+dorfischer ah, thanks. I'm occupied with so much stuff nowadays, music is postponed in my life until God knows when. Maybe if or when certain turmoils are safely transitioned? Let's see how it all turns out. Thanks again.
Thank you for presenting this very beautiful custom tuned instrument. I hope your tunings, notation, passion, and wisdom spread widely. Thank you for sending your paper. I skimmed it again more thoroughly. As you predicted, at least some of my assumptions and misunderstandings, have been corrected. I also just read through a very long, frustrating and circular Yahoo discussion from 2006, I believe from just before you completed your dissertation. In my opinion, if you demand an octave of nearly exactly 79 or 80 notes, then your just octave, fourths, fifths, subset of 159 is very reasonable and possibly ideal. Mathematically, however, it may not be quite as elegant as 53edo, the extra comma before the fifth in particular. You clearly require more nuanced notes than 53 but desire "not too many notes". No equal division has more pure fourths and fifths than 53edo until 200edo (and 200 is not a significant improvement anyway). Therefore, if it's not too large a note space, I imagine 106edo is ideal for your purposes (even if they're not all used, strung on a qanun). Just like 53edo, 106edo contains nearly exactly pure pythagorean and numerous harmonic intervals. Additionally, 106edo contains the midpoint between the fourth and fifth as suggested by others, indeed also the midpoints between all tones, and doesn't require uneven commas. Otherwise, if 159 provides something specific and necessary that 53 and 106 do not (which I can't imagine), then of course, 159edo (or 200edo) would seem to be perfect. Or course, I may be mistaken again (it happens :D). I wish you luck and success. I look forward to hearing and seeing your future projects.
106-EDO is not ideal, because you cannot construct meaningful alternative cycles of fifths with its impure fifths. They are either too narrow or too wide. The Töre-Karadeniz system is a 41-note subset of that and it doesn't resonate well. The 159-tET impure fifths, on the other hand, are just at the edge of tolerability.
@@OzanYarman the 53, 106, 159, and every multiple of 53edo (short of a million) has the exact same fifth. The 53edo fifth (31°) is less than 0.006% from perfect purity (3/2). Anything can be tempered, adjusted, inserted to get truly perfect fifths (for which no human can discern a difference) as you've done. We could give 12tet perfect fifths by raising the 7° about 2¢, but such hacks won't make it mathematically elegant.
By fifths, I suppose you don't mean perfect fifths, but a collection of several similar notes surrounding (and including) the perfect fifth, such as 30°, 31°, 32° (and some in between). I can't speak about your requirements nor the particulars of maqam, but I can discuss symmetry and harmonic purity. The three 530edo "fifths" previously mentioned have cent values of roughly -23, 0, +23¢ from the perfect fifth. 106edo gives you exactly that plus additional values exactly in between and beyond (11.3¢). Alternatively, 159edo also gives you exactly 53edo's "fifths" and two more (rather than one more: 1/3 and 2/3 or about 7.5¢) in between. However 79,80 MOS 159 are bastards similar to 53, 106, and 159 but with none of their symmetries (with or without your inserted comma and adjusted perfect fourth and fifth). Or rather, new symmetries, a coincidence of notes, periodically selected from the standard EDOs 53, 106, and 159. To be specific, 159 is already a superset of 53, which is (for more than practical purposes) is already perfect. 159 only provides additional symmetric notes, with a period of 3 (every 3 notes is exactly in 53edo). 79,80 MOS has a period of 2 (aka generator) which only sometimes includes a pure note from 53edo -- 33% of the notes, while 67% are from 159edo but not 53edo with no obvious justification except "a desire for more notes". In contrast, all of the notes in 106edo are symmetrical and justified, either exactly in 53edo or exactly in between. 79 or 80 (from a purely mathematical perspective) seems as arbitrary as 12tet. Compromises that squeeze a specific number of notes into a fixed physical instrument. IMO, either you just select the best set of notes (such as JI) disregarding mathematical symmetries of the set entirely, or you select specific subset of notes from a perfect superset (such as 106edo or 159edo) which does have mathematically perfect symmetries. It seems to me that 79,80 is pointing at 79.5°, which doesn't exist in 159edo, but does exist as 53° in 106edo.
