User talk:Rperlner: Difference between revisions

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:::: I'm not saying that complete chords on other scale degrees aren't usable at all, but you still have to be careful with the few that you can actually get away with when the Tonic chord is reduced to just the Tonic and the Mediant. A notorious example of a chord that you don't want to have in complete form under any circumstances is the Submediant chord as it contains the entire Locrian tonic chord, and makes it seem like the Submediant chord is actually the tonal center. An even more notorious example is the chord built on the flat-2 as that chord is particularly likely to be tonicized if it is in complete form, and it requires careful setups and follow-ups to use it even in incomplete form. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 19:23, 6 December 2020 (UTC)

== Email exchange with Dr. Ozan Yarman ==

I am posting an email exchange I had with Dr Ozan Yarman on the possible naming of the tridecimal neutral thirds comma (512/507) "Huzamma".

--------

Hello Dr. Yarman,

My name is Ray Perlner. I am interested in microtonal composition and have recently been looking into Turkish and Arabic traditions in tuning.

I recently joined Xenharmonic wiki, a major online resource on the theory of musical tuning. One of my first edits has been to add to the list of commas -- the comma that is implied to be tempered out when using quarter-tone accidentals to notate 13-limit intervals, 512/507. As a follow up, I have been looking into choosing a catchier name for the comma than the present name, "tridecimal neutral thirds comma."

In discussing this on my talk page ( https://en.xen.wiki/w/User_talk:Rperlner ) with another user, Aura, we came upon a possible name for the comma, the "Huzamma," based on the Arabic Maqam Huzam, on the grounds that it is notated with quarter-tone accidentals, and may be used in a way that implies 13-limit intervals. But, neither of us was entirely sure about the latter point and we wanted to consult someone more knowledgeable about the subject before committing to the name. Aura, who is a big fan of your work in 159EDO and has also worked with 159EDO, recommended you. Do you have any thoughts on the 13-limit implications of Maqam Huzam, or the naming of the 512/507 comma?

Thank You,

Ray Perlner

--------

Dear Ray, very glad you wrote to me. Sorry for my delay in responding to you and to Aura. I've been exhausted these past days and had to rest the whole day until late hours.

Now, back to the tridecimal neutral thirds comma. If I understand you correctly, one initially has, for instance,

13/10 454.214 cents

and

72/55 466.278 cents

55/42 466.851 cents

representing the Karjighar makam's ascending "perde hisar" in the former case (tonic is acute Bb), and the Huzzam makam's ascending "perde hisar" in the latter case (tonic is C). For the descending melody scenarios these ratios go down a notch (13/10 may become Huzzam's "perde huzzam" in descent).

Were the desire to temper them to a single median or mean note, one would first need find the primes to generate them and temper one or more of those primes to approximate values so as to converge to a single note. But you more specifically require, if I understand correctly,

13/10 times 512/507 = 6656 / 5070 = 256/195 = 471.2036 cents for the "ascending or nominal perde huzzam" which is "perde hisar"

or otherwise

55/42 divided by 512/507 = 27,885 / 21,504 = 9295 / 7168 = 449.8611 cents for the descending or the real namesake "perde huzzam".

Let's pick the former route for simplicity. Thus we have "13/10" as the lowerbound and "256/195" as the upperbound, while the actual target is somewhere between. The prime factors for 256/195 are "2^8 / (3*5*13)". The prime factors for 13/10 are straightforwardly "13 / (2*5)". We can dismiss the "13th harmonic" specifically and focus instead on the octave "2" and/or the octave+fifth "3" and/or the two octaves+major third "5".

Therefore, as an example:

[1199 + 1199 + 1199 + 1199 + 1199 + 1199 + 1199 + 1199 cents] - [ 1909.9446 + 2780 + 4,440.5277 cents]

=

[4,440.5277] - [1199 + 2780]

making 461.5277 cents as some sort of median where we tempered out the 512/507 comma by dint of 1 cent clipped octaves and somewhat wider fifths and narrower major thirds than pure.

