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Meta: this whole conversation amounts to a bunch of people who don't really understand tuning talking over-confidently about it. There are communities of expert

Meta: this whole conversation amounts to a bunch of people who don't really understand tuning talking over-confidently about it. There are communities of experts on the subject, and if you bother to engage with any of them, you can learn. But you don't learn by starting out sure that you already know everything. > The Tritone for instance, never appears in the harmonic series The first of multiple tritones that show up is the one from harmonic 5 to harmonic 7. We're not talking weird abstract, esoteric harmonics here. The major scale has SOMETHING to do with harmonics of course. It's true that Just Intonation purists can be dogmatic and make claims that don't hold up to scrutiny, but jumping to the conclusion that their claims have NOTHING to them is even more stupid a position. The major scale became the reference scale in chordal music specifically because of the way it facilitates blended harmonies in closely related chords. It's because people discovered the blend of the major chord which is a thing because of how harmonics work. And you put three overlapping major chords together and you get the major scale. Before chordal-harmony, other modes and scales were just as or more prominent.

PaulDavisThe1st 5y ago
The harmonic series does not define the major scale, which is a heptatonic (7 tone) scale, at least not any more (or less) than it defines any other scale. The harmonic series helps to explain the relationships between the twelve tones that we (people composing and performing in "western" musical traditions) use to divide the octave. It's likely not a coincidence that many other cultures, despite their use of additional tones within the octave, also seem to "stumbled" as we did onto the properties we get from 12T-per-octave (regardless of the precise tuning of those 12 tones). I'm not sure where you are getting your information about tritones from. Everything I've learnt about tritones would say that you're wrong to claim they occur between the 5th and 7th harmonic. Got any references on that? Also, this thing about communities of experts ... one of the problems with this is that at least in the USA and Europe, the majority of the community of experts appears to have deliberately constrained their expertise to a somewhat narrow view of tuning. There's a reason why Bohlen-Pierce and the tunings of Harry Partch are considered "out there": it's not just that they are quite challenging for 12T(ET) ears to listen to, but also that our musical academies have shrunk the possibilities for tuning down to a sadly constrained range. Consider for example, the bulk of musical set theory, which is incredibly interesting at the scale (mode) level, but still appears from the literature to overwhelming assume only a handful of possible tuning systems (and a big chunk of it considers only one possible tuning system).
- quadrangle 5y ago
  I wasn't saying that the major scale is defined by harmonics, I'm saying that the harmonics which define what tones blend into chords are the reason for the major scale becoming our primary reference scale, whether or not it is tempered in the end. The tritone point doesn't need any reference. Go and play the 5th harmonic and then the 7th harmonic on a string. That's an interval of a tritone. Tritone means 3 whole steps, 3 whole tones. It's a general scale-based interval amount. The 7/5 ratio is 583¢, that's a tritone. It's an interval that takes 3 whole tones to reach. Put in traditional language, the 5th harmonic is a major third (2 octaves above the fundamental) and the 7th is the minor 7th (2 octaves above the fundamental). And the interval from a major third to a minor seventh is a tritone. There's no references needed. > the majority of the community of experts appears to have deliberately constrained their expertise to a somewhat narrow view of tuning Exactly, that's my point. All those so-called experts are basically ignorant to be blunt. What I mean is that there ARE people out there (on the margins to a degree), all the people who develop https://en.xen.wiki/ https://en.xen.wiki/ for example, and from their (okay, our, I'm one of them) perspective, all the chatter here is a mix of thoughtful people like you trying to talk some sense with a bunch of ignorant folks who are clueless. So, you have more than some clues, you seem to have some knowledge, but you would be a beginning student in the world of people who actually understand the topic of tuning. So, understanding of this stuff exists in the world, and the reasons that it remains on the margins are themselves also understood. Suffice to say, Partch being a reference known by the already small subset of clued-in people is already pretty tiny. His work is foundational but quirky and old and nowhere near reaching real understanding. A lot of people into tuning are intentionally weird sounding, so it's hard to separate that form the topic. And if you're NOT weird sounding, then nobody is noticing the tuning. As soon as the tuning draws your attention, it's already weird. It's all too much to get into here. It does seem that there's some prospect of breaking out of this situation in the next few years finally, but don't hold your breath.
  - PaulDavisThe1st 5y ago
    > Go and play the 5th harmonic and then the 7th harmonic on a string. You're using "harmonic" here in a way this is disconnected from a lot of the rest of the discussion here. We are not talking about scale degrees or anything like that, but the physical harmonic series. The 5th and 7th partial of the harmonic series has nothing to do with the 11th, which the basis for the ratio that normally is identified as the tritone, modulo some culture-specific tweaks to fit in with other musical practice (eg. definining it as 64:45 or 7:5 or sqrt(2) in various tuning systems). > There's no references needed. There's plenty of existing references that make it clear that the tritone is based on the 11th harmonic of the harmonic series, folded down into the octave as a ratio of 11:8. The "tritone is 3 whole steps" is a tuning-specific simplification of this. And yeah, I know the xen site, and have a learned a lot from it. I still see some fairly clear impositions of "worldviews" on some of the material there, maybe not as bad as it would be at a music school, but not quite as context-free as some people would prefer. I'm the author of a cross-platform DAW, and one of my goals for the next few years it to get support for arbitrary tuning systems deeply embedded into the software.

