This is a chapter out 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) 11. Northern Indian Rāgas In this segment, we will have a closer look at some Northern Indian rāgas, compare them to Turkish and Arabic scales and modes as well as other Northern Indian rāgas, and set them in a jazz context. Please note that an Indian musician would neither do any of the subsequent nor would he agree with it. Indian musicians, for the most part, stay within a rāga and do not modulate to others too much, though ascending and descending raags differ in terms of added and/or altered tones. Each rāga follows distinct rules that determine its performance. Hence, the ensuing is solely from a Western point of view and nothing a Hindustani musician would agree with. a. The Northern Indian Tetra- and Pentachords Just like Turkish makamlar or Arabic maqamat, Northern Indian rāgas are also composed of tetrachords, which can span both a perfect as well as an augmented fourth; with a, depending on the raag and/or the performer, potential variance of ± 21.506 cents, a Didymean comma each. According to some mathematicians, there are 43 different possible tetrachords only within the equal-tempered 12-tone system [Hook: p. 14]. Now, imagine the possible number of tetrachords within other musical systems and tunings, such as in the Turkish A-E-U or the Northern Indian musical system. Below, the individual composition of each of Bhatkhande's thaats. As we can see, there are thaats that share the same lower and thaats that share the same upper tetrachord. By adding the perfect fifth (G) to each lower tetrachord, it becomes the according pentachord. Thaat Poorvang Uttarang lower tetrachord upper tetrachord Bilāval C D E F G A B C Ionian tetrachord + Ionian tetrachord Khamāj C D E F G A B ♭ C Ionian tetrachord + Aeolian tetrachord Kāfi C D E ♭ F G A B ♭ C Aeolian tetrachord + Aeolian tetrachord Āsāvari C D E ♭ F G A ♭ B ♭ C Aeolian tetrachord + Phrygian tetrachord Bhairavī C D ♭ E ♭ F G A ♭ B ♭ C Phrygian tetrachord + Phrygian tetrachord Kalyān C D E F# G A B C Lydian tetrachord + Ionian tetrachord Mārvā C D ♭ E F# G A B C Lydian ♭ 9 tetrachord + Ionian tetrachord Poorvī C D ♭ E F# G A ♭ B C Lydian ♭ 9 tetrachord + Hicâz/Hijāz tetrachord Tōḍī C D ♭ E ♭ F# G A ♭ B C Athar Kurd tetrachord + Hicâz/Hijāz tetrachord Bhairav C D ♭ E ♭ F G A B C Phrygian tetrachord + Ionian tetrachord Though the Poorvī thaat (just as the Tōḍī thaat) has no Western equivalent, its interval sequence is in Greece known as Drómos Pireótikos (Greek Δρόμος πειραιώτικος). There, its lower pentachord of C - D ♭ - E - F# - G, a Lydian ♭ 9 pentachord, is referred to as Pireótikos pentachord . As a tetrachord, which is to be found in both the Mārvā and the Poorvī thaat, it can also be interpreted as an Arabic Hijāz Murassa‘ pentachord without 4th scale degree (see p. 36). Re -interpreting certain sequences or building blocks of a scale or mode is a very useful tool for modulation, as we have already seen. For instance, the sequence of D - E - F# - G in Kalyān can be interpreted as an Ionian tetrachord on D to which further subsequent or overlapping building blocks can be attached. 98 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 0 996.090 1200.000 Maqam Husayni: 165.004 315.641 498.045 701.955 884.359 0 996.090 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 0 996.090 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]. 99 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 0 996.090 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 0 996.090 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. 