning of determining intervals, for the Turkish and Indian scales and modes, respectively. Both of which are theoretical constructs . So even this comparison might be a superficial one. ET Dorian: 200.000 300.000 500.000 700.000 800.000 1000.000 1200.000 Kāfī thaat: 182.404 315.641 498.045 701.955 884.359 1017.596 1200.000 Makam Hüseynî: 180.450 294.135 498.045 701.955 882.405 1 996.090 1200.000 Maqam Husayni: 165.004 315.641 498.045 701.955 884.359 1 996.090 1200.000 As we can see, the Arabic variant is, except for the 2nd scalar degree, much closer to the Indian than the Turkish variant. Keep in mind that the Arabic variant of the scale is much older than the Turkish. The third and the seventh of the Turkish variant vary by a Didymean comma (21.506 cents) that the Indian variant is sharper. The 2nd and the 6th scale degree, on the other hand, vary by 1.954 cents each that the Indian variant is sharper. The interval of 1.954 cents is referred to as schisma (ratio 32805/32768; at times, also spelled skhisma). It represents the interval between the Didymean comma of 21.506 cents (see p. 47) and the Pythagorean comma of 23.460 cents (see p. 5). The Turkish A-E-U Hüseynî is equivalent to the Babylonian mode Embūbum [Hewitt: p. 83]. Next in our initial table, we have Phrygian , the Indian Bhairavī thaat , and the Turkish makam Kürdî . Again, they all look the same in notation. Because the Arabs do not have a binding theory as the Turks or the Hindustani musicians, we are in the following only going to compare these three variants. ET Phrygian: 100.000 300.000 500.000 700.000 800.000 1000.000 1200.000 Bhairavī thaat: 111.731 315.641 498.045 701.955 813.686 1017.596 1200.000 Makam Kürdî: 0 90.225 294.135 498.045 701.955 792.180 1 996.090 1200.000 In this comparison, the only match is the perfect fourth and the perfect fifth. All other intervals of the Indian variant are by precisely 21.506 cents sharper, a Didymean comma. Bhairavī's interval sequence is equal to that of Dorian tuned according to Ptolemy's intense diatonic shade [Hewitt: fig. 8.3] (see p. 11). Kürdî is equivalent to the Pythagorean Dorian [Hewitt: fig. 3.8]. Both scales are a variant of ancient Greek Dorian , today's ET Phrygian. If the 3rd scale degree (E ♭ ) in the Bhairavī thaat becomes very flat ( 294.135 cents) , such as in Raag Bilāskhānī Tōḍī , the interval has the same value as in the Turkish variant. In that case, the lower tetrachord changes from Ptolemy's intense diatonic tetrachord (16/15 - 6/5 - 4/3) [Hewitt: fig. 8.1] to that of Didymus' diatonic tuning (16/15 - 32/27 - 4/3) [Hewitt: fig. 8.4] (also see p. 11). If we flatten the 2nd degree of Kürdî to 62.565 cents (ratio 648/625) and the 6th to 764.916 cents (ratio 14/9), we receive Archytas' (435/410-355/350 BCE) diatonic scale [Hewitt: fig. 1.2]. 1 Now let us have a look at Mixolydian , the Khamāj thaat , and Acem ET Mixolydian: 200.000 400.000 500.000 700.000 900.000 1000.000 1200.000 Khamāj thaat: 182.404 386.314 498.045 701.955 884.359 1017.596 1200.000 Makam Acem: 203.910 407.820 498.045 701.955 905.865 1 996.090 1200.000 Again, a Didymean comma variance between 2nd, 3rd, and 6th scale degree. This time, the 2nd, 3rd, and 6th scale degree of the Turkish variant is sharper than the Indian. The seventh is by a Didynean comma flatter than the Indian variant. The interval sequence of Acem is equal to the ancient Greek Hypophrygian , which's interval sequence in ancient Babylonia was referred to as Pītum . Though there it was heptatonic because it lacked the octave [Hewitt: fig. 5.7]. If in the Khamāj thaat komal ni (B ♭ ) becomes very flat (996.090 cents), the interval sequence is equal to Hypophyrygian tuned according to Ptolemy's intense diatonic shade [Hewitt: fig. 8.3]. Next, Aeolian , the Āsāvari thaat , and Bûselik ET Aeolian: 200.000 300.000 500.000 700.000 800.000 1000.000 1200.000 Āsāvari thaat: 182.404 315.641 498.045 701.955 813.686 1017.596 1200.000 Makam Bûselik: 203.910 294.135 498.045 701.955 792.180 1 996.090 1200.000 The variance of the 3rd, 6th, and 7th interval is again by a Didymean comma that the Indian variant is sharper. The second of Bûselik is by a Didymean comma sharper than the Indian variant. In ancient Greece, the interval sequence of Bûselik was referred to as Hypodorian [Hewitt: fig. 6.11] and in ancient Babylonia as the mode Kitmum [Hewitt: p. 83]. If in Raag Āsāvari, we use komal re (D ♭ ) instead of the natural D, as some Hindustani musicians suggest (see p. 55), we get the same interval sequence as that of the Bhairavī thaat Double harmonic major , the Bhairav thaat , and Zîrgûle'li Hicâz in comparison. Double harm. major: 100.000 400.000 500.000 700.000 800.000 1100.000 1200.000 Bhairav thaat: 111.731 386.314 498.045 701.955 813.686 1088.269 1200.000 Makam Zîrg. Hicâz: 113.685 384.360 