Under these circumstances, tempering out the 512/507 comma does indeed reduce the nominal "perde hisar" of Huzzam makam and its "perde huzzam" counterpart in descent to be the same pitch. Thus, verily, you may rename 512/507 to "hüzzama" or the "hisarite/hisarine comma".

Yet, bear in mind that it is in fact Karjighar makam that rather delineates 13-limit ratios while Huzzam maqam may rather delineate 11-limit ratios. That is because Karjighar concludes like Ushshaq, which transcends the 11-limit or quarter-tonal perde segah to an evel lower tridecimal perde segah which many, including myself, call "perde ushshaq".

Cordially,

Dr. Oz.

--------

Dear Dr. Oz.

Thanks for the reply. It was in fact quite prompt from my perspective. Do not worry about needing rest. We all do. What you write makes sense, but I think my guess about tempering of 512/507 in Maqam Huzam may have been subtly different from what you thought I had in mind.

The interval I suspected might be tempered was in fact that between the 1st and 3rd scale degrees of Maqam Huzam (perde segah and perde neva, I believe.) Here the idea is that the context of the other perdes in the Maqam may suggest this interval is either 16/13 or 39/32 (differing by the 512/507 comma I need a name for.) Here I suspect the other perdes in the Maqam may be heard as being related to the tonic by relatively simple intervals that either suggest perde neva should be at 16/13 or 39/32. In particular the only simple intervals that are near the roughly 450 cent interval from perde segah to perde hisar are 9/7 and 13/10. If this interval is the latter, it would suggest to me that perde neva should be an interval of 16/15th lower, i.e. at 39/32. Likewise, the next scale degree after hisar (I assume it is perde gevast or perde mahur. I typically see it written as b natural when the tonic is e half flat. e.g. https://www.maqamworld.com/en/maqam/huzam.php) is roughly 450 cents below the octave above the tonic, so one might assume it is 20/13 if perde hisar is 13/10. This would suggest that perde neva should be a just major 3rd below perde mahur here, and therefore tuned to 16/13.

In sum, if we can interpret the full scale as something like 1: 13/12 : 16/13 or 39/32 : 13/10 : 20/13 : 13/8 : 20/11: 2, it seems like tempering 512/507 could be important to the musical structure of Maqam Huzam. Alternatively, one could see the 512/507 comma as related from a purely notational perspective to any scale where the 13/12 interval is written using quartertone accidentals in a notation that assumes two chromatic quartertones are equal to a chromatic semitone.

Let me know if the above seems reasonable. Also, you mention the low perde segah that occurs in the Karjighar and Ushshaq Maqams a ratio of approximately 13/12 above the tonic. This might make sense to me in the context of a 12:13:14:16 tetrachord, but this would make the tuning of perde cargah surprisingly low, given that it is written as a note often played on open strings on an Oud for example. Can you give some insight into what is going on here?

Best,

Ray

--------

Dear Ray, 13-limit is too low for Hüzzam in the Turkish understanding. But perde hisar, instead of the tonic perde segah, can be focused on to temper out 512/507 the way I indicated or in a similar fashion.

Cordially,

Dr. Oz.

--------

Dear Dr. Oz.

Thank you for your responses. May I reproduce this exchange (with proper attribution) on my talk page.

Best,

Ray

--------

Dear Ray,

Just to be on the safe side, I tried the scale you indicated:

0: 1/1 0.000000 unison, perfect prime

1: 13/12 138.572661 tridecimal 2/3-tone

2: 16/13 359.472338 tridecimal neutral third

3: 39/32 342.482663 39th harmonic, Zalzal wosta of Ibn Sina

4: 13/10 454.213948 tridecimal semi-diminished fourth

5: 20/13 745.786052 tridecimal semi-augmented fifth

6: 13/8 840.527662 tridecimal neutral sixth

7: 20/11 1034.995772 large minor seventh

8: 2/1 1200.000000 octave

and confirm that 13/10 should be replaced by 4/3 if one should insist on a 13-limit architecture for conformity with an outlandish Turkish understanding of Hüzzam:

