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I am making this new thread to revive what I posted in another thread, but this time trying to start it off better by being more comprehensive in coverage of the diversity to expect based upon looking at what we have on Earth.
This time, I will start on the music system side. Consider how on Earth, Western music has long been dominated by systems of 12 notes per octave (although exceptions exist, going back into the late Renaissance), while cultures elsewhere have their own systems of not necessarily 12 notes per octave. I have not enough knowledge of the history of music systems outside of European tradition to say much, although I do have a passing familiarity with some examples of what exists today, so I will mostly stick to the European side, while recognizing that Earth also has many non-European musical traditions, which I will touch on later as much as I can, and we should expect no less for Golarion.
For Western European music, which hails from ancient Greek and Roman music, and before that Mesopotamian music, scales were originally based upon intervals between notes initially consisting of ratios of powers of 3 with powers of 2, with some ratios later being adapted in recognition of the usability of higher primes to reduce the number of powers of 3 -- so ~3/2 (fifth), ~4/3 (fourth), ~9/8 (whole tone --> also ~10/9 and ~8/7), ~16/9 (minor seventh --> also ~9/5 and ~7/4), ~32/27 (minor third --> ~6/5), ~81/64 (major third --> ~5/4), etc. (The "~" is to acknowledge that the ratios are often inexact in many tuning systems, although in the Mesopotamian variant commonly known as Pythagorean tuning, they are required to be exact, and Pythagorean tuning is exactly the same as strict 3-limit just intonation.) Using ratios of 3/2 and other powers there of (like 4/3) sets up what today is known as a circle of fifths, with the fifth being ~3/2. (I wonder who came up with that terminology, naming the octave-reduced third harmonic the "fifth", and naming the octave-reduced fifth harmonic the "major third".) But this really amounted to an (in principle) infinite helix of fifths. Although the use of higher primes (usually only up to prime 5 and sometimes 7) is often spoken of as a Renaissance invention, some of the scholars of Antiquity (such as Archytas and Claudius Ptolemy) also made use of primes 5 and 7, and it seems that Medieval and early Renaissance adherence to strict Pythagorean tuning (using only ratios containing 3 and 2 and powers thereof) was a matter of backsliding.
In the Renaissance (at least as early as 1495), meantone was invented (with early pioneers including Pietro Aron, Lodovico Fogliani, Gioseffo Zarlino, and Francisco deSalinas), replacing strict 3-limit just intonation with approximate 5-limit just intonation. This flattens the fifth (hence ~3/2) by some set fraction of the syntonic comma (81/80) and equates ~9/8 with ~10/9 to perfect the major third (5/4, in 1/4-comma or quarter-comma meantone, the dominant variety, literally choosing the geometric mean between 9/8 and 10/9) or rarely the minor third (6/5, in 1/3-comma meantone) or achieve a state in between (in 2/7-comma meantone) or also rarely even going beyond to perfect 10/9 (in half-comma meantone).
This also included 12-tone equal temperament, also known today as 12 equal divisions of the octave (12EDO), discovered in both Europe and China in the 1500s (in China possibly even earlier) -- this is almost the same as 1/11-comma meantone, and exactly 1/12 Pythagorean comma meantone. But at the time, most people did not like the way it sounded -- the major thirds are considerably sharp of 5/4 but not all the way to 81/64, while the minor thirds are considerably flat of 6/5 but not all the way to 32/27. The closest convenient ratios are 63/59 and take your pick of 25/21 or 16/19, respectively -- these are respectable ratios, but energy transfer between strings doesn't work very well with such complicated ratios, thus causing it to sound somewhat dull and yet rough unless an instrument is designed with extra power and resonance to compensate, like a modern piano, pipe organ, or synthesizer (the latter not having to bother with resonance at all unless it is designed to emulate resonance). Thus, 12EDO took a long time to catch on, and meanwhile other meantone tunings (primarily quarter-comma meantone) took over to support tertian harmony (that using major and minor thirds and chords composed by stacking these). Both Pythagorean tuning and most meantone tunings, having infinite helices of fifths, have wolf intervals (especially the wolf fifth) if you cut the number of notes per octave short, so that the player is forced to use the nearest available note in the now-broken chain of fifths (forced into an imperfect circle) when modulating beyond a restricted set of key signatures.
