# mean tone and alternative tuning systems



## obwan

can anyone actually identify or give me a list of songs composed in other tuning systems such as mean tone.

I am aware that especially with early music, unless you know the correct tuning system sometimes the song will not sound right, or at least certain notes may seem if they have been copied down wrong or something.

i just want to know of some examples so i can see the theory in action so to speak.

thanks


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## BabyGiraffe

Meantone temperament is not one of the "other tuning system". 12 equal is kind of Meantone. 5 and 7 equal - too.
Meantone replaced Pythagorean tuning, so we can say that most classical music is in Meantone, so pre-romantic classical music can be performed in 12 equal or in any other meantone division of octave (also in 5 or 7 equal, but some this will require some rewriting).
You can find all Meantone division of octave by summing 5 and 7. 5+7 = 12, 12+7= 19, 19+7=26, 26+5=31 or 19+12=31 etc
Some of these don't work quite well = 12+5=17 -> Meantone mapping of this is worse than "Superpythagorean" or "Helmholtz" temperaments, so in terms of microtonal slang, Meantone is in 17c equal and the other ones are 17p. (12 equal is unambigious until 13-limit, so no such terminology is used for 5,7 and 11-limit temperaments in it, but it has 4 variations in 13 limit).

About "xenharmonic" microtonal music - use youtube search and you will find plenty of it, most of the time it's quite amateurish in terms of composition or production... so better check commercial recordings of Arabic or Turkish pop or folk music. (The smallest equal temperaments that supports "Oriental" music is 17 equal; check for example this -> https://en.wikipedia.org/wiki/Bağlama#Bağlama_scale , this baglama scale is close to 17 tones out of 24 equal when we convert ratios to cents

0: 1/1 0.000000 unison, perfect prime
1: 18/17 98.954592 Arabic lute index finger
2: 12/11 150.637059 3/4-tone, undecimal neutral second
3: 9/8 203.910002 major whole tone
4: 81/68 302.864594 Persian wosta
5: 27/22 354.547060 neutral third, Zalzal wosta of al-Farabi
6: 81/64 407.820003 Pythagorean major third
7: 4/3 498.044999 perfect fourth
8: 24/17 596.999591 1st septendecimal tritone
9: 16/11 648.682058 undecimal semi-diminished fifth
10: 3/2 701.955001 perfect fifth
11: 27/17 800.909593 septendecimal minor sixth
12: 18/11 852.592059 undecimal neutral sixth
13: 27/16 905.865003 Pythagorean major sixth
14: 16/9 996.089998 Pythagorean minor seventh
15: 32/17 1095.044590 17th subharmonic
16: 64/33 1146.727057 33rd subharmonic
17: 2/1 1200.000000 octave)

You can think of 24 equal as two unrelated 12 equals (so meantone) or as non-meantone system.


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## millionrainbows

obwan said:


> can anyone actually identify or give me a list of songs composed in other tuning systems such as mean tone.
> 
> I am aware that especially with early music, unless you know the correct tuning system sometimes the song will not sound right, or at least certain notes may seem if they have been copied down wrong or something.
> 
> i just want to know of some examples so i can see the theory in action so to speak.
> 
> thanks


"Any plan that describes the adjustments to the sizes of some or all of the twelve fifth intervals in the circle of fifths so that they accommodate *pure **octaves* and produce *certain sizes of **major thirds* is called a _temperament."
_
Thus, mean tone tunings take place within a perfect octave, and their purpose is to produce better major thirds.

I think Peter Watchorn's harpsichord versions of Bach would be good listening for you.










Also, for other tunings, listen to Wendy Carlos' Beauty In The Beast.


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## millionrainbows

Also, see Enid Katahn's recordings:

















These are hard to find. Here is a link:
https://www.allmusic.com/album/beethoven-in-the-temperaments-mw0001816174


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