0: 1/1 0.000000 unison, perfect prime

1: 13/12 138.572661 tridecimal 2/3-tone

2: 16/13 359.472338 tridecimal neutral third

3: 4/3 498.044999 perfect fourth

4: 20/13 745.786052 tridecimal semi-augmented fifth

5: 13/8 840.527662 tridecimal neutral sixth

6: 117/64 1044.437664

7: 15/8 1088.268715 classic major seventh

8: 2/1 1200.000000 octave

In such a case, where would you have the tridecimal neutral thirds comma eliminated if not regarding between 16/13 and 4/3? Thus, maybe by keeping 4/3 in place and raising the whole structure tonic-wise up by a third or fourth of a syntonic comma?

How about then my Hüzzam (Turkish Segah, Huzzam and Mustear ver.2 with perde segah on E by Dr. Oz.) key-transposed to C:

0: 1/1 0.000000 unison, perfect prime

1: 392/363 133.060927

2: 40/33 333.040771

3: 175/132 488.180391

4: 147/110 501.975158

5: 3/2 701.955001 perfect fifth

6: 196/121 835.015928 two (undecimal diminished fourth or major third)

7: 20/11 1034.995772 large minor seventh

8: 12544/6655 1097.384272

9: 441/220 1203.930158 Werckmeister's undecimal septenarian schisma +1 octave

where I already understand your 512/507 to be tempered out in the desired manner?

Also, I missed the part about 12:13:14:16 earlier. To tell the truth, some people in Turkey insist perde chargah gets lowered by dint of just such an Ushshaq tetrachord in descent perhaps?

By all means, do refer to what I wrote here in its entirety on your Talk page. I would be interested in what other microtonalists engaged with maqam/makam/mugham/dastgah/etc... think about the whole issue.

Cordially,

Dr. Oz.

--------

--[[User:Rperlner|Rperlner]] ([[User talk:Rperlner|talk]]) 00:04, 9 December 2020 (UTC)

