# Sonantometry as Algebra of Harmony



## commator (Jun 6, 2007)

I need your judgement of some ideas on tonal functions of the higher order.

http://sonantometry.blogspot.com


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## commator (Jun 6, 2007)

commator said:


> I need your judgement of some ideas on tonal functions of the higher order.
> 
> http://sonantometry.blogspot.com


The article of blog http://sonantometry.blogspot.com was updated and continued.


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## Leporello87 (Mar 25, 2007)

This looks quite interesting (from a very quick cursory glance). I studied quite a bit of mathematics in college. I'll have to read through this more carefully when I get a chance, thanks for the link.


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## commator (Jun 6, 2007)

Leporello87 said:


> This looks quite interesting (from a very quick cursory glance). I studied quite a bit of mathematics in college. I'll have to read through this more carefully when I get a chance, thanks for the link.


Thank you so much for the warm words. I hope in the nearest time to finish math introduction and to continue with score analysis. At first I'm going to show mobility of grade II in diatonic major-minor scale of 5-limit Just Intonation.


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## zlya (Apr 9, 2007)

I see that you can assign a note to a degree in your 53-tone EQ based on its tonal function. Ok, very interesting. Why? What are you trying to do? Are you trying to show the advantages of one system of intonation over another? Are you going to use this 53-tone EQ system in analysis? What is the goal of this study?

Looks interesting so far.


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## commator (Jun 6, 2007)

zlya said:


> I see that you can assign a note to a degree in your 53-tone EQ based on its tonal function. Ok, very interesting. Why? What are you trying to do? Are you trying to show the advantages of one system of intonation over another? Are you going to use this 53-tone EQ system in analysis? What is the goal of this study?
> 
> Looks interesting so far.


Your questions are good. Thank you.

I'll answer each of them. My native language is Russian so excuse me some delay to form English answers.


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## commator (Jun 6, 2007)

zlya said:


> I see that you can assign a note to a degree in your 53-tone EQ based on its tonal function. Ok, very interesting. Why?...


The 53EDO tuning is very close to 5-limit Just Intonation. So it is possible to approximate infinite 5-limit JI by means of finite 53EDO. This tuning contain own comma which in Wikipedia named Holdrian. This comma used like 5-limit JI Dydimus comma.

5-limit JI can be approximated also by means 31EDO for example. The 31EDO not contain comma like conventional 12EDO, and scores for 12EDO may be played without any analysis if they supposed 5-limit JI as ideal.

The sonantometrical analysis let us to know where and how many commas we must sharp or flat note pitch to play 12EDO scores in 53EDO and approximate JI sound.

The notes with sonantometrical formulas which contain M, 2M, 3M must be flattened with one two and three commas. The formulas with m, 2m, 3m requre note sharping with one, two and three commas.

So in 53EDO it needful to assign additional accidental to note.


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## commator (Jun 6, 2007)

zlya said:


> ...What are you trying to do? Are you trying to show the advantages of one system of intonation over another? Are you going to use this 53-tone EQ system in analysis? What is the goal of this study?...


First of all I'm trying to be sure that it's possible to play all tonal music in 53EDO. My three-year practice let me hope that it so. But it is very hard to make analysis manually and the ways to give this work to computer are needful. I'm trying to find them.

I'm sure 53EDO is a way to have good approximation of JI keyboard and it will have success in near future. It is a good way to integrate all tonal music systems in one theory.

No doubt 31EDO more practical, as sharp-flat divided keyboard which have very close to JI third and seventh. But the fact of comma escape make this tuning unsuitable for investigations in theory of JI and tonality.

My goal is to make some steps in these deepnesses.

Last year Pam & Phil Fluke in England repared 53EDO Bosanquet Enharmonium. It now playable but the scores are needful for playing...


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## zlya (Apr 9, 2007)

Ah, so you're designing a new keyboard? I see. Very interesting. Won't it be rather large?


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## commator (Jun 6, 2007)

zlya said:


> Ah, so you're designing a new keyboard? I see. Very interesting. Won't it be rather large?


No, I'm not designing new keyboard, but this process is in progress thanks to other people.

J. S. Allen: http://www.bikexprt.com/music/bosanqet.htm
A. D. Fokker: http://www.xs4all.nl/~huygensf/english/instrum.html
R. H. M. Bosanquet: http://tardis.dl.ac.uk/FreeReed/English/organ_book/node17.html#SECTION000172000000000000000

I'm developing method which can be understandable for educated musicians to have possibility for play existing scores by such keyboards. Also for writing new music for such keyboards.


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## commator (Jun 6, 2007)

commator said:


> I need your judgement of some ideas on tonal functions of the higher order.
> 
> http://sonantometry.blogspot.com


Now added links to example of score and MIDI-model in the beginning of the article http://sonantometry.blogspot.com

Feel free to comment.


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## commator (Jun 6, 2007)

Last news for those who may be interested:

Has completed two new articles for international conferences. 
In them I do inform some results of researches within the frames of my project COMMATOR. http://commator.googlepages.com/

Has participated in two international forums: 
in India http://www.itcsra.org/sra_story/sra...ents_links/sra_story_events_seminars/frsm.pdf
and Portugal http://www.sigmap.org/SIGMAP2008/
In proceedings of FRSM2008 and SIGMAP2008 my articles are already published.

FRSM2008: Project Commator and Sonantometry
SIGMAP2008: "APPROXIMATION OF 5-LIMIT JUST INTONATION - Computer MIDI Modeling in Negative Systems of Equal Divisions of the Octave"

Professor Patrizio Barbieri http://commator.googlepages.com/barbieri 
has already written a couple of good words about my researches in his new book. http://www.patriziobarbieri.it/1.htm

Suddenly googled there own name on a Web accessible page 602. 
It is Page 8 of unit Name Index. http://www.patriziobarbieri.it/pdf/name_index.pdf


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