498.045 701.955 815.640 1086.315 1200.000 In this comparison, we can observe that sometimes an interval in one variant is by a schisma (1.954 cents) sharper than its counterpart and sometimes it is by a schisma flatter. The Lydian mode compared to the Kalyān thaat is as follows. ET Lydian: 200.000 400.000 600.000 700.000 900.000 1100.000 1200.000 Kalyān thaat: 182.404 386.314 590.224 701.955 884.359 1088.269 1200.000 The ET Lydian is, with a deviation of a few cents only, pretty close to the ancient Babylonian mode Niš Gabrim [Hewitt: p. 83]. In the Pythagorean tuning, it would be precisely the same interval sequence. The Lydian ♭ 9 scale and the Mārvā thaat Lydian ♭ 9: 100.000 400.000 600.000 700.000 900.000 1100.000 1200.000 Mārvā thaat: 111.731 386.314 590.224 701.955 884.359 1088.269 1200.000 Comparing Ionian major , the Bilāval thaat , and the in practice not existing Turkish makam Çârgâh and Râst ET Ionian: 200.000 400.000 500.000 700.000 900.000 1100.000 1200.000 Bilāval thaat: 182.404 386.314 498.045 701.955 884.359 1088.269 1200.000 Makam Çârgâh: 203.910 407.820 498.045 701.955 905.865 1109.775 1200.000 Makam Râst: 203.910 384.360 498.045 701.955 905.865 1086.315 1200.000 Though it is not used in Turkey and represents nothing but an artificially designed theoretical invention , in ancient Babylonia, Çârgâh's precise interval sequence was known as the mode Nīd Quablim , which is corresponding to the ancient Greek Lydian mode [Hewitt: p. 83]. In Çârgâh, the variance between the Turkish and Indian variant is by a Didymean comma that Çârgâh is, except for the perfect fourth and perfect fifth, sharper than the Indian variant. 2 In Râst Makamı, the third and seventh is by a Pythagorean comma flatter than that in Çârgâh. The third and seventh in Râst is also by a schisma flatter than in the Indian variant. The second in Râst and Çârgâh is the same. Makam Râst is closer to the Indian variant than Çârgâh. Though visually Çârgâh is closer because it contains no 'special accidental' . On paper, the Bilāval thaat and Çârgâh Makamı both look exactly like C major (Ionian). There are two more ancient Babylonian modes. Išartum: C - D ♭ - E ♭ - F - G - A ♭ - B ♭ ( Phrygian ) and Quablītum: C - D ♭ - E ♭ - F - G ♭ - A ♭ - B ♭ ( Locrian ) [Hewitt: p. 83]. If we have a look at makam Acem again, which is equal to the ancient Babylonian mode Pītum, we can observe that the cent-wise deviation is very little compared to the equal-tempered variant of that scale. The highest being 7.820 cents. As a rule of thumb, the frequency of one hertz (Hz for short) is equal to the interval of roughly four cents. So 440 Hz (= pitch standard A) by around eight cents sharper are 442 Hz (see p. 110). The next ET half tone is 100 cents sharper (A#/B ♭ ) and has a value of 466.164 Hz. The Babylonian intervals correspond to those of the Pythagorean tuning because of the Babylonian cyclic tuning of Nīš Gabrim, which goes up by a perfect fifth (3/2) and down by a perfect fourth (4/3). Again, up by a perfect fifth, down by a perfect fourth, and so on. Until finally the augmented fourth is reached [Hewitt: p. 80]. Therefore, you receive the same interval values in both tunings. Note that all Babylonian modes are heptatonic In conclusion, what looks the same on paper can indeed be very different, as we have seen in the previous. Finally yet importantly, we are also going to have a look at those raags that have no counterpart in the Western music tradition: those of the Poorvī thaat (though, at times referred to as 'Gypsy major') and the Tōḍi thaat Poorvī thaat: 111.731 386.314 590.224 701.955 813.686 1088.269 1200.000 Tōḍi thaat: 111.731 315.641 590.224 701.955 813.686 1088.269 1200.000 The Poorvī (on paper, in Greece referred to as Drómos Pireótikos ) and Tōḍi thaat have no Western equivalent and hence are particularly interesting for improvisation. Though the set of intervals composing a scale stays the same within a thaat, the vādī and the samvādī can indeed vary from one rāga to another. This should be considered depending on which Western scale or mode you want to use that very raag in. If we take, for instance, the Bhairavī thaat. Raag Malkauns is of that thaat and its vādī and samvādī is F and C, respectively. Bilāskhānī Tōḍī is, according to Bhatkhande, of the same thaat but has A ♭ as the vādī and a very flat E ♭ as the samvādī. The Bhairavī thaat can be regarded as Phrygian. So, if in C Phrygian, F and C are vādī and samvādī, respectively, these two tones transposed by a minor third are A ♭ and E ♭ , respectively. So if switching, for example, from C Phrygian to E ♭ Mixolydian, the 3rd mode of C Phrygian, such things should be taken into consideration. The common phrases can be applied accordingly. Such features make the Poorvī and Tōḍi thaat even more interesting for modulations. 3