@@ Line 107: / Line 107: @@
 :::: I'm not saying that complete chords on other scale degrees aren't usable at all, but you still have to be careful with the few that you can actually get away with when the Tonic chord is reduced to just the Tonic and the Mediant.  A notorious example of a chord that you don't want to have in complete form under any circumstances is the Submediant chord as it contains the entire Locrian tonic chord, and makes it seem like the Submediant chord is actually the tonal center.  An even more notorious example is the chord built on the flat-2 as that chord is particularly likely to be tonicized if it is in complete form, and it requires careful setups and follow-ups to use it even in incomplete form. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 19:23, 6 December 2020 (UTC)
+== Email exchange with Dr. Ozan Yarman ==
+I am posting an email exchange I had with Dr Ozan Yarman on the possible naming of the tridecimal neutral thirds comma (512/507) "Huzamma".
+--------
+Hello Dr. Yarman,
+My name is Ray Perlner. I am interested in microtonal composition and have recently been looking into Turkish and Arabic traditions in tuning.
+I recently joined Xenharmonic wiki,  a major online resource on the theory of musical tuning. One of my first edits has been to add to the list of commas -- the comma that is implied to be tempered out when using quarter-tone accidentals to notate 13-limit intervals, 512/507. As a follow up, I have been looking into choosing a catchier name for the comma than the present name, "tridecimal neutral thirds comma."
+In discussing this on my talk page  ( https://en.xen.wiki/w/User_talk:Rperlner ) with another user, Aura, we came upon a possible name for the comma, the "Huzamma," based on the Arabic Maqam Huzam, on the grounds that it is notated with quarter-tone accidentals, and may be used in a way that implies 13-limit intervals. But, neither of us was entirely sure about the latter point and we wanted to consult someone more knowledgeable about the subject before committing to the name. Aura, who is a big fan of your work in 159EDO and has also worked with 159EDO, recommended you. Do you have any thoughts on the 13-limit implications of Maqam Huzam, or the naming of the 512/507 comma?
+Thank You,
+Ray Perlner
+--------
+Dear Ray, very glad you wrote to me. Sorry for my delay in responding to you and to Aura. I've been exhausted these past days and had to rest the whole day until late hours.
+Now, back to the tridecimal neutral thirds comma. If I understand you correctly, one initially has, for instance,
+/10	454.214 cents
+and
+/55	466.278 cents
+/42	466.851 cents
+representing the Karjighar makam's ascending "perde hisar" in the former case (tonic is acute Bb), and the Huzzam makam's ascending "perde hisar" in the latter case (tonic is C). For the descending melody scenarios these ratios go down a notch (13/10 may become Huzzam's "perde huzzam" in descent).
+Were the desire to temper them to a single median or mean note, one would first need find the primes to generate them and temper one or more of those primes to approximate values so as to converge to a single note. But you more specifically require, if I understand correctly,
+/10 times 512/507 = 6656 / 5070 = 256/195 = 471.2036 cents for the "ascending or nominal perde huzzam" which is "perde hisar"
+or otherwise
+/42 divided by 512/507 =  27,885 / 21,504 = 9295 / 7168 = 449.8611 cents for the descending or the real namesake "perde huzzam".
+Let's pick the former route for simplicity. Thus we have "13/10" as the lowerbound and "256/195" as the upperbound, while the actual target is somewhere between. The prime factors for 256/195 are "2^8 / (3*5*13)". The prime factors for 13/10 are straightforwardly "13 / (2*5)". We can dismiss the "13th harmonic" specifically and focus instead on the octave "2" and/or the octave+fifth "3" and/or the two octaves+major third "5".
+Therefore, as an example:
+[1199 + 1199 + 1199 + 1199 + 1199 + 1199 + 1199 + 1199 cents] - [ 1909.9446 + 2780 + 4,440.5277 cents]
+=
+[4,440.5277] - [1199 + 2780]
+making 461.5277 cents as some sort of median where we tempered out the 512/507 comma by dint of 1 cent clipped octaves and somewhat wider fifths and narrower major thirds than pure.
+Under these circumstances, tempering out the 512/507 comma does indeed reduce the nominal "perde hisar" of Huzzam makam and its "perde huzzam" counterpart in descent to be the same pitch. Thus, verily, you may rename 512/507 to "hüzzama" or the "hisarite/hisarine comma".
+Yet, bear in mind that it is in fact Karjighar makam that rather delineates 13-limit ratios while Huzzam maqam may rather delineate 11-limit ratios. That is because Karjighar concludes like Ushshaq, which transcends the 11-limit or quarter-tonal perde segah to an evel lower tridecimal perde segah which many, including myself, call "perde ushshaq".
+Cordially,
+Dr. Oz.
+--------
+Dear Dr. Oz.
+Thanks for the reply. It was in fact quite prompt from my perspective. Do not worry about needing rest. We all do. What you write makes sense, but I think my guess about tempering of 512/507 in Maqam Huzam may have been subtly different from what you thought I had in mind.
