Do you think something like 371 edo is safe? I am thinking a multiple of 53 might be my best option because I only plan to compose in Pythagorean just intonation. Part of me is curious if something similar is the case with my other problems. I am no doubt using the program in a way that is not used by really anyone else, and the crashes and bugs are happening when I go off the beaten path so to speak. Changing note heads to a great degree, thicknesses of stems and their length, note spacing, rhythmic dot spacing. I am using time signatures with 1 as a denominatoor like 12/1 and 8/1 and 6/1 in combination with all these other things. I do wonder if the tuning issue is in anyway related to the myriad of other issues I am having. Because as I am using the program it is operating like it is an open beta and not a finished product, and from my communication with other Dorico users who are using Dorico in more conventional ways, even more conventional microtuning like 31 edo and 19 edo, they are not having any of the issues I am, and a lot of them have accused me of trolling.But vp til now every new project I have started has become useless because of a DIFFERENT glitch. It is a different glitch every time that causes me to have to abandon the project entirely because basically the program stops obeying my commands, even with restarts, even with ctrl z, it is like the file gets to a point and it becomes corrupted and I can no longer craft and shape it without a terrible crash or the engraving going crazy, or the playback getting messed up or out of synch with the green play bar, or the tempo slowing down dramatically without remedy, or the mixer becoming something apart from the playback, where I can mute things and they continue to be heard, I can turn the sliders for volume up and down and the volume remains the same. Sometimes all instruments start plaing on one track and not at all on the others. Every project brings an avalanche of project destroying glitches, so I am hoping getting the tuning thing straigtened out at least provides so me clarity on the rest of the issues.
Someone here also I think said that Dorico will only allow custom ccidentals to bend a note half an octave. Is this true? Because if it is that means that large edos become useless for Pythagorean tuning, and it also would explain why my sextuple sharp accidental caused glitching and launched the note E up an octave on the staff and did not alter the note as I programmed it to. This is very bad, because then there is no way to modulate to far out keys or use far out notes without misspelling notes and adding accidentals other than compound sharps or flats. If that is the case 53 edo may be the only option if I would like the ability to modulate from one side of the chain of fifths to the other side, because even if I used 106 edo, that would involve accidentals altering a note more than half an octave. Am I correct in my words here?
665EDO has considerably purer fifths than 371EDO and it works without bugs with non-440 reference pitches, including your 432. Itâs also better in tune for 3-limit than 12000EDO. The half-octave problem is a little confusing to think about but I donât think the choice of EDO is relevant because in Pythagorean you use the same accidentals in any EDO you choose for playback. I think you can get around the problem by including accidentals with Pythagorean-comma inflections. F# is enharmonically Gb^ where the ^ stands for âcomma upâ. So canât you always spell a note enharmonically so that itâs never altered by more than half an octave?
Yes, It seems misspelling notes is the only way around it. I thought about it last night, and what I decided on is 15,960 EDO, because that is 665x12, and I tested it and it works with A at 432 Hz.
In terms of the accidentals bending only a half octave, I think I will write in Pythagorean53. So I will think of my system as having 77 notes per octave which shall give me Fbbbbb through B#xx, five accidentals for each note, and not going over the tritone point of failure for the program to pitch bend. And then if I want to modulate around the âcircle of fifthsâ I will cross over at the 53 point, where the mercator comma is or would be and loop around there and misspell the notes that way. They might be less is tune, but functionally I think as a system is works better than having ups and downs. In a way it is interesting that with 77 notes per octave where D is the center pitch, you get full sets of five flats and five sharps (on letters A-G) on the two notes that bookend the diatonic scale F and B. So the 15,690 edo is just for purityâs sake of the intervals, but I will think as if I have 77 notes per octave with a modulation warp point to the other end of the chain of fifths at 53, essentially making Ebbbb enharmonically âequivalentâ with Gxx even though they may be around four cents off, when I wiĹżh to âcircle aroundâ and when I wiĹżh to remain pure and donât need to circle I have . I really only need the far out notes for quarter tones two commas down from the upper note in a passing note sequence or in an appoggiatura. I am just very happy to have found a solution that is working. The program is still not rememebring my tonailty system as default: whenever a new project is ccreated and I click on the first measure it always says it is in 12 tet. I do hope to find a solution to that, but that is at least a glitch that I can deal with if I have to.
- There is no need to use 15,960 (which is 665x24 rather than 665x12) because the tuning of the fifth will be exactly the same in it and 665EDO. 3:2 is mapped to the exact same step in both EDOs so youâd just be stacking steps of 665. In other words, 665 has such a pure fifth that dividing its steps further into 24 steps does not improve it - those small steps will never be used.
- âSave as Defaultâ in the Tonality System editor does not make the Tonality System the startup system. It saves it in the list of tonality systems that is always available from the Tonality Systems menu when you start a new project. If you want to start a Dorico project with your Pythagorean system already set up, you should save a template with your tonality system (File > Save as Project Template). Then, when you open Dorico, choose Create New, and youâll find your template in the list: open that.
Just out of curiosity and obviously not to criticize:
how does one arrive at
?
