Yahoo Tuning Groups Ultimate Backup tuning Mr. Keenan's standard for interval naming

http://dkeenan.com/Music/IntervalNaming.htm

Mr. Keenan has specified in the above link (in his own terms) a consistent approach for the interval denominations:

Index Prefix for Prefix for
unisons, fourths, seconds, thirds,
fifths, octaves sixths, sevenths,
ninths
----- ----------------- -----------------
-4 double diminished subdiminished
-3 subdiminished diminished
-2 diminished subminor
-1 sub minor
0 (perfect) neutral
+1 super (major)
+2 augmented supermajor
+3 superaugmented augmented
+4 double augmented superaugmented

Forgive my general ignorance in these matters, but I'm not particularly in alignment with the usage of the same indexing with varying jargons, such as a sub fifth being the deviation-wise correspondent of a minor third, seeing as the problems that arise with this methodology is well defined by the author himself.

Maybe it is more acceptable to reserve the usage of minor and major terms for those intervals differing by a semi-tone instead of a syntonic comma or diesis, and eliminate the confusion altogether. My suggestion is to dispense with the usage of 9:10 as a minor tone (second), and adopt the term `curbed or extenuated whole tone` instead. Also, the jargons for `diminished` and `augmented` intervals ought to be broadly understood as to mean an increase or decrease in the subject interval size anywhere from 24:25 (~70c) to 13:14 (~130c).

Thus there should at least be ~70c distance between a tone and its augmented or diminished cousin, which would pretty much fall in the order of the regular understanding of major and minor intervals. For example:

4:5 is an harmonic major third or diminished fourth
5:6 is an harmonic minor third or diminished major third or augmented second.

I apologize for any mistakes I might have done.

Cordially,
Ozan Yarman

🔗monz <monz@tonalsoft.com>

hello Ozan,

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:

> http://dkeenan.com/Music/IntervalNaming.htm
>
> Mr. Keenan has specified in the above link (in his own terms) a
consistent approach for the interval denominations:
>
>> Index Prefix for Prefix for
>> unisons, fourths, seconds, thirds,
>> fifths, octaves sixths, sevenths,
>> ninths
>> ----- ----------------- -----------------
>> -4 double diminished subdiminished
>> -3 subdiminished diminished
>> -2 diminished subminor
>> -1 sub minor
>> 0 (perfect) neutral
>> +1 super (major)
>> +2 augmented supermajor
>> +3 superaugmented augmented
>> +4 double augmented superaugmented
>
> Forgive my general ignorance in these matters, but I'm not
> particularly in alignment with the usage of the same indexing
> with varying jargons, such as a sub fifth being the
> deviation-wise correspondent of a minor third, seeing as
> the problems that arise with this methodology is well defined
> by the author himself.
>
> Maybe it is more acceptable to reserve the usage of minor
> and major terms for those intervals differing by a semi-tone
> instead of a syntonic comma or diesis, and eliminate the
> confusion altogether. My suggestion is to dispense with the
> usage of 9:10 as a minor tone (second), and adopt the term
> `curbed or extenuated whole tone` instead. Also, the jargons
> for `diminished` and `augmented` intervals ought to be broadly
> understood as to mean an increase or decrease in the subject
> interval size anywhere from 24:25 (~70c) to 13:14 (~130c).
>
> Thus there should at least be ~70c distance between a tone and
> its augmented or diminished cousin, which would pretty much
> fall in the order of the regular understanding of major and
> minor intervals. For example:
>
> 4:5 is an harmonic major third or diminished fourth
> 5:6 is an harmonic minor third or diminished major third
> or augmented second.
>
> I apologize for any mistakes I might have done.
>
> Cordially,
> Ozan Yarman

indeed, the fact that "major" and "minor" have specific
musical meanings is exactly the cause of the confusion.

these two words were originally simply the Latin words
for "big" and "small" respectively.

it was the constant association of certain aesthetic
effects ("flavors") with major and minor chords and scales,
once the era of tonality got underway c.1600, which
causes musicians to think of "major" and "minor" as
having a certain sound or other association.

with respect to the older meaning, "minor tone" for
10:9 and "major tone" for 9:8 makes perfect sense.

the real problem arises because today's interest in
microtonality finds many more sizes of a particular
interval in the vicinity of the older standardized ones,
and hence there is need for a longer list of descriptive
adjectives.

ultimately, using numbers to describe the intervals
(whether ratios, monzos, or logarithmic values like cents)
is really the only good way to do it. the descriptive
words can only serve to help classify.

