The following EMail comment was received a few days ago: my replies are included - CEHL
>Date: Wed, 25 Feb 1998 20:56:19 -0500
>To: "Charles E. H. Lucy"
>Subject: Pitch, Pi, And Other Musical Paradoxes
>Dear Mr. Lucy,
>Your fascinating work is sure to benefit musicians and listeners.
>I hope to be able to make practical use of it soon.
>I found your 60-scale chart enlightening. There are several small concerns I'd like to address:
>The melodic major scale (descending) is correctly described as Aeolian.
>However, the Locrian scale is shown.
>The Slendro scale shown includes note 3 in the chain, contrary to the legend.
>The Pelog scale shown is 22 steps long, not 21, and includes note 5 in the chain, contrary to the legend.
Thank you for the corrections. You are totally correct, and I have
amended 60scales.gif to the appropriate values.
To view table of more than sixty scales and their codes (60scales.html)
CEHL 27th Feb '98.
>Also, on the "Scalemaking" page, you speak of the "Greek
names" of modes.
>According to an article on Greece in the New Grove Dictionary of Music and
>Musicians, ancient Greek names for species of the octave included the following (on white keys):
>Apparently, the Greeks counted intervals from top to bottom. When medieval
>ecclesiastical scholars tried to interpret the ancient texts, they counted
>from bottom to top, jumbling the information. The names on the table are the
Interesting! I had used other reference books. I realise that I had
developed a particular prejudice against Dr. Stanley Sadie, the editor
About ten years ago, I phoned him to check some detail, and he was extremely haughty to me. I shall check this out as soon as I get the opportunity. Maybe I should include both sets of names.
Assuming that you are once again perfectly correct; it is small wonder there has been such confusion amongst musicians on how to name scales and modes. Perhaps the idea of scalecoding will help to clarify the situation.
CEHL 27th Feb '98
>On the chart on that same page, the Locrian scale is shown as having
>one-half steps between C and D, instead of the actual one step.
Thank you. Again you are correct. This was a typo on my HTML table construction. I have moved the column left by one step and aligned it correctly.
I appreciate your comments.
CEHL 27th Feb '98
Charlie Anon's website (http://www.rev.net/~aloe/couchpotato) - (Lotsa useful links)
Date: Fri, 13 Mar 1998 09:55:15 -0800 (PST)
From: John Chalmers (firstname.lastname@example.org)
To: Alternative Tuning List email@example.com
Charles: The ancient Greek names for the heptatonic modes are correct in your post. To avoid accidentals, the key of C major is used and the various modes occur as octave species in the order Mixolydian (B-b), Lydian (C-c), Phrygian (D-d), Dorian (E-e), Hypolydian (F-f), Hypophrygian (G-g), and Hypodorian (a-a'). Hypolydian (F-f), Hypophrygian (G-g), and Hypodorian (a-a'). The extinct Ionian mode was a G mode and the Aeolian and Locrian were A modes, but it is not known how these differed from the HP and HD modes. The Mixolydian was also called Hyperdorian and the lower A mode (on the note Proslambanomenos) was called Hypermixolydian and Hyperphrygian. (In Argos, it was outlawed because it had no ethos of its own, but was merely a lower octave repetition of the Hypodorian.) Greek music was based on a 15-tone two-octave gamut running in our notation from A-a-a', to which an accidental b-flat was added to illustrate modulation at the fourth. This system could be taken at various pitch levels (see below). The absolute pitch is not known and may have been irrelevant in any case.
In musical practice, these modes were transposed so that the modal
patterns of all 7 species moved into the middle range of the two octave
system. Thus a system of pitch keys developed at roughly semitonal intervals.
These keys took the names of the modes and new names (Hyperionian, etc.)
were coined to complete a set of 15 keys or TONOI. The center of the system
was also changed from Dorian (E) to Hypolydian (F) and two series of names
were applied (high and low Dorian, etc.).
