Even More Exotic Scales!

At the end of the Part 8, you may have noticed I wrote “in our twelve-tone system.” Western music currently divides an octave into twelve equal parts, and the tuning we use is called 12TET, for 12 tone equal temperament. Prior to the 18th century, we used twelve tones, but they weren’t equally divided. Scales in the earlier Western systems (which was used by Bach, Mozart, and others) had twelve tones, but they weren’t equally divided – you can find some recordings of -period’ instruments using the earlier tunings, and you can probably hear a difference in the scales. But the scales used have the same names I’ve outlined in this series, because they use the same twelve tones.

The reason Western tuning changed was because of a mathematical oddity in scales – a “perfect” octave has one note vibrating exactly twice as fast as the other. In a “perfect” fifth, one note vibrates exactly one-and-a-half times faster than the other. Twelve perfect fifths make seven perfect octaves, but if you take a starting frequency and multiply it by 150% twelve times, you don’t get the same result as doubling it seven times. The first person to figure this out was Pythagoras (yep, the triangle guy) and the difference is called the “Pythagorean comma”. What it means in practical terms is that we can’t have all our notes perfectly in tune – if we try to get some sounds really, truly, perfectly in tune with others, we force OTHER tones to be out of tune! Our Western solution was to make every note equally spaced, which makes every note except the octave just a bit out of tune.

Other cultures have taken different approaches to the problem of the Pythagorean comma, and their solutions have divided the octave into some other division than 12. That means you won’t be able to just fret these scales – you’ll have to selectively bend notes to hit pitches that are between our twelve tones. I’ll outline two of these systems for you to experiment with.

In the Arabian peninsula music theorists took a mathematical approach, and the theory (which dates back about 1200 years) divides the octave into 17 parts. But it’s not quite as simple as dividing by 17! Most of the music of the middle east and North Africa is vocal, or accompanied by instruments like the oud, which is fretless – so they’re not constrained by “fixed intonation”. As a result, there are regional differences that have developed in their scales. What I’m calling “Arabian” is a broad description; it covers music from the Arabian peninsula all the way up to the Black Sea, as well as much of north Africa and the Southwestern parts of the former Soviet Union.

Modern Arabian music uses at least 24 different pitches to the octave, and the placement of those pitches can be a little different in Iraq than they are in Algeria! If you’re really interested in this sort of music, listen to it closely and use what you hear!

But here’s the basic structure: Arabian scales are called “maqams”, and each maqam is made up of two or more “jins”, which are fragments of 3 to 5 notes. The jins may follow one another, or they may overlap (i.e., the last two notes of one jin may also be the first two notes of the next jin), or they may be separated by one or two other tones, usually equivalent to our half steps and whole steps. This means there are a HUGE number of possible maqams, so I’m going to focus just on the jins. I’ll start them all from C; you’ll need to transpose them up to create whole maqams from these. The Hijaz, Bayati, and Sikah are the ones most commonly heard.

We’ll start with the ones that can be played without bends:

C-Db-Eb-F is the Kurd jin. It’s the same as the beginning of our Phrygian scale.

C-D-Eb-F is the Nahawand jin. It’s the same as the beginning of our minor scales.

C-Db-Eb-Fb is the Zamzama jin.

C-D-Eb-F#-G is the Nawa Athar jin, and

C-Db-Eb-F#-G is the Athar Kurd (it’s the Nawa Athar with the second note flatted)

Now we start bending. Here you’ll have to use your ears, because the differences can be small.

C-D-E* (the E is played just slightly flat, so you bend from D# about 90% of the way to E) is the Ajam.

C-D-E** (with the E just a little more flat than in the Ajam – maybe 80% of the way to E) is the Jiharkah.

C-D-Eb*-F is the Busalik

C-Db*-E***-F (with E bent sharp by about 10%) is the Hijaz.

Several jins make use of notes about halfway between our pitches. I’ll indicate those with the notes on either side, as in Db/D – you bend halfway from Db to D to get the right sound:

C-Db/D-Eb/E is the Sikah jin. If you want, you can bend the C to be C/C#, and just follow it with D and E.

C-D/Eb-Eb/E is the Mustaar. You can also go from C/C# to Eb and then E.