-monz

🔗Ozan Yarman <ozanyarman@superonline.com>

Dear Joseph,

It is a priviledge for me to correspond with you finally. It's been only a year since I became acquainted with your presence, your work and revolutionizing contributions along with other prevelant ground-shakers among the tuning list. I am particularly flabbergasted with the depth of your grasp of the middle-eastern music theory beginning with Kindi, Zalzal and Farabi. Furthermore, your tonal encyclopedia deserves an ovation.

More likely than not, my confession regarding the general ignorance around these parts of the much improved and extended theoretical novelties propagated by avant-garde microtonalists is probably nothing new to you. Nevertheless, I feel inclined to apologize for my lack of knowledge and resources, and hope that you will not refuse to provide your much needed expertise as the occasion warrants it.

I have recently come to terms with Mr. Keenan's suggestion concerning the utilization of fractions and colons for pitches and intervals respectively (with one minor reservation being my insistance that we keep the tradition of writing pitches with the format 3/2, 4/3, etc. as a means to specify just where to put our finger down on an open vibrating string).

Concerning the `major` and `minor` dichotomy, it is without a question of doubt that the older methodology is in perfect harmony with the naming of 9:10 and 8:9 when we are talking about historical temperaments. In this regard, the subsequent requirements for the naming of other intervals is not a drastic problem as you say, since we have better numerical references to define pitches and intervals today. Nevertheless, a mathematically profound categorization should be in alignment with a pragmatical classification of names for intervals, would you not agree? As new intervals come into play, should we just do without the names, or invent new appellations to go along with these? And if it is the latter, ought we to act without restraint, or abide by a set of standards commonly accepted by the `major`ity? (pun intended)

Cordially,
Ozan Yarman

🔗monz <monz@tonalsoft.com>

hi Ozan,

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:
> Dear Joseph,

it's fine if you call me "monz" like everyone else around here.
i don't like formality.

> It is a priviledge for me to correspond with you finally.
> It's been only a year since I became acquainted with your
> presence, your work and revolutionizing contributions along
> with other prevelant ground-shakers among the tuning list.
> I am particularly flabbergasted with the depth of your grasp
> of the middle-eastern music theory beginning with Kindi,
> Zalzal and Farabi. Furthermore, your tonal encyclopedia
> deserves an ovation.

thanks so much for all the kind words.

in truth, i really don't know all that much about middle-eastern
music-theory ... i simply presented what i found in Helmholtz's
book in a way which i find more suited to the modern mind.
i haven't studied it any deeper than that, and haven't read
any of the original Arab sources in translation ... and my
very limited knowledge of the Arabic language precludes
reading the originals themselves.

> More likely than not, my confession regarding the general
> ignorance around these parts of the much improved and extended
> theoretical novelties propagated by avant-garde microtonalists
> is probably nothing new to you. Nevertheless, I feel inclined
> to apologize for my lack of knowledge and resources, and hope
> that you will not refuse to provide your much needed expertise
> as the occasion warrants it.

i'll be happy to help you as much as i can ... but as you
may note from the length of time it took me to respond to
this, i am very busy these days and haven't been keeping
a very close eye on the tuning lists.

> <snip>
>
> Concerning the `major` and `minor` dichotomy, it is without
> a question of doubt that the older methodology is in perfect
> harmony with the naming of 9:10 and 8:9 when we are talking
> about historical temperaments.

well, in fact the names "minor tone" and "major tone" came up
with regard to the study of 5-limit JI in the late 1400s.
of course, a consideration of the fact that there *are* those
two differently-sized "tones" is what led almost immediately
to the invention of meantone temperament ... but the terminology
itself arose out of just-intonation first.