100 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. c. Improvising with Rāgas Now, from some in-depth just intonation comparisons on to some just in notation comparisons and a closer look at the intervallic structure of some rāgas. This is very helpful and necessary if we want to use those scales and modes in improvisation. The anhemitonic major pentatonic Raag Bhoopali is basically a C Lydian (or also major , depending on your interpretation) scale without 4th and 7th scale degree and is in notation identical with Bulgarian pentatonic No II. Within the Japanese Ryo scale , whose basic scale is the pentatonic above, one can add an F or F# as well as a B or B ♭ to the scale. Lateef gives this scale with both of the sharper intervals (F# and B) [Lateef: p. 115]. Raag Kirvani is an ordinary harmonic minor scale but not part of any of Bhatkhande's thaats, consequently not present in the table above. Kirvani is in notation equal to the ascending Maqam Nahāwand 101 Kirvani's performance does not follow strict rules. D, E ♭ , and A ♭ are the strong tones. The descending is the same as the ascending. However, in his 'Thesaurus of Scales and Melodic Patterns,' Nicolas Slonimsky gives a nice pattern that begins with Kirvani and dissolves into Raag Āsāvari . Of course, he calls it neither Kirvani nor Āsāvari. This time, it is written in Indian Sargam notation . So it has to be sung [adapt.; Slonimsky: pattern No 429]. Sa ma dha Pa ga dha Ni ni This melodic pattern, which Slonimsky files under 'Ultrapolation of three notes' ("Ultrapolation is the addition of a note above the next principal tone" [Slonimsky: p. ii]) is composed of a series of arpeggios of the intervals fourth, major third, and one whole tone down (C - F - A - G; C6sus4, inverted: Fadd9 or Am7 ♯ 5), climbs up in minor thirds. So, the second arpeggio (ga - dha - Sa' - ni) begins on E ♭ (E ♭ - A ♭ - C - B ♭ ; E ♭ 6sus4, inv.: A ♭ add9 or Cm7 ♯ 5), the third on F#, and so forth. But, why sing? There is an old Arabic story in which the student wants to impress his teacher and plays something very fast and technical on his instrument. After the student had finished, the teacher asked him to now sing what he had just played. The moral of the story is that if you cannot sing what you play – it is pointless. The following hemitonic minor pentatonic , which is sometimes referred to as Hira Chôshi [Kostka: p. 484], contains the very tones of Raag Kirvani , though giving it a very unique sound due to its intervallic structure. xcv What is fascinating about pentatonic scales is not only that, due to their open composition , one can excessively fill in the blanks by adding passing tones, but one can also blend them by overlapping them. This allows you to build hybrids and get entirely new rows and scales to improvise with. Below we have that pentatonic on C overlapped from the 5th scale degree on by the same pentatonic transposed by a perfect fifth to G (G - A - B ♭ - D - E ♭ - G). This very row adds, because of its odd intervallic composition of wide interval leaps and the three half steps in its center, a nice flavor to any E ♭ maj7 or – due to the wide interval leap between E ♭ and G – even E ♭ min7. It is also pretty nice to pull triads or, of course, also more complex chords from. A rāga that fits perfectly with the set of intervals above is Raag Bhairavī Bhairavī is basically nothing other than a C Phrygian scale, though the phrase F - F# - F can be used, and D flat and B flat can become a natural D and a natural B, respectively. The descending scale is no different from the ascending one. Bhairavī is a Hindu goddess associated with the Mahavidyas (Sanskrit महािवा ), a group of ten aspects of Adi Parashakti in Hinduism. Bhairavī means nothing other than terror . With the above-mentioned alterations applied to Bhairavī, we get one of Lateef's synthetic scales [Lateef: p. 126, scale No 7]. If one strips Raag Bhairavī down to a pentatonic by leaving out the 2nd and 5th scale degree as to eliminate all half steps, one gets the anhemitonic minor pentatonic Raag Malkauns , which is also of the Bhairavī thaat and which is in notation identical with the Bulgarian pentatonic No IV and in China known as Man Gong pentatonic. Or, we can strip it down to the enharmonic scale of Olympus on C , in India referred to as Raag Gunakri of the 102 Bhairav thaat or also as the ascending Komal Rishabh Āsāvari of the eponymous thaat. Āsāvari adds tones to the descending, whereas Gunakri does not. This makes this pentatonic quite interesting. In traditional Japanese music, this scale, based on the original