A temperament basically defines a set of pitches and how they relate to one another. The organisation of these relationships should be considered to achieve certain objectives such as better harmony.
Just intonation is the most harmonious tuning. However, it is impractical because 12 pure fifths are not equal to 7 octaves. This is called the Pythagorean comma. This comma must be spread across the 12 fifths to create a practical tuning. The act of doing this is called tempering.
12-tone equal temperament causes every interval except for the octave to deviate from its ratio in 5-limit just intonation. However, it resolves the Pythagorean comma very well which makes it practical.
My temperament gets closer to just intonation by keeping 6 fifths pure whilst tempering the other 6 fifths. All the fifths are within an acceptable limit (a sixth of the Pythagorean comma).
I have mimicked the symmetry of 12-tone equal temperament to make my temperament as practical as possible. The circle of fifths of my temperament is symmetrical.
All temperaments are compromises. Every 12-TET interval except for the octave is out of tune relative to its corresponding ratio in 5-limit just intonation which means 12-TET is the least harmonic compromise. Well temperaments improve harmony so they are better compromises.
There is more information on this website:
http://just-intonation.org/intonation"
Just intonation aims at maximal harmony, tuning all intervals with rational frequency ratios, but it can be used only in a single musical key. The ET, which is characterized by a constant irrational semitone ratio 21/12, works in all keys but all intervals except for the octave are out of tune. In between there is a large variety of historical unequal temperaments, seeking for a compromise between harmony and scale invariance to a different extent. The ET, today’s dominating Western temperament, is the least harmonic one, but over the last two centuries humanity got used to these discrepancies. Still, many musicians keep on expressing their discomfort with the harmonic shortcomings of the ET."------------------------------
Roshan Kakiya
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Original Message:
Sent: 08-23-2018 07:49
From: Alan Eder
Subject: Roshan Kakiya's Well Temperament
What is a temperament but the relationship of pitches to each other?
Alan
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Alan Eder, RPT
Herb Alpert School of Music
California Institute of the Arts
Valencia, CA
661.904.6483
Original Message:
Sent: 08-22-2018 14:03
From: Roshan Kakiya
Subject: Roshan Kakiya's Well Temperament
I have not produced aural directions for my temperament.
I have updated my original post by including the offsets from 12-tone equal temperament in cents, my aims and a breakdown of the features of my temperament.
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Roshan Kakiya
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Original Message:
Sent: 08-22-2018 12:12
From: Benjamin Sanchez
Subject: Roshan Kakiya's Well Temperament
Aha! Speaking in terms of cents is something I get, and I'm going to give this temperament a try soon... that is, as soon as I can figure out how to program it into my ETD.
I'm assuming you haven't yet come up with aural directions for this temperament? If not no worries, just curious.
Thanks,
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Benjamin Sanchez
Professional Piano Services
(805)315-8050
www.professional-piano-services.com
BenPianoPro@comcast.net
Original Message:
Sent: 08-21-2018 20:58
From: Roshan Kakiya
Subject: Roshan Kakiya's Well Temperament
Roshan Kakiya's Well Temperament
C = 0.00 cents
C# = 101.96 cents
D = 200.00 cents
D# = 301.96 cents
E = 400.00 cents
F = 501.96 cents
F# = 600.00 cents
G = 701.96 cents
G# = 800.00 cents
A = 901.96 cents
A# = 1000.00 cents
B = 1101.96 cents
C = 1200.00 cents
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Roshan Kakiya
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