# Origins / history / universality of the pentatonic, diatonic, and 12-tone scales



## BrahmsWasAGreatMelodist

Can anyone recommend reading which explores these topics and/or share their own knowledge / thoughts?

This is a really interesting topic which I would like to know more about.

All input is appreciated.

Edit: not just in the West either


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## tdc

As far as I can tell the history of music in terms of the Western classical tradition is concerned, has been a gradual process of discovery. The harmonic origins beginning with Pythagoras, I believe these mathematical principles led to the dividing of the octave into 12 notes. By reading things like Fux's manual on counterpoint, you can see that early on modes and hexachords were favored, and the concept of tonality and keys as used in the common practice era being gradually formed in the Baroque era. Charles Rosen's book _The Classical Style_ provides interesting insight in terms of tonality, diatonic scales, the circle of 5ths and how these things were perceived in the Classical era.

As far as I know the use of the pentatonic scale in classical music was not something heavily in use until the modern era and was largely inspired by non-Western musical traditions like Gamelan and African music and perhaps also blues.


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## tdc

I think other ways of dividing the octave can be derived using Pythagorean principles. My feeling is that it is possible the numbers 12 and 7 were ultimately favored because of their astrological significance, being numbers that symbolize solar and lunar cycles. "As above, so below', this is merely speculation, though.


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## BrahmsWasAGreatMelodist

tdc said:


> I think other ways of dividing the octave can be derived using Pythagorean principles. My feeling is that it is possible the numbers 12 and 7 were ultimately favored because of their astrological significance, being numbers that symbolize solar and lunar cycles. "As above, so below', this is merely speculation, though.


Well that's some speculation!

I'm equally curious about the history and evolution of scales / temperaments in other, non-Western cultures.


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## tdc

tdc said:


> I think other ways of dividing the octave can be derived using Pythagorean principles. My feeling is that* it is possible the numbers 12 and 7 were ultimately favored because of their astrological significance, being numbers that symbolize solar and lunar cycles*. "As above, so below', this is merely speculation, though.


For clarity I'm simply referring to 12 months in a year, and 7 days in a week. Was going to edit this information into the post but my time limit was up!


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## BabyGiraffe

BrahmsWasAGreatMelodist said:


> Well that's some speculation!
> 
> I'm equally curious about the history and evolution of scales / temperaments in other, non-Western cultures.


Babylonian
https://www.jstor.org/stable/737674?seq=1 (Summary: they tuned in fifths and fourths thousands of years before Pythagoras was born. The whole idea that there were no musical system until Pythagoras is actually hilarious, I don't know why this nonsense is still being spread.)

Greek music theory based mainly on tetrachords and extension of it along references to other books: (free download)
http://eamusic.dartmouth.edu/~larry/published_articles/divisions_of_the_tetrachord/index.html
I don't remember, if division of octave into 72 parts was mentioned, but this is Orthodox Church music theory all over Eastern Europe/North Africa/Middle East. Can be traced back to theories of Aristoxenus.

https://en.wikipedia.org/wiki/Aristoxenus

Roman music:
https://www.amazon.com/Ptolemy-Harmonics-Translation-Commentary-Bibliotheca/dp/9004115919 (division of string lengths)

Indian music:
https://digitalcommons.unl.edu/univstudiespapers/45/ (free download)
And some sources on Arabic scales I found:

Abu Nasr al-Farabi (d.950).

Kitab al-Musiqa al-Kabir [Grand Treatise on Music].
reprint: Gattas 'Abd al-Malik Hashaba, Dar al-katib al-'arabi, Cairo, 1967.
French translation by F.R. d'Erlanger, 1930

Ibn Sina [Avicenna] (d. 1037).

Kitabu a-Sifa.
French translation by F.R. d'Erlanger, 1935.

Auicene perhypatetici philosophi: ac medicorum facile primi opera in luce redacta...
Latin translation published in 1508.
Facsimile edition, Minerva, Frankfurt am Main, 1961.

Safi ad-Din al-Urmawi (d. 1291).

Al-Risala al-Sharafiya fi'l-nisab al-ta'lifiya.

Sezgin, F. (ed.). Book on the Cyclic Forms of Musical Modes: Kitab al-Adwar
and Treatise dedicated to Sharaf al-Din on Proportions in Musical Composition:
Al-Risala al-Sharafiya fi'l-nisab al-ta'lifiya
by Safi al-Din al-Urmawi Abd al-Mu'mim ibn Ysuf ibn Fakhir (d. 1294 A.D.).
Institute for the History of Arabic-Islamic Science, Ser. C vol. 6, Frankfurt a.M., 1984.

Hefny, Mahmoud el. 1931.

Ibn Sinas Musiklehre.
PhD diss., Otto Hellwig, Berlin.

Touma, Habib Hassan. 1995.

"Basics of Ratio in Arab Music. The schismatic Permutation of Safiyyuddin al-Urmawi",
Lux Oriente. Festschrift Robert GÃ¼nther zum 65. Geburtstag.
Gustav Bosse-Verlag, Kassel.


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## tdc

BabyGiraffe said:


> Babylonian
> https://www.jstor.org/stable/737674?seq=1 (Summary: they tuned in fifths and fourths thousands of years before Pythagoras was born. The whole idea that there were no musical system until Pythagoras is actually hilarious, I don't know why this nonsense is still being spread.)