> In this regard, the subsequent requirements for the naming
> of other intervals is not a drastic problem as you say, since
> we have better numerical references to define pitches and
> intervals today. Nevertheless, a mathematically profound
> categorization should be in alignment with a pragmatical
> classification of names for intervals, would you not agree?

i absolutely and totally agree. in fact, Dave Keenan's scheme
for categorizing the different sizes of "comma" arose at least
in part from something i did several years ago:

http://tonalsoft.com/enc/index2.htm?../td/monzo/o483-26new5limitnames.
htm

delete the line-break to make that link work, or just use this:

http://tinyurl.com/55hpz

> As new intervals come into play, should we just do without
> the names, or invent new appellations to go along with these?
> And if it is the latter, ought we to act without restraint,
> or abide by a set of standards commonly accepted by the
> `major`ity? (pun intended)

well ... if you peruse the archives of this list, you'll see
that i am in the minority as one of those who welcome a
proliferation of new names, but the majority who do not
agree with me here will argue vehemently against such a
proliferation.

i like creating new names because i believe that one short
term to express an idea which otherwise would require a
whole phrase, makes further discourse easier. since i write
and monitor the Encyclopaedia of Tuning, it doesn't seem to
me to be a big deal to create a new term, and write a definition
which is publicly available for all to use (and add to!).

-monz

🔗Ozan Yarman <ozanyarman@superonline.com>

Dear Paul,

As per your request, I forward our discussion to the tuning list. It has been most fulfilling to benefit from your insightful thoughts. I look forward to the next episode of our dialogue.

As for my careless description of the Huzzam Maqam, what I meant to say is that the distance between Eb and F# which would normally correspond to an interval with the ratio 19683/16384 or a size of 317.5950 cents contracts in favor of raising the diatonical Eb to a very sharp hypothetical D# as if it were a conduit of E at a distance of 19:18, and lower the diatonical F# to Gb as if it were a conduit of F 20:19 far in the same manner. Nevertheless, we express such maqams using diatonical accidentals, even though they would not be considered so diatonical in Western theory.

On the other hand, I do not believe that historical 12 tone octave temperaments need any notation other than the Staff Notation in use today. One only needs to add a disclaimer to specify what temperament the musician has to perform.

Regarding my Spectral Notation proposal, I have developed it a little further and wish to hear your comments.

Cordially,
Ozan Yarman

----- Original Message -----
From: wally paulrus
To: Ozan Yarman
Sent: 09 Kasım 2004 Salı 21:35
Subject: Re: Mr. Keenan's standard for interval naming

Hi Ozan!

>I apologize for my absent-mindedness, my neglect was not deliberate.

No problem!

>I
>prepared a collective reply to your last 3 posts as a means to cement
>our
>amicable correspondence:

Excellent! And feel free to forward any or all of my remarks to the list and/or George, as you see fit. Certainly if George was the one making any unfounded assertions about how I would notate microtonal music, you should set him straight with the reactions I sent you.

>You have outlined perfectly the issue with Mr. Keenan's approach that I
>botched in my turgid explanation. Indeed, I am in `perfect` alignment
>with
>you that 3/2 `plus` 9/8 should make 27/16, thus a pythagorean major
>sixth,
>as opposed to 5/3 which is a just major sixth and thence a didymus'
>comma (81/80) lower, which support your thesis that each sound system
>should be attributed a unique intervallic lexicon, with which I am
>again in
>`perfect` alignment.

I just meant that, whatever exact ratios or irrational specifications are supposedly mapped to the interval names, that a 'perfect fifth' plus a 'major second' should equal a 'major sixth', and if it doesn't, musicians are going to get way too confused by the system.

>What I meant by "a sub fifth being the deviation-wise correspondent of
>a
>minor third", is that Mr. Keenan has assigned the same -1 index prefix
>to
>both a `sub fifth` and a `minor third`.

Yes but this is not in reference to a comparable 'zero' point in the two cases, so I'm afraid you're reading too much into the 'sameness' of the two '-1's.

>Barring the mathematical
>corrections
>to his indices, that would make a narrow fifth the semantic equivalent
>of a
>minor third instead of a perfect fifth.

I'm afraid this looks like an incorrect characterization of Dave Keenan's system. Your conclusion would only follow if a 'perfect fifth' was somehow the semantic equivalent of a 'neutral third', but nothing in Dave Keenan's system supports such a view. In fact, almost everything Dave's done supports an opposite view, that a neutral third would tend to be regarded, semantically and notationally, as a deviation from some other inteval, while the perfect fifth would be the most basic interval after the octave. So it appears to me that you are taking this one table of Dave's out of context, and imbuing it with meaning it does not have.

