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Fw: [tuning] The combined 12MP19 scale

🔗Mario Pizarro <piagui@...>

12/4/2010 4:47:07 AM

----- Original Message -----
From: Mario Pizarro
To: tuning yahoogroups
Cc: John H. Chalmers ; Brad Lehman ; Carl Lumma
Sent: Friday, December 03, 2010 9:42 PM
Subject: [tuning] The combined 12MP19 scale

To the tuning list,

I have interesting news for you. First you´d better believe that two scales can live together; in this case a 19 Microtonal scale plus a bran-new 12 tone intonation. I called this combination as the 12MP19 scale and PIAGUI IV to the 12 tone intonation. I´m sure you will like it, it´s a result of two insomne nights.

THE PIAGUI IV INTONATION (12 TONES)
---------------------------------------------------------------- FIFTHS --------MAJ. 3ds. --------MIN. 3ds.
C = 1 ----------------------------- 0 cents ----------- 700.9775 ----- 400.9775 -------- 300
C# = 1.060061465 ------------ 100.9775 --------- 700.9775 ----- 400.9775 -------- 300
D = 1.12373030958 --------- 201.955 ---------- 698.045 ------- 398.045 ---------- 300
Eb = 1.189207115 ------------ 300 ----------------- 700.9775 ----- 400.9775 ---------300
E = 1.26063263652 -------- 400.9775 --------- 700.9775 ----- 400.9775 -------- 300
F = 1.3363480795 ----------- 501.955 ---------- 698.045 ------- 398.045 ---------- 300
F# = 1.41421356237---------- 600 ----------------- 700.9775 ----- 400.9775 -------- 300
G = 1.49915330075 --------- 700.9775 --------- 700.9775 ----- 400.9775 -------- 300
Ab = 1.58919464426 --------- 801.955 ----------- 698.045 ------- 398.045 ---------- 300
A = 1.68179283051---------- 900 ----------------- 700.9775 ----- 400.9775 --------- 300
Bb = 1.78280377174---------- 1000.9775 -------- 700.9775 ----- 400.9775 -------- 300
B = 1.88988157808 --------- 1101.955 ---------- 698.045 ------- 398.045 --------- 300
2C = 2 ----------------------------- 1200 ---------------- 700.9775 ----- 400.9775 -------- 300
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<

MICROTONAL INTONATION (19)

0) 0

1) 44.5369 cents

2) 122.26845 ------------------- (0 + 201.955/2) = 100.9775 = C#

3) 201.955 --------- D
------------------------------------------------------------------------------------------
4) 244.5369
------------------------------------------------------------------------------------------
5) 300 ---------------- Eb

6) 344.5369
----------------------------[(300 + 501.955)/2] = 400.9775 = E
7) 422.26845

8) 501.955 -------------------- F
--------------------------------------------------------------------------------------------
9) 544.5369
--------------------------------------------------------------------------------------------
10) 600 -------------------------- F#

11) 644.5369
----------------------------[(600 + 801.955)/2] = 700.9775 = G
12) 722.26845

13) 801.955 ---------------------- Ab
-----------------------------------------------------------------------------------------------
14) 844.5369
-----------------------------------------------------------------------------------------------
15) 900 ----------------------------- A

16) 944.5369
----------------------------[(900 + 1101.955)/2] = 1000.9775 = Bb
17) 1022.26845

18) 1101.955 ------------------------ B
-------------------------------------------------------------------------------------------------
19) 1144.5369
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<

Thanks

Mario

Lima, December 3, 2010

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🔗Mario Pizarro <piagui@...>

12/4/2010 5:12:36 AM

----- Original Message -----
From: Mario Pizarro
To: tuning yahoogroups
Cc: John H. Chalmers ; Brad Lehman
Sent: Saturday, December 04, 2010 7:47 AM
Subject: Fw: [tuning] The combined 12MP19 scale

----- Original Message -----
From: Mario Pizarro
To: tuning yahoogroups
Cc: John H. Chalmers ; Brad Lehman ; Carl Lumma
Sent: Friday, December 03, 2010 9:42 PM
Subject: [tuning] The combined 12MP19 scale

To the tuning list,

I have interesting news for you. First you´d better believe that two scales can live together; in this case a 19 Microtonal scale plus a bran-new 12 tone intonation. I called this combination as the 12MP19 scale and PIAGUI IV to the 12 tone intonation. I´m sure you will like it, it´s a result of two insomne nights.