To try to get around the problem of wolf intervals, a couple of approaches were tried. One approach is to provide extra notes to allow for more modulation. This includes some systems of split flats/sharps, as seen on some harpsichords and pipe organs of the early Baroque; split frets on lutes and viols perform an analogous function. Although many instruments did not have this feature, it is reasonably easy to find videos of such instruments, with split keys for G♯/A♭, often also for D♯/E♭, and less commonly additional split keys. In rare cases this resulted in harpsichords having 19 or more notes per octave (at this point also inserting a key between B/C and another between E/F). In the case of Nicola Vicentino's Arcicembalo and Arciorgano of ~1555, this went all the way up to 36 notes per octave, although with terrible ergonomics (distributing them between 2 keyboards engaging the same rank of strings or pipes, or in the case of Vito Trasuntino's Clavemusicum Omnitonum of 1606 (see same article as for Arcicembalo), 31 notes per octave with still challenging but more manageable ergonomics.
The other approach is to bend pitches to get the helix of fifths to close into a finite circle, with the wolf interval being spread enough around the circle to stop being objectionable. This includes the above-mentioned 12EDO, but that is not the only number of notes capable of supporting a closed circle, and if the above approach of adding split flat/sharps is used, larger sizes are possible. Other sizes tried in Western Europe included 19EDO, which is nearly identical to 1/3-comma meantone and flattens the fifth nearly to 112/75; 31EDO, which is a bit sharp of quarter-comma meantone and was also one of the tuning systems(*) used by the above-mentioned Nicola Vicentino (and is compatible with the above-mentioned Clavemusicum Omnitonum and its modern derivatives); 43EDO, which is nearly identical to 1/5-comma meantone, 50EDO, which is a bit sharp of 2/7-comma meantone, and 55EDO, which is a bit flat of 1/6-comma meantone.
(*)Nicola Vicentino also had the alternative idea to use extended quarter-comma meantone on the lower manual of the Arcicembalo and Arciorgano, and tune the upper manual at pitch a quarter comma above the lower manual, to be able to get both pure major thirds (5/4) and pure perfect fifths (3/2); however, the tuning diagram in the Wikipedia article does not appear to match either tuning system.
In Western Europe, these larger sizes did not catch on, probably because the pipe organ was very important in Western Europe, and adding more organ pipes is very expensive and takes a lot of space; even on a clavichord, harpsichord, or piano, adding more strings to get more notes per octave is no light matter, not only because of expense, but also because it cuts into adding more strings to get more volume. Also, 31 notes per octave seems to be the practical limit of the Halberstadt (clavichord/harpsichord/piano-style) keyboard, so while a very small number of 31EDO-capable instruments were built, this kept 43EDO and 50EDO (and other large tuning systems such as 41EDO that were NOT meantone, although reportedly one experimental 41EDO piano was built) from being more than a theoretical prospect in Western Europe (but not in some parts of Earth that did not have such large and expensive instruments -- see below). Leopold and Wolfgang Amadeus Mozart did recommend using a subset of 55EDO (approximating 1/6-comma meantone), but had to contend with a mess of different players disagreeing on tuning systems (and even with violinists lacking a mathematical understanding of how finger position spacing changes along the violin strings), as documented in Mozart's Teaching of Intonation by John Hind Chesnut, Journal of the American Musicological Society Vol. 30, No. 2 (Summer, 1977), pp. 254-271 (18 pages), Published By: University of California Press.