>Another note on the disparities between the tonal systems of East and
>West
>is my finding that the diatonic progression of a maqam requires the
>sharps
>and flats to be interchanged with each other, so much so that the
>central
>notes of the Hijaz tetrachord (D, Eb, F#, G) in the Huzzam maqam
>contract in
>favor of raising the Eb to the level of a very shrill D# as a conduit
>to E.

This confuses me -- are you saying D# is higher than Eb? If so, what 'contracts?' And where does E come in; why would one need a 'conduit' to it if it does not occur in the maqam?

>Nevertheless, I have to admit that I'm very partial
>to
>reserving the natural unaltered note-heads on the staff to ditonic
>pythagorean values unless a chosen temperament demands otherwise (such
>as
>5-edo or 7-edo).

These are rather unlikely temperament for Western notation! What about something like, say, meantone temperament, which happened to dominant and shape Western music in its formative years (c. 1480-1780)? And what about an adaptive tuning that maintains the advantages of meantone while adjusting each chord to be just within itself?

>Using colors in order to distinguish irregular
>temperaments
>seems to be the only

Irregular temperaments include Werckmeister (III), Kirnberger (II, III), etc. The differences between one irregular temperament and another can be very tiny in some cases. Using colors to distinguish one irregular temperament from another sounds like a =n extremely tall order, one not likely to be able to usefully communicate much information. Surely I've misunderstood you somehow?

>circumbendibus

I don't know this word.

>that makes sense at this point. I,
>for
>one, cannot think of any other way to adjudicate between the
>secterianist
>musicians of the East with the conservative ones in the West.

Wow, that sounds profound, but I have no idea what it means.

>I know that my language requires some polish,

Not at all. Your english is superior to that of many native speaking scholars. Bravo!

I hope we can continue in this manner for some time to come.

Best,
Paul

------------------------------------------------------------------------------

Hello Ozan,

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:

> I do not favor the clumping of the apotome and the limma together
>actually, but it is possible to temper the limma out and adopt a 36-
>edo system.

Technically speaking, if you temper the limma out, you get a 5-tET
system, not 36-tET, let alone any edo . . . and that's assuming you
started with Pythagorean (3-limit JI) -- otherwise an equal tuning
doesn't result from tempering the limma out at all . . . I'd love to
find out what you were really thinking here and help you put it into
terms that our 'tuning scientists' will understand.

>Seeing as this results in 12-edo elaborated exactly 3 times, or 72-
>edo simplified by 2, it appears to be the next step to take for the
>Maqam World which has adopted 24-edo since Allah knows when.

Far be it from me to claim expertise on such matters, but the
intervals of 36-equal may be appropriate for certain Persian and/or
Byzantine scales, but would seem a very poor fit for typical Arabic
maqamat.

>Considering the lower boundaries Mr. Keenan gives in this table:

Don't be too 'impressed' by this table. Almost all of the boundaries
Dave proposed were derived through some very contorted, ad-hoc logic,
and should not be taken as the result of either deep tuning
investigations or anything empirical.

>
>
>
> Square of lowerbound
> .. 2-exponent
> ...... 3-exponent
> ................ Lowerbound (cents)
> ................................. Size range name
> -------------------------------------------------
> .. [ 0, 0 > ....... 0 ........... schismina
> .. [-84, 53 > ..... 1.807522933 . schisma
> .. [ 317,-200 > ... 4.499913461 . kleisma
> .. [-19, 12 > .... 11.73000519 .. comma
> .. [-57, 36 > .... 35.19001558 .. small-diesis
> .. [ 8, -5 > ..... 45.11249784 .. (medium-)diesis
> .. [-11, 7 > ..... 56.84250303 .. large-diesis
> .. [-30, 19 > .... 68.57250822 .. small-semitone
> .. [ 35, -22 > ... 78.49499048 .. limma
> .. [-3, 2 > ..... 101.9550009 ... large-semitone
> .. [ 62, -39 > .. 111.8774831 ... apotome
> .. [-106, 67 > .. 115.492529
>
>
> it is obvious that I have to calibrate the figures in this way:

Not sure what you're getting at here, or why. Where did this sudden
interest in 36 come from?

