How Many Scales Are There In Music?

How many musical scales are there as a mathematical equation

Learning scales is a fundamental part of learning any instrument. They can improve sightreading, improvisation, and technique.

But how many scales are there? The short answer is that there are 48 total major and minor scales. The long answer? It could be more than 200, more than 25,000 or infinity depending on the definition.

Definition 1: Counted If It is a Major or Minor Scale

The most rigid definition of a scale is: a scale is one of the standard major and minor scales. The majority of music today is centered around these scales. This includes folk music of many cultures, pop music and western classical music of the past 500 years.

There are 12 major scales – one for each of the 12 notes in an octave. There are 3 types of minor scales: natural, harmonic and melodic, so 3* 12 =36 minor scales. This gives a total of 48 scales.

Definition 2: Counted If It Is a Common Type of Scale

Let’s upgrade the answer. Here is a list of common musical scale types.

Scale# of TypesTotal
Major112
Minor3 (Harmonic, Melodic, Natural)36
Blues2 (Major, Minor)24
Pentatonic2 (Major, Minor)24
Mode7 (Ionian [major scale], Dorian, Phrygian, Lydian, Mixolydian, Aeolian [natural minor scale], Locrian)84 (60 if excluding Aeolean and Ionian)
Whole Tone112
Chromatic112
Diminished2 (Whole-half, Half-whole)24
Grand Total204

With our new definition we have a total of 204 scales.

Some of these scales use the same set of notes. Perhaps you are already familiar with relative major/minor scales such as C major and A minor which use the same notes but different starting points.

Below is a list of scales that use the same set of notes but different starting points.

  • Major with natural minor – A major key’s relative minor key have the same notes
  • Major with minor pentatonix
  • Major with minor Blues
  • Whole tone with whole tone – in fact there are only 2 sets of notes used in a whole tone scale. One of them is C D E F♯ G♯ A♯ and the other is C♯ D♯ F G A B.
  • Chromatic with chromatic – there is only one set of notes used in the chromatic scale – that set is all of the notes.
  • Diminished with diminished – Diminished scales include 8 distinct notes per octave following a pattern of alternating whole and half notes. There are only 3 sets of notes used in diminished scales.

Definition 3: Counted If It Has 8 Notes per Octave

This definition is inspired by John D. Cook’s article on the number of scales, and is a bit more nuanced.

Definition 3: A scale is a set of 8 unique notes in which the highest and lowest notes are one octave apart and adjacent note are no more than a minor 3rd apart.

Why is this a reasonable definition? Notice that the harmonic minor scale has a leap of a minor 3rd between its 6th and seventh scale degrees.

Harmonic Minor Scale Example With  Minor 3rd Between A♭ and B

So a scale can include minor 3rds right? Well, if we create a scale of only minor 3rd intervals we end up with a diminished chord. If played in an ascending/descending order this would typically be called an arpeggio not a scale.

Diminished Chord with Minor Thirds Marked Throughout

Definition 3 excludes the diminished chord as a scale, but includes the Harmonic Minor Scale. According to this definition there are 266 possible scales. However, unfortunately our beloved whole-tone, diminished, blues and chromatic scales are excluded because they have too many/few notes…

Definition 4: Counts If It Is a Subset of the 12 Chromatic Notes

A subset of the 12 chromatic notes is any collection of 12 or less notes with no duplicates. So far all the scales we have discussed fit this definition. But here are more examples:

With this flexible definition of a scale and a bit of math we can show that there are 24576 possible scales. That linked article is an interesting read, to understand it you will want to understand factorials and combinations.

Definition 5: Including Non-WesternTunings

So far our discussion has been on the 12 tone per octave system commonly used in western music. Our most recent calculation of 24576 essentially answers “how many piano scales are there?”

But not all music is played on the piano. Let’s head to traditional Indian music for even more scales!

Ragas or raags are something like the equivalent of modes/scales in western music. The actual definition is more nuanced; some claim they are between a scale and a tune. The notes used in the Raag Purvi could be converted to C D♭ E F♯ G A♭ B which is not one of the standard western scales. Here is a piece that uses the Raag Purvi; I find it to be bizarre (to my western ears), sad, unsettling, and gorgeous.

Here is a breakdown of Indian classical music compared with western music equivalents.

Indian Classical MusicNotes per octaveExplanationWestern Equivalent
Swar12Octave is split into 12 notes called swarNotes of chromatic scale
Thaat7A selection of 7 of 12 notes that can be played in ascending order.Scale/Mode
Raga5-7A selection of 5 – 7 notes from a Thaat; it must have ascending (Aaroha) and descending (Avaroha) notes and must convey an emotion/sentiment.Scale/Mode/Melody
Shruti22The 12 swar are modified depending on the raga. The modification is less than a half step – it’s an interval called the shrutti.Quarter step?

Uh oh. What’s up with this shruti character; why are there 22 of them in the octave!? This throws our 12 note per octave assumption out the window. Time to make an even more flexible scale definition.

Definition 5: A scale is an ascending or descending sequence of pitches.

There are infinite pitches so it follows that there are infinite scales according to this definition.

Value in Exploring Non-Standard Scale Types

Generally theory should serve practice, so what is the value of these infinite obscure scales?

Well generally the notes of scale are the building blocks of melodies and harmonies. Most melodies fit inside one, or possibly 2-3, scales. So infinite scales allows for infinite conceivable melodies and harmonies. Most of this “music” would be so bizarre it might seem pointless.

With that in mind consider the following pie chart.

Pie Chart expressing explored vs unexplored music and meaningful vs meaningless music.

So this chart obviously isn’t scientific or accurate in any way (hence the fun font:), and splitting music between “meaningful” and “meaningless” seems problematic. Nonetheless, consider the dark red triangle labelled “meaningful unexplored.” This triangle is what motivates composers to spend countless hours perfecting their craft. Why? Because composers generally create new (unexplored) music that they hope connects with others (is meaningful).

In effect the red triangle is the horizon of music waiting to be discovered.

Perhaps by exploring these obscure theoretic scale types, we dig deeper into the depths of human experience, expressing and communicating in new, profound ways.

Conclusion

How many scales are there in music? Well that depends on the definition. Really it can range anywhere from dozens, to hundreds, to thousands, and to infinity.

So what is next in your musical explorations? Here are some ideas:

  1. Explore the modes – my favorites are Mixolydian and Dorian. I’d even say that as I improvise I prefer using modes to standard major/minor scales.
  2. Learn how to play common scales.
  3. Explore Indian music and ragas.

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