Yes, really this makes sense, though I wasn't aware there was documented evidence of Babylonian tuning systems. I think people
connect music systems with Pythagoras because he is the earliest name of a figure whose mathematical principles can be linked to tuning and harmonic principles, but perhaps there are other earlier names I'm not aware of.

As they say there is nothing new under the sun.



BabyGiraffe said:


> I don't remember, if division of octave into 72 parts was mentioned, but this is Orthodox Church music theory all over Eastern Europe/North Africa/Middle East. Can be traced back to theories of Aristoxenus.
> https://en.wikipedia.org/wiki/Aristoxenus


Maybe just coincidence, but it is interesting to me that 72 is another highly significant astrological number, related to the precession of the equinoxes:

"72: Number of years required for the equinoctial sun to complete a precessional shift of one degree along the ecliptic. This means that 72 years = 1 "day" of Precession. 72 x 360 = 25920 or 1 "Great Year". "

https://www.cosmic-core.org/free/ar...tial,The pre-eminent number in the code is 72.


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## tdc

The Chaldeans were renowned astrologers.

"The fame of the Chaldeans was still solid at the time of Cicero (106-43 BC), who in one of his speeches mentions "Chaldean astrologers", and speaks of them more than once in his De divinatione. Other classical Latin writers who speak of them as distinguished for their knowledge of astronomy and astrology are Pliny, Valerius Maximus, Aulus Gellius, Cato, Lucretius, Juvenal. Horace in his Carpe diem ode speaks of the "Babylonian calculations" (Babylonii numeri), the horoscopes of astrologers consulted regarding the future."

https://en.wikipedia.org/wiki/Chaldea


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## BabyGiraffe

tdc said:


> As they say there is nothing new under the sun.


https://en.wikipedia.org/wiki/Paleolithic_flutes

"Dated and tested independently by two laboratories, in England and Germany, the artifacts are authentic products of the Homo sapiens Aurignacian archaeological culture, made in between 43,000 and 35,000 years ago. "

Astrology/sacred geometry and similar are very funny. I wonder, if ancient people would mystify most of the constants in physics and mathematics, if they knew about them.

https://en.wikipedia.org/wiki/Anthropic_principle#Metaphysical_interpretations


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## RogerWaters

BrahmsWasAGreatMelodist said:


> Can anyone recommend reading which explores these topics and/or share their own knowledge / thoughts?
> 
> This is a really interesting topic which I would like to know more about.
> 
> All input is appreciated.
> 
> Edit: not just in the West either


Have you seen this?






It may run against what tdc says about the rationalist origins of western music. Rather, Bernstein argues that harmonic development is more 'empirical', stemming from the physical nature of overtones.


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## Bwv 1080

Pentatonic scales seem ubiquitous outside of the Mediterranean/Near East.


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## cheregi

https://puretones.sadharani.com/ is an amazing resource - especially the three long articles under the category 'background of puretones' - for explaining in detail the history and development of Indian tuning systems. What I learned about the physics of the functioning of the tanpura kind of blew my mind.



RogerWaters said:


> It may run against what tdc says about the rationalist origins of western music. Rather, Bernstein argues that harmonic development is more 'empirical', stemming from the physical nature of overtones.


I'm not watching the whole video, but just in response to this comment - as far as I understand it's almost impossible to develop a musical system that _doesn't_ stem from the physical nature of overtones; but from that starting point it's far from guaranteed that you'll end up with specifically 12 and 7 as important numbers, right?


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## EdwardBast

The most relevant early development for western art music was the modal system of the Ancient Greeks. They used seven-note diatonic modes (Dorian, Phrygian, Lydian, Mixolydian) which they built from tetrachords, but they also employed chromatic tetrachords (a minor third and two semitones) and enharmonic tetrachords (a major third and two quarter tones). 

Medieval European theorists tried to appropriate the diatonic modes of the Greeks but they got it all wrong, so the Dorian church mode (for example), is not the same as the Greek Dorian. And I believe the Greek Phrygian is actually the same as the modern major scale. The Europeans got everything upside down.


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## BabyGiraffe

Modern major = Greek Lydian
Dorian = Phrygian
Phrygian = Dorian
Lydian = Hypolydian
Mixolydian = Hypophrygian or Ionian
Minor = Hyperphrygian
Locrian = Mixolydian or Hyperdorian



cheregi said:


> it's far from guaranteed that you'll end up with specifically 12 and 7 as important numbers, right?


Only 12, 19, 31 equal are anywhere close to harmonic series when we look into small equal temperaments. Still, European music used unequal tunings and with unequal tuning any gamut of arbitrary number of pitches can be good (all these unequal tunings can be thought as a scale from some big equal temperament, for example classical European meantone tunings are something like selection of 12 notes out of 55, 50, 31 etc equal)


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## cheregi

BabyGiraffe said:


> all these unequal tunings can be thought as a scale from some big equal temperament, for example classical European meantone tunings are something like selection of 12 notes out of 55, 50, 31 etc equal)


That's interesting, I've never thought to see things this way, as opposed to the 'historical-time' point of view of seeing equal temperament as a sort of arbitrary modification of preexisting unequal divisions.


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## Enthalpy

Don't imagine European scales as subsets of the equal-tempered 12 tones.

Traditional music in Greece, Romania, Bulgaria and elsewhere occasionally uses scales that don't fit on a piano, fourth-tones or sixth-tones approximately. That has been the case over millennia and lives up to now.

Or hunting horns. They use the 11th natural mode, a nearly perfect definition of a quarter-tone, falling in the middle of a minor third 12/10. Or bagpipes.


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