A pretty well done blog on harmony:
https://www.garygarrett.me/?page_id=1922
Btw if you want to hear the difference between just intonation and equal tempered tunings:
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Here is a book on musical composition:
I find this one pretty valuable because it concentrates on song form beyond harmony. More specifically, it focuses on the interactions between harmony, register, texture, tempo, dynamics, rhythm, etc. rather than on any of them alone.
Thatās why, you should have some basic background in those concepts, otherwise the text will be difficult to understand. The introduction lists the requirements and if those donāt speak to you, it is probably best to postpone reading this book.
Taking things to another level, check out the videos and educational material from Galen DeGraf.
To start perhaps look at his video on post-tonal trichord set classes, or his video on
composing rhythmic paradoxes.
He has videos outside of straight music theory as well, like on improving musical notation using video notation, and musical example pieces, and analysis.
When you discovery other things heās presented feel free to discuss them below in this thread.
Iād love to see software / hardware that allows his accelerate decelerate tempo paradoxes to be more easily created.
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Some more ideas in this post exploring some advanced music theory this time from Levi McClain.
Here he is exploring ideas in polymicrotonality. ( A microtonal approach to polytonality. ) This gets into some approaches for the specific note selection from various microtonal tuning systems.
If you have a good understanding of traditional polytonality then watch this video where i have it queued, otherwise roll it back to the start and watch the introduction.
Warning : There is an ad embedded in the middle of this.
He touches lightly on a variety of approaches here and there is lots of room for your own personal exploration. I found the ideas of microplanning especially interesting. He is really just scratching the surface in this video.
It occurs to me that there is no absolute reason to either have one microplanning systen throughout a composition, or for that matter, for the different microtonal branches be connected with a traditional modal system.
Again like with my last post, hardware or software to assist with these exploration would be nice. Electronic sound creation by its nature is very useful in exploring these polymicrotonalities.
Sidebar : With microplaning, what about using a standard keyboard, with a low note defining which part of the system you are in, with then the seven white notes being a seven note selection ( or 6 with a duplicate ) from that specific microplane.
By the way, judging from this video and others, this presenter, is also quite a good musician. ( Though not a singer. ) Go ahead and share and explore others of his videos below.
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Thank you for the interesting video!
My personal conclusion from the video is that the concept of microplaning seems to translate more naturally to playing two differently tuned instruments together rather than putting it all together on a single āpolytunedā instrument. Plus, having two varying layers of sound texture makes the sonic result more palatable to our equal-temperament educated ears.
The disadvantage of most tuning systems other than equal tempered is that they require the definition of a base or reference tone and that they then only work within that context. Unthinkable for most keyboard players who are used to switching keys all the time.
Technically, there is no reason that any modern keyboard synth would not be able to do all this (eg Korg Kronos can do to some extent) but beyond defining fixed base tone tuning tables, most manufacturers donāt seem to dare investing much time into this topic.
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More Levi McClain ā Klingon Music Theory this time.
Actually theory on three separate ideas of what Klingon music might be.
This is more fun than serious, although it does get into some more advanced music theory topics, for instance of composition and musical reinterpretation into other tuning systems other than our traditional 12 tone equal temperament.
There is also some good Star Trek reference and research for those interested in Star Trek Theory.
Unfortunately this video is very seriously flawed by rookie innumeracy errors. ( And another embedded ad. ) For starters there is no digit ā3ā in the ternary number base. ( Doh ! ) Plus 11 in the ternary base is NOT eleven. He is also confused some with dozenal arithmetic. Youād think heād have to have studied some of this mathematics to have gained his music theory knowledge but apparently not. So smile and skip over this ignorant nonsense in the video, and enjoy the rest.
ADDED :
Perhaps he is counting in ternary using bijective numeration. It gets complicated, so wonāt go into great detail, but this has to do with number systems without a ā0ā digit so you canāt have ā10ā. But ā11ā is still not eleven.
Good foundations for composing in 9-EDO here.
I like the general idea of creating your own philosophy, and theoretic systems to create your own musical realm. ( Like in his second idea of Klingon Music Theory. )
Microtonal Solfeges is also a nice idea.
Also of interest is his microtonal playing of the Exquis. That seems pretty Star Trek.
Also for those who havenāt it might be good to explore Ian Ringās Scale Finder website.
https://ianring.com/musictheory/scales/finder/
( Sorry for all the late edits on this page, it escaped from me too early, by error. )
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Hereās a very good ( and short ) intro to the basic triads in 31 EDO.
What it has is the equivalent of the major and minor chord we know in 12 EDO, but then adds a neutral triad, a super major, and a sub minor. There is also a suspended triad considered here as well.
Zheanna Erose very well explains the composition of these triads in 31, as well as giving a musically descriptive essence of their sounds to help give them contexts for your composition and playing.
This is all very basic, and builds on an understanding of the 12 equal temperament triads. Basic, so little reference to 7th chords, other than for the neutral chord and sub minor, and no mention at all for any higher harmonics.
She put together another very very short video that quickly shows the extended seventh chords. Almost no detail in this video, but you can work out the voicings on these on your own if you want.
If you get interested in those in 31, check out, another video of hers that shows the overtone scale in 31.
You can play modally in 31, as well as use it in alternative, but somewhat familiar functional harmony ways with its own way of voice leading and progressions and resolutions and cadences.
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This song theory book seems to be under creative commons license:
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Starting with the chord map (or harmonic scale) presented in this book, more specifically in the chapter on chord progressions, and based on the aforementioned book Harmonic Experience by Mathieu, Iāve extended the harmonic scale by adding chromatic chords from other modes that are typically borrowed in tonal harmony:
This circular map is a nice tool to trace your chord progressions when composing. It can be spelled out in 12 keys. The book shows you how to use it. I find it a pretty easy way to remember the function of each chord within a key and also an easy way to navigate in less common keys.
The chromatic chords in the outer ring, which is my own extension to this chart, are limited to the five root notes shown in the chart. Iāve also written their original function next to them, eg V of IV for VIIb. Their position compared to the primary functions is not chosen randomly but directly related with their relative harmonic distance in terms of common or closest tones (think Tonnetz or tonal lattice). Iāve left out Ib and Vb. VIIb (backdoor) and IIb (tritone substitute) can be used as a substitute to V7, while IIIb and VIb would be used more often as a substitute to IV. VIb also allows for aug6, as a substitute to V7.
I watched through these lectures 3 times around 10 years ago and it helped a lot of things to fall into place (even if his phonology hypothesis is incorrect it can be a useful analogy).
Another thing thatās helped me a lot is singing. The act of finding and producing the right frequencies with your body makes you feel and understand music in a physical way.
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Is it worth finding the DVDs/Blu-Rays for these?
Thatās been quite nice for me, though translating that to song has been a process Iām still working through.
Itās all readily available on youtube (and the internet archive) so I donāt see a need. Bernstein is dead so doesnāt need your money 
Iāve found just being able to feel the notes in my body has helped in a lot of subtle ways.
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Sure sure. I didnāt see all the lectures available on either (or in higher quality rips), and agree, the primary persons receiving residuals on them would be whatever family estate and iām sure theyāre doing fine.
I understand on some level (hence why Iāve been focusing on vocal coaching to supplement synthwork) but can always use lectures like these to help fill in gaps.
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The way he explains the development of harmony from monophonic plainsong to 20th century extended tonality and atonality is really nice.
Heās as passionate as he is knowledgable + a virtuosic performer and speaker to boot.
EDIT: this channelās great if you already have a decent understand of theory. His analyses are the most in-depth Iāve seen on youtube.
https://www.youtube.com/@syroyid-class