@@vegahimsa3057 The 7.5 cents above and below the of 53-EDO (31st degree) are necessary to construct scales that have SEVERAL flavors of neutral seconds AND to acquire a chromatic 12-tone cycle AND to transpose everything over any degree besides optimizing many more desiderata. 79 or 80 MOS 159-tET are symmetric in the sense of MOMENT OF SYMMETRY. Watch Moriarty's UA-cam video for that. I do not approve of your usage of the term BASTARD, nor do I approve of your cliche fetishm for glorifying the or of some given intervals. My modified meantone temperament tuned Feurich piano resonates most delectably even though it violates your notion of purity over many transpositions and modulations. I do not have much more patience to discuss this matter over here besides. You might perhaps direct all your energy to the Xenharmonic Alliance II facebook group.
In effect you HAVE selected an 80 note subset of 159edo (disregarding the adjustment before the fifth). As you explained in the Yahoo group, there's no particular reason for MOS159, only that a bunch of mathematicians mentioned it, for reasons which probably don't address your actual requirements. It seems that both 80 (or 79) and 159 are arbitrary or at best coincidental. The former, because it's a Goldilocks number, not too big, and not too small, that can be squeezed into an instrument. The latter because it shares the mathematical elegance of 53. The combination (79.5MOS159) just happens to be about half. What you really want (and I'd argue, all of harmonic and music theory since Pythagoras has wanted) is an instrument that can be tuned to mathematical elegance OR a mathematical compromise that can be squeezed into an instrument (and understood by mortal humans). Nothing short of 53edo and its precise supersets (such as 106, 159, etc) is mathematically elegant. So if 53 notes is not enough, it seems your next best choices, your only elegant solutions, are 106edo, 159edo or larger. I'm not familiar with any 41 subset of a 53 multiple. I imagine it fails, not because it's derived from a 53edo derivative, but fails due to the choice of 41.
Bu kanundaki ses düzenini Terpstra klavye web uygulamasına taşıdım. Arıza işaretlerini Sagittal notasyonu çağrıştıracak Unicode ok karakterlerinden seçtim ve frekansı A = 440 Hz (Hüseyni) olacak şekilde ayarladım. Çalmaya hazırdır. Linki ek olarak aşağıya iliştiriyorum, görünmüyorsa filtreye takılmıştır:
I have an Armenian Qanun with 26 strings and two mandals under each string. I need to fine tune this qanun and I am not sure how. Can any body tell me what are the tones on these strings starting from the bottom? And will both mandals be down or up while tuning?
Armenian qanuns, to the best of my knowledge, implement 12-tone equal temperament semitones. If you need to fine tune it, you will end up at best with well temperaments and modified meantone temperaments, but they will all be cyclic. If you want to destroy the cyclic nature of the mandal setting, you can try to implement JI ratios for the naturals (1 mandal ups). Turkish qanuns have the space between the nut mandal and the semitone madal divided into 5/6/7 equidistant parts, all yielding multiples of 12-tET such as 60, 72, 84 equal divisions of the octave. With these "marketplace qanuns" you really have no escape from the 12-tET idiom. What you need, instead, is to mathematically implement a clever tuning such as my 79-tone system to acquire all the microtonal detail to play all modes and maqams everywhere (at whatever transposition you want)...
I didnt know that turkish qanoun have 79 strings. Turkish qanoun are more around 72 strings whereas egyptian and syrian are aroun 75 strings up to 80 strings
+Saad Mnissar +seaatlast This qanun is special due to the placement of 19 mandals per tricordi from note A2 until E5. The mandals are 15.1 cents apart, except for the mandal just below the note G, the distance to which is 22.2 cents up therefrom. The tuning is thus a quasi-equal, irregular, yet symmetric structure allowing transpositions everywhere with minimal damage (max. 7.5 cents detuning of any pitch).
I am grateful that such a video exists in English!
This is mesmerising. I learned so much! Eagerly awaiting part 2. (and 3 and 4 etc' ;)
+dorfischer ah, thanks. I'm occupied with so much stuff nowadays, music is postponed in my life until God knows when. Maybe if or when certain turmoils are safely transitioned? Let's see how it all turns out. Thanks again.
ua-cam.com/video/vR2koucP0ao/v-deo.html
Bravíssimo, maestro! Başına ellerine sağlık!