koto tuning, is called (Hon) Kumoi Chôshi . Other theorists call this interval sequence In scale or also Miyako-Bushi scale . In the In scale, F and B are added as pien tones. Kumoi Chôshi is the 4th mode of Hira Chôshi , another koto tuning. Most Japanese koto pentatonics are modes of this scale. In Ethiopian traditional music, it is known as the Ambassel scale [Hewitt: p. 168]. In comparison, the precise interval sequence of Raag Gunakri is as follows: 111.731 cents - 498.045 cents -701.955 cents - 813.686 cents - 1200.000 cents. According to Helmholtz, Olympus (7th cent. BCE) stripped this scale down from the ancient Greek Dorian scale . He moreover assumes that Olympus brought the 5-tone scale with him from Asia and only borrowed the use of the half tone from the ancient Greek music tradition. The Chinese as well as the Gaels of Ireland and Scotland still stick exclusively to anhemitonic pentatonics [Helmholtz: p. 426]. Harry Partch gives the interval sequence for the Olympus pentatonic with the ratios of 9/8, 6/5, 3/2, and 8/5, which is 203.910 cents - 316.98 cents - 701.955 cents - 813.686 cents, respectively. This is the 3rd mode (beginning on F) of the pentatonic above. Plutarch describes yet another pentatonic by Olympus, in which he added a whole-tone step to each half of the octave (C - E ♭ - F - G - B ♭ - C) of the ancient Greek prototype scale from page 11 [Wolf: p. 9]. This very pentatonic is equal to the Bulgarian pentatonic No I , which, in turn, in notation is identical with Raag Dhani . Mode II of the Olympus pentatonic is C- E - F# - G - B - C, Terry Burrows' version of Hira Chôshi [Burrows: p. 90]. Mode III is C - D - E ♭ - G - A ♭ - C. Mode IV is C - D ♭ - F - G ♭ - B ♭ - C, which Lateef refers to as "Hon-Kumoi-Joshi" [Lateef: p. 113] ( hon is Japanese for 'true' or 'real') and Slonimsky as his version of Hira Chôshi [Slonimsky: scale No 1153]. Mode V is C - E - F - A - B - C, which is also to be found in ancient Greek music [West: p. 289]. Plutarch also mentions a mode called Spondeion scale , which looks quite similar to the Olympus pentatonic in notation. Its precise interval sequence is 150.637 cents - 498.045 cents - 701.955 cents - 852.592 cents - 1200.000 cents [Hewitt: fig. 11.7]. The Japanese hemitonic Insen pentatonic , in India referred to as Raag Bairagi , has a different ascending but can use the Olympus pentatonic in the descending. The ascending sequence of F - G - B ♭ - C followed by the descending sequence C - A ♭ - G - F gives a pretty nice flavor. An A or likewise a natural B instead of the B ♭ in the ascending sounds pretty nice as well. Both pentatonics go very well with Hümâyûn Makamı . Omitting the 3rd degree in its Hicâz tetrachord also produces a nice East Asian flavor. The hemitonic pentatonic that we stripped from Raag Kirvani (C - D - E ♭ - G - A ♭ - C) from the previous page fits nicely in the ascending, too. Raising the second of the ascending Insen pentatonic by a half tone but keeping the descending leading tone (D ♭ ) likewise sounds very sweet and sour. The sound of the descending leading tone of the Olympus pentatonic is very characteristic. By raising the second of the hemitonic Insen pentatonic by a half tone, we receive the anhemitonic Bulgarian pentatonic No III Insen pentatonic ascending Olympus pentatonic descending The 3rd mode of the Insen pentatonic is the ascending variant of Raag Āsāvari with a major second (D instead of D ♭ , see p. 55). Mode II of the Insen pentatonic is C - E - F# - A - B - C, which in India is referred to as Raag Sohani of the Mārvā thaat. Mode IV is C - E ♭ - F - G ♭ - B ♭ - C, a Locrian pentatonic , in India referred to as Raag Jayakauns of the Kāfī thaat. Mode V is C - D - E ♭ - G - A - C, which at times also is referred to as Kumoi Chôshi (aka 'Wise One' pentatonic , see p. 89). The Insen pentatonic with a diminished fifth gives mode IV of the Olympus pentatonic. Another hemitonic minor pentatonic that can be stripped from Raag Bhairavī is Slonimsky's variant of the Javanese Pélog pentatonic [Slonimsky: scale 1144]. Pélog means beautiful in Javanese. The modes of the Pélog pentatonic are as follows. 