# Music: 12 Notes/Octave - No Known Explanation?? **URL:** \ **Category:** Factual Questions\ **Created:** [February 6, 2009, 12:10am UTC](https://boards.straightdope.com/t/music-12-notes-octave-no-known-explanation/484645 "2009-02-06T00:10:57Z")\ **Posts on this page:** 8\ **Page:** 3
**Author:** ![pulykamell](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pulykamell/32/3166_2.png) [@pulykamell](https://boards.straightdope.com/u/pulykamell)\ **Post date:** [February 6, 2009, 2:49am UTC](https://boards.straightdope.com/t/music-12-notes-octave-no-known-explanation/484645/41 "2009-02-06T02:49:12Z")
> [@ZenBeam](#): > > When I was in college, I worked out that 19 notes / octave would work well, and built a guitar with 19 frets/octave. It was made from free discard parts from a local guitar store, but it sounded good (well, in-tune). Fascinating. How did you divide the scale? Did you maintain perfect fourths and fifths, and subdivide from there? Did you maintain major and minor thirds? Did you throw in a third between those two, by any chance? I’m curious how you fell upon the 19… ---
**Author:** ![Bad\_Astronaut](https://avatars.discourse-cdn.com/v4/letter/b/e19adc/32.png) [@Bad\_Astronaut](https://boards.straightdope.com/u/Bad_Astronaut)\ **Post date:** [February 6, 2009, 2:53am UTC](https://boards.straightdope.com/t/music-12-notes-octave-no-known-explanation/484645/42 "2009-02-06T02:53:27Z")
> [@pulykamell](#): > > Fascinating. How did you divide the scale? Did you maintain perfect fourths and fifths, and subdivide from there? Did you maintain major and minor thirds? Did you throw in a third between those two, by any chance? I’m curious how you fell upon the 19… He’s not alone: > **[19 equal temperament](https://en.wikipedia.org/wiki/19_equal_temperament)** > > In music, 19 equal temperament, called 19 TET, 19 EDO ("Equal Division of the Octave"), 19-ED2 ("Equal Division of 2:1) or 19 ET, is the tempered scale derived by dividing the octave into 19 equal steps (equal frequency ratios). Each step represents a frequency ratio of 19√2, or 63.16 cents (Playⓘ). > The fact that traditional western music maps unambiguously onto this scale (unless it presupposes 12-EDO enharmonic equivalences) makes it easier to perform such music in this tuning than in many oth... I’ve learned a lot about musical theory today. Edit: Also interesting, from that article: > [@](#): > > The composer Joel Mandelbaum wrote his Ph.D. thesis (1961) on the properties of the 19-et tuning, and advocated for its use. In his thesis he demonstrated why he believed that this system represents the only viable system with a number of divisions between 12 and 22, and furthermore that the next smallest number of divisions resulting in a significant improvement in match to natural intervals is the 31 equal temperament. ---
**Author:** ![ZenBeam](https://avatars.discourse-cdn.com/v4/letter/z/3ab097/32.png) [@ZenBeam](https://boards.straightdope.com/u/ZenBeam)\ **Post date:** [February 6, 2009, 3:46am UTC](https://boards.straightdope.com/t/music-12-notes-octave-no-known-explanation/484645/43 "2009-02-06T03:46:05Z")
Yeah, equal tempered. I came across [this page on tuning](http://www.endino.com/archive/tuningnightmares.html) where the author had a quality one made. Waaaay at the bottom of the page, and he even has a picture. ---
**Author:** ![GorillaMan](https://avatars.discourse-cdn.com/v4/letter/g/50afbb/32.png) [@GorillaMan](https://boards.straightdope.com/u/GorillaMan)\ **Post date:** [February 6, 2009, 10:42am UTC](https://boards.straightdope.com/t/music-12-notes-octave-no-known-explanation/484645/44 "2009-02-06T10:42:59Z")
Not so long ago I saw a quarter-tone guitar, i.e. 24 equal intervals per octave. It sounded hideous. > [@Bad\_Astronaut](#): > > Nevermind. This point is of no importance. It was pretty much meant as a joke when I mentioned seconds in the first place. As long as we all agree that 440 Hz is an arbitrary choice, it’s not worth discussing further. Wow, something everyone agrees on, in a music theory thread!! 🙂 ---