C-Db/D-Eb-F is the Bayati.

C-D-Eb/E-F is the Rast.

C-Db/D-Eb-Fb is the Saba.

The music of India consists of an entirely different system, called raga. When I studied Indian music in a college class, we were taught that there were 72 ragas – I’ve since learned that wasn’t exactly true (it’s more like 300!) The music of Southern India follows a system of “Carnatic” ragas; Northern India uses “Hindustani” ragas. They have different origins, so while there is overlap, it’s either coincidental or the result of unrecorded past influences from the other system. What I was being taught was a Southern system (as it turns out, it’s not even the only Southern system!), which does have 72, but there are modifications used that push that to 100 or so.

Ragas have cultural and religious implications; some are to be performed at certain times of the day, or during certain seasons of the year. I admit I’ve never really gotten a good grasp on that aspect of ragas. But I do understand at least a bit about how they work musically – ragas, like our Western diatonic scales, each consist of seven notes in an octave.

Every raga contains two fixed notes, Sa (our “do”, or C) and Pa (our “sol”, or G). Because of this, raga melodies can have cadences that are virtually identical to those in Western music. But the other five notes in a raga can take either two forms (like our D or Db) or three forms – like Db, D, or D#. Some of their pitches are identical in sound, like our F# and Gb.

Ancient ragas divided an octave into 22 divisions called shruti. In most parts of India this has given way to a twelve tone system – that’s the one I’ll present here. But drawing on the shruti heritage, the 12 tones that make up ragas aren’t equally spaced. So we’ll need to start with a slightly different scale. The one I’m presenting I can’t pretend is standard� but that’s because there ISN’T a standard! The actual divisions of the octave can vary from place to place, and even from one performance to another.

But to make this at least a bit accessible, I’m going to simplify the tones. I’ve worked this section from recordings of ragas, and where the pitch is within 5 cents or so of what we use, I’ll just make them equivalent (a cent in music is 1/100th of a half step). You’ll need to adjust a couple of tones in the ragas:

C# will be about 10% flatter than our C#; bend up the C below most of the way to C#
A will be about 15% flatter than our A; bend up from the G# below

Got that? Ok, on with the scales. I’m showing all of them with sharp tones to keep things simple, and to avoid having to go into how shruti are named.