103 Mode II Mode III Mode IV Mode V Mode II can be considered an Ionian pentatonic and mode III a Mixolydian (or genderless ) pentatonic . The Turkish makam Râst changes from Ionian in the ascending to Mixolydian (in Turkey, known as Acem'li Râst Makamı ) in the descending, as does Drómos Rast (Gr. Δρόμος Ράστ) in the Greek music tradition. The ascending leading tone shifts by a half step from B down to B ♭ . Now, switch their a- and descending scales with one another. Beautiful. Drómos Rast ascending / Ionian (major) Drómos Rast descending / Mixolydian Mode II of the Pélog pentatonic Mode III of the Pélog pentatonic The primary chords for Rast used in the Greek music tradition are I, IV, v, VII (on the asc. leading tone), as well as the V. The secondary chords are ii, iii-dim, vi, and I-7. At least two of the modes derived from the Pélog pentatonic are in India known as rāgas . Mode II is in India known as Raag Hansdhwani of the Bilāval thaat. Mode III is in India referred to as the in the ascending pentatonic Raag Gorakh Kalyan of the Khamāj thaat. In Carnatic Indian music, mode V is known as Nāgasvarāvaḻi . The seven bells of the church tower Onze-Lieve-Vrouwetoren in Amersfoort, the Netherlands, are tuned according to mode IV because it is possible to play quite a number of Gregorian melodies with this tuning [Dutch Carillon News: p. 4]. Raag Bilāskhānī Tōḍi is a hemitonic minor pentatonic rāga that can also be stripped from Bhairavī. Raag Bilāskhānī Tōḍi ascending Raag Bilāskhānī Tōḍi descending It is like arranging flowers in a vase. Scale Ikebana. Once we flatten – or re -arrange – the G by a half tone to F# and add a natural B to the ascending Bilāskhānī Tōḍī, we get the intervallic structure of Raag Miyāṅ kī Tōḍī Miyāṅ kī Tōḍī ascending can be described as a leading whole-tone scale with a flattened 2nd and 3rd scale degree. Speaking of minor scales, we will have a look at Maqam Nahāwand and Raag Malkauns , which look just like 'brothers from another mother.' Again, like with Drómos Rast and the Pélog pentatonic, switch their a- and descending scales with one another. Nahāwand switches from harmonic minor in the ascending to natural minor in the descending. 104 Maqam Nahāwand ascending Maqam Nahāwand descending Raag Malkauns ascending Raag Malkauns descending A strong emphasis lies on the F, while the C is the second strongest tone in Malkauns. Malkauns is in notation identical with the Bulgarian pentatonic No IV and belongs to the Bhairavī thaat, which is considered Phrygian . On page 78, we compared the Bulgarian pentatonics to Indian rāgas. These pentatonics are all modes of each other. This becomes quite interesting when it comes to modulation. For example, the Bulgarian pentatonic No V (in Japan, referred to as Nogi Chôshi ), is in notation identical with both Raag Sindhura and Raag Narayani. But Raag Sindhura belongs to the Kāfī thaat, which is considered Dorian ; and Raag Narayani belongs to the Khamāj thaat, which is considered Mixolydian . Dhani and Nayaki Kanada, Bulgarian pentatonics No I and No III, respectively, are both of the Kāfī thaat, thus considered Dorian . But pentatonic No III is the third mode of pentatonic No I. Such things result in whole new possibilities for modulation. Not to forget their Turko/Arabic counterparts' relations. If we raise the seventh of Malkauns by a half tone to an ascending leading tone , we get Raag Chandrakauns Next, a descending pattern in Raag Nayaki Kanada of the Kāfi thaat Since the Kāfi thaat's mother scale ( Dorian ) is symmetrical and hence composed of complementary intervals (major second - minor seventh, minor third - major sixth, perfect fourth - perfect fifth), we can strip the following three pentatonics from it. Each also composed of complementary intervals and hence of palindromic symmetry The second pentatonic above is a minor 6th pentatonic. The last pentatonic is the Bulgarian pentatonic No III or in India referred to as Raag Nayaki Kanada . Nayaki Kanada is on paper in the ascending identical with the Bulgarian pentatonic