+The interval I suspected might be tempered was in fact that between the 1st and 3rd scale degrees of Maqam Huzam (perde segah and perde neva, I believe.) Here the idea is that the context of the other perdes in the Maqam may suggest this interval is either 16/13 or 39/32 (differing by the 512/507 comma I need a name for.) Here I suspect the other perdes in the Maqam may be heard as being related to the tonic by relatively simple intervals that either suggest perde neva should be at 16/13 or 39/32. In particular the only simple intervals that are near the roughly 450 cent interval from perde segah to perde hisar are 9/7 and 13/10. If this interval is the latter, it would suggest to me that perde neva should be an interval of 16/15th lower, i.e. at 39/32. Likewise, the next scale degree after hisar (I assume it is perde gevast or perde mahur. I typically see it written as b natural when the tonic is e half flat. e.g. https://www.maqamworld.com/en/maqam/huzam.php) is roughly 450 cents below the octave above the tonic, so one might assume it is 20/13 if perde hisar is 13/10. This would suggest that perde neva should be a just major 3rd below perde mahur here, and therefore tuned to 16/13.
+In sum, if we can interpret the full scale as something like 1: 13/12 : 16/13 or 39/32 : 13/10 : 20/13 : 13/8 : 20/11: 2, it seems like tempering 512/507 could be important to the musical structure of Maqam Huzam. Alternatively, one could see the 512/507 comma as related from a purely notational perspective to any scale where the 13/12 interval is written using quartertone accidentals in a notation that assumes two chromatic quartertones are equal to a chromatic semitone.
+Let me know if the above seems reasonable. Also, you mention the low perde segah that occurs in the Karjighar and Ushshaq Maqams a ratio of approximately 13/12 above the tonic. This might make sense to me in the context of a 12:13:14:16 tetrachord, but this would make the tuning of perde cargah surprisingly low, given that it is written as a note often played on open strings on an Oud for example. Can you give some insight into what is going on here?
+Best,
+Ray
+--------
+Dear Ray, 13-limit is too low for Hüzzam in the Turkish understanding. But perde hisar, instead of the tonic perde segah, can be focused on to temper out 512/507 the way I indicated or in a similar fashion.
+Cordially,
+Dr. Oz.
+--------
+Dear Dr. Oz.
+Thank you for your responses. May I reproduce this exchange (with proper attribution) on my talk page.
+Best,
+Ray
+--------
+Dear Ray,
+Just to be on the safe side, I tried the scale you indicated:
+:          1/1               0.000000 unison, perfect prime
+:         13/12            138.572661 tridecimal 2/3-tone
+:         16/13            359.472338 tridecimal neutral third
+:         39/32            342.482663 39th harmonic, Zalzal wosta of Ibn Sina
+:         13/10            454.213948 tridecimal semi-diminished fourth
+:         20/13            745.786052 tridecimal semi-augmented fifth
+:         13/8             840.527662 tridecimal neutral sixth
+:         20/11           1034.995772 large minor seventh
+:          2/1            1200.000000 octave
+and confirm that 13/10 should be replaced by 4/3 if one should insist on a 13-limit architecture for conformity with an outlandish Turkish understanding of Hüzzam:
+:          1/1               0.000000 unison, perfect prime
+:         13/12            138.572661 tridecimal 2/3-tone
+:         16/13            359.472338 tridecimal neutral third
+:          4/3             498.044999 perfect fourth
+:         20/13            745.786052 tridecimal semi-augmented fifth
+:         13/8             840.527662 tridecimal neutral sixth
+:        117/64           1044.437664
+:         15/8            1088.268715 classic major seventh
+:          2/1            1200.000000 octave
+In such a case, where would you have the tridecimal neutral thirds comma eliminated if not regarding between 16/13 and 4/3? Thus, maybe by keeping 4/3 in place and raising the whole structure tonic-wise up by a third or fourth of a syntonic comma?
+How about then my Hüzzam (Turkish Segah, Huzzam and Mustear ver.2 with perde segah on E by Dr. Oz.) key-transposed to C:
+:          1/1               0.000000 unison, perfect prime
+:        392/363           133.060927
+:         40/33            333.040771
+:        175/132           488.180391
+:        147/110           501.975158
+:          3/2             701.955001 perfect fifth
+:        196/121           835.015928 two (undecimal diminished fourth or major third)
+:         20/11           1034.995772 large minor seventh
+:      12544/6655         1097.384272
+:        441/220          1203.930158 Werckmeister's undecimal septenarian schisma +1 octave
+where I already understand your 512/507 to be tempered out in the desired manner?
+Also, I missed the part about 12:13:14:16 earlier. To tell the truth, some people in Turkey insist perde chargah gets lowered by dint of just such an Ushshaq tetrachord in descent perhaps?
+By all means, do refer to what I wrote here in its entirety on your Talk page. I would be interested in what other microtonalists engaged with maqam/makam/mugham/dastgah/etc... think about the whole issue.
+Cordially,
+Dr. Oz.
+--------
+--[[User:Rperlner|Rperlner]] ([[User talk:Rperlner|talk]]) 00:04, 9 December 2020 (UTC)