In the Middle Ages, confusion arose between the keys and the modes and the order of the modal names was reversed. Schlesinger attributes this error to Boethius. Later, other ecclesiastical names were invented as musical practice changed. The plagal/authentic distinction developed at that time.
To avoid confusion, one should always specify whether Greek or ecclesiastical nomenclature is being used unless the context is clear.
Date: Sun, 15 Mar 1998 07:50:44 -0500
From: firstname.lastname@example.org (Joseph L Monzo)
Subject: Re: TUNING digest 1353, Topic No. 1: modes
John Chalmers' answer to the confusion between ancient Greek and medieval ecclesiastical modes is correct, however, so is the original statement that the medieval theorists determined the modal structure from the opposite direction. In determining the particular modal scale, the Greeks started "counting notes" at the highest note and went downward, while medieval musicians started at the lowest pitch and ascended. Spacing the intervals in the same order as the Greeks, but in the opposite direction, gave the ecclesiastical correspondences Chalmers described.
Joseph L. Monzo
Date: Sun, 15 Mar 1998 15:22:24 -0800 (PST)
From: John Chalmers (email@example.com)
To: Charles Lucy firstname.lastname@example.org
Subject: Re: Ambiguous Mode and scale names (aliases?)
Charles: I just posted this to the List, but you may want a separate copy. The relationship between the Greek and Ecclesiastical modal nomenclatures is a confusing topic and I think somewhat more complex than the result of simple intervallic inversion, though this is a good way to remember the orders.
In the natural key (C major, no accidentals), the order of the Greek modes (ascending) is Mixolydian (B), Lydian (c), Phrygian (d), Dorian (e), Hypolydian (f), Hypophrygian (g) and Hypodorian (a). The corresponding interval patterns (ascending) are (in generalized diatonic tuning):
M S T T S T T T
L T T S T T T S
P T S T T T S T
D S T T T S T T
HL T T T S T T S
HP T T S T T S T
HD T S T T S T T
Retrograding these interval patterns or doing the equivalent operation of inverting the scales around the octave yields the following pairs:
It is true that the order of the M L P D HL modes is reversed to HL D P L M, but the HP and HD modes do not fit the pattern unless the HD mode is taken an octave lower to low A (on proslambanomenos). Then the inversion pattern fits exactly. However, I do not think this is the way the system developed historically, though I admit that the effect is the same.
Although the modes may be thought of as sections of the diatonic scale starting on different notes, the Greeks actually transposed all their modes to the same register. Thus there developed a set of pitch keys named after the modes which they transposed into the central two octave range. The Dorian key and mode were the center point. The Phrygian key was a tone higher so that the sequence D-d now fell on the notes that formerly represented the E mode. The Hypolydian was a tone higher still (two tones in all) and the Mixolydian a semitone above this. Similarly, the Hypolydian key was a semitone below the Dorian (to bring the sequence f-f' into the center range), the Hypophrygian a tone and 1/2, and the Hypodorian a tone below this.
These pitch keys ran in the ascending order HD HP HL D P L M which
corresponds to the Ecclesiastical modes Aeolian or Hypodorian (A), Hypophrygian
(B), Ionian or Hypolydian (c), Dorian (d), Phrygian (e) Lydian (f), and
Mixolydian (g). In other words, the ecclesiastical modes are in the order
of the pitch keys, the Greek in the order of their starting notes.
This is a simplified account as there was another series of late Greek pitch keys interleaved between these (so that keys stood at semitonal intervals) and the entire system was transposed so that the f mode (Hypolydian still) was the center rather than the e mode (Dorian). The topic is further complicated by there being more than one set of ecclesiastical names depending upon the writer and the period.
Thank you John C. , Joseph L. Monzo and Charlie Anon, who posed
the original query. So to summarise (and for all practical modern purposes),
we have the following result:
|Scale of White Notes||Ecclesiastic
|or in order of fifths:|
CEHL 16th March 98
Table of more than sixty scales and their codes (60scales.html)
Instructions for Lucy Scalecoding