No III, whereas the descending is a hybrid of pentatonic No I and III . The Bulgarian pentatonic No III is in Japan being called Gaku Chôshi and in China referred to as the Jin Yu pentatonic . It is also very common across Africa. The Jin Yu, the Man Gong, and the Man Jue pentatonic are, just as the five Bulgarian pentatonics, all modes of one another. Thus, Gaku Chôshi and Nogi Chôshi are modes of one another as well. The ascending Nayaki Kanada has, moreover, the same intervallic structure as the Japanese Yō scale , while the descending Yō scale is somewhat different compared to Raag Nayaki Kanada, which is omitting the sixth (A) entirely. Playing the descending Yō scale ascending, we get another Japanese scale, the Ritsu scale , which in notation is similar to the Bulgarian pentatonic No V. In fact, there is no definite Yō scale because it actually is a hybrid of the Minyō scale (C - E ♭ - F - G - B ♭ - C), which in notation is identical with Raag Dhani and the Bulgarian pentatonic No I , 105 and the Ritsu scale (C - D - [E ♭ ] - F - G - A - [B ♭ ] - C) [McQueen Tokita: p. 5]. In the Ritsu scale, the pien tones E ♭ and B ♭ can be added to the scale. Jewish cantor and composer Solomon Rosowsky developed out of the pentatonic interval sequence above his variant of the Pentateuch mode by adding an E and a B ♭ to the scale (see p. 82). If we flatten the B ♭ in the Minyō scale by a half step to A, we again receive a minor 6th pentatonic What about an ascending Raag Bahār pattern , containing both the natural B and the B flat of the a- and the descending Maqam Nahāwand , respectively? In Bahār, we have a common opening phrase of a Csus4 arpeggio (C - F - G) followed by an E ♭ sus2 arpeggio (E ♭ - F - B ♭ ), both of which contain the F as the 2nd scale degree, followed by A - B - C. If we now take the F as our root and add those three latter tones, the result is an incomplete F7 ♯ 11 chord. The missing E ♭ is, of course, also part of Bahār. If we use the B flat instead of the natural B of the scale, we get an F11 chord. Note that, though a rāga might contain two variants of the same svara, the two forms should never be performed in succession. The sequence of C - E ♭ - F - G - B ♭ - C gives a C minor pentatonic . Due to its structure, it can also be interpreted as G Aeolian without 2nd and 5th scale degrees and, of course, all imaginable altered modes thereof. F Aeolian without 3rd and 7th scale degree or B ♭ Aeolian without 3rd and 7th scale degree can also be considered, though they both contain no third . Double-stop chord progressions in rock or pop music do not always contain the third either. Raag Bahār descending pattern Bahār's descending row of C - B ♭ - G - F with the following major third down from the G to E ♭ , the seventh, gives an F9sus4 chord. The sound of F9sus4 is not that much different from that of F11 (F - A - C - E ♭ - G - B ♭ ), if at all. Both chords fit perfectly over the dominant bebop scale on F. Both chords also sound nice succeeding Igor Stravinsky's (1882-1971) bitonal Petrushka chord, which is an F# major triad over a C major triad. So we have C - D ♭ - E - F# - G - B ♭ , a tritone scale. The corresponding svaras are Sa, re, Ga, Ma, Pa, and ni. The Petrushka chord is mainly associated with Stravinsky, although Franz Liszt (1811-1886) used it already 80 years earlier in his 'Malediction Concerto,' though he merged F with B major; "F contra H, diabolus in musica." It is worth noting that some rāgas, for example, those of the Tōḍi thaat, sound pretty nice performed over the Petrushka chord, Just try to play, for instance, Miyāṅ kī Tōḍī over the Petrushka chord, which can be interpreted as a C7 ♭ 9 ♯ 11 chord, followed by Bahār over an F9sus4 (or F11) chord. Just improvise back and forth between these two chords. If in doubt, always go for a C-dominant seventh chord when trying C-based scales in order to get a taste for its flavor. The sound of the Petrushka chord is widely considered messed up. But arpeggiated or in some voicings, it can indeed sound pretty decent. Another nice chord in this regard is Scriabin's mystic