1. Have tunings in Eastern music been chosen based on mathematical calculations or cultural considerations?
2. Tunings are diverse in eastern countries, and many countries have their own tunings, which in many cases differs greatly. When these tunings were chosen in those countries, did math and physics play a role in their selections, or were only ear and cultural considerations influential?

Thanks!

 

Don´t confuse tunings with scales.

 

both of course. and more than that.

math, physics, trial and error...

then the move to polyphonic music and then the need to build instruments with fixed frequencies influenced the theorists - and the other way round.

 

Both (some ancient Oriental music theorists used stacking perfect fifths as a starting point, but had to derive neutral type of thirds and sixths - since such intervals were used in actual music; and even 12 equal may have been used thousand of years ago by Babylonians (or at least, they knew how to roughly calculate it on their tablets... (It was adopted for use in Europe on lutes and guitars around 15-16 century, so these type of instruments are were not adopted in the classical music orchestra*- they were out of tune with other type of instruments back in the day in Europe!))
*they were associated with secular music.

 

Can you tell me which tuning in which eastern country is based on math? (By math, I mean mathematical formulas, not playing with numbers.)

The fretboards of most Eastern instruments have irregular shapes. These irregular shapes and lines show that math hasn't played a major role in tuning those instruments.

It might be said that if mathematical formulas were considered in eastern countries' tunings, the music of those countries would be non-cultural commodities there.

 

They were just slaughtering an animal and the intestine from the innards was lying around and a person had an intuition, he stretched the intestine on a wooden board and fastened it above and below, then gradually he made the intestine tighter, he found the sound very much Inspired and expired with it for a number of years. At the top there was a lower-sounding gut string and underneath a higher-sounding gut string. The first stringed instrument was born either from the intestines or from the tendons of an animal.Then the next person came and had an inspiration to make some wood around it, that was the first sound body and so it went on, it was optimized and refined.

Several thousand years passed and today there are steel strings and plastic strings and the musical device is called a guitar, for example. To answer your question, in my opinion, all aspects play a role in the development of instruments. You cannot look at it in isolation, you have to imagine the overall picture. Some people visited other countries and brought their habits and musical instruments home with them. where they were then tuned and used differently depending on the culture.When some cultures got electricity, a lot changed again. pickups were invented and the other electrical devices we use today.

 

1- you're asking the same question twice
2- mathematical vs. cultural is a false dichotomy. they're not mutually exclusive, as mathematics is part of culture. and "irregular" shapes, as you call them, are still mathematical. you're just dividing with different numbers.

 

It was an interesting story, and probably was the true one.

One of the most important reasons that Eastern countries have bound themselves to their indigenous cultures and don't untie is musical cultures in their countries. At the heart of all Eastern music is the tuning issue, the prime fodder in their music. Many of these tunings have reached the next generations chest-to-chest, but musicians in those countries do not have strong mathematical reasons for their tunings, and when they want to explain their music, they use the principles of Western music and compare with it.

If you know any Eastern country that has come up with a musical formula for their tunings, please mention that country.

 

Too convoluted to answer without disrespect. That's like microtones and people asking in western music why aren't notes like D# and Eb called one or the other.
You take into account the nature of an instrument, that a microtone note is not the same as a microtone scale though the note can exist within the scale, or, that in western terminology the D# and Eb exist because of instruments that have been known to have a saying ascend in sharps and descend in flats. So basically on a violin, a D# is not the same note as an Eb, though in equal-tempered pitch it is or on fretted instruments. That is a poor example but it illustrates a shitload of research just to answer that statement adequately and that is not as complex as your question.

In Arab music the Maqamat is a series of scale structures yet it is still part of their religion. same for some Hebrew music.

SOME music is interwoven with their culture and religion and some is the nature of the instrument, some it is both... You'd have to take every country, every instrument and associate or disassociate it with their culture to answer that with any true answer. Music has math in it so math is there, that is a given. Physics? every instrument also has some form of physics associated with it to sound a note however simple or complex.

@Marseilles - If you want a thorough answer to this, I'd suggest looking in all the University libraries via a search globally. A lot of people have spent a lot of time in research on these very topics. You will find some academics have devoted entire theses/dissertations to a single area of your question. when you search, do not limit it only to ethnic music. Because you have mentioned cultures, physics and mathematics, use 'Indigenous' as part of your search coupled with the other areas. You will find 300 page - 1,000 page documents with more detail and accuracy than anyone can post here. Nowadays, the Universities allow their published academic documents to be publicly available, so it's worth the search time.

 

Last edited: Sep 20, 2021

go to academia.edu and search articles on Babylonian and Sumerian music (most of this is researched thanks to surviving tablets).
Btw, do you think anything will remain from us in 4000-6000 years from now (considering there will probably be an environmental collapse before 2050)? It is quite lucky we still have such evidences (even if there were any similar civilizations in Europe or Africa, there are very few remains surviving - for example the oldest golden treasure found is from Europe (around 6000 years ago), but nothing is known for the civilization).
And if you are interested in something more contemporary, there exist
books on Ancient Greek, Arabic, Roman, Chinese (interestingly, they used at some point 7 and even briefly 14 ET) music.
https://www.oldest.org/music/musical-instruments/

 

Mathematics is mathematics and culture is culture. Math is always constant, but culture changes over time.