Highest Regards,
Paul

---
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🔗George D. Secor <gdsecor@yahoo.com>

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:
> Dear Paul,
>
> As per your request, I forward our discussion to the tuning list.
It has been most fulfilling to benefit from your insightful thoughts.
I look forward to the next episode of our dialogue.
>
> ----- Original Message -----
> From: wally paulrus
> To: Ozan Yarman
> ...
> Hello Ozan,
>
> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...>
wrote:
> >Considering the lower boundaries Mr. Keenan gives in this table:
>
> Don't be too 'impressed' by this table. Almost all of the
boundaries
> Dave proposed were derived through some very contorted, ad-hoc
logic,
> and should not be taken as the result of either deep tuning
> investigations or anything empirical.
> ...
> Highest Regards,
> Paul

Paul,

I have the impression that lately you (like Dave) have been keeping a
low profile, but since Ozan has included your comment (above) in his
message, I feel obligated to respond.

Now that Dave has made a final correction to the above-mentioned
table (which we both agreed was long overdue), I must respectfully
disagree, very strongly and completely, with your opinion of Dave's
methodology.

Here is the corrected table:

Square of lowerbound
.. 2-exponent
...... 3-exponent
................ Lowerbound (cents)
................................. Size range name
-------------------------------------------------
.. [ 0, 0 > ....... 0 ........... schismina
.. [-84, 53 > ..... 1.807522933 . schisma
.. [ 317,-200 > ... 4.499913461 . kleisma
.. [-19, 12 > .... 11.73000519 .. comma
.. [ 27, -17 > ... 33.38249264 .. small-diesis
.. [ 8, -5 > ..... 45.11249784 .. (medium-)diesis
.. [-11, 7 > ..... 56.84250303 .. large-diesis
.. [-30, 19 > .... 68.57250822 .. small-semitone
.. [-49, 31 > .... 80.30251341 .. limma
.. [-3, 2 > ..... 101.9550009 ... large-semitone
.. [ 62, -39 > .. 111.8774831 ... apotome
.. [-106, 67 > .. 115.492529

You will find the specifics and reasons for the correction in this
message (about 4/7 of the way down; search for "lower boundaries"):

/tuning/topicId_56133.html#56232

The only thing that might be consider "arbitrary" about the
methodology that was used in arriving at the above boundaries is in
the number of comma-categories (and therefore the number of size
boundaries) that we judged to be sufficient for microtonal notational
purposes. But it can be demonstrated that the locations of those
boundaries, which are defined very precisely, are not the slightest
bit arbitrary.

We specified that nominals in our notation be pitches in a
Pythagorean sequence, i.e., no prime factors greater than 3, and that
the comma-ratios or "accidentals" be distinguished from one another
by two criteria: 1) prime content greater than 3; and 2) size
category. True, there are other possible sets of nominals, but I
believe that we have selected that which would be considered least
arbitrary.

Our Sagittal notation project has addressed the question: what is the
most convenient and logical way to name the various Sagittal symbols
(which are now capable of dividing the apotome into at least 233
parts, a resolution of < 0.5 cents), and we found, time after time,
that given the above two criteria, pairs of comma-ratios with the
same prime content > 3 (which provide alternate spellings for the
same pitch) are size-equidistant (as measured in cents) from specific
irrational intervals, which became the boundaries for differentiating
between these comma-ratios. Yet you claim that our tuning
investigation has not been "deep" enough? How many more pitches must
we attempt to notate (spelled in how many different ways) in order
for you to be satisfied that we have been thorough enough for all
practical (and enough impractical) purposes?

And what is that you find "ad-hoc", "contorted", or
otherwise "arbitrary" about this?

BTW, Paul, good to hear from you (even if only indirectly). :-)

--George

🔗Ozan Yarman <ozanyarman@superonline.com>

I hope I haven't messed up things or anything like that.

All the best,
Ozan Yarman

----- Original Message -----
From: George D. Secor
To: tuning@yahoogroups.com
Sent: 17 Kasım 2004 Çarşamba 20:37
Subject: [tuning] Re: Mr. Keenan's standard for interval naming

Paul,

I have the impression that lately you (like Dave) have been keeping a
low profile, but since Ozan has included your comment (above) in his
message, I feel obligated to respond.

Here is the corrected table:

You will find the specifics and reasons for the correction in this
message (about 4/7 of the way down; search for "lower boundaries"):

/tuning/topicId_56133.html#56232

And what is that you find "ad-hoc", "contorted", or
otherwise "arbitrary" about this?

BTW, Paul, good to hear from you (even if only indirectly). :-)

--George