chord, which consists of C - F# - B ♭ - E - A - D and which Scriabin himself referred to as the 'chord of the Pleroma,' which describes the totality of divine powers and literally translates as fullness . All those odd chords seem to have been invented for these kinds of exotic scales and modes. Maqam Athar Kurd (a hybrid of Maqam Nawa Athar and Maqam Kurd ) is in notation equal to the descending Raag Miyāṅ kī Tōḍī . The pentachord of C - D ♭ - E ♭ - F# - G (in Miyāṅ kī Tōḍī only used in the desc.) is the Arabic Athar Kurd pentachord . In Turkish music theory, there is no such pentachord. Athar Kurd is cohemitonic and has a diminished , a perfect , as well as an augmented fifth . Two succeeding half steps with the perfect fifth in their center. The 8th mode of the dominant bebop scale on D ♭ further adds a natural F to that tetrachord. And on top of that, with the added B ♭ , we get another passing tone – into the ascending leading tone. The natural G is gone again in this scale. 106 In his 'Thesaurus,' Slonimsky files this very scale (to which Lateef erroneously refers to as 'Maqam ‘Irāq;' (see p. 70) under the category 'Non-Symmetric Interpolation' [Slonimsky: pattern No 51], "the insertion of one or several notes between the principal tones" [Slonimsky: p. ii]. In pattern No 50, under the same categorization, he gives Scriabin's Prometheus scale (C - D - E - F# - A - B ♭ - C), a scale that is derived from Scriabin's mystic chord. The Prometheus scale is a perfect tool to modulate from one dom. bebop scale to another one fifth apart. The dom. bebop scale on C contains a B ♭ , the dom. bebop scale on G contains an F#, all other intervals in both scales are natural. The Prometheus scale on C contains both the B ♭ and the F#. Social psychologist Erich Fromm (1900-1980) once put it this way: "In love, the paradox occurs that two beings become one and yet remain two." Not belonging to anything but still involved with everything. In Buddhism, moreover, there is a key doctrine referred to as Pratītyasamutpāda (Sanskrit ती यसमु पाद ), it says that all things arise in dependence upon other things. We can further strip the latter two scales down to one almost identical (A ♭ becomes A) symmetric scale that moreover divides the octave into four equal parts : four minor thirds. The tritone G ♭ divides the octave into two equal parts. We can also strip Maqam Athar Kurd down to the hemitonic pentatonic rāga Raag Shrī We can strip down this scale down even further. In his 'The Technique of my Musical Language,' Messiaen gives a what he calls incomplete MOLT No 5 [Messiaen: fig. 343]. This variant is the same scale as Raag Shrī, just without the ascending leading tone B. Lendvai refers to this interval sequence as a so-called '1:5 model,' which is an infinite row of minor seconds and perfect fourths [Lendvai: p. 30]. It is also composed of two tritones , C - F# and D ♭ - G. It eliminates the tritone F - B from MOLT No 5, which would make it complete. So, in the complete MOLT No 5, the B – like in Raag Shrī – is present. Messiaen considered MOLT No 5 an ' incomplete MOLT No 4, ' since MOLT No 5 contains all tones of the latter [Messiaen: p. 91] (also see p. 79). Tritones are the key ingredient of any dominant 7th chord. The tones of a G7 chord are G - B - D - F. The interval B - F is a tritone. Contrary to the fourth or the fifth, a tritone always stays a tritone, no matter if one is going up or down on the circle of fifths, as it divides the octave into two equal parts . Hence, both tones are at diametrically opposite points on the circle of fifths. By adding all tones of the B to the F major scale, we receive the entire 12-tone chromatic scale. This applies to all tones situated at diametrically opposite points on the closed circle of fifths. But why is an orange like a bell? Because they both can be 'peeled' or stripped . By stripping down two or more apparently quite different scales or modes to their lowest common denominator , one can effortlessly 'tailor' a relationship between them. The lowest c ommon denominator in this very riddle is the miraculous pair