Do you know why Micro-Tone is discussed in music?
The answer is that people don't look for mathematical formulas and assume tuning problems are solved with Micro-Tones.

In other words:
Micto-Tone doesn't allow people to look for mathematical formulas, and whenever they run into a problem, they take refuge in Micro-Tone and falsely pretend to have solved the Tuning problem. Micro-Tone is not the definitive answer.

 

See ! You have a great reason to go and research papers on this, The reason I say this is because a great part of academia is proving or disproving something. You have an inquisitive mind, use it. Mathematical formulas exist in them and I am confident you will find an academic who is on the same investigative path as yourself that can answer and confirm your suspicions. You will also probably find one on the opposite side of it. Microtones are a western label to allow a level of understanding. It's like a man saying "A bird flys". Another man says "Why does it fly?" One person will say "because it's part of the bird's nature". Then you will get another who will want to know the mathematics and physics of it. They called it "Flight". I see microtones as the same type of label for something very convoluted. Icarus in mythology shows that man wanted to know the workings of an inherent nature that is not of their own. Do the same, it's probably the only way you will get the correct answers you seek.

 

Last edited: Sep 21, 2021

Thank you for leading me to extensive studies.

If these huge studies that you're talking about have achieved great results, then where is the music that these massive scientific studies have made?

 

I want an Eastern mathematical formula. A formula been made only in the East for their instruments and music.

 

First you are welcome.
Second, that point is extremely valid. It's like the statement you've probably heard that in technology, medicine, music and education and more, humankind is supposed to be the most advanced it has ever achieved compared to any other point in history. YET - the entire world is in random lockdown over a microscopic virus nobody knows enough about.
Humankind is really fast off the mark discovering and hypothesising and theorising over any area scholastically, but incredibly slow in implementing anything with absolute confidence in practice safely, well or decisively.

 

Because some people believe it's an Eastern virus, and eastern viruses aren't easily formulable.

Wait a second, part of me says maybe the Orientals themselves have not deliberately used straightforward formulas in their music that westerners will forever be confused.

 

I'd say these considerations were musical, techical and aesthetic. In the modern european equal temperament we can play in all major and minor scales without retuning an instrument and sounding out of tune. We can transpose musical pieces, use modulations. Not all temperaments (european or not, it's not important) allow it. We also don't have to deal with very unpleasant intervals such as wolf fifth that is unavoidable in natural temperaments based on consonances. But all our music is slightly out of tune, we got accustomated to it and don't notice it.

Was it culture? Or math? I think both of them. I agree that in this case math is just a tool.

 

Sorry, no. Math is a part of culture. Math evolves and changes over time. Math is a family of very exact formal languages to describe different domains. Mosly quantitative but this isn't nessecary. These languages are creations of people.

Microtones are pure math. They are based on the idea of mathematical relation between two tones and don't take into consideration how these tones sound together. Music was born from relations between tones evaluated by ear only.

There is no such a formula. It doesn't exist. The European music knew many temperaments with different mathematical foundation and even without them. All early temperaments were created 'by ear', mathematical foundations appeared later.

 

Go read pictures of tablets written in cuneiform in ancient Akkadian and using base 60 for the math parts... It's all about authentic formulas in your mind, right?
Dude, if you are interested in learning anything about this sort of stuff, PM me to send you links to articles and books, but I think you just continue to troll instead of having genuine interest.

 

The Chinese 12 Lyu and 14 Lyu are also mathematical models with a resonant harmonious and discordant mathematical model for scales and modes and transits. If remember correctly the Wake Forrest University has published a few papers on Chinese music theory and it's mathematical model.

Though I am certain there are also many Chinese sources, I do not have the capability of reading them, maybe someday I'll embark on that adventure.

The Babylonian system is what western music theory is based on through as music theory transited through the old Hellenistic Greeks. Those same Babylonians are why we count to 12 twice a day on our clocks, each 12 period is divided into 2 morning, afternoon, evening, night and a circle has 360 gradations (base 6 math). Pythagoras may have made basic geometry famous in Greece but even vulgar Babylonians were using the Pythagorean theorem to survey land and calculate areas a for a millennia before Pythagoras was born.

While you're sports fan take on who's team we should all be on West vs East is kind of cute, it's trite and boring. If you really actually understand math and are curious a search engine is your friend. If you continue to want to discuss this here you are going to have to prove you have the math chops to understand what people are going to throw your way so that they will at least know they are not wasting their time on someone who is asking a question for which they can not even understand the answer for.

The whataboutisims and circular arguments aren't really helping your cause, nobody here has a duty to answer you this altruism in it's purest form don't confuse it with anything else.