On Thu, Jan 3, 2019 at 4:15 PM -0800, "Roshan Kakiya via Piano Technicians Guild"
Original Message------
5-limit tuning
https://en.wikipedia.org/wiki/Five-limit_tuning#The_just_ratios
| Intervals |
Ratios |
Cents |
12-TET |
Offsets |
| Unison |
1/1 |
0.00 |
0.00 |
0.00 |
| Minor Second |
16/15 |
111.73 |
100.00 |
11.73 |
| Major Second |
9/8 |
203.91 |
200.00 |
3.91 |
| Minor Third |
6/5 |
315.64 |
300.00 |
15.64 |
| Major Third |
5/4 |
386.31 |
400.00 |
-13.69 |
| Perfect Fourth |
4/3 |
498.04 |
500.00 |
-1.96 |
| Tritone |
45/32 |
590.22 |
600.00 |
-9.78 |
| Perfect Fifth |
3/2 |
701.96 |
700.00 |
1.96 |
| Minor Sixth |
8/5 |
813.69 |
800.00 |
13.69 |
| Major Sixth |
5/3 |
884.36 |
900.00 |
-15.64 |
| Minor Seventh |
16/9 |
996.09 |
1000.00 |
-3.91 |
| Major Seventh |
15/8 |
1088.27 |
1100.00 |
-11.73 |
| Octave |
2/1 |
1200.00 |
1200.00 |
0.00 |
7-limit tuning
https://en.wikipedia.org/wiki/7-limit_tuning#Lattice_and_tonality_diamond
| Intervals |
Ratios |
Cents |
12-TET |
Offsets |
| Unison |
1/1 |
0.00 |
0.00 |
0.00 |
| Minor Second |
8/7 |
231.17 |
100.00 |
131.17 |
| Major Second |
7/6 |
266.87 |
200.00 |
66.87 |
| Minor Third |
6/5 |
315.64 |
300.00 |
15.64 |
| Major Third |
5/4 |
386.31 |
400.00 |
-13.69 |
| Perfect Fourth |
4/3 |
498.04 |
500.00 |
-1.96 |
| Tritone |
7/5 |
582.51 |
600.00 |
-17.49 |
| Perfect Fifth |
3/2 |
701.96 |
700.00 |
1.96 |
| Minor Sixth |
8/5 |
813.69 |
800.00 |
13.69 |
| Major Sixth |
5/3 |
884.36 |
900.00 |
-15.64 |
| Minor Seventh |
12/7 |
933.13 |
1000.00 |
-66.87 |
| Major Seventh |
7/4 |
968.83 |
1100.00 |
-131.17 |
| Octave |
2/1 |
1200.00 |
1200.00 |
0.00 |
------------------------------
Roshan Kakiya
------------------------------
Original Message:
Sent: 12-31-2018 16:17
From: David Love
Subject: Just intonation offets
Anyone know these Just intonation temperaments and the offsets so I can program them?
5-limit and 7-limit
------------------------------
David Love RPT
www.davidlovepianos.com
davidlovepianos@comcast.net
415 407 8320
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