Cok iyi
süper
Thank you for presenting this very beautiful custom tuned instrument. I hope your tunings, notation, passion, and wisdom spread widely.
Thank you for sending your paper. I skimmed it again more thoroughly. As you predicted, at least some of my assumptions and misunderstandings, have been corrected. I also just read through a very long, frustrating and circular Yahoo discussion from 2006, I believe from just before you completed your dissertation.
In my opinion, if you demand an octave of nearly exactly 79 or 80 notes, then your just octave, fourths, fifths, subset of 159 is very reasonable and possibly ideal. Mathematically, however, it may not be quite as elegant as 53edo, the extra comma before the fifth in particular. You clearly require more nuanced notes than 53 but desire "not too many notes". No equal division has more pure fourths and fifths than 53edo until 200edo (and 200 is not a significant improvement anyway). Therefore, if it's not too large a note space, I imagine 106edo is ideal for your purposes (even if they're not all used, strung on a qanun). Just like 53edo, 106edo contains nearly exactly pure pythagorean and numerous harmonic intervals. Additionally, 106edo contains the midpoint between the fourth and fifth as suggested by others, indeed also the midpoints between all tones, and doesn't require uneven commas. Otherwise, if 159 provides something specific and necessary that 53 and 106 do not (which I can't imagine), then of course, 159edo (or 200edo) would seem to be perfect.
Or course, I may be mistaken again (it happens :D). I wish you luck and success. I look forward to hearing and seeing your future projects.
106-EDO is not ideal, because you cannot construct meaningful alternative cycles of fifths with its impure fifths. They are either too narrow or too wide. The Töre-Karadeniz system is a 41-note subset of that and it doesn't resonate well. The 159-tET impure fifths, on the other hand, are just at the edge of tolerability.
@@OzanYarman the 53, 106, 159, and every multiple of 53edo (short of a million) has the exact same fifth. The 53edo fifth (31°) is less than 0.006% from perfect purity (3/2). Anything can be tempered, adjusted, inserted to get truly perfect fifths (for which no human can discern a difference) as you've done. We could give 12tet perfect fifths by raising the 7° about 2¢, but such hacks won't make it mathematically elegant.
By fifths, I suppose you don't mean perfect fifths, but a collection of several similar notes surrounding (and including) the perfect fifth, such as 30°, 31°, 32° (and some in between). I can't speak about your requirements nor the particulars of maqam, but I can discuss symmetry and harmonic purity. The three 530edo "fifths" previously mentioned have cent values of roughly -23, 0, +23¢ from the perfect fifth. 106edo gives you exactly that plus additional values exactly in between and beyond (11.3¢). Alternatively, 159edo also gives you exactly 53edo's "fifths" and two more (rather than one more: 1/3 and 2/3 or about 7.5¢) in between.
However 79,80 MOS 159 are bastards similar to 53, 106, and 159 but with none of their symmetries (with or without your inserted comma and adjusted perfect fourth and fifth). Or rather, new symmetries, a coincidence of notes, periodically selected from the standard EDOs 53, 106, and 159. To be specific, 159 is already a superset of 53, which is (for more than practical purposes) is already perfect. 159 only provides additional symmetric notes, with a period of 3 (every 3 notes is exactly in 53edo). 79,80 MOS has a period of 2 (aka generator) which only sometimes includes a pure note from 53edo -- 33% of the notes, while 67% are from 159edo but not 53edo with no obvious justification except "a desire for more notes". In contrast, all of the notes in 106edo are symmetrical and justified, either exactly in 53edo or exactly in between.
79 or 80 (from a purely mathematical perspective) seems as arbitrary as 12tet. Compromises that squeeze a specific number of notes into a fixed physical instrument. IMO, either you just select the best set of notes (such as JI) disregarding mathematical symmetries of the set entirely, or you select specific subset of notes from a perfect superset (such as 106edo or 159edo) which does have mathematically perfect symmetries.
It seems to me that 79,80 is pointing at 79.5°, which doesn't exist in 159edo, but does exist as 53° in 106edo.
