4 ms·

It just means that melodies and harmonies are “supposed to be” sung and thus continuously pitched, where the ears of the musicians guide them to the proper harm

It just means that melodies and harmonies are “supposed to be” sung and thus continuously pitched, where the ears of the musicians guide them to the proper harmonies. This is not feasible with keyboard or fretted instruments, so we have to make compromises if we want to play polytonal music on a single piano. 12-TET is a compromise that stood the test of time: ultimately a slightly “clangy” dominant seventh is preferable to the corrupt fifths and thirds you get with unequal temperaments. I really don’t think there’s much more to it than that, except composers with picky ears should just bite the bullet with 17-TET or something. (I am a guitarist and sometimes I wish I had flatter thirds and tritones without having to bend the strings.) As shown off-handedly in the Werckmeister Harmonies novel and film, composers who get too deep into the weeds of temperament systems often find themselves confusing form with function and waging ideological battles, forgetting that the point of the exercise is create interesting music.

klodolph 2y ago
Note that the technical term for this is “just”.
analog31 2y ago
Has anybody made a guitar with double frets? I once saw a viola da gamba performance, and the VdG had some double frets, so I asked about it. Their purpose is to allow for some options when playing those thirds and tritones. Since the frets are tied on, you can have as many as you want, and they're also movable, so you can play around with temperaments if you want.
- klodolph 2y ago
  Does that work for just major thirds? They’re only 14 cents away from equal temperament, and I would think that the frets would be too close together, if you moved them into place for just major thirds.
  - analog31 2y ago
    Possibly. I didn't catch too many of the details, but he did demonstrate the sound and it was noticeable. The two frets were just a few mm apart, and a bass gamba has a fairly long scale length, comparable to a cello.
zahlman 2y ago
>12-TET is a compromise that stood the test of time: ultimately a slightly “clangy” dominant seventh is preferable to the corrupt fifths and thirds you get with unequal temperaments. The dominance of 12TET is not only about how well it approximates certain intervals. Equal temperaments in general are specifically about being able to transpose music freely without altering the "character" of the music. On the other hand, specifically having 12 notes in an octave turns out to produce some rather nice music-theoretical properties. Many equal-temperament tunings are regular diatonic tunings (https://en.wikipedia.org/wiki/Regular_diatonic_tuning https://en.wikipedia.org/wiki/Regular_diatonic_tuning), but 12TET is unique in that the size (as in, logarithmic pitch ratio) of the semitone is exactly half that of the whole tone. >composers with picky ears should just bite the bullet with 17-TET or something. For what it's worth, 17-TET (https://en.wikipedia.org/wiki/17_equal_temperament https://en.wikipedia.org/wiki/17_equal_temperament) has exceptionally "bad" thirds, both major and minor. It has an excellent semitone, since the just chromatic semitone is equal to the difference between the just major third and just minor third.) 19-TET (approximates third-comma meantone, and has an excellent minor third) and 31-TET (approximates quarter-comma meantone, and has an excellent major third) are common choices. 53-TET allows for approximating "zero meantone" - i.e. an almost exact perfect fifth - and a single such step is quite close in size to the syntonic comma. This has fairly dubious value in itself, since it's a lot of notes and the 2-cent difference between a 12TET perfect fifth and a just perfect fifth is not discernible for most people. However, as I understand it, some traditional Indian and Arabic tunings can be understood as subsets of 53TET. Electronic musicians with an interest in such exotic systems (or just microtonality in general) have a surprisingly complex system of jargon for describing tuning - since many of the systems they use don't depend on traditional music theory. Sometimes these systems are chosen for deliberate dissonance; some don't have pure octaves. (In this world (https://en.xen.wiki/w/Main_Page https://en.xen.wiki/w/Main_Page), equal temperament tunings are often labeled as "edo" - "equal division of the octave" - rather than TET.)

klodolph 2y ago

Note that the technical term for this is “just”.

analog31 2y ago

Has anybody made a guitar with double frets? I once saw a viola da gamba performance, and the VdG had some double frets, so I asked about it. Their purpose is to allow for some options when playing those thirds and tritones. Since the frets are tied on, you can have as many as you want, and they're also movable, so you can play around with temperaments if you want.

klodolph 2y ago
Does that work for just major thirds? They’re only 14 cents away from equal temperament, and I would think that the frets would be too close together, if you moved them into place for just major thirds.
- analog31 2y ago
  Possibly. I didn't catch too many of the details, but he did demonstrate the sound and it was noticeable. The two frets were just a few mm apart, and a bass gamba has a fairly long scale length, comparable to a cello.

zahlman 2y ago

>12-TET is a compromise that stood the test of time: ultimately a slightly “clangy” dominant seventh is preferable to the corrupt fifths and thirds you get with unequal temperaments. The dominance of 12TET is not only about how well it approximates certain intervals. Equal temperaments in general are specifically about being able to transpose music freely without altering the "character" of the music. On the other hand, specifically having 12 notes in an octave turns out to produce some rather nice music-theoretical properties. Many equal-temperament tunings are regular diatonic tunings (https://en.wikipedia.org/wiki/Regular_diatonic_tuning https://en.wikipedia.org/wiki/Regular_diatonic_tuning), but 12TET is unique in that the size (as in, logarithmic pitch ratio) of the semitone is exactly half that of the whole tone. >composers with picky ears should just bite the bullet with 17-TET or something. For what it's worth, 17-TET (https://en.wikipedia.org/wiki/17_equal_temperament https://en.wikipedia.org/wiki/17_equal_temperament) has exceptionally "bad" thirds, both major and minor. It has an excellent semitone, since the just chromatic semitone is equal to the difference between the just major third and just minor third.) 19-TET (approximates third-comma meantone, and has an excellent minor third) and 31-TET (approximates quarter-comma meantone, and has an excellent major third) are common choices. 53-TET allows for approximating "zero meantone" - i.e. an almost exact perfect fifth - and a single such step is quite close in size to the syntonic comma. This has fairly dubious value in itself, since it's a lot of notes and the 2-cent difference between a 12TET perfect fifth and a just perfect fifth is not discernible for most people. However, as I understand it, some traditional Indian and Arabic tunings can be understood as subsets of 53TET. Electronic musicians with an interest in such exotic systems (or just microtonality in general) have a surprisingly complex system of jargon for describing tuning - since many of the systems they use don't depend on traditional music theory. Sometimes these systems are chosen for deliberate dissonance; some don't have pure octaves. (In this world (https://en.xen.wiki/w/Main_Page https://en.xen.wiki/w/Main_Page), equal temperament tunings are often labeled as "edo" - "equal division of the octave" - rather than TET.)