THE PIAGUI IV INTONATION (12 TONES)
---------------------------------------------------------------- FIFTHS --------MAJ. 3ds. --------MIN. 3ds.
C = 1 ----------------------------- 0 cents ----------- 700.9775 ----- 400.9775 -------- 300
C# = 1.060061465 ------------ 100.9775 --------- 700.9775 ----- 400.9775 -------- 300
D = 1.12373030958 --------- 201.955 ---------- 698.045 ------- 398.045 ---------- 300
Eb = 1.189207115 ------------ 300 ----------------- 700.9775 ----- 400.9775 ---------300
E = 1.26063263652 -------- 400.9775 --------- 700.9775 ----- 400.9775 -------- 300
F = 1.3363480795 ----------- 501.955 ---------- 698.045 ------- 398.045 ---------- 300
F# = 1.41421356237---------- 600 ----------------- 700.9775 ----- 400.9775 -------- 300
G = 1.49915330075 --------- 700.9775 --------- 700.9775 ----- 400.9775 -------- 300
Ab = 1.58919464426 --------- 801.955 ----------- 698.045 ------- 398.045 ---------- 300
A = 1.68179283051---------- 900 ----------------- 700.9775 ----- 400.9775 --------- 300
Bb = 1.78280377174---------- 1000.9775 -------- 700.9775 ----- 400.9775 -------- 300
B = 1.88988157808 --------- 1101.955 ---------- 698.045 ------- 398.045 --------- 300
2C = 2 ----------------------------- 1200 ---------------- 700.9775 ----- 400.9775 -------- 300
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<

MICROTONAL INTONATION (19)

0) 0

1) 44.5369 cents

2) 122.26845 ------------------- (0 + 201.955/2) = 100.9775 = C#

3) 201.955 --------- D
------------------------------------------------------------------------------------------
4) 244.5369
------------------------------------------------------------------------------------------
5) 300 ---------------- Eb

6) 344.5369
----------------------------[(300 + 501.955)/2] = 400.9775 = E
7) 422.26845

8) 501.955 -------------------- F
--------------------------------------------------------------------------------------------
9) 544.5369
--------------------------------------------------------------------------------------------
10) 600 -------------------------- F#

11) 644.5369
----------------------------[(600 + 801.955)/2] = 700.9775 = G
12) 722.26845

13) 801.955 ---------------------- Ab
-----------------------------------------------------------------------------------------------
14) 844.5369
-----------------------------------------------------------------------------------------------
15) 900 ----------------------------- A

16) 944.5369
----------------------------[(900 + 1101.955)/2] = 1000.9775 = Bb
17) 1022.26845

18) 1101.955 ------------------------ B
-------------------------------------------------------------------------------------------------
19) 1144.5369
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<

Thanks

Mario

Lima, December 3, 2010

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ESET NOD32 Antivirus ha comprobado este mensaje.

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ESET NOD32 Antivirus ha comprobado este mensaje.

http://www.eset.com

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ESET NOD32 Antivirus ha comprobado este mensaje.

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🔗John H. Chalmers <JHCHALMERS@...>

12/4/2010 12:25:45 PM

Thank you, I see you've been busy. Sorry about the sleepless nights. It looks like an interesting set of intervals. I count 20, but you can delete F# as the tritone (semioctave) shouldn't exist in 19-tet or any approximation to it, IMO. Alas, I don't have time at the moment to tune it up in Scala or Csound and listen to it.

An approach I would take is too keep the diatonic set pretty much the same, but split each of the chromatic semitones into two intervals and the diatonic semitones E-F and B-C. The goal is to create a tuning that sounds like 19-tet, but hopefully has better fifths and major thirds without damaging the excellent minor thirds.

--John