Since instruments having 12 notes per octave won (in Western Europe) on practicality grounds, but 12EDO had yet to catch on (at least beyond small instrumental ensembles that lacked a keyboard instrument), mid-to-late Baroque and Classical through early-mid Romantic music went through a phase of using well-tempered tuning systems, with inventors such as Andreas Werckmeister, Johann Sebastian Bach himself, Johann Philipp Kirnberger, Jean-Philippe Rameau, Leopold and Wolfgang Amadeus Mozart, Francesco Antonio Vallotti, and Thomas Young. These systems make major thirds more pure in parts of the circle of fifths and fifths more pure in others, so that no intervals are so far off as to constitute a wolf interval, and all key signatures are playable (as in J. S. Bach's Well-Tempered Clavier), with the most commonly used key signatures sounding the best overall and the others having distinct flavors but not sounding so badly off as to be objectionable. Instrumental evolution and increasingly large orchestras and other ensembles combined with the mess of tuning systems that the Mozarts had to contend with drove Western European (and by this time also American) tuning systems towards standardization on 12EDO, although at the cost of loss of musical flavor. A side benefit of 12EDO and its well-tempered cousins is that for all its roughness in approximating 5-limit just intonation, it also gives a free (although even rougher) approximation of 7-limit just intonation, which can be of use when one is able to bend pitches to favor 7-limit or 5-limit intervals as needed, as is often done in traditional jazz and blues and some types of music derived from them.
I do want to touch upon some of Earth's other musical traditions which closed the circle of fifths (when they even use fifths as a scale generator at all -- some temperaments use a different generator) at different values, although I must apologize for not knowing more about them, and for having left out some of them (such as pre-European American) due to complete lack of knowledge.
- • In traditional music of the Kingdom of Georgia (Sakartvelo, later Georgia SSR, and now the independent nation of Georgia), closing the helix of fifths (if that is even what was used there) to a circle resulted in 7 notes per octave, well-tempered.
• The traditional music of Thailand reportedly also uses 7 notes per octave, but the information I have seen about the tempering of those notes is inconsistent.
• In parts of Africa, closing the circle early resulted in 5 divisions of the octave (not sure if equal), with the octave stretched to work with the inharmonic instruments that could be made and maintained with limited materials availability in a hot climate that is not friendly to most European instruments.
• Some music (Slendro) in Indonesia does the same thing, while some other music (Pelog) in Indonesia uses 9 divisions of the octave (not sure if equal) with 7 of the 9 notes normally being used.
• Arabic music since the 1700s uses quarter tones (24 notes per octave if all possible quarter-tones are included, but Arabic music does not necessarily distribute them evenly); while Arabic music leading up to the 1700s reportedly used a system of 17 notes per octave, although not equally distributed.
• At least some classical Indian music uses a system called Shruti, which has well over 12 notes per octave (often 22), not equally distributed.
• And Turkish music theory teaches 53 divisions of the octave (53EDO is barely flat relative to extended Pythagorean tuning), although not all of the notes are normally used.
Even in Western Europe, the idea of something other than 12 notes per octave never went away completely, and the Twentieth Century saw composers such as Ivan wyschnegradsky, Charles Ives, and Alois Hába experiment with more notes per octave -- usually 24EDO, which has the strange property of being the easiest higher-than-12EDO system for players in the Western European tradition to adapt to from a performance perspective, but very hard to actually compose for due to having twin circles of fifths that do not communicate with each other by any intervals having only primes 2, 3, and 5, instead requiring intervals such as 11/8 and its combinations with the other primes (technically prime 7 also works for doing this in 24EDO, but badly -- if you are going to be stuck with a multiple of 12EDO, 36EDO is much better for prime 7). Compositions in 24EDO that actually use notes from both circles of fifths at the same time or in rapid succession counterintuitively sound much more bizarre than compositions in some temperaments with more bizarre-seeming numbers, such as 17EDO, 19EDO, 26EDO, 31EDO, 41EDO, 46EDO, 50EDO, or 53EDO; or even 34EDO, which has twin circles of fifths, but is able to connect them using ratios that include prime 5. In the last couple of decades, the advent of (somewhat) affordable generalized/isomorphic keyboards and soft synthesizers that actually sound good (while not being limited to notes that can be produced on the installed base of fixed pitch acoustic instruments) has led to an explosion of microtonal/xenharmonic music composition that can be found on YouTube (and with more digging or a helpful Xenharmonic Wiki article link, also on other places).