PaulDavisThe1st 5y ago

The harmonic series does not define the major scale, which is a heptatonic (7 tone) scale, at least not any more (or less) than it defines any other scale. The harmonic series helps to explain the relationships between the twelve tones that we (people composing and performing in "western" musical traditions) use to divide the octave. It's likely not a coincidence that many other cultures, despite their use of additional tones within the octave, also seem to "stumbled" as we did onto the properties we get from 12T-per-octave (regardless of the precise tuning of those 12 tones). I'm not sure where you are getting your information about tritones from. Everything I've learnt about tritones would say that you're wrong to claim they occur between the 5th and 7th harmonic. Got any references on that? Also, this thing about communities of experts ... one of the problems with this is that at least in the USA and Europe, the majority of the community of experts appears to have deliberately constrained their expertise to a somewhat narrow view of tuning. There's a reason why Bohlen-Pierce and the tunings of Harry Partch are considered "out there": it's not just that they are quite challenging for 12T(ET) ears to listen to, but also that our musical academies have shrunk the possibilities for tuning down to a sadly constrained range. Consider for example, the bulk of musical set theory, which is incredibly interesting at the scale (mode) level, but still appears from the literature to overwhelming assume only a handful of possible tuning systems (and a big chunk of it considers only one possible tuning system).

quadrangle 5y ago
I wasn't saying that the major scale is defined by harmonics, I'm saying that the harmonics which define what tones blend into chords are the reason for the major scale becoming our primary reference scale, whether or not it is tempered in the end. The tritone point doesn't need any reference. Go and play the 5th harmonic and then the 7th harmonic on a string. That's an interval of a tritone. Tritone means 3 whole steps, 3 whole tones. It's a general scale-based interval amount. The 7/5 ratio is 583¢, that's a tritone. It's an interval that takes 3 whole tones to reach. Put in traditional language, the 5th harmonic is a major third (2 octaves above the fundamental) and the 7th is the minor 7th (2 octaves above the fundamental). And the interval from a major third to a minor seventh is a tritone. There's no references needed. > the majority of the community of experts appears to have deliberately constrained their expertise to a somewhat narrow view of tuning Exactly, that's my point. All those so-called experts are basically ignorant to be blunt. What I mean is that there ARE people out there (on the margins to a degree), all the people who develop https://en.xen.wiki/ https://en.xen.wiki/ for example, and from their (okay, our, I'm one of them) perspective, all the chatter here is a mix of thoughtful people like you trying to talk some sense with a bunch of ignorant folks who are clueless. So, you have more than some clues, you seem to have some knowledge, but you would be a beginning student in the world of people who actually understand the topic of tuning. So, understanding of this stuff exists in the world, and the reasons that it remains on the margins are themselves also understood. Suffice to say, Partch being a reference known by the already small subset of clued-in people is already pretty tiny. His work is foundational but quirky and old and nowhere near reaching real understanding. A lot of people into tuning are intentionally weird sounding, so it's hard to separate that form the topic. And if you're NOT weird sounding, then nobody is noticing the tuning. As soon as the tuning draws your attention, it's already weird. It's all too much to get into here. It does seem that there's some prospect of breaking out of this situation in the next few years finally, but don't hold your breath.
- PaulDavisThe1st 5y ago
  > Go and play the 5th harmonic and then the 7th harmonic on a string. You're using "harmonic" here in a way this is disconnected from a lot of the rest of the discussion here. We are not talking about scale degrees or anything like that, but the physical harmonic series. The 5th and 7th partial of the harmonic series has nothing to do with the 11th, which the basis for the ratio that normally is identified as the tritone, modulo some culture-specific tweaks to fit in with other musical practice (eg. definining it as 64:45 or 7:5 or sqrt(2) in various tuning systems). > There's no references needed. There's plenty of existing references that make it clear that the tritone is based on the 11th harmonic of the harmonic series, folded down into the octave as a ratio of 11:8. The "tritone is 3 whole steps" is a tuning-specific simplification of this. And yeah, I know the xen site, and have a learned a lot from it. I still see some fairly clear impositions of "worldviews" on some of the material there, maybe not as bad as it would be at a music school, but not quite as context-free as some people would prefer. I'm the author of a cross-platform DAW, and one of my goals for the next few years it to get support for arbitrary tuning systems deeply embedded into the software.