of the homophone words 'to peel ' and 'to peal ,' since patently nothing else links these two at all. The 4-tone scale above is, except for the natural sixth, alive in both of the latter 'complete scales' and thus a neat little gizmo to modulate between those two particular scales. The natural sixth (A) acts as the port of entry Tailoring scales and modes by adding or removing tones to make certain sequences fit with other scales and modes is a very useful gadget in our modulation utility belt . What you receive is one scale with which you can solo over two or even more different chord changes and by filling it up, modulate from one to the other. You get the best of both worlds without losing touch with one another. Any exit can also be an entrance and vice versa. 107 Alexander the Great (356-323 BCE) once proclaimed: "There is nothing impossible to him who will try." Everything is impossible until somebody does it and as already said earlier: to define is to limit . The same scale or mode can exist in many shapes and under many names, as we have seen in this chapter. There is no 'one truth,' everything is a matter of definition and perspective . "Everything we hear is an opinion, not a fact. Everything we see is a perspective, not the truth" [Marcus Aurelius (121-180)]. For a painter, the color white is the absence of color; for a physicist, white light (sunlight) contains all wavelengths (colors) of the visible light. For a painter, the color black is the sum of all colors; for a physicist, it is the absence of light (color). "One could therefore say the true name is that which all symbols, which signify an object, have in common" [Wittgenstein: 3.3411]. "Most questions and propositions of the philosophers result from the fact that we do not understand the logic of our language" [Wittgenstein: 4.003]. Our consciousness perceiving the world is the cause of all perception of form and matter. Things are attributed with names a priori . The concepts fixed by mere words only gradually come closer to the real knowledge, which can only be gained through perception. Both rectify each other. But, only when these two meet and are firmly bonded, the maturity of knowledge is reached. "Deep knowledge is not knowledge of the thing itself, but knowledge of a thing like the thing. Then, you gain not one knowledge, but two knowledges. Of the thing. And of the original thing, which is like the thing" [George Bernard Shaw]. The moment these two pieces of knowledge meet is the moment one steps out of the cave and into the light and sees the things one before only saw the shadows of. "Truth is one, but the wise men know it as many" [Rigveda 1.164.46]. An auxiliary diminished scale on F (F - G - A ♭ - B ♭ - B - C# - D - E - F) also fits nicely to pull chords from in order to build chord changes for rāgas that contain those very tones of thaats Kāfi , Āsāvari , and Bhairavī . There are only two kinds of diminished scales : the whole tone - half tone, the auxiliary diminished scale , which we have here; and the half tone - whole tone, which is referred to as the auxiliary diminished dominant scale . There are only three scales each of these two different diminished scale forms, the others just being modes of them. Some rāgas look like a jazz pattern. Just like Raag Gaud Sarang Raag Gaud Sarang ascending pattern The ascending Gaud Sarang pattern above is basically a C Lydian scale going up in a characteristic sequence of thirds. A perfect fourth from the G to the C, again a minor third from the B to the D, and one whole step back to the C, the octave. C - E - D - F - E - G and so on is a common ascending opening phrase of this rāga. The pattern continues this structure. F and E are the resting tones. Note that in Gaud Sarang both the F sharp and the natural F can be used. Of course, not in succession. Raag Gaud Sarang descending pattern Such a nice pattern. Yet there is another pentatonic raag, which is from the same thaat as Gaud Sarang, thus containing the same set of intervals, but which is not categorized under the Bulgarian pentatonics, though it is in China k