Information about the above tuning systems can be found on both Wikipedia and on the Xenharmonic Wiki, which has links to various non-closed regular temperaments including meantone and various non-meantone linear temperaments (some similar to meantone and some very dissimilar and not even using fifths as a generator), just intonation, historical tuning systems, and (as of this posting) equal divisions of the octave of every size up through 321EDO before starting to skip sizes, and thereafter selected sizes up through 5407372813EDO. (Note that this site usually converts EDO to lowercase, which is unfortunate, since warts that modify usage of a tuning system are also in lowercase.) The Xenharmonic Wiki also has information about equal step tuning systems that do not treat the octave as supreme, such as Bohlen-Pierce (13 equal divisions of the twelfth). Many of the Xenharmonic Wiki articles on tuning systems have links to music (on YouTube or otherwise) using those tuning systems. Both of these sources and links from them contributed to much of this post.
On the instrumental side, and now getting to the Pathfinder Campaign Setting, canonically some Western instruments from the Baroque through High Classical eras have been listed as being present in Avistan, and that a few threads have popped up about music on Golarion every so often (like this one and this one) as well as my own previous failed attempt), but has anything more detailed come up on this? (And searching for microtonal music on these messageboards formerly brought up exactly 1 hit that was not viewable, and now it doesn't come up at all.)
Also on the instrumental side, Golarion has working magic, which should enable the development of arcanaphones, which would be Golarion's equivalent of synthesizers, but using magic instead of electricity to generate sound. Given the existence of fairly low-level magic for making convincing sounds of things that aren't really there, the cost of such instruments should be only moderately outrageous -- out of reach of most of the common people, but easily in reach for the nobility and upper merchant classes.
Environments commonly used on Golarion but not commonly used on Earth would be expected to have an influence on music-making. For instance, those living underground and having easy access to stone and metal but not to wood or most other organics could find themselves pushed in the direction of making instruments of the idiophone families, consisting of struck bars or rods, which would have highly inharmonic partials, thereby causing effective harmonic relations between notes to be different from those produced by stringed, woodwind, and brass instruments; yet they would also be able to make brass instruments and even metal "woodwind" instruents and pipe organs, both of which would tend to have more conventional harmonics. And they just might want an arcanaphone (see above) to glue it all together. And if they had short fingers, it would tend to drive them to develop keyboards of layout radically different from the Halberstadt (piano/harpsichord/organ-style) keyboard familiar to us; such radically different keyboards started to appear at least as early as the 1800s on Earth, so their development on Golarion would not be completely unexpected). And if they had enough wealth, as the Dwarves are reputed to have (along with great longevity), their nobility might even be inclined to splurge for something like a pipe organ having as many as 50 notes per octave as well as numerous ranks, that would cause Earth-based accountants (even those working for nobility) to take fright.
I got interested in this subject from stumbling upon microtonal music on YouTube, which has seen a recent great radiation of microtonal music that actually sounds good (as noted above). And then the Xenharmonic Wiki (linked above) has been a great resource -- even if fairly rough around the edges -- for learning the mathematical details of music, even if some of it does seem to require a degree from a college of magic in mathematics. Even i I never produce any music (microtonal or otherwise) myself, it has been a wild ride in learning what it is that makes our dominant Western system of 12 equally tempered notes per octave actually work.
And since Paizo is now working especially hard to flesh out parts of Golarion that are culturally different from Earth's Western Europe even after accounting for technological differences, this seems like a good time to flesh out the music of Golarion, both Avistani and otherwise.