Kanakangi = C-C#-D-F-G-G#-A-C
Ratnangi = C-C#-D-F-G-G#-A#-C
Ganamurti = C-C#-D-F-G-G#-B-C
Vanaspati = C-D#-D-F-G-A-A#-C
Manavati = C-D#-D-F-G-A-B-C
Tanarupi = C-D#-D-F-G-A#-B-C
Senavati = C-C#-D#-F-G-G#-A-C
Hanumatodi = C-C#-D#-F-G-G#-A#-C
Dhenuka = C-C#-D#-F-G-G#-B-C
Natakapriya = C-C#-D#-F-G-A-A#-C
Kokilapriya = C-C#-D#-F-G-A-B-C
Rupavati = C-C#-D#-F-G-A#-B-C
Gayakapriya = C-C#-E-F-G-G#-A-C
Vakulabharanam = C-C#-E-F-G-G#-A#-C
Mayamalavagowla = C-C#-E-F-G-G#-B-C
Chakravakam = C-C#-E-F-G-A-A#-C
Suryakantam = C-C#-E-F-G-A-B-C
Hatakambari = C-C#-E-F-G-A#-B-C
Jhankaradhwani = C-D-D#-F-G-G#-A-C
Natabhairavi = C-D-D#-F-G-G#-A#-C
Keeravani = C-D-D#-F-G-G#-B-C
Kharaharapriya = C-D-D#-F-G-A-A#-C
Gourimanohari = C-D-D#-F-G-A-B-C
Varunapriya = C-D-D#-F-G-A#-B-C
Mararanjani = C-D-E-F-G-G#-A-C
Charukesi = C-D-E-F-G-G#-A#-C
Sarasangi = C-D-E-F-G-G#-B-C
Harikambhoji = C-D-E-F-G-A-A#-C
Dheerasankarabharanam = C-D-E-F-G-A-B-C (not quite our major scale, because A is a bit flat)
Naganandini = C-D-E-F-G-A#-B-C
Yagapriya = C-D#-E-F-G-G#-A-C
Ragavardhini = C-D#-E-F-G-G#-A#-C
Gangeyabhushani = C-D#-E-F-G-G#-B-C
Vagadheeswari = C-D#-E-F-G-A-A#-C
Shulini = C-D#-E-F-G-A-B-C
Chalanata = C-D#-E-F-G-A#-B-C
Salagam = C-C#-D-F#-G-G#-A-C
Jalamavam = C-C#-D-F#-G-G#-A#-C
Jhalavarali = C-C#-D-F#-G-G#-B-C
Navaneetam = C-C#-D-F#-G-A-A#-C
Pavani = C-C#-D-F#-G-A-B-C
Raghupriya = C-C#-D-F#-G-A#-B-C
Gavambhodi = C-C#-D#-F#-G-G#-A-C
Bhavapriya = C-C#-D#-F#-G-G#-A#-C
Shubhapantuvarali = C-C#-D#-F#-G-G#-B-C
Shadvidamargini = C-C#-D#-F#-G-A-A#-C
Suvamangi = C-C#-D#-F#-G-A-B-C
Divyamani = C-C#-D#-F#-G-A#-B-C
Dhavalambari = C-C#-E-F#-G-G#-A-C
Namanarayani = C-C#-E-F#-G-G#-A#-C
Kamavardani = C-C#-E-F#-G-G#-B-C
Ramapriya = C-C#-E-F#-G-A-A#-C
Gamanashrama = C-C#-E-F#-G-A-B-C
Vishwambari = C-C#-E-F#-G-A#-B-C
Shamalangi = C-D-D#-F#-G-G#-A-C
Shanmukhapriya = C-D-D#-F#-G-G#-A#-C
Simhendramadhyamam = C-D-D#-F#-G-G#-B-C
Hemavati = C-D-D#-F#-G-A-A#-C
Dharmavati = C-D-D#-F#-G-A-B-C
Neetimati = C-D-D#-F#-G-A#-B-C
Kantamani = C-D-E-F#-G-G#-A-C
Rishabhapriya = C-D-E-F#-G-G#-A#-C
Latangi = C-D-E-F#-G-G#-B-C
Vachaspati = C-D-E-F#-G-A-A#-C
Mechakalyani = C-D-E-F#-G-A-B-C
Chitambari = C-D-E-F#-G-A#-B-C
Suchantra = C-D#-E-F#-G-G#-A-C
Jyoti swarupini = C-D#-E-F#-G-G#-A#-C
Dhatuvardani = C-D#-E-F#-G-G#-B-C
Nasikabhushani = C-D#-E-F#-G-A-A#-C
Kosalam = C-D#-E-F#-G-A-B-C
Rasikapriya = C-D#-E-F#-G-A#-B-C

Many, many more scales are possible. I’ve only touched on the ones that are commonly used in Western music with the 12TET scale, and those that are culturally widespread. But theorists and composers are continually experimenting – tuning systems now exist that divide an octave into 15, 17, 19, 22, 24, 31, 34, 41, 53, and 72 equal divisions, and unequal tuning systems are also possible… from the historical ones like the Werkmeister tunings used by Bach to tomorrow’s innovations.

I hope this series has given your fingers some food for thought!

Tom (“Noteboat”) Serb is a longtime Guitar Noise contributor and founder of the Midwest Music Academyin Plainfield, Illinois. This advice first appeared in Volume 4 # 22 of Guitar Noise News. Sign-up for our newsletter to receive more free tips like this by email.

More from Everything You Ever Wanted to Know About Scales

• Everything You Ever Wanted to Know About Scales – Part 1
• Everything You Ever Wanted to Know About Scales – Part 2
• Everything You Ever Wanted to Know About Scales – Part 3
• Everything You Ever Wanted to Know About Scales – Part 4
• Everything You Ever Wanted to Know About Scales – Part 5
• Everything You Ever Wanted to Know About Scales – Part 6
• Everything You Ever Wanted to Know About Scales – Part 7
• Everything You Ever Wanted to Know About Scales – Part 8