Iâm really well versed in tunings of all sorts and have seen quite extensive diagrams like Salinas, but never came to a subdivision which amounts to a granulation of 0,077 cents (if I calculated this right). Is this some extrapolated Pythagorean tuning? Practically this would be a fluctuation far beneath auditory discretion of 2-3 cents, hence my interest. I suppose it removes beatings in some special intervals, right?
Yes, exactly, this division of the octave has a stupendously pure fifth (3:2), with only 0.000002-cent error, and in Pythagorean tuning all the intervals and accidentals are defined by fifths, so on paper, thatâs an ideal tuning unit. The oft-cited JND (Just Noticeable Difference) of a couple of cents concerns melodic intervals, and as you note, that extreme purity can only be noticeable in the beating rates of very stable synth sounds, kind of laboratory conditions. I was surprised to actually hear a difference in the beating of fifths in 12,000EDO and 15,6101EDO in Dorico when played on a straight sawtooth wave, using Steinbergâs Retrologue VSTi. I assume that few synths can cope with such precision and of course with sampled acoustic sounds this is all completely meaningless, the tuning of the samples varies a lot, and the sounds themselves are far from stable.
Note that even if we say 15,601-EDO, those minuscule units of 0.079 cents are not used as steps in the music; the idea is that if you want as pure fifths as possible, 9126 of these small units gives a much purer fifth than 702 cents.
Ok, I understand, so this is not meant for human singers/players.
Next question: if you tune all pythagorean intervals to such high precision, and - I presume - connect 2/3/4/⌠voice chords: how do you solve the constant drifting of pitch? Because this would be inevitable, as far as I understood
If I may presume to answer this briefly: They donât. Thatâs what the multiple accidentals are for.
There is no pitch drift in Pythagorean tuing unless one really works for it. You can see a pitch drift in Pythagorean comma in my video The LaĹżt Woęds of Dauid on Youtube on my channel Remember God Holy Bible 1611. In that piece it slowly modulates from G major to Fx major.
Thank you for informing me of this. Unfortunately 665 edo does not work either in 432 Hz. Only when there is one or two voices it works, but with 4 part harmony it is mostly squealing again. Also what I said above 15,960 edo also does not work at all. When I tried it last night it worked fora single piano line with single bass notes. But today converting a four part hymn that was in 15,601 edo and 440 Hz, when I changed it to 15,960 and also 665e edo it s squealling commenced again. I am not sure what to do. I just lost about 2 to 3 hours of work today making all my accidentals again and key signatures in the 15,960 edo.
I can try 1330 or some multiple of 53edo next I guess.
I just tried 665EDO in 432Hz with four instruments and four-part chords on each staff and it does work here, so thereâs something else going on in your file or computer. (Perhaps you accidentally went back to a large EDO?). 1330EDO does not improve the tuning; the mapping of the fifth would be that of 665EDO. About multiples of 53 Iâm not sure; the tuning of the fifths will be identical to that in 53EDO unless you go to a very large multiple: I havenât tried to find one.
Ok, I see: you are going purely Pythagorean and use pyth, thirds - then of course there is no problem. So this is a 3-limit system, if I have the terminology right
Yes, you got it. Contrary to what I and most others have been told 81/64 thirds are just intonation and are not only quite usable but ideal, even in triadic harmony. I know it is a big controversial statement, but if it interests you, trying it out, you may be very surprised.
Hmm. Well the only thing I can think of that could be an issue is that when I tuned in 665edo I made it by editing my tuning for 15,960edo. The score was already in Ab major in 15,960 with a custom flat pertaining to that edo. When I tried 665 I changed the spaces between all the diatonic notes, and then changed the custom flat to 63 steps. Then I click on the first measure changed to the 665 tuning and selected the Ab custom keysignature. Perhaps because the Ab custom key signature was created with a flat from another edo, when I changed the value of that custom flat, it did not translate over to the flats in the custom key signature. I may have to remake all the key signatures, or at least the Ab one to see if that changes anything.
Nope, I just tried deleting and remaking the Ab major key signature with the new flat, and it is still mostly loud squealing. It is possible the file is corrupted as all my other files have become and I need to try it in a new file? Dorico support thas still not returned my email about this.
Do try 665EDO in a new file. Copypasting notes from one Tonality System into another often causes problems and should be avoided.
No, no problem with hearing on my side. I tune my harpsichord to some flavour of Meantone or whatever, depending on what Iâm going to play. And my Organetto - it being a medieval instrument - I keep mostly in pythagorean (tuning by the fourths, because that is more precise), so in the end itâs just stylistic hearing. For some pieces from around the change in the 15th century, say early Franco-Flemian one has to decide by ear, which type of tuning fits better. On my fretted instruments it can be none of them of course âŚ
Thank you, yes, I just tried chords on a violin in a new file and it works perfectly in 665. Hopefully I can now finish a song, lol. Thank you for your help.
Thatâs right, and itâs essential to know: Changing the key sig does not change the notes, either in 12-EDO or here. Where the tonality system has an exact equivalent accidental (in terms of octave proportion on the same staff note), that accidental will show. In the much more likely event there isnât one, no accidental is displayed, but the pitch still plays as it was assigned.
When you want to hear slightly different accidentals, you have to reassign them all.