Teaching and classifying tunings

First of all I would like to apologize for starting a discussion
abouth "teaching tunings" a few weeks ago and not responding, since I got
disconected from the internet for a few weeks with my removal.

I would also like to say thank you to Neil, Johnny and Paul for
responding to the subject which I consider very important.

I finally got to understand limits, utonality and otonality in
1/2 an hour of explanation from Brian Lee, who I would also like to thank.
I had "Genesis of a New Music" at home for two years and I never got to
totally understand it. Is anybody on the list using U-tonality (equal
space fretting) for composition. I would be interested on hear something
more about it.

Johnny said:
"Also, a list of listening materials that
correspond to each and every lesson might be adviseable.
Most important is the real time singing of intervals, perhaps a new
interval each and every lesson"

I'm finding through Carnatic music that the only way to
distinguish the difference of the pitches (and ornamentation around
the tone) on the similar ragas, is to actually sing a traditional catchy
tune. Putting everything into numnbers made it really confussing.
So I agree with your point and would also like to ask you what vocal
(or choral) material can be use for beginners for the different groups
of tunings already classified by Paul through his 15 week tuning course
proposal:

>1. Introduce the octave as an acoustical phenomenon
>2. Introduce the 3-limit consonances and Pythagorean tunings
>3. Pythagorean tunings as applied to pentatonic scales: Chinese Music
>4. 7-ET representations of pentatonic scales allowing modulational freedom:
>Thai music
>5. Pythagorean tunings as applied to the heptatonic scale: Organum
>6. Discuss the pythagorean comma; introduce 12-ET representations of the
>heptatonic scale
>7. Non-just non-equal-tempered scales: African and much other music
>9. Schismatic tuning of late middle ages and medieval Arabic tuning as
>Pythagorean approximations to the 5-limit
>10. Just intonation: Indian music (I've heard some santoor music where the
>intonation is very clearly just 5-limit).
>11. Discuss the syntonic comma; introduce meantone temperament: Renaissance
>music
>12. Equal-tempered versions of meantone -- 31, 19, is 12 good enough?
>13. Circulating temperaments/well temperament: Bach and "key colors"
>14. 12-TET becomes standard :( , Arabic music measured and played in
>"quarter-tones"
>15. Equal tempered versions of just intonation: 53, 34, maybe compare
>22-equal with 22 sruti of Indian music to show how JI structures are
>preserved
>16. Atonality, set theory, Balzano and 20-TET and other numerological
>constructs.
>17. Introduce the 7-limit consonances
>18. Augmented sixth chords as meantone approximations to the 7-limit
>19. Introduce the 9- and 11-limit consonances in JI: Partch, Johnston, etc.
>20. Equal-tempered representations of higher consonances: Huygens, Fokker,
>and 31; Herf, Sims and 72, proposals of 41-tone and 171-tone equal
>temperaments
>21. Inharmonic timbres, tunings to go with them: Gamelan music, modern
>explorations
>22. Non-octave scales in history and modern non-octave tunings such as
>Pierce's 13 per 3:1
>23-30. Creative ensemble projects

This is also for anybody else who could suggest any other vocal works connected
to
any tuning different than the 12 Tet !!!!!

I have translated into english the index of a book which is used
by the Spanish Conservatoir as reference for the subject of acoustics :
"Afinacion y temperamento en la musica Occidental". This is also a good
classification of tunings (Only western I'm afraid):
***********************************************************************

TUNING AND TEMPERAMENT IN WESTERN MUSIC

1. GREECE. THE PYTHAGORIC TUNING

The Greek musical system
The pythagoreans
Timeo's scale
Aristogenes
Greek divisions of the tetrachord
Analysis of the pythagorean tuning

2. JUST INTONATION

The tuning of Ramo's monochord
Inestability in Just Intonation
The divission of Fogliano's monochord
The divission of the comma
Zarlino
The "perfect system" of Salinas

3. THE SCIENTIFIC REVOLUTION AND THE ORIGIN OF THE ACOUSTICAL SCIENCE.
THE HARMONICS

Number 7. Seventh intervals

4. INTRODUCING TEMPERAMENT. MEANTONE TEMPERAMENTS.

Mesotonic temperaments
1/4 comma Meantone temperament. Mayor thirds
1/3 comma Meantone temperament. Minor thirds
2/7 comma Meantone temperament
Evaluation of meantone temperaments
Erasthotenes' "Mesolabio"

5. THE CIRCULARITY OF MEANTONE TEMPERAMENTS. EQUAL DIVISSIONS

1/3 comma temperament. 19 divissions of the octave
Nicola Vicentino's archicembalo. 31 divissions of the octave
1/4 comma temperament. 31 divissions of the octave
2/7 comma temperament. 50 divissions of the octave
Survival of the 19 and 31 divissions per octave

6. OTHER VARIETIES OF THE MEANTONE TEMPERAMENT

1/5 comma temperament. 43 divissions of the octave
2/9 comma temperament. 74 divissions of the octave
1/6 comma temperament. 55 divissions of the octave
Quartertone temperament. 24 equal divissions of the octave
Pythagorean tunings: 53 and 17 divissions of the octave
Pythagorean tuning of thirds of tone in 17 divissions of the octave
Comparative table
Other Meantone temperaments
Other systems with multiple divission of the octave

7. EQUAL TEMPERAMENT

8. IRREGULAR TEMPERAMENTS

Irregular temperaments of XVI century. Modification of the pythagorean
tuning
Irregular temperaments of XVII century
Well temperaments
Werkmeinster I, 1/4 comma
Werkmeinster II, 1/3 of comma
Neidhart I, 1/12 and 1/16 comma
Valotti, 1/6 comma
Marpurg "I" , 1/3 comma
Kirnberger, 1/2 comma
French temperaments
***********************************************************************


Tony Salinas


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