**Author:** ![Carson\_O\_Genic](https://avatars.discourse-cdn.com/v4/letter/c/cdc98d/32.png) [@Carson\_O\_Genic](https://boards.straightdope.com/u/Carson_O_Genic)\ **Post date:** [February 6, 2009, 1:00pm UTC](https://boards.straightdope.com/t/music-12-notes-octave-no-known-explanation/484645/45 "2009-02-06T13:00:03Z")
> [@ZenBeam](#): > > Yeah, equal tempered. I came across [this page on tuning](http://www.endino.com/archive/tuningnightmares.html) where the author had a quality one made. Waaaay at the bottom of the page, and he even has a picture. ``` Using a milling machine with glass scale readout to place fretslots and subsequent fret dressing with same along with metered compensation and controlled pressure fretting and attack controlled picking leads to the following conclusion: "Guitars? Tuning? Intonation? Is that a joke?" ``` …which your link says with greater eloquence. ---
**Author:** ![ZenBeam](https://avatars.discourse-cdn.com/v4/letter/z/3ab097/32.png) [@ZenBeam](https://boards.straightdope.com/u/ZenBeam)\ **Post date:** [February 6, 2009, 1:45pm UTC](https://boards.straightdope.com/t/music-12-notes-octave-no-known-explanation/484645/46 "2009-02-06T13:45:53Z")
> [@pulykamell](#): > > Fascinating. How did you divide the scale? Did you maintain perfect fourths and fifths, and subdivide from there? Did you maintain major and minor thirds? Did you throw in a third between those two, by any chance? I’m curious how you fell upon the 19… Since all six strings use the same frets, the “correct” placement for a fret to achieve this would be different for each string. However, I remember seeing a guitar (well, a picture, probably in an ad) that had a fretboard that did do this, with short little frets that were slightly different for each string (so no string bending for you!). It was for 12 frets/octave, not 19. IIRC, there were multiple fretboards that could be switched out, each tuned for a different key. ---
**Author:** ![bordelond](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bordelond/32/150_2.png) [@bordelond](https://boards.straightdope.com/u/bordelond)\ **Post date:** [February 6, 2009, 5:05pm UTC](https://boards.straightdope.com/t/music-12-notes-octave-no-known-explanation/484645/47 "2009-02-06T17:05:00Z")
> [@GorillaMan](#): > > Not so long ago I saw a quarter-tone guitar, i.e. 24 equal intervals per octave. It sounded hideous. Was it like [this](http://www.youtube.com/watch?v=Scu76cBCfu0&feature=related)? Funny thing about it is that, yeah, it sounds really “different” but there’s something familiar about it, too. What’s familiar about it is that it sounds “Greek” … like the music you’ll hear at local Greek-heritage festivals 😃 ---
**Author:** ![GorillaMan](https://avatars.discourse-cdn.com/v4/letter/g/50afbb/32.png) [@GorillaMan](https://boards.straightdope.com/u/GorillaMan)\ **Post date:** [February 6, 2009, 5:10pm UTC](https://boards.straightdope.com/t/music-12-notes-octave-no-known-explanation/484645/48 "2009-02-06T17:10:23Z")
> [@bordelond](#): > > Was it like [this](http://www.youtube.com/watch?v=Scu76cBCfu0&feature=related)? > > Funny thing about it is that, yeah, it sounds really “different” but there’s something familiar about it, too. What’s familiar about it is that it sounds “Greek” … like the music you’ll hear at local Greek-heritage festivals 😃 The one I saw had 24 frets per octave all the way up, not just the additional one as there - which sounds good! 🙂 [Previous page](https://boards.straightdope.com/t/music-12-notes-octave-no-known-explanation/484645.md?page=2)