@@vegahimsa3057 The 7.5 cents above and below the of 53-EDO (31st degree) are necessary to construct scales that have SEVERAL flavors of neutral seconds AND to acquire a chromatic 12-tone cycle AND to transpose everything over any degree besides optimizing many more desiderata. 79 or 80 MOS 159-tET are symmetric in the sense of MOMENT OF SYMMETRY. Watch Moriarty's UA-cam video for that. I do not approve of your usage of the term BASTARD, nor do I approve of your cliche fetishm for glorifying the or of some given intervals. My modified meantone temperament tuned Feurich piano resonates most delectably even though it violates your notion of purity over many transpositions and modulations. I do not have much more patience to discuss this matter over here besides. You might perhaps direct all your energy to the Xenharmonic Alliance II facebook group.
In effect you HAVE selected an 80 note subset of 159edo (disregarding the adjustment before the fifth). As you explained in the Yahoo group, there's no particular reason for MOS159, only that a bunch of mathematicians mentioned it, for reasons which probably don't address your actual requirements. It seems that both 80 (or 79) and 159 are arbitrary or at best coincidental. The former, because it's a Goldilocks number, not too big, and not too small, that can be squeezed into an instrument. The latter because it shares the mathematical elegance of 53. The combination (79.5MOS159) just happens to be about half.
What you really want (and I'd argue, all of harmonic and music theory since Pythagoras has wanted) is an instrument that can be tuned to mathematical elegance OR a mathematical compromise that can be squeezed into an instrument (and understood by mortal humans).
Nothing short of 53edo and its precise supersets (such as 106, 159, etc) is mathematically elegant. So if 53 notes is not enough, it seems your next best choices, your only elegant solutions, are 106edo, 159edo or larger.
I'm not familiar with any 41 subset of a 53 multiple. I imagine it fails, not because it's derived from a 53edo derivative, but fails due to the choice of 41.
Bu kanundaki ses düzenini Terpstra klavye web uygulamasına taşıdım. Arıza işaretlerini Sagittal notasyonu çağrıştıracak Unicode ok karakterlerinden seçtim ve frekansı A = 440 Hz (Hüseyni) olacak şekilde ayarladım. Çalmaya hazırdır. Linki ek olarak aşağıya iliştiriyorum, görünmüyorsa filtreye takılmıştır:
tinyurl.com/4wsh2zv7
tinyurl.com/4wsh2zv7
I have an Armenian Qanun with 26 strings and two mandals under each string. I need to fine tune this qanun and I am not sure how. Can any body tell me what are the tones on these strings starting from the bottom? And will both mandals be down or up while tuning?
Armenian qanuns, to the best of my knowledge, implement 12-tone equal temperament semitones. If you need to fine tune it, you will end up at best with well temperaments and modified meantone temperaments, but they will all be cyclic. If you want to destroy the cyclic nature of the mandal setting, you can try to implement JI ratios for the naturals (1 mandal ups). Turkish qanuns have the space between the nut mandal and the semitone madal divided into 5/6/7 equidistant parts, all yielding multiples of 12-tET such as 60, 72, 84 equal divisions of the octave. With these "marketplace qanuns" you really have no escape from the 12-tET idiom. What you need, instead, is to mathematically implement a clever tuning such as my 79-tone system to acquire all the microtonal detail to play all modes and maqams everywhere (at whatever transposition you want)...
I didnt know that turkish qanoun have 79 strings. Turkish qanoun are more around 72 strings whereas egyptian and syrian are aroun 75 strings up to 80 strings
the discussed topic is about 79 distinct PITCHES in an octave, not strings.
Wow!!!
Birtanesiniz lütfen 🙏 hoşçakalın
Svp je veux explication en français si c est possible
Is this the turkish qanun?
Yes it is... the mandal installation is different though.
@@OzanYarman oh can I know about that more please?
@@_kenula_damsith_ Indeed, you can check out www.ozanyarman.com/79toneqanun.html
what instrument is this?
+Saad Mnissar +seaatlast
This qanun is special due to the placement of 19 mandals per tricordi from note A2 until E5. The mandals are 15.1 cents apart, except for the mandal just below the note G, the distance to which is 22.2 cents up therefrom. The tuning is thus a quasi-equal, irregular, yet symmetric structure allowing transpositions everywhere with minimal damage (max. 7.5 cents detuning of any pitch).
amazing!
+seaatlast read pertinent details @ www.ozanyarman.com/79toneqanun.html
kanun
Furkan Kılıç Thanks!